Notices of the American Mathematical Society (ISSN 0002· 9920) Is Published Monthly Except Bimonthly in June/ July by Voting Information for 2006 AMS Election

of the American Mathematical Society August2006 Volume 53, Number 7

The Differential Geometry and Physical Basis for the Applications of Feynman Diagrams page 744

A Fellows Program for the AMS page 754

Salt Lake City Meeting page 834 Cincinnati Meeting page 836 Storrs Meeting page 838

A Henan horseshoe (page 768) Masters of Mathematics A Historic Evolution of Ideas

Euler through Time ANew look at Old Themes V. S. Varadarajan, University of California, Los Angeles, CA

This book synthesizes hundreds of years of thought on Eulerian theories to place the work of the world's most prolific mathematician into the context of today's thinking. The primary focus is on Euler's work on infinite series and products and its influence on modern thought. The author examines Euler products and ties his work to the climactic developments reached by number theorists and the Langlands program.

2006; 302 pages; Hardcover; ISBN-I 0: 0-8218-3580-7; ISBN-13: 978-0-8218-3580-7; List US$59;AII AMS members US$47; Order code EULER

Bourbaki ASecret Society of Mathematicians Maurice Mashaal, Pour la Science, Paris, France This book lifi:s the veil from a secret society in which spirited debate, good humor, and a unified purpose helped generate the most influential mathematical treatise of the 20th century. It chronicles how the Bourbaki group saw its mission grow into creation of a universal collection of mathematical tools, shaping thought on mathematics from 1950 to the 1970s. Remarkable photographs and rich anecdotes enliven the text. 2006; approximately 168 pages; Softcover; ISBN-I 0: 0-8218-3967-5; ISBN-13: 978-0-8218-3967-6; List US$29;AII AMS members US$23; Order code BOURBAKI US$23; Order code BOURBAKI

Euclid's Phaenomena The Coxeter Legacy ATranslation and Study of a Reflections and Projections Hellenistic Treatise in Spherical Chandler Davis and Erich W. Ellers, Astronomy University of Toronto, ON, Canada, J. L. Berggren, Simon Fraser Editors University, Burnaby, BC, Canada, Comp rehensive collection of articles that and R. S. D. Thomas, University of captures the essence of Coxeter's legacy Manitoba, Winnipeg, Manitoba, Canada combination of storytelling and up-to-date information reflects the breadth of Coxetcr's contributions both within and outside math­ Thi s translati on of Euclid's Phaenomena, includes ex tensive ematics. The book includes a rich variety of beautiful illustrations. commentary that enhan ces the context and value of this impor­ ta nt histori c work. Readers get a fa scinating look at how Euclid A w ·publication of the AM.S and The Fields Institute fOr Research in Mathematical Sciences advanced knowledge in astronomy without the tools of trigonom­ (Toronto, Ontario, Canada). etry and spherical geometry. 2006; 320 pages; Hardcover; ISBN-I 0: 0-8218-3722-2; ISBN-13: 978-0-8218-3722-1 ; List US$69; All AMS members US$ 55; Order code COXETER (:0publishcd \\ ~ t h the London Mathematical Society beginning wi th Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. T he LMS is registered \vith tbc Chari ry Comm.issioncrs.

History of Mathematics. Volume 29; 2006; 132 pages; Softcover; ISBN-I 0: 0-8218-4072-X; ISBN - 13: 978-0-8218-4072-6; List US$29;AII AMS members US$23; Order code HMATH/29

For many more publications of interest, visit the AMS Bookstore ®AMS www.ams.org/bookstore AMERICAN M/.THBMAl'ICAL SOCIETY l-800-321-4AMS (4267), in the U.S. and Canada, or 1-401-455-4000 (worldwide); fax: 1-40 1-455-4046; email: [email protected]. American Mathematical Society, 20 I Charles Street, Providence, Rl 02904-2294 USA Open Access Mathematics Journals from Hindawi

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Mathematical Problems in Engineering Theory, Methods, and ApplicationS NEW f6 FORTHCOMING from Birkhauser

Vortices in the Magnetic Complex Variables History of Banach Spaces Ginzburg-landau Model with Applications and Linear Operators S. PONNUSAMY, Indian Institute of Technology, Madras, ALBRECHT PIETSCH, University of lena, Germany ETIENNE SANDIER, Universite Paris-12 Val-de-Marne, Chennai, India; HERB SILVERMAN, College of Charleston, Creteil, France; SYLVIA SERFATY, CMIA, Ecole Normale Banach spaces figure prominently in the study of func­ Superieure de Cachon, France sc tional analysis, having applications to integral and Complex numbers can be viewed in several ways: as an book presents the mathematical study of vortices differential equations, approximation theory, harmonic Thi ~ element in a field, as a point in the plane, and as a two­ of the two-dimensional Ginzburg-Landau model, an analysis, convex geometry, numerical mathematics, dimensional vector. Examined properly, each perspec­ im(1ortant phenomenological model used to describe analytic complexity, and probability theory. This work is tive provides crucial insight into the interrelations bet­ sup1erconductivity. The vortices, identified as quantized devoted to a comprehensive treatment of the history of ween the complex number system and its parent, the ani6unts of vorticity of the superconducting current Banach spaces and (abstract bounded) linear oper­ real number system. The authors explore these relation­ localized near points, are the objects of many obser­ ators. While other comprehensive texts on Banach ships by adopting both generalization and specialization vational and experimental studies, both past and pre­ spaces focus on developments before 1950, this one is methods to move from real variables to complex variab­ se~t. The Ginzburg-Landau functionals considered mainly devoted to the second half of the 20th century. les, and vice versa, while simultaneously examining their include both the model cases with and without a Banach space theory is presented as a part of a broad analytic and geometric characteristics. magnetic field. mathematics context, using tools from such areas as set The engaging exposition is replete with discussions, The work acts a guide to the various branches of Ginz­ theory, topology, algebra, combinatorics, probability remarks, questions, and exercises, motivating not only burg-Landau studies, provides context for the study of theory, and logic. Equal emphasis is given to both spaces understanding on the part of the reader, but also de­ vortices, discusses current research and results, and and operators. veloping the tools needed to think critically about mathe­ presents a list of open problems in the field. It will 2006/APPROX., 880 PP., 821LLUS./HARDCOVER berlefit mathematicians, physicists, and graduate stu­ matical problems. The material includes numerous examples and applications relevant to engineering stu­ ISBN 0-8176-4367-2/$109.00 (TENT.) dents having either an introductory or an advanced dents, along with some techniques to evaluate various knowledge of the subject. types of integrals. 20d6/APPROX. 290 PP., 151LLUS./HARDCOVER Mathematical Analysis 2006/X, 510 PP., 1091LLUS./HARDCOVER ISBN 0-8176-4316-8/$69.95 (TENT.) Linear and Metric Structures ISBN 0-8176-4457-1/$59.95 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS and Continuity ANP THEIR APPLICATIONS MARIANO GIAQUINTA, Scuola Normale Superiore, Pisa, AGeometric Approach Italy; GIUSEPPE MODICA, Universitii degli Studi di Firenze, Italy Number Theory to Differential Forms DAVID BACHMAN, Pitzer College, Claremont, CA This self-contained work on linear and metric struc­ An Introduction via the Distribution tures focuses on studying continuity and its applications of Primes This text presents differential forms from a geometric to finite- and infinite-dimensional spaces. The book, BENJAMIN FINE, Fairfield University, Fairfield, CT; perspective accessible at the sophomore undergradu­ replete with examples, observations, exercises, and GERHARD ROSENBERGER, Universitiit Dortmund, ate level. The book begins with basic concepts such as illustrations, may be used in a classroom setting, for Germany partial differentiation and multiple integration and self-study by advanced undergraduate and graduate gently develops the entire machinery of differential students, and as a valuable reference for researchers This book provides an introduction and overview of forms. The author approaches the subject with the idea in mathematics, physics, and engineering. number theory based on the distribution and properties that complex concepts can be built up by analogy from of primes. This unique approach provides both a firm simpler cases, which, being inherently geometric, often 2006/XVIII, 470 PP., 1281LLUS. background in the standard material as well as an over­ HARDCOVER/ISBN 0-8176-4374-5/$149.00 can be best understood visually. Each new concept is view of the whole discipline. All the essential topics are SOFTCOVER/ISBN 0-8176-4375-3/$69.95 presented with a natural picture that students can easily covered: fundamental theorem of arithmetic, theory of grasp. congruences, quadratic reciprocity, arithmetic func­ Also by M. GIAQUINTA and G. MODICA: tions, and the distribution of primes. Analytic number The text is designed to support three distinct course theory and algebraic number theory both receive a solid tracks: third semester (multivariable) calculus, sopho­ Mathematical Analysis introductory treatment. more-level vector calculus, and an advanced under­ Functions of One Variable graduate or beginning graduate topics course for The book's user-friendly style, historical context, and physics or mathematics majors. Contains excellent 2003/XII, 353 PP./HARDCOVER wide range of exercises ranging from simple to quite motivation, numerous illustrations and solutions to ISBN 0-8176-4312-5/$89.95 difficult (with solutions and hints provided for select selected problems in an appendix. ones) make it ideal for self study as well as classroom use in upper-level undergraduate and beginning 2006/APPROX. 160 PP., 331LLUS./HARDCOVER Mathematical Analysis graduate-level courses. ISBN 0-8176-4499-7/$39.95 (TENT.) Approximation and Discrete Processes

2006IAPPROX., 320 PP., 11 ILLUS/HARDCOVER 2005/XII, 388 PP., 1521LLUS. ISBN 0-8176-4472-5/$49.95 HARDCOVER/ISBN 0-8176-4313-3/$149.00 SOFTCOVER/ISBN 0-8176-4337-0/$69.95

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August 2006

Communications

764 WHAT IS ... a Strange Attractor? David Ruelle

766 Teruhisa Matsusaka (1926-2006) j(inos Kollar

771 Textbook Tempest Students and Professors Decry Price Surges Allyn jackson Features 775 2005AnnualSurveyofthe Mathematical Sciences in 7 44 The Differential Geometry and Physical Basis the United States (Second for the Applications of Feynman Diagrams Report) (and Doctoral Degrees L. Conferred 2004-2005, Samuel Marateck Supplementary List) The author uses the occasion of the issue of a stamp Ellen E. Kirkman, ]ames W honoring Richard Feynman by the United States Postal Maxwell, and Colleen A. Service to explore the mathematics and physics sug­ Rose gested in the stamp's design.

Commentary 7 54 A Fellows Program for the AMS

741 Opinion: Complex The AMS Council has placed a proposal for a Fellows NUMB3RS Program on the ballot for the 2006 elections. The pro­ posal, essays for and against by Ron Stern and David Sarah]. Greenwald Eisenbud, and introductory comments by James Arthur, 742 Letters to the Editor appear in this special section.

761 Reality Conditions­ A Book Review Reviewed by john Swallow Not·ces Departments of the American Mathematical Society Mathematics People ...... 790 Naur Rece ives Turing Award, Aumann Awarded von Neumann EDITOR: Andy Magid Prize, Plaskota Awarded 2006 Infor mation-Based Complexity ASSOCIATE EDITORS: Prize, Ferran Sunyer i Balaguer Prize Awarded, Massey Receives Susanne C. Brenner, Bill Casselman (Graphics Editor), Blackwell-Tapia Award, National Academy of Sciences Elections, Robert J. Daverman, Nathaniel Dean, Rick Durrett, Susan Friedlander, Robion Kirby, Steven G. Krantz, American Academy Elections, Cobb and D'Ambrosio Receive Elliott H. Lieb, Mark Saul, Karen E. Smith, Audrey ICMI Medals, USA Mathematical Olympiad. Terras, Lisa Traynor SENIOR WRITER and DEPUTY EDITOR: Mathematics Opportunities ...... 793 Allyn Jackson NSF Focused Research Groups, NSF Mathematical Sciences MANAGING EDITOR: Sandra Frost Postdoctoral Research Fellowships, Call for Submissions for CONTRIBUTING WRITER: Elaine Kehoe Sunyer i Balaguer Prize, Call for Nominations for 2006 PRODUCTION ASSISTANT: Muriel Toupin Information-Based Complexity Awar d. PRODUCTION: Kyle Antonevich, Stephen Moye, Erin Murphy, Lori Nero, Karen Ouellette, Donna For Your Information ...... 794 Salter, Deborah Smith, Peter Sykes National Mathematics Advisory Panel Members Announced, ADVERTISING SALES: Anne Newcomb Mathematics Institutes Infor mational Website.

SUBSCRIPTION INFORMATION: Subscription prices Inside the AMS ...... 796 for Volume 53 (2006) are US$430 list; US$344 institu­ Mathematical Imagery Page on AMS Website, Fan China tional member; US$258 individual member. (The sub­ scription price for members is included in the annual Exchange Program Names Awardees, Histor y Volumes Now dues.) A late charge of 10% of the subscription price Online, Deaths of AMS Members. will be imposed upon orders received from nonmem­ bers after January 1 of the subscription year. Add for Reference and Book list ...... 797 postage: Surface delivery outside the United States and India-US$20; in India-US$40; expedited delivery to destinations in North America-US$35; elsewhere­ Mathematics Calendar ...... 820 US$87. Subscriptions and orders for AMS publications should be addressed to the American Mathematical New Publications Offered by the AMS ...... 825 Society, P.O . Box 845904, Boston, MA 02284-5904 USA. All orders must be prepaid. Classified Advertising ...... 832 ADVERTISING: Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Meetings & Conferences of the AMS ...... 834 Advertising material or questions may be faxed to 401-331-3842 (indicate "Notices advertising" on fax Meetings and Conferences Table of Contents ...... 855 cover sheet). SUBMISSIONS: Articles and letters may be sent to the editor by email at noti ces@math . ou. edu, by fax at 405-325-5765, or by postal mail at Department of Mathematics, 601 Elm, PHSC 423, University of Okla­ homa, Norman, OK 73019·0001. Email is preferred. Correspondence with the managing editor may be sent to noti ces@ams . o rg. For more information, see the section "Reference and Book List". NOTICES ON THE AMS WEBSITE: Most of this publi­ cation is available electronically through the AMS web­ site, the Society's resource for delivering electronic From the products and services. Use the URL htt p : I /WNW. ams. o r g/not i ces / to access the Notices on the website. AMS Secretary

(Notices of the American Mathematical Society (ISSN 0002· 9920) is published monthly except bimonthly in june/ July by Voting Information for 2006 AMS Election ...... 803 the American Mathematical Society at 201 Charles Street, Prov· !. .... idence, RI 02904·2294 USA, GST No. 12189 2046 RT****. Pe· I I riodicals postage paid at Providence, Rl, and additional mail· Report of the Executive Director, State of AMS, 2006 . . f. .... :804 ing offices. POSTMASTER: Send address change notices to Notices oftheAmerican Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248 USA.] Publication here of the So· Report of the Treasurer, 2005 ...... 810 ciety's street address and the other information in brackets above is a technical requirement of the U.S. Postal Service. Tel: 401·455·4000, email: noti ces@ams. org. Call for Nominations for David P. Robbins Prize ...... 817 ©Copyright 2006 by the American Mathematical Society. All rights reserved. Printed in the United States of America.The paper used in this journal is acid-free and falls within the guidelines established. to ensure permanence and durability . Opinions expressed in signed Notices articles are those of the authors and do not necessarily reflect opinions of the editors or policies of the American Mathematical Society. Opinion

exposing students to mathematicians whose style of doing Complex NUJYIB3RS mathematics is identifiable to the students as being similar to the way they do mathematics. Additional stud­ Mathematicians appreciate that NUMB3RSis on television ies and full bibliographic references can be found at raising public awareness about the importance, beauty, and http://SimpsonsMath.com/wim.html#impacts. usefulness of mathematics, but in its second season, it has We as teachers are responsible for what we bring into been promoted as more than mere entertainment. The our own classrooms, but NCTM's name is associated with fact that the CBS website now offers classroom work­ the NUMB3RS worksheets, and so some may incorrectly sheets as part of an educational initiative cosponsored by assume that any difficulties or cautions are discussed in CBS, Texas Instruments (TI), and the National Council of the teacher's notes. In a session on NUMB3RS cospon­ Teachers of Mathematics (NCTM), and that recent items in sored by the AMS, MAA, and TI at the Joint Mathematics publications of the AMS and the Mathematical Association Meetings, Johnny Lott, past president of NCTM, mentioned of America (MAA) suggest that this initiative is a good way that the worksheet authors receive from TI a summary of to attract students to the mathematics profession blurs the all or part of an episode, and sometimes think, "What can distinction between NUMB3RS as television entertainment we do now? Can we do anything with this?" He said that and NUMB3RS as school curriculum. We should think care­ the worksheet writers are under intense time pressure to fully about how to use NUMB3RS and whether the math­ post worksheets before a show airs. Since the scripts they ematical community should endorse the show to the ex­ receive can differ from the final version, this can cause fun­ tent that it has. damental problems; many of the worksheets explore events The violence, sexual innuendos, and representations of that never happen on air or even contradict episode events. mathematicians on the show are complex for use with In addition, the worksheets do not contain links to the tra­ students. In an interview with NCTM, Gary Lorden, one of ditional curriculum, and he said, "We have no idea what the show's mathematics consultants, says, "I think it would teachers are doing with this and how teachers are using be great if they made [the relationship between Charlie, them." Until class testing, surveying, and revisions occur, the main character, and Amita, his former graduate stu­ at a minimum, there should be some kind of teacher forum dent] more of a collaboration and less of a beautiful as­ to discuss what works and what doesn't. sistant sort of thing." One of the CBS website questions Of course, TV portrayals of most professions are to some for students was whether Amita wrote a love letter to degree inaccurate glorifications and stereotypes; why Charlie, and some episodes have explored a romantic re­ should a portrayal of a mathematician be any different? lationship between them. She is still a student, obtaining If we are to follow President Bush's remarks from there­ a second Ph.D. in a related field. This could affect her fu­ cent State of the Union address, namely that "we need to ture career and would violate faculty guidelines at some encourage children to take more math and science," then institutions. For example, what happens when she needs we must identify and correct inaccurate portrayals of our a letter of recommendation (in the case they have a bad profession, especially stereotypes that could keep stu­ breakup, in the case they stay together, etc.)? If we are going dents out of math classes. Popular culture can be a pow­ to use Amita in the classroom, all of this comes along with erful way to engage students, but care must be taken to that use. Alex Kasman, who runs the Mathematical Fiction use it effectively. Without careful research and reflection website, points out a number of problems with Charlie, in­ related to the benefits and difficulties with using NUMB3RS, cluding social and emotional problems. In addition, Char­ we run the risk of having the positives outweighed by the lie often fits the stereotype of the gifted mathematician negatives. who readily finds the right answer. In the second season, the mathematics on the show has made less sense, such -Sarah]. Greenwald as "deep current sets", even though the worksheets are ad­ Appalachian State University vertised as exposing students to real-life mathematics [email protected] used in FBI cases. While these representations can work Editor's Note: Many newspaper and magazine articles well for the television show, they can be problematic for about the NUMB3RS television program have appeared in classroom use. the popular press. For summaries of these and other pop­ In fact, research studies have shown that stereotypical ular articles about mathematics, visit the AMS Math Digest, representations of mathematicians can actually discour­ http://www.ams.org/mathmedia/mathdigest. age students from pursuing more mathematics. For ex­ ample, one study showed that television commercials that are gender-stereotypic caused women to indicate less in­ terest in quantitative career fields than those who had not been exposed to the commercials. To encourage students to study mathematics, numerous authors recommend

AUGUST 2006 NOTICES OF THE AMS 741 Letters to the Editor highly-educated reader population re­ a general framework all of us function ally so inarticulate as to have to use in. Recently, all these thoughts came in such language in what appear to be or­ mind when the debate about electronic Mathematical Theory of Genetic dinary conversational or narrative set­ SEis and making them public online Code Needed tings? And, even if this has become erupted at OSU. We read a series of ar­ the case, does this scholarly journal ticles in a student newspaper the Lantern I again raise the possibility of devel­ have to publish it? oping a mathematical theory of the ge­ about SEiforms, RMPwebsite (http: I I - P. V. O'Neil ratemyprofessors.com)orrumors netic code. I again suggest that the ex­ University of Alabama at isting theory of codes could be used about federal standardized tests. A stu­ Birmingham dent Timo Atkinson is frank and straight­ to do this. At present coding theo­ [email protected] rists develop their subject, bio­ forward: "When we fill out these evalu­ ations, we answer questions that are chemists work on the sequencing (Received April 24, 2006) problem and related matters, and not geared toward how much you there is virtually no communication learned, but rather instructor organi­ zation and teaching effectiveness." The between them. Another Nobel Prize Winning students' perception ofTEACHING EF­ The potential benefits of better Mathematician communication between mathemati­ FECTIVENESS has nothing to do with In a letter in the April 2006 issue, Sir HOW MUCH YOU LEARNED. A teacher cians and biochemists are great, and Michael Atiyah mentions that the only the potential medical benefits to the who is a students' hero pictured by An­ mathematician to win a Nobel Prize nie Hall gives students the grade of their general public are still greater. Here for Literature was Bertrand Russell. is an example: own choice. As we learn on his RMPpage: This is not true: in 1904, the Nobel "The guy is flippin nuts. The class is like There is a class of degenerative dis­ Prize for Literature was awarded to eases in which the DNA of an affected a quarter long circus but in the end you the spanish mathematician Jose get to give yourself whatever grade you person behaves in the following way. Echegaray. First the DNA appears to be random. want." "Very easy class, but you won't -Francese Rossello learn much." "Veryverygreatteacher." As the disease begins, the DNA breaks University of the Balearic Islands "Very amusing professor, but not very up into long segments of equal length. [email protected] As the disease progresses these seg­ instructive." High eval rating is guar­ anteed. ments break up into shorter segments (Received April 28, 2006) of the same length. This process is But his colleague in Engineering repeated until the DNA degenerates College has perfect RMP rating 5.0 completely and becomes something Student Evaluations, Grades, with the following comments: "Easi­ like TAGTAGTAGTAGTAG .... and the Internet est class I've taken in a long time. Biochemists are puzzled by this Over the last thirty years, the system ... class is four days a week, but you phenomenon, but mathematicians of student evaluation of teachers in only have to go twice to get the ma­ need not be. The pattern of degener­ colleges evolved-step by step-as a terial. Tests are EXACTLY like the ation is precisely analogous to the be­ result of an implicit plot by academic homework, no surprises. Really nice havior of a linear recursive sequence administrators (who are unable to fill teacher and a good guy." "Bring him over GF(4) or Z(4) when terms in the classes by students properly prepared a bottle of scotch and you've got an denominator of the generating func­ to attend these classes) and by un­ A [happy face]." A Business College tion are specialized to zero. This ex­ qualified students (who want to be student is almost poetic: "Practice ample, and many others, suggest that awarded high grades without either questions are for chumps, and Sam­ DNA consists at least in part of linear having or getting skills and knowl­ ple exams is how we roll." (In 1998 the recursive sequences. edge). For great educational experi­ Notices published my letter on how de­ At present there is no mathemati­ ence- nobody talks about great edu­ structive sample tests are for under­ cal theory of the genetic code. But cation-teachers are an obstacle or a graduate mathematical education.) perhaps we could keep the idea of nuisance. They should be intimidated Will these pedagogical methods such a theory alive, until we have and pushed to certify illiteracy by per­ make the OSU a national leader in col­ world enough and time to examine it. fect grades. The use of student eval­ lege education? Or are they, together -Sherwood Washburn uation (SEI scores) by administrators with SEI procedures, pillars of an Seton Hall University in making personnel decisions on EDUCATION-LITE model of a store SherwoWashbu@aol .com promotion, tenure, and salary ad­ where sophisticated customers are justments became the whip which shopping for cheaper grades and dis­ (Received April 4, 2006) keeps the faculty in line and keeps counted diplomas? grade inflation (or to say it more sim­ -Boris Mityagin Fecal Language ply; cheating of the public) intact. Ohio State University I notice an increasingly common use These abstract comments are not [email protected] of fecal language in Notices articles necessarily related to Ohio State Uni­ (e.g., page 539 of May 2006). Is our versity or my department but they give (Received May 3, 2006)

742 NOTICES OF THE AMS VOLUME 53, NUMBER 7 :: Math Imagery Home :: Galleries & Museums :: Anicles & Resources :: Mos t viewed ::

The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals. Rose windows, oriental rugs. mosaics and tilings. mathematician1 Geometric forms were fundamental to the cubists and many abstract like a P.ainter or poet, expressionists, and award - winning sculptors have used topology as is a maker of patterns. the basis for their pieces. Dutch artist M.C. Escher represe nted If his pattem6 arc more infinity. MObius bands. tessellations. deformations. reflections. permanent than theirs, Platonic solids. spirals, symmetry. and the hyperbolic plane in his it is becaU5e the9 are works. made with ideas. Mathematicians and artists continue to create stunning works in all -G.H.Ha.-.!!j, media and to explore the visualization of mathematics --origami. At.tatheMatk.ian... ~ computer- generated landscapes, tesselations. fractals, anamorphic an. and more.

Explore the world of mathematiCs and art, send an e- p featured worl

Thomas Hull " The mathematics of origami This is a "Jersi on of the Ow- Hull ·Fi"Je should be a fami liar sight to those who through geometry textbooks. Read about Callery. Dear Peter, --- Thomas Hull. Photograph by Nancy Here's one of the a-postcards from the site.

--- Anne M. Burns Nancy

Peoplesymmetr ha"Jeies . longThe dbeenisco"Jery fasci ofn ated,~w~~i t:~h:(~·:~{.~~.~~~~~~~~~~~~~~~~~ IIIII greater wealth of patterns, some series of works. The co"Jer illustration on this 1 symmetric under a group generated by two MObius transformations. These are not distance­ pre serving, but they do preserve angles between curves and they map circles to circles. See Double Cusp Croup by David J. Wright In Notices of the American Mathematical Socie ty !December 2004, p. 1322).

AF:TICU::; 8 F.:E:SOUF.:CE:S · M.C. Escher: the Official WebSite Mathematics and Ait . (The theme for Mathematics The KnotPiot Sne Awareneu Month in 20031 Bridges . Mat hem atical Conneclfons in An, Music. and International Society of the Arts. Mathematics and SCience Architecture Images and Mathema!ics, MathArChlves Maths and Art: the whist/estop tour, by Lewis Mathematics Mustwm (Iapan) Oartnell Kalen dar. by Herwig Hauser Geometry in Art & Architecture, by Paul Ca lter \Da rtmouth Co ll ege) Harmony and Proportion , by John Boyd · Brent Viewpoints: Mathemalics and An. by Annallsa CrJnn ell (franklin & Marshall College) and Marc Frantz (lnd lanll University! Mathematics and Art, the April 2003 Featt.ne Co lumn by Joe Malktvitch Art & Music, MathArchi"Jt S www.ams.org/mathimagery The Differential Geometry and Physical Basis for the Applications of Feynman Diagrams SarnuelL.Afarateck

n May 11 of last year, the late Richard General relativity sparked mathematicians' in­ Feynrnan's birthday, a stamp was ded­ terest in parallel transport, eventually leading to icated to Feynrnan at the post office in the development of fiber bundles in differential 0 Far Rockaway, New York, Feynrnan's geometry. After physicists achieved success using boyhood home. (At the same time, the gauge theory, mathematicians applied it to differ­ United States Postal Service issued three other ential geometry. The story begins with Maxwell's stamps honoring the scientists Josiah Willard Gibbs equations. In this story the vector potential A goes and Barbara McClintock, and the mathematician from being a mathematical construct used to fa­ John von Neumann.) cilitate problem solution in electromagnetism to The design of the stamp tells a wonderful story. taking center stage by causing the shift in the in­ The Feynrnan diagrams on it show how Feynrnan's terference pattern in the Aharonov-Bohm solenoid work, originally applicable to QED, for which he won effect. As the generalized four-vector All, it be­ the Nobel Prize, was then later used to elucidate comes the gauge field that mediates the electro­ the electro weak force. The design is meaningful to magnetic interaction and the electroweak and both mathematicians and physicists. For mathe­ strong interactions in the standard model of maticians, it demonstrates the application of dif­ physics; All is understood as the connection on ferential geometry. For physicists, it depicts the ver­ fiber-bundles in differential geometry. The modern ification of QED; the application of the Yang-Mills reader would be unaccustomed to the form in equations; and the establishment and experimen­ which Maxwell equations first appeared. They are tal verification of the electroweak force, the first easily recognizable when expressed using vector step in the creation of the standard model. The analysis in the Heaviside-Gibbs formulation. physicists used gauge theory to achieve this and were for the most part unaware of the develop­ Maxwell's Equations ments in differential geometry. Similarly, mathe­ The equations used to establish Maxwell's equations maticians developed fiber bundle theory without in vacuo expressed in Heaviside-Lorentz rational­ knowing that it could be applied to physics. We ized units are: should, however, remember that in general rela­ tivity, Einstein introduced geometry into physics. (1) \7 · E = p (Gauss's law) And as we will relate below, Weyl did so for elec­ tromagnetism. (2) \7 · B = 0 (No magnetic monopoles)

Samuel L. Marateck is a senior lecturer at the Courant In­ (3) \7 x B = j (Ampere's law) stitute ofMathematical Sciences, New York University. His email address is marateck@cs. nyu. edu. (4) \7 x E = -oB /ot (Faraday's and Lenz's law)

744 NOTICES OF THE AMS VOLUME 53, NUMBER 7 where E and B are respectively the electric and p-form and Mis a p + 1 dimension oriented man­ magnetic fields; p and j are the charge density and ifold with boundary oM. For the purposes of this electric current. The continuity equation which dic­ article a manifold is simply a space that is locally tates the conservation of charge, Euclidean. The remark is that equation (8), i.e., d 2 = 0, is related to the principle that the bound­ (5) v-i+op/ot=o, ary of a region has no boundary, i.e., o2 M = 0 . This last principle once noticed, is geometrically ob­ indicates that Maxwell's equations describe a local vious. The fact that d 2 = 0 complements theory, since you cannot destroy a charge locally o2M = 0 can be seen from faz M W = foM dw = and recreate it at a distant point instantaneously. fM d2w = 0. Indeed Yang1 notes that equation (8) The concept that the theory should be local is the complements o2 M = 0 which, as we show later, is cornerstone of the gauge theory used in quantum in keeping with his championing of geometry's in­ field theory, resulting in the Yang-Mills theory, the fluence on field theory. basis of the standard model. Gauge lnvariance Maxwell realized that since In a 1918 article Hermann Weyl2 tried to combine (6) 'V·'VxB=O, electromagnetism and gravity by requiring the the­ ory to be invariant under a local scale change of equation (3) is inconsistent with (5); he altered (3) the metric, i.e., g v ~ g veiX(x l, where x is a 4- to read 11 11 vector. This attempt was unsuccessful and was (3 ') v x :B = j + a£ ; at criticized by Einstein for being inconsistent with observed physical results. It predicted that a vec­ Thus a local conservation law mandated the addi­ tor parallel transported from point p to q would tion of the a£ ;at term. Although equations (1), (2), have a length that was path dependent. Similarly, (3') and (4) are collectively known as Maxwell's the time interval between ticks of a clock would also equations, Maxwell himself was responsible only depend on the path on which the clock was trans­ for (3'). ported. The article did, however, introduce Maxwell calculated the speed of a wave propa­ • the term "gauge invariance"; his term was Eich­ gated by the final set of equations and found its invarianz. It refers to invariance under his scale velocity very close to the speed of light. He thus change. The first use of "gauge invariance" in hypothesized that light was an electromagnetic English3 was in Weyl's translation4 of his famous wave. Since the curl of a vector cannot be calculated 1929 paper. in two dimensions, Maxwell's equations indicate • the geometric interpretation of electromagnet­ that light, as we know it, cannot exist in a two­ ism. dimensional world. This is the first clue that elec­ • the beginnings of nonabelian gauge theory. The tromagnetism is bound up with geometry. ln fact, similarity of Weyl's theory to nonabelian gauge equation (6) is the vector analysis equivalent of the theory is more striking in his 1929 paper. differential geometry result stating that if {3 is a p-form and d/3 is its exterior derivative, then d(d/3) By 1929 Maxwell's equations had been com­ ord2 /3=0. bined with quantum mechanics to produce the Unlike the laws ofNewtonianmechanics, Maxwell's start of quantum electrodynamics. In his 1929 ar­ equations carry over to relativistic frames. The non­ ticle5 Weyl turned from trying to unify electro­ homogeneous equations, (1) and (3'), become magnetism and gravity to following a suggestion originally thought to have been made by Fritz Lon­ (7) don in his 192 7 article6 and introduced as a phase while the homogeneous equations, (2) and (4), be­ factor an exponential in which the phase Oi is pre­ come ceded by the imaginary unit i, e.g., e+iqC<(xl, in the wave function for the wave equations (for instance, (8) E1Xf3Y 8 Fyii = o13 o, the Dirac equation is (i;yllo11 - m)l/J = 0). It is here where EIX{3yii is the Levi-Civita symbol, FJlV = oil AV that Weyl correctly formulated gauge theory as a AP, A 0 is the scalar potential, and Ai's (i = 1, -av 1 Yang, C. N., Physics Today 6 (1980), 42. 2, 3) the components of the vector potential Note A. 2 that both equations (7) and (8) are manifestly co­ Weyl, Hermann, Sitzwingsber. Preuss. Akad., Berlin, 1919, p. 465. variant. In a later section we will show that equa­ tion (8) is due to the principle d 2 w = 0, where w 3 See jackson, ]. D., and Okun, L. B., Rev. Mod. Phys. 73 is a p-form. (2001), 663. The following remark can be understood in dif­ 4 Weyl, H., Proc. Natl. Acad. Sci. 15 (1929), 32. ferential geometry terms by using the generalized 5 Weyl, Hermann, Z. f Phys. 330 (1929), 56. Stoke's theorem: fM dw = faM w, where w is a 6 London, Fritz, Z. f Phys. 42 (1927), 375.

AUGUST 2006 NOTICES OF THE AMS 745 symmetry principle from which electromagnetism charge q must be conserved.ll Thus gauge invari­ could be derived. It was to become the driving ance dictates charge conservation. By Noether's force in the development of quantum field theory. theorem, a conserved current is associated with a In their 2001 Rev. Mod. Phys. paper, Jackson and symmetry. Here the symmetry is the nonphysical Okun point out that in a 1926 paper7 predating Lon­ rotation invariance in an internal space called a don's, Fock showed that for a quantum theory of fiber. In electromagnetism the rotations form the charged particles interacting with the electromag­ group U(l), the group of unitary !-dimensional netic field, invariance under a gauge transforma­ matrices. U(l) is an example of a gauge group, and tion of the potentials required multiplication of the the fiber is 5 1, the circle. wave function by the now well-known phase fac­ A fiber bundle is determined by two manifolds tor. Many subsequent authors incorrectly cited the and the structure group G which acts on the fiber: date of Fock's paper as 1927. Weyl's 1929 article­ the first manifold, called the total space E, consists along with his 1918 one, and Fock's and London's, of many copies of the fiber F-one for each point and other key articles-appears in translation in a in the second manifold, the base manifold Mwhich work by O'Raifeartaigh8 with his comments. Yang9 discusses Weyl's gauge theory results as reported for our discussion is the space-time manifold. The fibers are said to project down to the base mani­ by Pauli10 as a source for Yang-Mills gauge theory (although Yang did not find out until much later fold. A principal fiber bundle12 is a fiber bundle in that these were Weyl's results): which the structure group G acts on the total space Ein such a way that each fiber is mapped onto it­ ... I was very much impressed with the self and the action of an individual fiber looks like idea that charge conservation was re­ the action of the structure group on itself by left­ lated to the invariance of the theory translation. In particular, the fiber Fis diffeomor­ under phase changes and even more phic to the structure group G. impressed with the fact the gauge­ The gauge principle shows how electromagnet­ invariance determined all the electro­ ism can be introduced into quantum mechanics. magnetic interactions .... The transformation o/1 ~ o/1 + iqAJl is also called For the wave equations to be gauge invariant, i.e., the minimal principle and the operation o/1 + iqAJl have the same form after the gauge transformation is the covariant derivative of differential geometry, as before, the local phase transformation D = d + iqA, where A is the connection on a fiber

746 NOTICES OF THE AMS VOLUME 53, NUMBER 7 which, as we will see in the next section, is the field interference term in the superposition of the so­ strength F defined as F = dA. lution for the upper path and of that for the lower path produces a difference in the phase of the Differential Geometry electrons' wave function called a phase shift. Here the phase shift is (q I en) pA(x)dx. By Stoke's theo­ Differential geometry-principally developed by rem, the phase shift is (q I eh)cp, where ¢ is the Levi-Civita, Cartan, Poincare, de Rham, Whitney, magnetic flux in the solenoid, f B · dS. Mathemat­ Hodge, Chern, Steemod and Ehresmann-led to ically, their proposal corresponds to the fact that the development of fiber bundle theory, which is even if the curvature (the electromagnetic field used in explaining the geometric content of strength) of the connection vanishes (as it does out­ Maxwell's equations. It was later used to explain side the solenoid), parallel transport along non­ Yang-Mills theory and to develop string theory. homotopic paths can still be path-dependent, pro­ The successes of gauge theory in physics sparked ducing a shift in the diffraction pattern. mathematicians' interest in it. In the 1970s Sir Chambers15 performed an experiment to test the Michael Atiyah initiated the study of the mathe­ Aharonov and Bohm (AB) effect. The experiment, matics of the Yang-Mills equations; and in 1983 his however, was criticized because of leakage from the student Simon Donaldson, using Yang-Mills theory, solenoid. Tonomura16 et al. performed beautiful ex­ discovered a unique property of smooth mani­ periments that indeed verified the AB prediction. folds13 in ~ 4 . Michael Freedman went on to prove Wu and Yang17 analyzed the prediction of that there exist multiple exotic differential struc­ Aharonov and Bohm and comment that different 4 tures only on ~ . It is known that in other dimen­ phase shifts (q 1en)¢ may describe the same in­ sions the standard differential structure on ~n is terference pattern, whereas the phase factor eUq /chl

The solution of (112m)(-in\7- qAic)2 !fJ+ - A 0dt + Axdx + Aydy + A 2 dz. Evaluating dA and qV!fJ = EljJ, the time-independent Schrbdinger's realizing that the wedge product dxi 1\ dxj = equation for a charged particle, is - dxj 1\ dxi and therefore dxj 1\ dxj = 0, where dx0 1/Jo(x)eUq /ch) Js(xl A(y)ds' (y) where 1/Jo(X) is the solution is dt, dx1 is dx, dx2 is dy and dx3 is dz, produces of the equation for A equals zero and s(x) repre­ a 2-form consisting of terms such as (oxAo+ sents each of the two paths. Here c is the speed of light, and n is Plank's constant divided by 2rr. The 15 chambers, R. G., Phys. Rev. Lett. 5 (1960), 3. 16 Tonomura,Akira, et. al., Phys. Rev. Lett. 48 (1982), 1443; 13 Donaldson, S. K., Bull. Amer. Math. Soc. 8 (1983), 81. and Phys. Rev. Lett. 56 (1986), 792. 14 Aharonov, Y., and Bohm, D., Phys. Rev. 115 (1959), 485. 17 Wu, T. T., and Yang, C. N., Phys. Rev. D 12( 1975), 3845.

AUGUST 2006 NOTICES OF THE AMS 747 orAx)dtdx and (oxAy - oyAx)dxdy. When all the is(-+++). Thus the Hodge star takes a spatial1-form components are evaluated, these terms become dxidt into a spatial 2-form and vice versa with a respectively \lAo + oA/ or and \l x A. The analysis sign change. up to now has been purely mathematical. To give The nonhomogeneous Maxwell's equations are it physical significance we associate these terms then expressed by with the field strengths Band E. In electromagnetic (15) d<' F = 0 (source-free) theory, two fundamental principles are \l · B = 0 (no magnetic monopoles) and for time-indepen­ (15') d<'F = 1'] (non-source-free) dent fields E = - \l A 0 (the electromagnetic field is

the gradient of the scalar potential), so consistency where the 2-form 1'F and the 3-form 1'] are respec­ dictates that in the time-dependent case, we assign tively the Hodge duals ofF and]. ''F and ''J are de­ the two terms to B and :E respectively: fined as

(11) B = \l X A and :E = -\lAo - orA. *F = - Bxdxdt - Bydydt - B2 dzdt (16) The gradient, curl, and divergence are spatial op­ + Exdydz + Ey dzdx + Ezdxdy erators-they involve the differentials dx, dy, and dz. The exterior derivative of a scalar is the gradi­ *1 = pdxdydz - fxdtdydz ent, the exterior derivative of a spatial1-form is the (17) - ]ydtdzdx- ] 2 dtdxdy curl, and the exterior derivative of a spatial two­ form is the divergence. In the 1-form A, the -A0 dt Thus the Hodge star reverses the roles of :E and B is a spatial scalar and when the exterior derivative from what they were in F. In ''f the coefficient of is applied gives rise to \l A 0 . The remaining terms the spatial1-form is now - B, which will produce in A are the coefficients of dx; constituting a spa­ the curl in the nonhomogeneous Maxwell's equa­ tial 1-form and thus produce \l x A. tions; and the coefficient of the spatial 2-form is We define the field strength F as F = dA, and E, which will produce the divergence. In IRI.n the from equation (10) we see that the field strength Hodge star operation on a p-form produces an is the curvature of the connection A. Using the (n-p)-form. Thus the form of Maxwell's equations equations in (11) and the 2-form dA, we get is dictated by the fact that we live in a four­ dimensional world. When the 1-formA undergoes F = Exdxdt + Eydydt + E2 dzdt (12) the local gauge transformation A ~ A + doc(x), dA + Bxdydz + Bydzdx + Bdxdy remains the same, since d 2 oc = 0. Since Band :E are where, for example, dxdt is the wedge product unchanged, Maxwell's theory is gauge invariant. dx 1\ dt. Since d2 A = 0 The Dirac and Electromagnetism (13) dF = 0. Lagrangians Evaluating dF gives the homogeneous Maxwell's To prepare for the discussion of the Yang-Mills equations. In equation (12), since theE part is a spa­ equations, let's investigate the Dirac and Electro­ tial1-form, when the exterior derivative is applied magnetism Lagrangians. The Dirac equation is it produces the \l x :E part of Maxwell's homoge­ neous equations. Since the B part of equation (12) (18) (iylloll - m)tJl = o, is a spatial2-form, it results in the \l · B part. Since where the speed of light, c, and Plank's constant dF = 0, F is said to be a closed 2-form. n are set to one. Its Lagrangian density is To get the expression for the nonhomogeneous Maxwell's equations, i.e., the equivalent of equation (19) (7), we use The Euler-Lagrange equations minimize the action (14) J = pdt + f xdx + ]ydy + f zd z S where S = f Ldx. Using the Euler-Lagrange equa­ tion where the differentiation is with respect to <[;, and calculate the Hodge dual using the Hodge star i.e., operator. The Hodge duals are defined18 by *Frxf3 = 1/2Erxf3y8FY8 and 1']rxf3y = Erxf3y8]8 . The (20) Hodge star19 operates on the differentials in equa­ tions (12) and (14) using ''(dxidt) = dxjdxk and yields equation (18). ,·,(dxjdxk) = -dxidt, where i, j, and k refer to x, y, The same gauge invariant argument used in the and z and are taken in cyclic order. The metric used "Gauge Invariance" section applies here. In order for the Lagrangian to be invariant under the phase 18 Misner, C. W., Thorne, K. S., and Wheeler, ]. A., Gravi­ transformation tjJ(x) - tjJ(x)e+iqrx(x), this transfor­ tation, Freeman, San Francisco 1973. mation has to be accompanied by the local gauge 19 Flanders, H., Differential Forms, Academic Press, 1963. transformation All -All - q- 1olloc(x) and oil has

748 NOTICES OF THE AMS VOLUME 53, NUMBER 7 to be replaced by oil + ieAw The Lagrangian den­ 1/13 7, for a good approximation we can neglect the sity becomes fact that the electromagnetic forces break this sym­ metry. By Noether's theorem, if there is a rota­ (21) L = ljj(iylloll- m)!JJ- eljjyll!JJAil. tional symmetry in isospin space, the total iso­ The last term is the equivalent of the interaction en­ topic spin is conserved. This hypothesis enables us ergy with the electromagnetic field, jll Aw In order to estimate relative rates of the strong interactions for the Euler-Lagrangian equation differentiated in which the final state has a given isospin. The spin with respect to All to yield the inhomogeneous matrices turn out to be the Pauli matrices

or equivalently Fllv = (ollEv - ovEil) + iE[Eil, Evl, The Yang-Mills Theory where E is the connection on a principal fiber bun­ The Yang-Mills theory incorporates isotopic spin dle, i.e., the gauge potential and where E is the symmetry introduced in 19 3 2 by Heisenberg, who coupling constant analagous to q in (9). Therefore, observed that the proton and neutron masses are as opposed to the electromagnetic field strength almost the same (938.272 MeV versus 939.566 MeV which is linear, their field strength is nonlinear. respectively). He hypothesized that if the electro­ They proposed using a local phase, magnetic field were turned off, the masses would be equal and the proton and neutron would react (27) !jJ(x) ~ !jJ(x)e - im1

AUGUST 2006 NOTICES OF THE AMS 749 as F = dB + ~ iE[B, B]. As opposed to the Maxwell's intermediate vector bosons, where GeVrepresents equations case, the exterior derivative of the cur­ a billion electron volts. The W ± was discovered23 vature dF does not equal zero because of the com­ in 1983 (its mass is now reported at 80.425 Gev ± mutator in the expression for the curvature. Thus 0.033 GeV), and later that year the Z 0 was discov­ the exterior derivative for the 2-form F has to be ered24 (its mass is now reported at a mass of 91.187 altered to include the connection Bin order to gen­ ± 0.002 GeV). eralize the homogeneous Maxwell's equations. The Euler-Lagrange equations for equation (28) The Yang-Mills Lagrangian give the Dirac equation (28) L =

750 NOTICES OF THE AMS VOLUME 53. NUMBER 7 occurring,26 and the W can radiate, producing a photon in W- W + :y. The Yang-Mills field strength contribution (also called the kinetic term) to the differential geome­ try Lagrangian density, where k is a constant is:

(33) L = -kTr(F 1\ *F).

The Euler-Lagrange equations produce d8 F = 0 (it is called the Bianchi Identity, which is purely geo­ metric), and in the absence of matter fields the field equation d8 * F = 0, where d8 is the exterior co­ variant derivative. These are the Yang-Mills equa­ tions in compact form. The Feynman Stamp In QED after Schwinger, Tomonaga and Feynman addressed the singularities produced by the self­ would not conserve energy and momentum. To energy of the electron by renormalizing the theory. see this you must first remember that since the pho­ They were then exceedingly successful in predict­ ton has zero mass due to the gauge invariance of ing phenomena such as the Lamb shift and anom­ electromagnetic theory, its energy and momentum alous magnetic moment of the electron. are equal. Thus {3, which equals ~ , has the value 1; Feynman introduced27 schematic diagrams, but {3 = ~ . so that the photon's velocity is always today called Feynman diagrams, to facilitate cal­ c, the speed of light. In the electron-positron cen- culations of particle interaction parameters. Ex­ ter of mass frame (more aptly called the ternal particles, represented b y lines (edges) con­ center of momentum frame, since the nected to only one vertex are real, i.e., observable. net momentum of all the particles is They are said to be on the mass shell, meaning their zero there), the electron and positron four-momentum squared equals their actual mass, momenta are equal and are in opposite i.e., m2 = £ 2 - p 2 • Internal particles are represented directions. The photon travels at the by lines that connect vertices and are therefore in­ speed of light, and therefore its mo­ termediate states-that is why they are said to me­ mentum cannot be zero; but there is no diate the interaction. They are virtual and are con­ particle to cancel its momentum, so the sidered to be off the mass shell. This means their interaction cannot occur. (For it to occur four-momentum squared differs from the value requires a Coloumb field from a nearby Figure 1. A pair of their actual mass. This is done so that four­ nucleus to provide a virtual photon that production vertex. momentum is conserved at each vertex. The ra­ transfers momentum, producing a nu­ tionale for this difference is the application of the clear recoil.) Therefore the :yin the di­ uncertainty principle t.E · M = 1'1. . Since M, the agram is internal. Its mass is off the time spent between external states is very small for mass shell and cannot equal its nor­ that short time period, t.E, and thus the difference mal value, i.e., zero. between the actual and calculated mass can be The diagram on the lower-left of the large. In the following Feynman diagrams, the time stamp (Figure 2) is also a vertex diagram axis is vertical upwards. and represents an electron-positron The diagram on the upper-left of the stamp (Fig­ pair annihilation producing a :y. Again, ure 1) is a vertex diagram and as such represents if all the particles are external, conser- Figure 2. A pair a component of a Feynman diagram. It illustrates vation energy and momentum prohibit annihilation v~rtex. the creation of an electron-positron }Jair from a pho­ the reaction from occurring; therefore ton, :y; it is called pair production. The :y is repre­ the :y must be virtual. sented by a wavy line. The Feynman-Stuckelberg in­ The diagram on the bottom to the terpretation of negative-energy solutions indicates right of Feynman (Figure 3) was meant that here the positron, the electron's antiparticle, to represent an electron-electron scat­ which is propagating forward in time, is in all ways tering with a single photon exchange. equivalent to an electron going backwards in time. This is called M0ller scattering. (It can, ·If all the particles here were external, the process however, represent any number of in­ teractions exchanging a photon.) The 26 This is indicated in Figure 1 of the Yang-Mills paper. See diagram represents the t-channel of also F. • Halzen. .and A. D. Martin, Quarks and Leptons, M0ller scattering; there is another dia- Figure 3. Electron­ john Wiley & Sons, 1984, p. 343. gram not shown here representing the electron (M 0IIer) 27 Feynman, R. P., Phys. Rev. 76 (1949), 769. u-channel contribution, where u, t and scattering.

AUGUST 2006 NOTICES OF THE AMS 751 another variable s are called the Mandelstam vari­ d ~ w- + u shown in Figure 6, and flavor-con­ ables. They are used in general to describe 2-body serving transitions, e.g., d ~ Z 0 + d of the elec­ ~ 2-body interactions. If you rotate the diagram troweak force-the u and d quarks have different in Figure 3 by 90°, you have the s -channel diagram values of flavor. The process in Figure 6 occurs for for electron-positron scattering, called Bhabha scat­ instance in {3 decay, where a neutron (udd) decays tering, shown in Figure 4 but not on the stamp. Here into a proton (udu) and electron and an antineu­ an electron and positron annihilate, trino. What happens is that the transition producing a virtual photon which in d ~ u + w- corresponds to a rotation in isospin turn produces an electron-positron pair. space. This rotation is caused by the virtual w­ There is also a t-channel contribution which mediates the decay. It in turn decays into an to Bhabha scattering. The cross-section electron and an antineutrino. The calculations for for Bhabha scattering can be easily ob­ these transitions all use the Yang-Mills theory. Al­ tained from the one for M0ller scatter­ though quarks are confined in hadrons (particles ing by interchanging the s and u in the that undergo strong interactions like the proton and cross-section expression in a process neutron), they are free to interact with the inter­ called crossing. Small angle Bhabha scat- mediate vector bosons. Figure 4. Electron- tering is used to test the luminosity in positron (Bhabha) e+-e - colliding beam accelerators. Who Designed the Stamp? scattering. To the right of the M0ller scattering Feynman's daughter, Michelle, was sent a provi­ diagram is a vertex correction to elec­ sional version of the stamp by the United States tron scattering, shown in Figure 5, Postal Service and advised on the design of it by, where the extra photon forms a loop. among others, Ralph Leighton, coauthor with It is used to calculate both the anom­ Richard Feynman of two popular books, and Cal­ alous magnetic moment of the electron Tech's Steven Frautschi and Kip Thorne. Frautschi and muon, also the anomalous mag­ and Leighton edited the Feynman diagrams, and netic moment contribution to the Lamb Frautschi rearranged them and composed the final shift.28 The other two contributions to design. The person who chose the original Feynman the Lamb shift are the vacuum polar- diagrams that form the basis for the stamp re­ Figure 5. Radiative ization and the electron mass renor­ mains a mystery. correction. malization. The Lamb shift explains the splitting in the spectrum of the 2S 1 and Acknowledgements 2" 2Pl levels of hydrogen, whereas Dirac 2" The author thanks Jeff Cheeger, Bob Ehrlich, ]. D. theory alone incorrectly predicted that Jackson, and C. N. Yang for their suggestions on these two levels should be degenerate. the article. Their contributions improved the paper. The low-order solution of the Dirac The author especially thanks]. D. Jackson for gen­ w- d equation predicts a value of 2 for the erously giving of his time, and periodically pro­ g-factor used in the expression for the viding advice since the author first corresponded magnetic moment of the electron. The with him many years ago. vertex correction shown in Figure 5, Figure 6. A flavor non- however, alters the g-factor, producing conserving transition an anomalous magnetic moment con­ vertex. tribution, written as 9 ; 2 . When this and higher-order contributions are included, the calculated value of 9 ; 2 for the elec­ tron is 1159 652 460(127)(75) x 10- 12 and the ex- perimental value is 1159 652 193(10) x 10- 12 , where the numbers in parenthesis are the errors. This seven-significant figure agreement is a spec­ tacular triumph for QED. We need not emphasize that the calculations for all these diagrams use the gauge principal for quantum electrodynamics. The other diagrams on the stamp are all vertex diagrams and show how Feynman's work, originally applicable to QED, was then later used to elucidate the electroweak force. This is exemplified on the stamp by flavor-changing transitions, e.g.,

28 See, for instance, Griffith, David, Introduction to Ele­ mentary Particles, John Wiley and Sons, 1987, p. 156.

752 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Be sure to register for the joint Mathematics Meetings in New Orleans, january 5-8, 2007

Photographs courtesy of John Nitsche, M.D.; A Fellows Program fortheAMS

Editor's Note: This special section was organized by AMS president James Arthur (University of Toronto) and AMS Coun­ cil member Susan Friedlander (University of Illinois at Chicago). -Andy Magid

t the Joint Meetings in San Antonio in remind ourselves that mathematicians will never­ January, the AMS Council debated theless gain respect from others if their demeanor whether to place a proposal for an AMS reflects the pride they have in their subject. If it A passes, we can take comfort in Fellows Program before the general knowing that math­ membership. As had been the case in ematics ultimately belongs to all of us, and that we past meetings, the discussion was extensive. It was are able to express gratitude to those who have also thoughtful, and at times, quite passionate. brought us new ideas. These sentiments are of The final vote was very close. After first agreeing course not always part of our day-to-day thinking, that the proposal would require two-thirds support but I believe they approximate something we should by members to be implemented, Council voted be aiming for. 13-11 in favor of bringing it forward. In any case, I hope that members will think The vote by members will be a part of the AMS about the proposal, discuss it with colleagues, and fall elections. The formal proposal that will ap­ above all, vote on it! In fact, it would not be out of pear on the ballot has been reproduced below. It place for those with strong views to campaign vig­ is accompanied by two essays. David Eisenbud orously in support of their position. A large vote, summarizes arguments that have been made whatever the outcome, would be a clear indication against the proposal from his perspective of Im­ of the strength of our Society. mediate Past President. Ron Stern describes the ar­ -]ames Arthur, President guments in favor of the proposal from his vantage point as Dean of Physical Sciences at University of California, Irvine. I thank both David and Ron for the time and thought they have invested in these essays. Many mathematicians have strong feelings about the wisdom of creating a class of Fellows within our membership. I was personally against the idea at the beginning, but after hearing eloquent argu­ ments in its favor, I am now sitting resolutely on the fence! I do believe that the discussion has been healthy, for it goes to the heart of how we regard the practice of mathematics. I trust that all of us will come to terms with the outcome, however the vote turns out. If the proposal is rejected (re­ member, it will need a two-thirds vote), we should

754 NOTICES OF THE AMS VOLUME 53, NUMBER 7 F. Each year all Fellows are invited to a recep­ A Proposal for a tion at the AMS annual meeting, and the new Fel­ lows are introduced at this reception, followed by Fellows Program of a press release. New Fellows receive a certificate and their names are listed on the AMS website. The names of new Fellows are also included in the theAMS Notices. G. If they are not already Fellows, the AMS pres­ The Goals of the Fellows Program are: ident and secretary are made Fellows when they • To create an enlarged class of mathematicians take office. recognized by their peers as distinguished for their contributions to the profession. II. Election Process • To honor not only the extraordinary but also the A New Fellows are elected each year after a nom­ excellent. ination process. Eligible voters consist of current • To lift the morale of the profession by provid­ Fellows who are also members of the Society. Both ing an honor more accessible than those cur­ the election and the nomination process are car­ rently available. ried out under the direction of the secretary with • To make mathematicians more competitive for help from the AMS staff. awards, promotions, and honors when they are B. The Election Committee will consist of nine being compared with colleagues from other dis­ members of the AMS who are also Fellows, each ciplines. serving a three-year term, and with three new mem­ • To support the advancement of more mathe­ bers appointed each year. The AMS president, in maticians in leadership positions in their own consultation with the Executive Committee of the institutions and in the broader society. Council, nominates the new members of the Elec­ tion Committee in November of each year. At the I. Program (steady-state) same time, the president nominates a continuing A The Fellows Program of the American Mathe­ member of the Election Committee to serve as matical Society recognizes members who have chair. The president's choices are approved by made outstanding contributions to the creation, ex­ Council at its January meeting. position, advancement, communication, and uti­ C. The Election Committee accepts nominations lization of mathematics. for Fellows between February 1 and March 31 each B. The responsibilities of the Fellows are: year. Nominations are made by members of the • To take part in the election of new Fellows, AMS. A member can nominate no more than 4 • To present a "public face" of excellence in nominees a year. mathematics, and D. To be eligible for nomination to Fellowship, • To advise the president and/or the Council on an individual must be an AMS member for the year public matters when requested. in which he or she is nominated as well as for the C. All AMS members are eligible to be elected Fel­ prior year. lows. E. A nominator must supply a package with the D. The target number of Fellows will be deter­ following information on the nominee: mined by the AMS Council as a percentage of the 1. A curriculum vitae of no more than five pages. 2. A citation of fifty words or less explaining the number of eligible members.1 The target percent­ person's accomplishments. age will be revisited by the Council at least once 3. A statement of cause of 500 words or less ex­ every ten years and may be increased or decreased plaining why the individual meets the criteria of in light of the history of the nomination and elec­ Fellowship. tion process. The intended size of each year's class 4. The signatures of the nominator and three ad­ of new Fellows should be set with this target size ditional AMS members who support the nomi­ in mind. nation, with at least two of these individuals cur­ E. Following an election process (see below), in­ rent Fellows. dividuals are invited to become Fellows. They may F. A person can be nominated no more than 3 decline and they may also resign as Fellows at any times in a 5-year period. time. G. Each year the January Council provides a 1 This proposal's recommendation to Council is 5% of eli­ guideline for the number of nominations to appear gible members. At present there are about 30,000 eligi­ on the ballot. The Election Committee assembles the ble members so the number of Fellows would be about ballot from the nominations bearing in mind this 1,500. guideline, diversity of every kind, and the quality

AUGUST 2006 NOTICES OF THE AMS 755 and quantity of the external nominations. The Elec­ 1. Given an invited AMS address (including at tion Committee has the discretion to make nomi­ Joint Meetings). nations itself to fulfill the general goals of the Fel­ 2. Been awarded an AMS prize. lowship. 3. Given an invited address at an ICM (Interna­ tional Congress of Mathematicians). H. The ballot is available electronically (only) and voting is conducted throughout the month of B. An additional 50 Fellows are selected by a com­ September each year. The curriculum vitae and ci­ mittee appointed by the president with the advice of the Executive Committee of the Council. Partic­ tation for each candidate will be available to all el­ ular attention will be paid to selecting AMS mem­ igible voters. Election is by plurality with the top bers recognized for their contributions to educa­ one-half of the candidates elected. In case of a tie, tion and service to the profession. more than one-half of the candidates may be elected. C. For the initial "seed pool" of Fellows there is no length of AMS membership required. Any per­ I. Those nominees elected are invited by the son who falls into one of the three categories above, president to become new Fellows of the AMS as of and who is an AMS member during the year in January 1 of the following year. which this program is initiated will be invited to become a Fellow. Ill. Initial Implementation D. At least ten (10), but no more than fifty (50), A. In the initial year of the program, all eligible AMS new Fellows are elected each year until the total members who have done one or more of the fol­ number of Fellows reaches 95% of the targeted lowing are invited to become AMS Fellows.2 size of the Fellowship.3

2 The seeding process described in III.A would produce of­ fers ofFellows status to more than BOO current AMS mem­ 3 If 1,000 Fellows are named through the initial seeding, bers. The group of Invited Speakers also includes ap­ then we estimate that a steady state of 1,500 would be proximately 400 additional individuals who are not achieved in approximately 10-20 years under the enclosed currently AMS members. plan.

756 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Fellows program flies in the face of this culture by rigidly ranking mathematicians. Sdence or Politics at • Politicization in a Fellows program would be distracting and destructive: One cannot imag­ theAMS?-A ine that the appointment of Fellows won't be a highly charged process! What favor can I do for Dr. Divisive Proposal X, who has just been appointed to the selection committee? Even worse, what pressure can I put on him, in seeing that his students are not tenured if David Eisenbud he doesn't help out the case I'm interested in. Would Dr. Y like to wield the power of a commit­ tee member? How will he campaign to become One of the most discussed issues before the AMS one? These questions may seem like fantastical Council during the time I was President was the bad dreams, though I personally know of such be­ question of whether the AMS should start a Fellows havior in connection with some other prizes. Even program. Both the Council and the Committee on if these extreme behaviors don't happen, I think it's the Profession were almost evenly divided on the quite likely that who becomes a Fellow will depend issue, but the Council voted by a small majority to a lot on who knows whom. Do we want this? put it to a vote of the whole membership, which is • Enormous work: To attempt to appoint Fel­ about to take place. lows in a way even remotely approaching fairness I'm writing this to urge you to vote against es­ and transparency will be a huge amount of work. tablishing such a program. Here are the reasons I Alas, the example of the way in which papers are think it's a bad idea. often refereed is not encouraging: I think the likely • The AMS should serve us all: The society outcome is that the necessary work will not be represents us in Washington, it organizes very pop­ done. Randomness and the appearance of ran­ ular meetings for us and it publishes wonderful domness, or worse, the appearance of favoritism, journals, attracting a wide range of interest, from will likely be strong. With enough work, maybe re­ the popular Notices to the abstruse journal. Anoint­ search could be judged in a fair way. But teaching? ing a small proportion of the membership as the Excellence of committee service? There may be a chosen will certainly give the impression, what­ few outstanding cases where judgment of any of ever the reality, that the AMS is "for" this fraction these qualities is easy, but accurately judging a more strongly than it is "for" the mass of its mem­ significant fraction of all the people in the field on bers. Kaplansky told his students to join the AMS these attributes? Hard to imagine. because it was the nearest thing we had to a union. • Wandering and uncertain criteria: Suppose The AMS is at its strongest when it takes action in for the sake of argument that the committees favor of us all. The vast majority of the AMS would picked to choose Fellows find the strength and, per­ not become Fellows, and one can only think they haps harder, make the time to do a great job of dis­ would suffer in relative prestige and influence in cerning whatever they think are the qualities of Fel­ the society because of this. This is not the way the lows. Nonetheless, the policy set by successive AMS should work. presidents in appointing the committees who will • Mathematics has a special culture: A Fellows decide membership will surely wander; the com­ program goes against one of the things that makes mittees' policies will wander even more. The diffi­ mathematics special and wonderful: its uniquely culty in deciding what is "good" is already clear in egalitarian culture. To say that mathematics is egal­ Plato. Thus a kind of drift is inevitable. Suspecting itarian is not to say that we don't care about qual­ that you were passed over because of this will not ity. Rather it's to say that we think quality can make being passed over any easier to take. How­ emerge anywhere, anytime. A spectacular advance ever hard the committees work, the process is un­ on an old problem in number theory made by likely to be seen as sensible by the majority of someone teaching at an institution without a Ph.D. mathematicians-those who do not become Fel­ program? It happened just recently in my own lows. backyard. Similarly, great teaching happens every­ • Polarization: Trying to be quantitative, the where, certainly not just at the major universities. Committee on the Profession did some research: On a more trivial level, this culture is typified by they surveyed a group of members to ask whether the fact that we almost always list authors of pa­ a Fellows program was worthwhile. The member­ pers alphabetically. This culture is a point of pride ship was roughly split. But there was space on the survey for many mathematicians-certainly for me. A for a free response, and those who read the responses observed that the strength of feeling on David Eisenbud is the director of the Mathematical Sciences the two sides did not seem to be equal: those in Research Institute and immediate past president of the AMS favor of a Fellows program were rather mild in (2003-04). His email address is de@msri. org. their preferences, but some of those opposed

AUGUST 2006 NOTICES OF THE AMS 757 expressed their positions in the strongest terms, to the advantage of the mathematical discipline to and said they'd resign if the AMS did something so make the people close to it feel at home in one or­ exclusionary. ganization. The AMS is, in my opinion, the out­ • Weakness of the argument in favor: Some standing candidate for this organization. Deliber­ people who think they will become Fellows will ately creating a schism dividing the AMS into certainly vote for the program simply because they Fellows and Non Fellows- the Ins and the Outs­ feel they deserve the honor. I hope that if the pro­ runs against this unity. It might even invite an­ gram is enacted, not too many of these are disap­ other wave of defections. pointed! I don't regard this as the sort of argument In short, I think that to create a Fellows program that should drive a Fellows program forward. would, for the sake of small and dubious benefits, There is a more altruistic argument made in risk damage to mathematics and its culture, and favor of a Fellows program- the main argument, injury to the AMS. I urge you to vote against it. from my point of view. Roughly: if more mathe­ maticians get (more) honors such as being named a Fellow, then Deans and Provosts will take math­ ematicians-and thus maybe mathematics-more seriously. It seems unlikely that this effect will op­ erate in the strongest departments, where, I would suspect, most of the Fellows will be employed. What about the departments that are not in the top 50? There the effect might be significant, indeed. But wouldn't the main effect be to increase the in­ fluence of individuals, not of mathematics as a dis­ cipline? The influence of a department or a disci­ pline depends a lot on the unity and enthusiasm with which the members work together. By simul­ taneously increasing the resentments within math­ ematics departments, it seems to me that the over­ all effect of a Fellows program on department standing might finally be negative. • The Good of the Society, the Good of Math­ ematics: Given the small turnout for AMS elec­ tions, it's quite possible that the Fellows program could pass if only those who thought they would become Fellows (likely to be more than those who really would become Fellows) voted for it. Such a vote would be a mistake: we should be voting for the good of the whole society, not our personal gain. Those who feel they are likely to become Fellows have a double obligation to think about whether a Fellows program is good for the society as a whole. Ninety years ago those who felt that the AMS was becoming too concerned with one part of mathe­ matics decided to vote with their feet: they formed the MAA. A little more than fifty years ago, the AMS lost the loyalty and interest of another big chunk of mathematics and mathematicians, in the for­ mation of SIAM. Justified and sensible as those moves may have been, I think that Mathematics it­ self lost in influence and coherence because of them. The AMS is weaker because of this, just as the U.S. would have been weaker if the South had seceded. In recent years, I believe the Society has moved thoughtfully and purposefully toward making it­ self into "the big house of Mathematics" where all mathematical concerns, teaching and applications included, are welcomed. Whichever part of math­ ematics is closest to your heart, I think it's strongly

758 NOTICES OF THE AMS VoLUME 53, NUMBER 7 fellow to learned and professional societies. This A Celebration of information appears in a variety of forms in uni­ versity publications, mailings to alumni, donors, speeches by our chancellor or provost, or other pub­ Sdence­ lic opportunities to boast about our institutions. Some individual fellows are featured in these pub­ Whynot lications, but it is usually the body count that is of most use. These counts also play a role in a vari­ mathematics? ety of nationally visible rankings. These routines and practices are repeated at every research university and institute and at the Ronald]. Stern corporate and national labs. This dissemination is a wonderful celebration of the important science that is undertaken and informs the public of ex­ Every November I receive a list of the roughly 200 citing advances in science. The election of fellows newly elected American Physical Society Fellows, has an immense ripple effect that enhances the of which our campus typically has two or three. I credibility of the societies and the sciences they rep­ routinely notify our communications office to pre­ resent. pare a news release based on the citation given for As a dean I attend many social events and speak each fellow. I then contact the science writer for our to many community groups. As a result I have de­ major local paper, Gary Robbins of the Orange veloped close relationships with hundreds of won­ County Register. The citations are typically too derful and often influential community members dense or cryptic for a public audience, so I work in Orange and Los Angeles County. These are in­ with our communications office and Gary to put dividuals who do read newspapers. They routinely the research in a general context and they prepare remark on having seen these articles and are im­ text that best relates to the public about the elected pressed with the scientific contributions made at fellows' contributions. Within a day or two the the research university that resides within their press release is prepared and an article appears in community. It gives them a sense of pride to be as­ the Orange County Register listing the elected fel­ sociated with such advances. There is a huge ap­ lows and a nice article about each fellow's contri­ petite for science in our community. Such state­ butions. The dozens of smaller community papers ments as "Ron, I just read that a couple of your throughout southern California routinely print the physics faculty were elected as a fellow for what news release. In addition, our weekly faculty /staff sounds like some real interesting stuff. Can you tell newsletter, which is read by our 10,000 employees, me more?" As a result, scientific accomplishments does the same. This is not our student rag, but a are discussed over coffee, at lunches, dinners, and publication designed for our faculty and staff that dozens of community social events. This scenario keeps them abreast of what is happening at our has been, and will continue to be, repeated hun­ main and medical campus. Occasionally the local dreds of times. PBS radio or TV station picks up the press release. My point is now evident. Election as fellow to For very topical or unusual work, the national press learned and professional societies results in a broad picks it up. In summary, the entire professional dissemination of scientific research to the entire community and roughly 2 million members of our academy and public. Also, there is the appearance community are exposed to physics. of a unified voice from within the scientific disci­ This scenario is repeated throughout the year pline. Most often the name of the elected faculty when the American Geophysical Union, American member is quickly forgotten. However, the overall Statistical Society, Association for Psychological picture that exciting scientific research is hap­ Science, and other professional societies announce pening at our university lingers. the election of their fellows. The lack of a fellows The quality of the research, teaching and service program for the American Chemical Society is as evaluated by our peers outside our institution is made up with the myriad of chemistry prizes they most important. In particular, a fellows program at award. Again our faculty routinely receive a cou­ the premiere academic professional societies has pe­ ple of their prizes each year and the public rela­ cuniary advantages. Since the scientific research tions scenario is the same. success of our faculty and researchers is acknowl­ Each year most institutions update a master list edged by a society without political or institutional of faculty that have received awards or election as bias, it makes it easier for me to argue for impor­ tant dollars that will enhance the research, teach­ Ronald Stern is dean of physical sciences and professor of ing, and service goals of our excellent science de­ mathematics at the University of California Irvine. His partments. Such judgments from professional and email address is rstern@uci. edu. learned societies certainly grease the wheels for

AUGUST 2006 NOTICES OF THE AMS 759 research budgets, enhancing the likelihood of new well as the perception that the AMS membership science initiatives and the overall growth of science will be split into first- and second-class citizenship. at our university. The first is a fact and the second is a perception. The success of these fellows programs in cele­ Our research and educational community is, hope­ brating and disseminating advances in the sciences fully, sufficiently mature to recognize excellence has, unfortunately, come at the expense of math­ without being divisive. ematics. I squirm when my community friends say "Ron, wow, I am impressed by all I read in the pa­ pers about your science faculty. Is your mathe­ matics department weak? I don't read much about them." Of course this is a wonderful opportunity to brag about what excellent faculty and research we in fact do have in our mathematics department. However, I am only influencing a handful of indi­ viduals, rather than the millions of readers of the press. Of course there are those rare occasions where one of our faculty is elected to the NAS or receives a Sloan and the press release and news­ paper routine is implemented. It is these rare op­ portunities that we do celebrate mathematics and inform, educate, and excite the public about what we do. As the preeminent mathematical society we now have the opportunity to celebrate mathematics and to provide on an annual basis an effective vehicle to disseminate the essence of our existence, our im­ portant and exciting research. If each year we elect no more than one-half of one percent of the then current membership of the Society as fellows, then each year 150 mathematicians will be recognized by their peers for election to the status of Fellow in the American Mathematical Society. Articles will appear in every newspaper in the nation about mathematicians and mathematics. There will be dis­ cussions over coffee, at lunch, and at dinner tables about what we create and discover. There will be a positive sense within your broad communities about the mathematical contributions your insti­ tution makes to the advancement of knowledge. We will finally broadcast and begin to recognize and reward excellence beyond the easily identifiable ex­ traordinary. There are some corollaries to an AMS Fellows Program. The old adage that excellence begets ex­ cellence is palpable at a research university. Those programs and individuals that are recognized as excellent are the first to be considered for further awards and recognition. Mathematics has had dif­ ficulty here largely due to our refusal as a com­ munity of scholars to assume a public responsibility to recognize excellence beyond the extraordinary. Regardless of the reasons, the result is that we do not operate on the same playing field as the other sciences. We are always a special case. As we all know, dealing with special cases can require ex­ ceptional effort, and they are easily overlooked. Of course there are less desirable corollaries to an AMS Fellows Program. There is the extra effort involved in the administration of the program as

760 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Book Review

Reality Conditions Reviewed by john Swallow

Reality Conditions mathematics? Rest AlexKasman assured: there is .no Mathematical Association ofAmerica, 2005 need to sound the 512 pages, US$29.95 alarm. In fact, what ISBN 08-838-5552-6 makes Reality Con­ ditions so effective Alex Kasman came to write his first collection and attractive is the of short stories, Reality Conditions, as a profes­ undeniable authen­ sional-that is, as a professional mathematician. ticity of Kasman's Not so long ago he sensed a growing interest, mathematical per­ mostly within the mathematical community, in the spective. Kasman's geme of mathematical fiction. He sought out a writing affirms that suitable database of reviews, and, discovering that mathematics is that none existed, he created one: the now widely­ vein of truth mined recognized Mathematical Fiction website [2]. He with a pickaxe of was then able to survey the literature, welcoming Short Mathematical Fiction logic, and he is as re- the assistance of the site's many visitors. Finding luctant as any of us something missing-gaps of "ideas, stories, and to trivialize the com­ facts" (page vii)-Kasman arrived at a true un­ plex, or to play fast and loose with the details. Kas­ solved problem or two, and he set to work writing. man knows what it means to be a mathematician: From murder mysteries to tall tales, from histori­ the sign of creativity and brilliance is an intuition cal reconstructions to alien encounters, the stories for what lies beneath a rock's contours, and yet suc­ in Reality Conditions are informative and charming, cess requires the simple labor of filing a nugget and occasionally even striking. Although their down to reveal the gem within. craftsmanship is not exquisite, they are sure to Part of Kasman's aim in Reality Conditions is to entertain readers both inside and outside the math­ introduce the laity to mathematics, to use short ematical community. stories as a pedagogical vehicle for teaching, and Some mathematicians may worry about the im­ his stories successfully meet this goal. Kasman in­ port of a geme with the appellation "mathemati­ troduces foundational notions of group theory cal fiction". After all, would we dare read fictional and topology, and a few ideas from algebraic geom­ etry even make their appearance. He examines the John Swallow is associate professor of mathematics at blurred boundaries separating 'pur~ and applied Davidson Cpllege. !fis email address is j oswa ll ow@ mathematics (and those separating mathematics davidson. edu. and physics), and he explores as well the aesthetic The author thanks the Universite de Bordeaux I for its hos­ sense in mathematics. For reasons of space and dif­ pitality during the writing of this review. ficulty, the portraits of foundational notions are

AUGUST 2006 NOTICES OF THE AMS 761 necessarily more realistic, while higher-level ab­ merit, and one that has already been achieved for stractions are rendered in more stylized sketches. the scientific community in science fiction. At the end of the book Kasman provides notes on Fortunately, authors of mathematical fiction each of his stories, reflecting his desire to instruct have many formulas available to assist them. One with accuracy while entertaining. Many of these might, for instance, embed a mathematical fact, say notes would work well to initiate discussions about from geometry or topology, in the physical world mathematical ideas; he draws attention to related and then scrutinize its consequences. Or one might mathematical concepts and published material and focus on the thoughts of a mathematically inclined delineates clearly what is truth and what is fiction. character, examining the psychology of doing math­ As important as mathematical concepts are to ematics from the first tremors of an initial hunch some of the stories, though, Kasman is also inter­ to the exuberance of-or disbelief in- the com­ ested in introducing readers to prominent issues pleted proof. A writer might also pen a detective in the mathematical community. The welcome and story expressing the thrill of the chase, or even support afforded to women in research, for in­ present some detailed mathematics together with stance, forms the backstory of one. Another story, a significant historical backstory. "Monster", is in part a satire on the increasing need A versatile writer, Kasman uses all of these, and to sell mathematics to the public. "Another New then some. "Eye of the Beholder", for example, Math" ruminates on the prospects for mathemat­ takes the Pythagorean notion that "all is number" ical expertise in the politics of school reform, while to an extreme conclusion. "Progress" asks, by pre­ the title story "Reality Conditions" raises the specter senting a sequence of mathematical examples, of the suppression of mathematics departments, whether mathematical judgments are a function of , reminiscent of events at the University of Rochester one's historical period, or derive instead from an in the mid-1990s. individual's maturity. Kasman employs stereotyp­ Kasman's appreciation for the foibles, anxieties, ical comic-book heroes who humorously condition and crimes of those at all levels of the academic reality to match mathematical theories of space, and hierarchy is especially delightful, and much of the he also finds room for deeper intellects, such as world of Reality Conditions is located close to the Bev in "Eye of the Beholder", who draw us into campus. We encounter students hoping for quick their consciousness. Some of Kasman's stories are solutions to. their daily homework, bright intel­ brief exercises in mathematical writing, rather than lects looking for love and seeking solace in coffee fully-formed short stories, and these mathemati­ shops, graduate students both awed and frustrated cal vignettes are similar to the shorter pieces in by their professors' brilliance. We recognize as­ Clifton Fadiman's anthology Fantasia Mathematica sistant professors as well as students-turned­ [1). Finally, in a genre not known for appropriat­ entrepreneurs who are desperate to show parents ing literary texts, "Reality Conditions" combines and peers that they haven't chosen unwisely. Fac­ elements of the Sumerian Epic of Gilgamesh with ulty long to be appreciated by their students and honest reflections on the challenges of a mathe­ respected by their professional colleagues. Stu­ matical career, as a way of approaching the quest dents and researchers alike are tempted to cheat­ for immortality. and then to rationalize the urge. The most striking stories reveal mathematical Occasionally, the transition from the story situations in unexpected circumstances. In "Mur­ proper to the introduction of a mathematical con­ der, she conjectured", Kasman introduces the cept, or the transition from the story to a mini­ reader to the mathematical process of discovery lecture on mathematical history, is too apparent and proof, but he has a New York Police Depart­ and abrupt. While we might initially conceive a ment psychologist, rather than her friend the story in terms of mathematics as content and fic­ mathematician, lead the mystery's investigation. tion as form, too transparent a division weakens The mathematician, while eager to be helpful, still the final result. Leaving the structural supports plays Watson to her Holmes. At the end we find the visible is the primary occupational hazard in museum guide, representing the general public, writing mathematical fiction. as interested as the mathematician in the mys­ Weaving mathematics and fiction together is tery's solution. certainly an art, and our expectations for the genre "Reality Conditions" takes up a fundamental are nontrivial. Mathematical fiction must explore question about existence: the extent to which na­ the intersection of the world of mathematics with ture and nurture define human life. While grant­ the rest of humanity. We expect to find illumi­ ing that both are crucial to an appreciation of any nated, for mathematicians and nonmathematicians individual's actions, the story avoids the debate alike, the interplay between mathematical concepts about their relative importance. Instead, "Reality and such disparate fields as philosophy, history, Conditions" considers the question from the point psychology, aesthetics, and perhaps even religion. of view of the individual, asking how each of us can A tall order, perhaps, but surely not one without know the conditions our own nature and nurture

762 NOTICES OF THE AMS VOLUME 53, NUMBER 7 have imposed on us. We see that we might spend authenticity even become advantageous in narra­ our life searching for the precise constraints, but tion by mathematicians. In "Reality Conditions," the learn only at the end what they had been. We come narrator Goldfarb displays a habit mathematicians to realize that mathematics similarly depends on know so well: inserting brief examples into expla­ foundational constraints, but that without doing nations almost reflexively, anticipating the charge mathematics, we cannot fully appreciate the bound­ that one's presentation has become too abstract. ary conditions. Remarking on the powerful odors that wafted from For the writer of mathematical fiction, more a nearby factory during his childhood, Goldfarb ex­ dangerous than the seeming paradox in the name plains, " .. .once they started making one, lemon "mathematical fiction" is a particularly mathe­ let's say, then they'd keep making it, vats and vat matical conceit: that the essence of elegance is to of it" (page 65), and his tic reappears again only two be found in the realm of ideas, that language is no sentences later, when he says, "When the scent more than the vehicle for the final apprehension changed, from lemon to mint for example, the of abstraction. But just as intuition alone does not world changed with it." With mannerisms like these, a mathematical proof make, creativity or brilliance Goldfarb dwells close to our hearts. in imagining backstories, characters, and action As a whole, the collection successfully meets the does not suffice for the writer. As one ofKasman's author's pedagogical goals, and the book would be characters puts it,"It is the things that are left out a worthy addition to a seminar for first-year under­ of the story that give it power" (page 99). The processes of grinding away the unnecessary and ir­ graduates on mathematical ideas and culture.ln fact, relevant, of perceiving how symbols and analogies with the disarming honesty and openness evidenced might connect, of simply polishing and repolish­ in the preface and the author's notes, the book would ing the prose, these are what generate strength be well received by a variety of audiences. For the and elegance in a piece of short fiction. student new to the world of mathematics, the Unfortunately, in this regard some of the stories stories provide an accessible and entertaining look in Reality Conditions fall short. In general, readers into some significant mathematics, as well as into seeking incisive descriptions and precise conno­ what it means to be a mathematician. For the math­ tations from an experienced wordsmith will be ematician, they offer an amusing perspective on disappointed. Even passing by the occasional mis­ everything from the oddities of mathematical tem­ spelling and dubiously placed modifier, readers peraments to the politics of professional reputation. may still yearn for more finesse when the action What many of us will appreciate most about Reality is slow, or when the narrator appears to be an in­ Conditions is the authentic snapshot it takes of the dependent observer of the action. Many descriptive human side of being a turn-of-the-century mathe­ details in "Unreasonable Effectiveness", for exam­ matician in America. ple, which is essentially a single conversation be­ Among the wider public, those who love math­ tween two characters, are rough and unconvincing. ematical fiction in the tradition of Fantasia The story moreover misses the opportunity to en­ Mathematica will certainly appreciate Reality gage the reader early on, settling too late into nar­ Conditions. It's even an odds-on bet that the read­ ration derived unambiguously from a particular ership will be greater still. In the wake of Sylvia character's point of view. The sullen voice that Bev Nasar's A Beautiful Mind, Ron Howard's movie of uses to open "Eye of the Beholder" is not always the same title, David Auburn's Proof, and Nick sustained as she goes back and forth between Falacci's and Cheryl Heuton's television series chronicling the past and commenting in the pre­ NUMB3RS, it's tempting to claim that mathemat­ sent. Sometimes Kasman's turns of phrase, recog­ ics is gaining ground in American culture. Nearly nizable as common mathematical speech patterns, fifty years ago, Fadiman observed that "an entirely work against our willing suspension of disbelief. new audience for popular works touching on The narrator of "Murder, she conjectured" sounds mathematics has developed" [1, p. xviii). Perhaps remarkably like someone we might encounter at it is so again, and more excellent mathematical teatime, a colleague giving a post-mortem on of­ fiction is just around the corner. fice hours: "Then, Beth and Trevor began asking questions. It was clear from the very beginning References that they did not have any straightforward ques­ [1] CLIFTON FADIMAN, compiler and editor, Fantasia Math­ tions to ask. Since they did not know exactly what ematica: Being a Set of Stories, Together with a Group they were hoping to learn, the questions were all of Oddments and Diversions, All Drawn from the Uni­ rather vague" (page 18). verse ofMathematics, Simon and Schuster, 1958, New However, when the stories are fast-paced-which York: Copernicus, 1997. is more often than not -or flashbacks are used [2] ALEX KAsMAN , The Mathematical Fiction Homepage, to shorten scenes, these sorts of shortcomings http://math.cofc.edu/faculty/kasman/ are much less serious. Markers of mathematical MATHFICT/default.html.

AUGUST 2006 NOTICES OF THE AMS 763 W H A T s a Strange Attractor? David Ruelle

Your computer will readily implement the map f We ask that A be attracting, i.e., that A have an open sending the point (u, v) E R2 to the point neighborhood U such that (v + 1- au2 ,bu) E R2, where a= 1.4 and b = 0.3. nr ?. ortu =A Ask your computer to plot the points Xn = fn(O, 0), and you will find that they accumulate, for n - oo, (one can then arrange that fU c U). Smale's Axiom on a convoluted fractal set A known as the Henan A also requires that f-periodic orbits be dense in attractor. This set is prototypical of what one wants A and that A contain a dense f-orbit (topological to call a strange attractor. Such objects often arise transitivity). when a diffeomorphism f stretches and folds an An Axiom A attractor is either a finite attract­ open set U and maps the closure fU inside U (this ing periodic orbit, or it is an infinite set, and the is a typical situation, not a necessary or a sufficient dimension of the expanding sub spaces E~ is > 0. condition). The strange attractor A is visualized In the latter case, A is a strange Axiom A attrac­ when a computer plots the points Xn = fnxo with tor: there are points y close to x in A such that the almost any initial value xo in U. The figures show distance between rnx and fny grows exponentially a two-dimensional example corresponding to the with n until this distance becomes of the order of Herron attractor, and a three-dimensional example the diameter of A. The exponential growth of corresponding to Smale's solenoid. It turns out that dist(fnx, fny) expresses chaos, or sensitivity to ini­ a small change in the values of a and b can destroy tial condition: if there is any imprecision on x, the the Herron attractor, but a small change off does predictability of fnx is lost for large n. Here, f not destroy the solenoid. stretches the set U and necessarily also "folds" We give now a definition of uniformly hyperbolic this set to put fU back in U, in agreement with the attractors, or Axiom A attractors. This will cover the notion of a strange attractor. Careful studies have case of the solenoid but not the Herron attractor. shown that various systems that occur in nature (One can also define nonattracting hyperbolic sets, are chaotic: their time evolution is described by low­ called basic sets, but they will not concern us.) Let dimensional dynamics with sensitivity to initial fbe a diffeomorphism of the compact manifold M, condition, for which strange Axiom A attractors and put some Riemann metric on M. Let A be a offer an excellent mathematical model. In partic­ compact invariant subset of M. We say that A is a ular, a proposal by Floris Takens and myself that hyperbolic set if one can continuously choose at hydrodynamic turbulence is chaotic in this sense each point x E A a contracting (or stable) subspace was eventually vindicated by experiment. It is on E~ and an expanding (or unstable) subspace E~ of this occasion that the name "strange attractor" TxM so that (Tf)£S·u = p.u and TM = Es Ell Eu. We seems to have been coined. thus assume that The theory of uniformly hyperbolic attractors, initiated by Dmitrii Anosov and Stephen Smale, II(Tf)XII < I lXII if 0 =1- X E Es shows that one can define stable and unstable manifolds llf, llxu c M: these are nonlinear ver­ II(Tf)-1 XII < I lXI I if 0 =I- X E Eu sions of the spaces E~,E~ c TxM, and they give a David Ruelle is professor emeritus at the Institut des Hautes global meaning to contracting and expanding di- Etudes Scientifiques, Bures-sur-Yvette, France, and Distin­ rections. One proves structural stability: if f is guished Visiting Professor in the mathematics department close to f, then f has an attractor A close to A, so at Rutgers Untversily. His email address is ruell e@i hes. fr. that fiA is topologically conjugate to fiA. Using

764 NOTICES OF THE AMS VOLUME 53, NUMBER 7 the density of periodic orbits, Smale proved local product struc­ ture: A is locally the product of a set in the contracting direction and a set in the expanding direction. (The set in the expanding direc­ tion is a manifold, while in the con­ tracting direction it is usually a fractal, for instance a Cantor set.) Yakov Sinai obtained a global con­ sequence of the product structure called symbolic dynamics (an im­ The He non map f sends the proved later treatment was given quadilateral U inside itself. by Rufus Bowen). Here is the result: The sets fU, f 2 U, f3 U are up to well-controlled ambiguities, plotted, and f3 U already Smale's solenoid map f sends the torus U inside one can associate with each point looks a lot like the Henon itself. Shown are U, fU, f 2 U, and you can x E A an infinite sequence of sym­ attractor n 1.,_ 0fn U. imagine the solenoid n1.,_ 0 fnU. bols( . .. , ~-1. ~o. ~1. ... ). The ~i in called a strange attractor and is in fact what you the sequence are taken from a finite set F and only see when a computer plots for you, say, the Henon certain successive pairs (~i. ~i+ 1 ) are allowed, but no other condition is imposed. Furthermore, re­ attractor. We may say that, to go beyond hyper­ bolicity, we have replaced the geometric concept placing x by fx replaces (... , ~ - 1, ~o. ~ , ... ) by the 1 of strange attractor by the ergodic concept of SRB shifted sequence (. .. , ~o. ~1, ~ 2 , . . . ). Symbolic dynamics thus replaces geometry (the diffeomor­ measure. phism f) by algebra (the shift on sequences of sym­ The great generality of Pesin theory comes at a price: it is hard bols). For example, using symbolic dynamics, one to know how things change when can count periodic points in A (i.e., give a formula the diffeomoq~_hism f is replaced by a nearby dif­ feomorphism for cardfn lA). One can also study {-invariant mea­ f. Here we reach the current fron­ sures on A, in particular so-called Gibbs measures: tier in the theory of smooth dynamical systems. they correspond to "thermal equilibrium states" Cvitanovic has proposed a fascinating description of the "pruning front" for an interacting one-dimensional spin system as associated with changes in studied in statistical mechanics when the sequence the Henon attractor. A theory of "Henon-like" dif­ feomorphisms has been developed (by Benedicks­ ( ... , ~ - 1, ~o. ~1. ... ) is interpreted as an infinite Carleson, Viana, L.-S. Young, and others) where the configuration of spins ~i in one dimension. For Lebesgue-almost-all points x in the neigh­ ~RB measure is analyzed, not for all perturbations off, but for a set borhood U of A, the time averages along the for­ f of positive measure of such per­ ward orbit (x, fx, ... 'rnx, ... ) tend to a probability turbations in some parameter space. Jacob Palis has proposed a beautiful set of conjectures to the measure JlSRB on A, and this measure does not de­ effect that for pend on x. This so-called SRB-measure is a Gibbs most diffeomorphisms f (in some measure, introduced by Yakov Sinai, myself, and sense), and most initial points x E M (in the sense Rufus Bowen. We have a detailed understanding of of Lebesgue measure), time averages correspond to a finite SRB measures and how they depend on f. number of SRB measures (or attractors if you like). But What now about non-Axiom A attractors? To it is also conceivable that for a large discuss them, we must introduce the wonderful set of diffeomorphisms f and of points x, the time averages idea by Yakov Pesin that the geometric condition are not even defined! of uniform hyperbolicity for dynamical systems can The beautiful pictures above are by Bill Cassel­ be replaced by an almost-everywhere analysis with man and David Austin. respect to any given ergodic measure Jl. Pesin the­ Further Reading ory allows one to define stable and unstable man­ [1] J.-P. EcKMANN and D. ifolds for 11-almost-all RUELLE, Ergodic theory of chaos and Y;·u x. Furthermore, those strange attractors,Rev. Mod. Phys. 57 (1985), 617-656. measures that can be called SRB measures have [2] L.-S. YouNG, What are SRB measures, and which dy­ been characterized by Fran<;ois Ledrappier, Jean­ namical systems have them?, ]. Statist. Phys. 108 Marie Strelcyn, and Lai-Sang Young. General SRB (2002), 733-754. measures are a beautiful measure-theoretic ver­ [3] C. BONATTI, L. DlAZ, and M. VIANA, Dynamics Beyond Uni­ sion of Axiom A attractors, without the uniform hy­ form Hyperbo/icity: A Global Geometric and Proba­ perbolicity assumption; they again describe time bilistic Approach, Springer, Berlin, 2005. averages for a set of positive Lebesgue measure in the manifold M. The support of a general SRB mea­ sure is typically a fractal object that deserves to be

AUGUST 2006 NOTICES OF THE AMS 765 Teruhisa Matsusaka (1926-2006) Janos Kollar

From his arrival at the After three years at Northwestern Unversity and a Unversity of Chicago in year at the Institute for Advanced Study, Princeton, 1954 until his retirement he went to Brandeis University in 1961 where he from Brandeis University stayed until1994, helping to build the department in 1994, Matsusaka has to its current prominence. Matsusaka was invited been a key figure of to address the Edinburgh International Congress American algebraic geom­ of Mathematicians in 1958, and he was elected to etry. He was a quiet math­ the American Academy of Arts and Sciences in ematician to whom alge­ 1966. braic geometry was a Most of the early works of Matsusaka are devoted personal friend whose to extending basic theorems of complex algebraic company one can best ap­ geometry to arbitrary fields, following the direction preciate away from the established by Weil. These theorems carry the name rush of the academic life. of the original authors who proved them over the Instead of going to con­ complex numbers, and very few of the young gen­ ferences or working with eration know that the existence of the Albanese and others, he most enjoyed Picard varieties [Mat52], the projectivity of Abelian Teruhisa Matsusaka sitting in his fishing boat varieties [Mat53], the Lefschetz theorem comput­ and thinking about math­ ing the Picard variety of a hyperplane section ematics. Yet for those who knew him well, his love [Mat 54], and the Torelli theorem that the polarized of the subject and his devotion to the deep under­ Jacobian determines a smooth curve [Mat58] are all standing of important problems was infectious. due to Matsusaka in the general case. Matsusaka received his Ph.D. in 1952 at Kyoto It is also in these early years that he proved a University, but the person with the greatest influ­ characterization of Jacobians, now known as the ence on his research career was Andre Weil. Dur­ Matsusaka criterion [Mat59]: ing the difficult years after the Second World War, Matsusaka worked on several problems connected A principally polarized Abelian variety of with Weil's Foundations of Algebraic Geometry. dimension g containing a curve (C c A, 8) is the This led to a correspondence and eventually Weil jacobian of C if and only if (g - 1)! · C is numeri­ invited Matsusaka to the University of Chicago cally equivalent to the self-intersection e g-l. (1954-57) where they became life-long friends. After these results Matsusaka turned his atten­ tion to the moduli problem of algebraic varieties, J(inos Kollar is professor of mathematics at Princeton and he devoted the rest of his career to this topic. University. His email address is koll ar@math. Nowadays moduli problems are built into the princeton.edu. basics of algebraic geometry, but in the 1950s and

766 NOTICES OF THE AMS VOLUME 53, NUMBER 7 1960s the existence and nature question when X is smooth and of moduli spaces was a major the characteristic is 0. open question, where even the Later Matsusaka showed that basic definitions were unsettled. the answer is also positive if X It was realized early on that is smooth, dimX :o; 3 [Mat81), the set of isomorphism classes and the characteristic is arbi­ of varieties of a given type does trary, or when X has rational not carry any reasonable alge­ singularities and the character­ braic structure. Some of the istic is 0 [Mat86). (The more gen­ worst examples are given by eral cases of smooth varieties in Abelian and K3 surfaces. positive characteristic and nor­ Matsusaka devoted thirty mal varieties in characteristic years of work to proving that 0 are still unknown.) the right objects to consider are Once boundedness holds, polarized varieties, that is, pairs one can parametrize all pairs (X, H) where Xis a projective va­ (X, H) with a given Hilbert poly­ riety and H is an ample divisor nomial by an open subset of class. the Chow variety (or Hilbert Two major preliminary ques­ scheme) of a fixed projective tions need to be settled before space IP'N. The remaining prob­ one can start building a sensible lem is that we obtain every moduli space, and both were (X, H) many times, since the solved by Matsusaka: is the Andre Wei I and Ryoko Matsusaka, embedding of X into IP'N is moduli problem separated and 1956. Photo by Teruhisa Matsusaka. unique only up to an automor­ bounded? phism of IP'N . This leads us to The separatedness problem concerns unique­ the question: when is the quotient of an algebraic ness of limits. Assume that (X1,H1) depend con­ variety by a group also an algebraic variety? In tinuously or algebraically on t where t =1= 0. Is it true some cases the answer is given by Mumford's geo­ that there is at most one pair (X0 , H0 ) that can be metric invariant theory or by Artin's theory of al­ viewed as the limit of this family? gebraic spaces, but a truly satisfactory general an­ It is easy to write down examples where this com­ swer is still lacking. Matsusaka's main contribution pletely fails if we allow X 0 to be singular. It is to this area is the theory of Q-varieties [Mat64). This harder to come up with smooth counterexamples, is the first clear instance in the literature where the but 1Jl' 1-bundles over curves give many. The basic currently popular "stacky viewpoint" appears in al­ paper of Matsusaka and Mumford [MM64) shows gebraic geometry. In both approaches the starting that these are the only obstructions: the limit is point is the dictum that one should not worry unique as long as X 0 is smooth and not birational about the existence of the quotient. Instead, one to a IP' 1-bundle. should work out a theory of the more general quo­ The boundedness problem asks about the total­ tient objects. Afterwards we may prove that the ity of all pairs (X, H). Maybe there are too many of quotient also exists in the classical sense, but at the them to be parametrized by the points of a single end this may turn out to be unimportant. algebraic variety? This happens already for curves: Following the theory of Weil, Matsusaka always we need infinitely many algebraic varieties to pa­ worked with varieties, so his theory is about quo­ rametrize all polarized curves (C, H), but we need tients of varieties by equivalence relations. By the only one variety if we fix the genus of C and the de­ time his book appeared in 1964, schemes took gree of H. Equivalently, we can fix the Hilbert poly­ over algebraic geometry, and the current theory of nomialx(C, Oc(tH)) = t ·(degree of H) + 1- g(C). stacks preserved only the basic philosophy of his Similarly, in higher dimensions we need to fix approach. the Hilbert polynomial Matsusaka's last published paper [Mat91) Hilbrx.HJ(t) := X(X, Ox(tH)) strengthens his Big Theorem by proving that only the two leading terms of the Hilbert polynomial first. It turns out that one can restate boundedness Hilbrx ,H)(t) matter. Namely, if dim X = n and His in the following form: ample (or just nef and big) then there is an effec­ For every polynomial p(t) find a constant tively computable function C(x, y, z) such that c = c(p(t)) such that if(X, H) is a polarized pair with p(t) = Hilbrx .HJ(t) then I cHI is very ample. 0 Hn n Kx . Hn- 1 n - 1 I Matsusaka's best known result [Mat72), dubbed I h (X, Ox(tH))- rz!t + 2(n _ 1)! t Matsusaka's Big Theorem by Lieberman and Mumford [LM75), gives the positive answer to this :o; C(Hn' Kx . Hn- 1' n)tn-2 ,

AUGUST 2006 NOTICES OF THE AMS 767 and a similar inequality holds when we replace About the Cover h0 (X, C:Jx(tH)) by X(X, Ox (tH)). Note that the Hirze­ A Henon horseshoe bruch-Riemann-Roch theorem computes This month's cover was suggested by Ruelle's x(X, Ox(tH)) exactly in terms of all the Chern article on strange attractors. It portrays an ap­ classes of X, whereas the above result needs only proximation to the non-wandering set n, as well the first Chern class Kx = -c1(X). as a portion of the homoclinic tangle, for the Henonmap References [LM75] D. LIEBERMAN and D. MUMFORD, Matsusaka's big the­ 2 f: (x,y) ~ (y, 1 - ay +bx) orem, Algebraic geometry (Proc. Sympos. Pure Math., with a= 6, b = 0.9. For these values, the Henan Vol. 29, Humboldt State Univ., Arcata, Calif., 1974), map does not possess an attractor, but instead Amer. Math. Soc., Providence, R.I., 1975, pp. 513-530. [Mat 52] TERUHISAMAT susAKA, On the algebraic construction offers an instance of one of Smale's horseshoes, of the Picard variety. II, ]ap.]. Math. 22 (1952), 51-62 and that is what· the cover more or less illus­ (195 3). trates. The logic is exhibited in more detail by the [Mat53] __ , Some theorems on Abelian varieties, Nat. following sequence of pictures: Sci. Rep. Ochanomizu Univ. 4 (1953), 22-35. [Mat54] __ , On the theorem of Castelnuovo-Enriques, Nat. Sci. Rep. Ochanomizu Univ. 4 (1954), 164-171. [Mat58] __ , On a theorem of Torelli, A mer.]. Math. 80 (1958), 784-800. [Mat59] __ , On a characterization of a Jacobian vari­ ety, Memo. Col/. Sci. Univ. Kyoto. Ser. A. Math. 32 (1959), 1-19. [Mat64] __ , Theory ofQ -varieties, Mathematical Soci­ ety of Japan, Tokyo, 1964. [Mat72] __ , Polarized varieties with a given Hilbert poly­ nomial, Amer.]. Math. 94 (1972), 1027-1077. [Mat81] _ _ , On polarized varieties of dimension 3. II, Amer.]. Math. 103 (1981), no. 2, 357-376. · [Mat86] __ , On polarized normal varieties. I, Nagoya Math.]. 104 (1986), 175-211. [Mat91] _ _ , On numerically effective divisors with positive self-intersection numbers, ]. Fac. Sci. Univ. Tokyo Sect. IA Math. 38 (1991), no. 1, 165-183. [MM64] T. MATSUSAKA and D. MUMFORD, Two fundamental theorems on deformations of polarized varieties, Amer.]. Math. 86 (1964), 668-684.

We begin with a region R bounded by parts of the stable manifold of one fixed point and the un­ stable manifold of the other. Any point outside R is taken off to infinity by iterates of either for f - 1, so 0 lies inside it. The next pictures show f(R) and f - 1(R), then [Z(R) and f - 2 (R). Each intersec­ tion fn(R) n f - n(R) also contains 0. The symbolic dynamics of this example, the same as those of the horseshoe, are simple. As Ruelle mentions, the more complicated symbolic dynamics of the classical Henan map with a = 1.4, b = 0.3 are specified by the pruning front conjecture. For more information, look at the AMS Feature Column for June 2006 (available at http://www.ams.org/featurecolumn/) and the book Classical and Quantum Chaos by Cvitanovi c and others, available at http://ChaosBook.org. - Bill Casselman Graphics Editor

768 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Animated Tube Plot > To make an animat ed tube plot 1

Scientific Word

Scientific Word® offers the same features as Scientific WorkPlace, without the computer algebra ______. system. Support the future of fllathefllatics Give to the American Mathematical Society Your donations support: Learn about giving opportunities and estate planning • Career paths of young mathematicians www.ams.org/giving-to-ams • Recognition of important work Contact the AMS • Public awareness and appreciation of Development Office mathematics 1.800.321.4267 • Inspiration of young scholars (U.S. and Canada) or (Epsilon Fund) 1.401.455.4000 www.ams.org (worldwide) 06/04 • International outreach email: [email protected] Textbook Tempest Students and Professors Decry Price Surges Allyn jackson

The past couple of years have seen enormous con­ of Education and also conducted interviews with troversy over rising prices for college textbooks. In a large number of individuals knowledgeable 2005 the state Public Interest Research Groups about textbook publishing and sales, including (PIRGs) issued an updated version of their scathing publishing executives, textbook wholesalers, and 2004 report Ripoff 101, which accused textbook pub­ representatives of companies operating college lishers of gouging students with high prices and of textbook stores. The GAO report provides an trying to undercut the used-textbook market. Later overview of the college textbook publishing in­ in 200 5 the Government Accountability Office (GAO) dustry and analyzes the factors that influence issued a report, prepared at the request of Congress, textbook pricing. The GAO circulated a draft of the on why college textbook prices had risen so much. report to various groups and included in the final Though far more sober in tone than the PIRG docu­ version responses from the National Association ment, the GAO report did not calm the waters, and of College Stores and from the Association of Amer­ a plethora of articles and opinion pieces continued ican Publishers (AAP). to appear in the media. Mathematics faculty have The main finding of the GAO report is that, yes, entered this fray with a petition, signed by 5 50 math­ textbook prices have gone up- a lot. Between 1986 ematics professors, calling on the publisher of a and 2004 college textbook prices rose 186%; by con­ best-selling calculus textbook to change its pricing trast, the Consumer Price Index (CPI), a general and revision policies. Just how this turmoil will shake measure of inflation calculated by the BLS, rose out is not yet clear, but some mathematics depart­ about 72% in that period. This finding is based on ments are taking matters into their own hands and a special data series, prepared by the BLS, on his­ negotiating reduced prices for the textbooks they toric prices of college textbooks. In its response to assign. the draft report, the AAP objected to some of the The Bottom Line: Have Prices Increased? BLS methodology used to produce the data and con­ tended that the BLS had greatly exaggerated the Have college textbook prices increased? In 2004 price increases. The Congress asked the GAO to investigate this ques­ GAO responded that while the tion and in case prices were found to have in­ BLS data has some limitations-and these are creased, to analyze the reasons. In response, the clearly spelled out in the report- it remains the GAO issued in late July 2005 the report College Text­ most reliable and complete source of statistics books: Enhanced Offerings Appear to Drive Recent available on college textbook prices. Price Increases. The GAO obtained data from the Another way of looking at the question of text­ Bureau of Labor Statistics (BLS) and the Department book cost is to ask, How much do students typi­ cally pay per year for textbooks? The state PIRGs Allyn jackson is senior writer and deputy editor of the examined this question in their 2004 report, Ripoff Notices. Her email address is axj@ams. org. 101: How the Current Practices of the Textbook

AUGUST 2006 NOTICES OF THE AMS 771 Industry Drive Up the Cost of College Textbooks impression with data is difficult. The GAO report (an updated version of the report was issued in Feb­ does not break down the textbook price data ruary 2005). The report contains results of a according to subject, so it is impossible to tell survey, conducted in the fall of 2003 by the Cali­ whether prices of mathematics textbooks have fol­ fornia PIRG, of 521 University of California stu­ lowed the trend for textbooks overall. In response dents. This survey found that students on UC to an inquiry about whether the BLS could produce campuses would spend an average of US$900 per data specific to college mathematics textbooks, year on textbooks for the 2003-2004 academic Mike Reese, a BLS commodities specialist for year. To provide historical perspective, the report textbooks, said that BLS data cannot be used to cites a UC Office of the President study estimating estimate textbook price changes in a specific that, in the 1996-1997 academic year, UC students academic subject. spent an average of US$642 on textbooks. These Data on prices of mathematics textbooks does two figures imply that the amount UC students exist, but behind considerable cost barriers, as the spent on textbooks rose about 40% from 1996 to data is typically in the hands of marketing research 2003. By contrast, the CPI rose about 17% in that firms, such as Monument Information Resource period. (MIR). Based in Princeton, New Jersey, MIR collects At least four other groups have tried to estimate information about textbooks used in over 1,800 what students typically pay per year for textbooks, courses in fifty disciplines and is the college text­ and most have come up with approximately the book industry's main source for marketing data. In same figure as that reported by PIRG. First, using response to a request from this reporter for his­ Department of Education data, the GAO estimated torical data on the prices of calculus textbooks, that a first-time, full-time student at a four-year MIR offered just three years of data at a cost of public institution paid an average of US$898 US$3,500. In fact, it would be possible through a for "books and supplies" during the 2003-2004 meticulous search of booksellers' and publishers' academic year. Second, the College Board put websites to gather three years of price data for this figure at US$894 for the 2005-2006 academic free on the Internet. However, three years is too year. Third, a report prepared in 2003 by the staff short a time frame to provide perspective on price of Senator Charles Schumer (D-NY) found that changes. freshman and sophomore college students in New York State spent an average of US$922 on text­ Reasonsforthelncreases books. By contrast, a fourth estimate, by the AAP, Why have college textbook prices gone up so much? puts the figure much lower. In its letter in response The main reason seems to be that textbooks today to the GAO report, the AAP performed its own are far more elaborate than in the past and often calculation, based on overall college textbook come with extensive ancillary materials. According sales and the number of college students nation­ to the GAO report, publishers say that they have wide, to conclude that students spend an average made substantial investments to develop CD-ROMs, of US$ 5 76 per year on textbooks. The AAP's letter software, and websites to support faculty instruc­ also attacked the GAO's estimates based on the tion and improve student learning. It has become Department of Education data, noting that the data a common practice to "bundle"' additional items­ lumps together "books and supplies" with no clear CD-ROMs, Web passwords, workbooks-together definition of what constitutes "supplies". with textbooks. The PIRG report derides these How hard do textbook costs hit students? For additional items as "bells and whistles" that pro­ those who pay US$30,000 a year in tuition, a vide little value to professors and students. PIRG US$150 textbook is not likely to register on the surveyed 156 college and university professors in radar screen of college costs. But for many other California and Oregon, and 65% of them said they students, especially those at two-year colleges, use these additional materials rarely or never. On textbooks constitute a large proportion of college the other hand, publishing representatives told expenses. The GAO report estimates that the cost the GAO that they develop these supplementary of books and supplies for students at private four­ materials in response to demand from faculty. One year colleges is just 8% of the cost of tuition and reason given for the demand is that college and fees, while at two-year colleges-where the con­ university faculty increasingly rely on part-time or centration of low-income students is higher-the adjunct instructors who need more support ma­ analogous figure is 72%. terials to carry out their teaching than do regular And what about mathematics textbooks? Judg­ faculty. Publishers also told the GAO that they ing by commentaries in news articles and on the develop student supplements to aid the many stu­ Internet, many mathematics faculty have the im­ dents who now arrive at college with inadequate pression that the textbooks they assign, particularly backgrounds. in lower-level courses, have risen substantially Opinions about the usefulness of the textbook in price in recent years. However, confirming this supplements are likely to vary greatly and to depend

772 NOTICES OF THE AMS VOLUME 53 NUMBER 7 on students' preferences, instructors' teaching styles, catalog; the prices are from the publishers' web­ the needs of the discipline, the type of institution, sites.) and a host of other factors that are difficult to quan­ The frequency of textbook revisions have exas­ tify. According to the GAO report, publishers have perated many. Newspapers delighted in carrying the gotten the message that not all the supplements they following quotation of Representative David Wu produce are wanted or needed, and they have be­ (D-OR), one of the members of Congress request­ come more flexible in their offerings of bundled ing the GAO report: "Calculus hasn't changed much materials. since Isaac Newton. Do we really need a new edi­ One point of contention much emphasized in the tion every few years?" The September 2005 issue PIRG report is the publishers' practice of charging of the Notices carried a letter to the editor from much lower prices for textbooks sold overseas. As Thomas M. Liggett, undergraduate vice chair in an example, the PIRG report noted that Calculus: the mathematics department at the University of Early Transcendentals, written by James Stewart California, Los Angeles. This letter objected to the and published by Thomson Learning, cost about appearance of the seventh edition of a textbook that US$132 in 2003, while in Britain the cost was less the department had used for years. "We have no than half that amount: £3 3, the equivalent of about problem with books that go into second or third US$62. Students have found that since textbook editions because of the desire to correct errors, im­ prices are often significantly lower overseas, it prove presentation, or change topics covered, based makes sense to purchase the books from foreign on the experience of users of the original version," online bookstores and have them reimported to the Liggett wrote. "But if the author can't get it right United States. Publishers have defended this dif­ by the third edition, he/she should give up. The ferential pricing by noting that they must set prices decision to publish a new edition should be based that are appropriate for the markets in which the on pedagogy, not money." The department passed books will be sold. Unlike in the U.S., in many coun­ a resolution that, if a textbook it was using went tries college textbooks are not required, so students into an edition beyond the third with no significant might decide not to buy the books at all if the pedagogical improvement, the department would prices are too high. immediately begin to look for a replacement. But more than bundling and differential pricing, Publishers told the GAO that the revision cycle what seems to irk students and professors is the of textbooks is driven by professors' demand for short revision cycle for textbooks. Many believe that the most up-to-date material and for new tech­ publishers speed up the revision cycle in order to nology applications. The GAO report mentions a undercut the used-textbook market. As the GAO survey of over one thousand college professors report notes, "New textbook sales are highest in that was commissioned by the AAP and carried out the first year an edition is available, with sales by Zogby International [6]. Eighty percent of the fac­ declining as the supply of used books becomes ulty polled for this survey said it is important that greater." Professors usually must assign the newest the content of the textbooks they assign be as cur­ edition of a textbook, since assigning an out-of­ rent as possible. (It should be noted that, judging print edition can make it difficult for all students by a table listing the twenty-eight academic de­ to obtain copies. The GAO report says that ten partments of the 1,000 survey respondents, one in­ years ago college textbooks were typically revised fers that no mathematics professors were included every four to five years, compared to every three in the survey.) As a specific example of the kind of to four years today. development that necessitates textbook revision, It is certainly not uncommon for lower-level one publisher cited to the GAO "a teaching ap­ mathematics textbooks to be revised often. For ex­ proach from the 1980s that has regained popularity ample, John Wiley publishes a popular calculus in calculus." Indeed, the past twenty years have seen textbook by Howard Anton et al. The book first extensive discussions within the mathematical came out in 1980; it was revised regularly every community about how best to teach calculus, and three or four years, with the eighth these discussions have led to a plethora of text­ edition appearing in 2005 (list price US$151). Cal­ books reflecting new teaching methodologies. culus with Analytic Geometry by Ron Larson et al., published by Houghton-Mifflin, first came out in Going to the Grassroots 1979 and appeared in its eighth edition in 2006 (list In early 2004 Bernard Russo, chair of the mathe­ price US$156). The top-selling college calculus matics department at the University of California, textbook is most likely Stewart's Calculus: Early Irvine, led a petition drive seeking changes from Transcendentals. This book had its first edition in the publisher Thomson Learning in its pricing 198 7 and has been revised on a regular four-year and revision policies for Stewart's Calculus: Early schedule since then (list price US$15 7 for the fifth Transcendentals. In particular, the petition called edition, published in 2003). (The information on on Thomson not to revise the current edition, which editions is from the Library of Congress online is the fifth edition, "until there has been significantly

AUGUST 2006 NOTICES OF THE AMS 773 new content in the field of calculus, applications of in at least five states, he noted, and several major calculus, and/or the teaching of calculus that would universities have launched task forces to study justify an update." It also called for sales materi­ ways to lower textbook costs. The appearance of als and sales representatives to disclose the full "low-frills" publishers and free online prices of textbooks and supplementary materials textbooks have also added to the pressures on and the amount of time the current editions will be traditional textbook publishers to lower their on the market. Within weeks, around 550 mathe­ prices. Rosenfeld predicted that the combination matics faculty across the nation had signed the of these factors means the situation "has the petition, which was sent in a letter dated April 6, potential to create a tipping point in the market." 2004, to the chief executive officer of Thomson With its 2004 report, PIRG set in motion a cam­ Learning. paign to lower textbook prices that has gained Around this time, the UCLA mathematics de­ national momentum and is clearly having an effect. partment negotiated an agreement with Thomson Some of the campaign's rhetoric became extreme, Learning to charge UCLA students US$20 less for portraying publishers as evil entities intent on three of Stewart's calculus textbooks that are squeezing as many dollars as possible out of published by Thomson. Not long thereafter, math­ struggling students. But the campaign highlighted ematics departments at several other universities legitimate concerns of students and faculty and followed suit and were able to negotiate similar forced publishers to recognize that they had a price reductions. In a January 2005 email message serious problem with their consumer base for to the petition signatories, Russo reported that the college textbooks. Change is surely on its way. As UC Irvine mathematics department negotiated retired publishing executive Edwin Beschler put it price reductions for delivery of the Stewart calcu­ in a 1999 letter to the editor of the Notices, "If the lus textbook in various formats, including on a educational establishment wishes to change the CD-ROM and as a loose-leaf textbook. "S everal rules of the game, it will follow as the night the faculty involved in these different negotiations day that publishers will adapt." have related that those developments would not have been possible without the efforts of students References and faculty last year to bring attention to this [1] College Textbooks: Enhanced Offerings Appear to Drive problem and therefore create a more favorable Recent Price Increases, Government Accountability negotiating environment," he wrote. Office, July 2005. Available at http: I lwww. gao. gov I cgi-binlgetrpt?GA0-05-806. Integral to these efforts has been the extensive [2] Ripoff 101: How the Current Practices ofthe Textbook work done by students through the state PIRGs, Industry Drive Up the Cost of College Textbooks, by which held press conferences, arranged meetings Merriah Fairchild, CALPIRG, 2004. with publishing representatives, and created a web­ [3] Ripoff 101: 2nd Edition. How the Publishing Industry's site (http: I I www. maketextbooksaffordabl e. Practices Needlessly Drive Up Textbook Costs. A National com). In 2005 a group of physics faculty launched Survey of Textbook Prices, State Public Research Interest their own petition, which addressed a widely used Groups, February 2005. Available at http: I lwww. physics textbook also published by Thomson Learn­ pirg.orglhighered. ing. Eventually the mathematicians and physicists [4] Trends in College Pricing, Trends in Higher Education Series, College Board, 2005. Available at http: I lwww. banded together to produce a joint call to action collegeboard.comlprod_downloadslpresslcostOSI addressing both the mathematics and physics trends_college_pricing_OS.pdf. textbooks published by Thomson. This joint [5] "Schumer reveals local college textbook prices are petition was signed by over 700 faculty at 150 skyrocketing-and proposes new $1,000 tax deduction institutions around the nation. to help cover cost", press release from the office The fever pitch of media attention that followed of Senator Charles E. Schumer, October 10, 2003. the appearance of the PIRG and GAO reports mod­ Available at http:llwww.senate.govl-schumerl erated a bit in 2006, but the issue of college text­ SchumerWebsitelpressroomlpress_releasesl book prices was still very much on the front burner PR02101. htm l. [6] The Attitudes of College Faculty on the Textbooks for many students and faculty. David Rosenfeld, pro­ Used In Their Courses, Zogby International, December gram director for the student PIRGs, said he knows 2004. Available at http:llwww.publishers.orgl of several institutions where departments in vari­ higheredl pdfsi AAP%20final%20report%20B.doc. ous academic subjects have negotiated their own price deals with textbook publishers. He noted that the spread of this practice seems to provide evidence that textbook prices are "grossly inflated". As he put it, "Sales reps seem perfectly empowered to make deep price cuts in their books from just a few squeaky wheels." Legislation aimed at easing the burden of high college textbook prices is pending

774 NOTICES OF THE AMS VOLUME 53 NUMBER 7 200 5 Annual Survey of the Mathematical Sciences in the United States (Second Report)

Updated Report on the 2004-2005 Doctoral Recipients Starting Salary Survey of the 2004-2005 Doctoral Recipients

Ellen E. Kirkman, ]ames W. Maxwell, and Colleen A. Rose

Update on the 2004-2005 This Second Report of the 2005 Annual Survey gives an update of the 2004-2005 new doctoral recipients from the First Report, which appeared Doctoral Recipients in the Notices of the AMS in February 2006, pages 230-45. The First Introduction Report gave salary data for faculty members in these same departments. The Annual Survey of the Mathematical Sciences It also had a section on new doctoral recipients in statistics that is not updated here. collects information each year about degree The 2005 Annual Survey represents the forty-ninth in an annual recipients, departments, faculties, and students in series begun in 1957 by the American Mathematical Society. The 2005 the mathematical sciences at four-year colleges and Survey is under the direction of the Data Committee, a joint committee universities in the United States. Information about of the American Mathematical Society, the American Statistical Association, recipients of doctoral degrees awarded between the Institute of Mathematical Statistics, and the Mathematical Association July 1, 2004, and June 30, 2005, was collected from of America. The current members of this committee are Richard Cleary, doctorate-granting departments beginning in late Amy Cohen-Corwin, Donald M. Davis, Nicholas M. Ercolani, Abbe H. Herzig, spring 2005. The "2005 Annual Survey First Report" Donald R. King, Ellen E. Kirkman (chair), David j. Lutzer, james W. (Notices, February 2006, pages 230-45) presented Maxwell (ex officio), Peter March, Polly Phipps, David E. Rohrlich, and Henry Schenck. The committee is assisted by AMS survey analyst Colleen survey results about 1,116 new doctoral recipients A. Rose. Comments or suggestions regarding this Survey Report may based on the data provided by the departments. be directed to the committee. Here we update this information using data obtained from 587 new doctoral recipients who responded to a questionnaire, Employment doctoral recipients appears at the end of this report Experiences of New Doctoral Recipients (EENDR), on pages 787-89. sent in early October 2005 to all new doctoral recipients. In addition, this report incorporates Updated Employment Status of 2004-2005 information on an additional 106 doctoral Doctoral Recipients recipients from departments that responded too The updated responses rates for the 2005 Survey late to have the information included in the First of New Doctoral Recipients appears on the next Report. Finally, we present the starting salaries and page. The total number of departments responding other employment information from the new in time for inclusion in this Second Report was doctoral recipients that responded to the EENDR 262; 22 more than were included in the 2005 First questionnaire. Report and 10 less than the number responding The names and thesis titles of the 2004-2005 doctoral recipients reported on in the First Report Ellen E. Kirkman is professor of mathematics, Wake Forest were published in "Doctoral Degrees Conferred" University. ]ames W Maxwell is AMS associate executive (Notices, February 2006, pages 258-76). A director for special projects. Colleen A. Rose is AMS survey supplemental listing of the 106 additional new analyst.

AUGUST 2006 NOTICES OF THE AMS 775 2005 Annual Survey of the Mathematical Sciences in the United States

Doctorates Granted Departmental Response Highlights Rates (updated April 2006) Group I (Pu)' 2 5 of 2 5 including 0 with 0 degrees • There were 1 ,222 doctoral recipients from U.S. institutions for Group I (Pr) 22 of 23 including 0 with 0 degrees 2004-2005, up 141 (13%) from the previous year. This is the Group II 56 of 56 including 3 with 0 degrees highest number of new Ph.D.'s reported since 1994-1995. Group Ill 73 of 73 including 22 with 0 degrees • The final unemployment rate for 2004-2005 doctoral recipi­ ents was 3.9%, comparable to the rates of the last 8 years. Group IV 66 of 87 including 1 with 0 degrees • The number of new doctoral recipients who are not U.S. citi­ Group Va 20 of 23 including 4 with 0 degrees zens is up 1 04 over last year's number, and is up 193 (36%) ' For defm1t1ons of groups see page 786. from 2000-2001. for inclusion in the 2004 Second Report. Definitions • The number of doctoral recipients who are U.S. citizens is 496, of the varous groups surveyed in the Annual Survey up 37 (8%) from last year's number. The percentage of U.S. can be found on page 786 of this report. citizens among all doctoral recipients this year is 41%, down from 42% last year; this is the lowest percentage of U.S. citi­ zens in the six years that the number of doctoral recipients Table 1A: Doctoral Recipients: in the Second Report has been broken down by citizenship. Fall and Final Counts • Females totaled 3 59 (29% of all new doctoral recipients), up Year Fall Final in number and down in percentage from 333 (31%) last year. Of the 496 U.S. citizen new doctoral recipients, 141 are female 1995-1996 1098 1099 (28%), down in number and percent from last year. The highest 1996-1997 1123 1130 percentage of females among the annual counts of doctoral 1997-1998 1163 1176 recipients was 34%, reported for 1998-1999. 1998-1999 1133 1135 • The number of doctoral recipients whose employment status 1999-2000 1119 1127 is unknown is 1 50, up 31 from last year's number of 119. • Of the 1 ,072 new doctoral recipients whose employment sta­ 2000-2001 1008 1065 tus is known, 1,018 reported having employment in fall2005 2001-2002 948 960 with 86% (875) finding employment in the U.S.; last year this 2002-2003 1017 1037 percentage was 87%. 2003-2004 1041 1081 • The number of new doctoral recipients taking positions in U.S. 2004-2005 1116 1222 business/industry and government was 176 in fall 2005, a 30% increase from last year's number. The percentage of doc­ Table 1A shows the fall and final counts of toral recipients employed in the U.S. taking positions in busi­ doctoral recipients in the mathematical sciences ness/industry and government has increased to 20%, from 1 7% awarded by U.S. institutions in each year from 199 5 in fall 2004. This increase reverses the trend of five years of through 2005. This year the total number of new decline in this percentage, from 31% in fall 2000. doctoral recipients is 1,222, up from the previous • Doctoral hires into U.S. academic positions are at a six-year year by 141. A detailed review of the responding lnigh, up by a total of 69 across the combined four-year math­ ematics departments (Groups I, II, Ill, M & B) and down by a total of 27 across the other academic reporting categories com­ Table 1 B: Doctoral Recipients: Citizenship bined. • Non-U.S. citizens accounted for 59% of those employed in the Year u.s. Non-U.S. TOTAL U.S. (last year this percentage was 58%). 2000-2001 532 533 1065 • There were 587 new doctoral recipients responding to the 2001 - 2002 428 532 960 EENDR survey; of the 523 who found employment in the U.S., 2002-2003 499 538 1037 56% reported obtaining a permanent position (last year this 2003-2004 459 622 1081 percentage was 49%). 2004-2005 • The percentage of temporarily employed respondents who re­ 496 726 1222 ported taking a postdoctoral position decreased from 77% in fall 2004 to 74% in fall 2005. The number of respondents who Table 1C: Doctoral Recipients by Type of reported taking a postdoctoral position in fall 2005 was 1 72, Degree-Granting Department down from 1 76 for fall 2004. Department Group' I (Pu) I (Pr) II Ill IV Va Number 266 181 222 160 301 92 Percent 22% 15% 18% 13% 25% 8%

' For definitions of groups see page 786.

776 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

Table 2A: Fall 2005 Employment Status of 2004-2005 Doctoral Recipients: Field of Thesis (updated April 2006)

FIELD OF THESIS

Real , Comp., Di scr. Math./ Numerical Linear Differential, Alg ebra Funct., & Com bin./ Analys is/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Appro xi· Optim./ Difference Math. Oth er/ TYPE OF EMPLOYER Theory Analysis Topology Comp. Sci. Probability Biostat. Math. mations Control Equations Educ. Unknown TOTAL

Group I (Public)' 16 8 13 7 1 0 7 5 2 18 0 1 78 Group I (Private) 13 4 16 6 1 1 4 1 1 9 0 0 56 Group II 19 9 11 4 3 2 5 6 1 7 1 0 68 Group Ill 3 10 1 9 1 11 2 4 1 3 1 1 47 Group IV 0 1 1 0 3 45 2 0 0 0 0 1 53 Group Va 1 0 0 0 0 0 4 3 2 2 0 0 12 Master's 12 4 5 6 6 1 5 9 4 2 13 3 0 79 Bachelor's 28 18 11 23 1 16 8 8 7 8 5 0 133 Two-Year College 3 1 5 3 2 1 1 1 0 0 1 0 18 Other Academic Dept.' 8 2 1 6 5 57 20 7 1 11 2 0 120 Research Institute/ 6 1 1 0 1 16 3 1 0 6 0 0 35 Other Nonprofit Government 1 1 1 1 0 15 5 7 3 3 0 0 37 Business and Industry 6 3 5 6 8 83 14 2 4 8 0 0 139 Non-U.S. Academic 27 9 18 16 4 17 14 8 4 9 1 0 127 Non-U.S. Nonacademic 2 1 0 0 3 9 0 1 0 0 0 0 16 Not Seeking Employment 3 0 1 1 0 4 1 0 0 2 0 0 12 Still Seeking Employment 4 2 3 9 0 9 6 1 1 7 0 0 42 Unknown (U.S.) 13 5 8 1 0 20 13 2 4 7 0 0 73 Unknown (non-U.S.)' 11 3 4 3 2 33 4 4 2 10 1 0 77 TOTAL 176 82 105 101 41 354 122 65 35 123 15 3 1222 Column I Male 145 66 81 81 34 197 90 47 24 90 5 3 863 Subtotals I Female 31 16 24 20 7 157 32 18 11 33 10 0 359 1 For definitions of groups see page 786. 2 These are departments outside the mathematical sciences. 3 Includes those whose status is reported as "unknown" or "still seeking employment". Table 28: Fall 2005 Employment Status of 2004-2005 Doctoral Recipients: Type of Degree-Granting Department (updated April 2006)

TYPE OF DOCTORAL DEGREE-GRANTING DEPARTMENT

Group I Group I Row (Public) (Private) Group II Group Ill Group IV Group Va Subtotals TYPE OF EMPLOYER Math. Math. Math. Math. Statistics Applied Math. TOTAL Male Female

Group I (Public)' 36 24 9 4 0 5 78 63 15 Group I (Private) 20 33 2 0 0 1 56 44 12 Group II 23 15 23 3 2 2 68 56 12 Group Ill 8 1 9 19 10 0 47 31 16 Group IV 0 3 2 2 45 1 53 30 23 Group Va 1 1 2 0 0 8 12 9 3 Master's 17 6 25 17 8 6 79 43 36 Bachelor's 26 9 49 33 13 3 133 100 33 Two-Year College 3 1 7 5 0 2 18 13 5 Other Academic Dept. 11 7 18 13 55 16 120 80 40 Research Institute/ 7 4 6 1 16 1 35 23 12 Other Nonprofit Government 8 2 6 2 12 7 37 20 17 Business and Industry 13 15 17 16 67 11 139 100 39 Non-U.S. Academic 45 28 17 13 17 7 127 96 31 Non-U.S. Nonacademic 1 4 2 0 9 0 16 12 4 Not Seeking Employment 2 3 1 1 4 1 12 7 5 Still Seeking Employment 8 8 5 7 6 8 42 25 17 Unknown (U.S.) 20 12 10 11 13 7 73 54 19 Unknown (non-U.S.)' 17 5 12 13 24 6 77 57 20 TOTAL 266 181 222 160 301 92 1222 863 359 Column I Male 212 148 172 101 168 62 863 Subtotals I Female 54 33 50 59 133 30 359 1 For definitions of groups see page 786. 2 These are departments outside the mathematical sciences. 3 Includes those whose status is reported as "unknown" or "still seeking employment".

AUGUST 2006 NOTICES OF THE AMS 777 2005 Annual Survey of the Mathematical Sciences in the United States

Table 2C: Field of Thesis of 2004-2005 Doctoral Recipients: by Type of Degree-Granting Department (updated April 2006)

FIELD OF THESIS

TYPE OF DOCTORAL Real, Comp., Discr. Math./ Numerical Linear Differential, Algebra Funct., & Com bin./ Analysis/ Nonlinear Integral, & DEGREE-GRANTING Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim ./ Difference Math . Other/ DEPARTMENT Theory Analys is Topology Camp. Sci. Probability Bios tat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public)' 74 26 39 27 6 11 25 11 8 37 2 0 266 Group I (Private) 52 9 41 19 10 2 19 7 3 19 0 0 181 Group II 40 25 20 26 13 6 22 21 11 37 0 1 222 Group Ill 10 22 4 22 4 32 21 9 3 20 13 0 160 Group IV 0 0 0 0 4 291 3 1 0 0 0 2 301 Group Va 0 0 1 7 4 12 32 16 10 10 0 0 92 TOTAL 176 82 105 101 41 354 122 65 35 123 15 3 1222 ' For defmJtJons of groups see page 786. significantly influenced by differences in Table 2D: Percentage of Employed New Doctoral responding departments between the two years. Recipients by Type of Employer Table 1B shows trends in the number of new doctoral recipients for the past five years broken down by U.S. Employed in U.S. Not Employed in U.S. NUMBER citizens and non-U.S. citizens. This year the EMPLOYED Academic' Nonacademic Academic Nonacademic number of new doctoral recipients who are U.S. citizens Fall 2001 63% 27% 9% 2% 914 is 496, an increase of 3 7 over last year. The number

Fall 2002 67% 22% 10% 1% 829 of non-U.S. citizen new doctoral recipients has climbed to 726, a 17%increase over last year. Fall 2003 70% 17% 12% 2% 792 Table 1C gives a breakdown of the 1,2 2 2 doctoral Fall 2004 72% 15% 12% 1% 910 degrees awarded in the mathematical sciences Fa ll 2005 69% 17% 12% 2% 1018 between July 1, 2004, and June 30,2005, by type of ' Includes Research Institutes and other non-profits. degree-granting department. Tables 2A, 2B, and 2C display updates of employ­ departments in 2004 and 2005 revealed that the ment data, found in these same tables in the First departments responding in both 2004 and 2005 Report, for the fall count of 2004- 2005 doctoral reported an increase of 13 5 new doctoral recipients; recipients plus 106 additional doctoral recipients re­ hence, the total increase from 2004 to 2005 is not ported late. These tables are partitioned by field of thesis research, by the survey group of their de-

Figure l: Percentage of New Doctoral Recipients Unemployed' Year Percentage 1981 0.0 1982 1.8 1983 2.2 1984 2.1 1985 0.8 1986 2.3 1987 3.0 1988 1.4 1989 3.0 1990 2.2 1991 5.0 6.0 +------r------~~------1992 6.7

1993 8.9 5.0+------.------r--~------~~--- 1994 10.7 1995 10.7 4.0 +------~------~~----~------~----~~ 1996 8.1 1997 3.8 3.0+------~--~~-+------~----~------1998 4.9 1999 4.7 2000 3.3 2001 3.7 2002 2.9 2003 5.0 N m ~ ~ ~ ~ oo m o N m ~ ~ ~ ~ oo m o N m ~ ~ 2004 4.4 oo oo oo oo oo oo oo oo oo m m m m m m m m m m o o o o o o 2005 3.9 m m m m m m m m m m m m m m m m m m m o o o o o o NNNNNN

' As reported in the respective Annual Survey Second Reports.

778 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

Table 3A: New Doctoral Recipients Employed in the U.S.

Degree-Granting Department Group'

I (Pu) I (Pr) II Ill IV Va TOTAL Academic2 Business/ Academic Business/ Academic Business/ Academic Business/ Academic Busine ss/ Academic Business/ Academic Business/ Industry & Industry & Industry & Industry & Indu stry & Industry & Industry & Government Government Government Government Government Gove rnment Government Fall 2001 159 31 71 19 126 40 80 31 108 96 30 27 574 244 Fall 2002 133 25 86 20 107 27 91 11 102 72 34 24 553 179 Fall 2003 123 24 90 16 118 13 61 10 119 54 40 14 551 131 Fall 2004 118 18 118 18 144 17 73 11 150 61 52 11 655 137 Fall 2005 152 21 104 17 152 23 97 18 149 80 45 19 699 176

1 For definitions of groups see page 786. 2 Includes Research Institutes and other non-profits. gree-granting department, and by type of employer. Table 3B: New Doctoral Recipients New doctoral recipients are grouped by field of Employed in U.S. Academic Positions thesis using the Mathematical Reviews 2000 Mathe­ matics Subject Classification list. A complete list Hiring Department Group' of these groups is available on the AMS website at HII IV Va M&B Other TOTAL www.ams.org/employment/Thesis_groupings. Fall 2001 214 49 11 178 122 574 pdf. At the time of this Second Report, the fall2005 Fall 2002 222 45 10 148 128 553 employment status of 1,072 of the 1,222 doctoral recipients was known. Fall 2003 216 39 9 158 129 551 The fall2005 unemployment rate for new doctoral Fall 2004 220 66 19 172 178 655 recipients, based on information gathered by the time Fall 2005 249 53 12 212 173 699 of the Second Report, was 3.9%. Figure 1 presents the 1 For definitions of groups see page 786. fall 1981 through fall 2005 trend in the final unemployment rate of new doctoral recipients. The Table 3C: Females as a Percentage of New counts on which these rates are determined do not Doctoral Recipients include those new doctoral recipients whose fall employment status was unknown at the time of the Department Group' Second Report. This year the number of recipients I (Pu) I(Pr) II Ill IV Va TOTAL whose employment status was reported as unknown % Female increased to 150 from 119last year. Produced 20% 18% 23% 37% 44% 33% 29% Of the 1,072 new doctoral recipients whose Hired 19% 21% 18% 34% 43% 25% 26% employment is known, 875 were employed in the U.S., 143 were employed outside the U.S., 42 were still ' For definitions of groups see page 786. seeking employment, and 12 were not seeking with theses in probability or statistics is the highest employment. at 36% (up from 26% last year). Table 2D presents the trend in the percentage of Table 3A breaks down the numbers of new employed new doctoral recipients by type of doctoral recipients employed in the U.S. in acad­ employer for the last five years. Academic emic positions or in business/ industry and employment includes those employed by research goverment by degree granting group shows that institutes and other nonprofits. The percentage of the the fall 2005 total number of doctoral recipients total employed new doctoral recipients that are in U.S. taking positions in business/industry and gover­ academic positions has dropped after five years of ment is 176; this number reflects an steadily increasing, and concomitantly the percentage increase of 30% over last year and is the highest of the total employed in U.S. nonacademic positions number reported since fall 2002. All groups have (U.S. government, U.S. business and industry) has shown an increase in number of graduates finding increased after five years of steady decreases. employment in business/industry and gover­ Among new doctoral recipients who are employed, ment, except Group 1 Private. the percentage taking nonacademic employment varied Table 3B shows that the number of new doctoral significantly by field of thesis. For those recipients taking U.S. academic positions has whose field of thesis is in the first three columns increased to a six-year high of 699, from 655 in in Table 2A, this percentage is the lowest at 7% 2004. Doctoral hires into U.S. academic positions (down from 8%), while the percentage for those are up in all groups except Groups IV (down to 53

AUGUST 2006 NOTICES OF THE AMS 779 2005 Annual Survey of the Mathematical Sciences in the United States

Table 3D: Citizenship of 2004-2005 Male Doctoral Recipients by Fall 2005 Employment Status

CITIZENSHIP TOTAL MALE NON-U .S . CITIZENS DOCTORAL U.S. CITIZENS TYPE OF EMPLOYER Permanent Visa Temporary Visa Unknown Visa RECIPIENTS U.S. Employer 283 so 270 9 612 U.S. Academic 233 33 219 7 492 Groups' I, II , Ill, and Va 92 13 94 4 203 Group IV 6 1 23 0 30 Non-Ph.D. Department 126 16 91 3 236 Re search Institute/Other Nonprofit 9 3 11 0 23 U.S. Nonacademic so 17 51 2 120 Non-U .S. Employer 21 1 71 15 108 Non-U.S. Academic 20 1 65 10 96 Non-U.S . Nonacademic 1 0 6 5 12 Not Seeking Employment 5 0 2 0 7 Still Seeking Employment 5 3 17 0 25 Subtotal 314 54 360 24 752 Unknown (U.S.) 37 1 10 6 54 Unknown (non-U.S.)' 4 2 41 10 57

TOTAL 355 57 411 40 863

1 For definitions of groups see page 786. ' Includes those whose status is reported as "unknown·· or "still seeking employment"'.

Table 3E: Citizenship of 2004-2005 Female Doctoral Recipients by Fall 2005 Employment Status

CITIZENSHIP TOTAL FEMALE NON-U .S. CITIZENS DOCTORAL U.S. CITIZENS TYPE OF EMPLOYER Permanent Visa Temporary Visa Unknown Visa RECIPIENTS U.S. Employer 117 32 111 3 263 U.S. Academic 95 26 84 2 207 Groups' I, II, Ill, and Va 21 9 27 1 58 Group IV 6 3 14 0 23 Non-Ph .D. Department 65 11 37 1 114 Research Institute/Other Nonprofit 3 3 6 0 12 U.S. Nonacademic 22 6 27 1 56 Non-U.S. Employer 3 1 23 8 35 Non-U.S. Academic 2 1 21 7 31 Non-U.S. Nonacademic 1 0 2 1 4 Not Seeking Employment 5 0 0 0 5 Still Seeking Employment 4 2 11 0 17 Subtotal 129 35 145 11 320 Unknown (U.S.) 10 4 3 2 19 Unknown (non-U.S.)' 2 0 15 3 20

TOTAL 141 39 163 16 359 1 For defmltlons of groups see page 786. ' Includes those whose status is reported as "unknown·· or "still seeking employment"'.

from 66last year), Va (down to 12 from 19last year) decreased from last year's percentages of 31% and and Other (down to 173 from 178 last year); the 27%, respectively, to this year's 29% and 26%. biggest percentage increases are in Group ill (38%) and Group B (28%). Doctoral hires into non-U.S. academic Table 3F: Number of New Doctoral positions increased by 18% to 127 from 108last year. Recipients Employed in the U.S. by Citizenship Table 3C gives information about the production and Type of Employer and hiring of female new doctoral recipients in CITIZENSHIP the doctoral-granting departments of this survey. From Table 3C we see that the percentage of females U.S. EMPLOYER U.S. Non-U.S. TOTAL hired ranges from a high of 43% in Group IV, followed Academic, Groups I-Va 125 189 314 by Group III at 34% to a low of 18% in Group II. The Academic, M&B, Other 203 182 385 percentage of female new doctoral recipients Nonacademic 72 104 176 produced is highest in Group IV (44%). The total TOTAL 400 475 875 percentage of females produced and hired has

780 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

Updated Information about 2004-2005 Doctoral Recipients by Sex and Citizenship Table 4A: Number (and Percentage) of Annual EENDR Tables 3D and 3E show the sex and citizenship Respondents Employed in the U.S. by job Status of the 1,222 new doctoral recipients and the fact that 875 new doctoral recipients found jobs in the Employed in U.S. Temporary U.S. this year. This is 82% of the 1,072 new doctoral Unknown Permanent Temporary Postdoctoral recipients whose employment status was known Permanent Total Total not available Permanent and 86% of the 1,018 known to have jobs in fall Total not available 2005. Last year these percentages were 82% and 87%, respectively. Fall 2001 266(56%) 205(43%) 1 07(52%) 143(70%) 42(29%) 2 Sex and citizenship are known for all of the Fall 2002 264(52%) 245(48%) 90(37%) 203(83%) 69(34%) 1 1,222 new doctoral recipients. The final count of Fall 2003 253(54%) 216(46%) 87(40%) 164(76%) 53(32%) -- new doctoral recipients who are U.S. citizens is 496 (41%) (down from 42% last year) this is the lowest Fall 2004 220(49%) 229(51 %) 81 (35%) 176(77%) 49(28%) -- percentage of U.S. citizens in the six years that the Fall 2005 291 (56%) 232(44%) 92(40%) 172(74%) 55(32%) -- number of doctoral recipients in the Second Report has been broken down by citizenship. Pages 235-8 of the First Report present further information Table 4B: Percentage of Annual EENDR Respondents Employed related to the citizenship of the 2004-2005 new in the U.S. by Employment Sector within job Status doctoral recipients. Employed in U.S. Of the 496 U.S. citizen new doctoral recipi­ ents reported for 2004-2005, 141 are female Permanent Temporary Academic1 Government Business/ Academic Government Business/ and 355 are male. Females accounted for 28% of Industry Industry the U.S. citizen total (down from 33% last year); the number of female U.S. citizens has Fall 2001 62% 6% 32% 95% 4% -- decreased by 10 from last year's count of 151, Fall 2002 70% 6% 23% 93% 6% 1% and the number of male U.S. citizens increased Fall 2003 76% 4% 20% 94% 3% 3% by 47 over last year's count of 308. Table 3F shows that non-U.S. citizens accounted Fall 2004 72% 5% 23% 97% 3% -- for 58% of those employed in the U.S. (the same as last Fall 2005 68% 5% 27% 96% 4% --

year). U.S. academic doctoral departments, Groups I ' Includes Research Institutes and other non-prof1ts. through Va, hired 40% U.S. citizens, while groups M, B, and all other academic departments hired 53% U.S. who were employed the highest response rate, 70%, citizens (last year these percentages were 41% and was from those employed in the U.S., while the 51%, respectively). U.S. citizens represented 41% of lowest, 39%, was from those in non-U.S. academic. those hired into nonacademic positions (last year The EENDR gathered details on employment 48%). Among all the 875 new 2004-2005 doctoral experiences not available through departments. recipients employed in the U.S., 20% took nonacademic The remainder of this section presents additional employment (government or business and industry.) information available on this subset of the This percentage is up from 17% in 2003-2004 and 2004-2005 doctoral recipients. from 19%in2002-2003. Figure 2: Age Distribution of 2004-2005 EENDR Respondents New Information from the EENDR Survey 80 Of the 1,116 new doctoral recipients reported in the First 70 Report, the 1,104 whose addresses were known were 60 sent the Employment 50 >-v Experiences of New Doctoral s::: QJ 40 Recipients (EENDR) survey in ~ October 2005, and 587 (53%) 0" ,_QJ 30 responded. The response Ll.. rates varied considerably 20 among the various subgroups -, of new doctoral recipients 10 defined by their employment ,....., I KHl-n-n ~ .r-1 n status as reported by 0 20 25 30 35 40 45 50 55 60 65 departments. Among those Age

AUGUST 2006 NOTICES OF THE AMS 781 2005 Annual Survey of the Mathematical Sciences in the United States

Table 4A gives the numbers and percentages of the AMS website at www. ams. org/empl oyment/ EENDR respondents taking permanent and surveyreports.html. temporary positions in the U.S for fall 2001 through fall 2005. This year we see that among the 523 employed in the U.S., 291 reported obtaining a permanent Starting Salary Survey of the position and 2 3 2 a temporary position. While these 2004-2005 Doctoral Recipients numbers both reflect an increase, the number of individuals obtaining permanent positions has The starting salary figures for 2005 were reached a five-year high. ln addition, the percentage compiled from information gathered on the EENDR of individuals taking permanent positions has questionnaires sent to individuals who received increased to 56%, while the percentage of those doctoral degrees in the mathematical sciences taking temporary positions has dropped to 44% during the 2004-2005 academic year from (the lowest reported since 43% in 2001). Of the 232 universities in the United States (see previous in temporary positions, 92 (40%) reported taking section for more details). temporary employment because a suitable The questionnaires were distributed to 1,104 permanent position was not available, and 172 recipients of degrees using addresses provided (7 4%) classified their position as postdoctoral. Of by the departments granting the degrees; 587 the 172 respondents taking positions they classified individuals responded between late October and as postdoctoral, 55 (32%) reported that a suitable April. Responses with insufficient data or from permanent position was not available. individuals who indicated they had part-time or non-U.S. employment were excluded. Numbers Table 4B shows the employment trends of permanent and temporary positions broken down of usable responses for each salary category are reported in the following tables. by sector for the last five years. Following last year's Readers should be warned that the data in this pattern the percentage of permanently employed report are obtained from a self-selected sample, and EENDR respondents taking employment in inferences from them may not be representative academia has declined this year, and there was an of the population. offsetting increase in the proportion of Key to Tables and Graphs. Salaries are listed permanently employed EENDR respondents taking in hundreds of dollars. Nine-month salaries are positions in business and industry. based on 9-10 months' teaching and/or research, Among the 291 who reported obtaining a not adding extra stipends for summer grants or permanent position in the U.S. in fall 2005, 68% summer teaching or the equivalent. Years listed were employed in academia (including less than 1% denote the survey cycle in which the doctorate was in research institutes and other nonprofits), 5% in received: for example: survey cycle July 1, 2004- government, and 27% in business or industry. June 30, 2005, is designated as 2005. Salaries are Women held 3 7% of the permanent positions. those reported for the fall immediately following Among the 232 individuals with temporary the survey cycle. M and F are male and female employment in the U.S. this year, 96% were respectively. Some persons receiving a doctoral employed in academia (including 9% in research degree had been employed in their present posi­ institutes and other nonprofits), 4% in government, tion for several years, so those who had "one year and less than 1% in business or industry. or less experience" were analyzed separately Figure 2 gives the age distribution of the 57 4 new from the total. Male and female figures are not doctoral recipients who responded to this question. provided when the number of salaries available The median age of new doctoral recipients was 30 for analysis in a particular category was five or years, while the mean age was 32 years. The first fewer. Also, quartile figures are not available for and third quartiles were 28 and 34 years, 1970 through 1980. All categories of "Teach­ respectively. ing/Teaching and Research" and "Research Only" contain those recipients employed at academic institutions only. Previous Annual Survey Reports Graphs. The graphs show standard boxplots The 2005 First Annual Survey Report was pub­ summarizing salary distribution information for the lished in the Notices in the February 2006 issue. For years 1998 through 2005. Values plotted for 1998 the last full year of reports, the 2004 First, Second, through 2004 are converted to 2005 dollars using and Third Annual Survey Reports were published the implicit price deflator prepared annually by in the Notices in the February, August, and Sep­ the Bureau of Economic Analysis, U.S. Department tember 2005 issues respectively. These reports of Commerce. and earlier reports, as well as a wealth of other For each boxplot the box shows the first quartile information from these surveys, are available on (Q1), the median (M), and the third quartile (Q3). The

782 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

Academic Teaching/Teaching and Research Academic Postdoctorates Only 9-1 0-Month Salaries 9-1 0-Month Salaries (in hundreds of dollars) (in hundreds of dollars) Reported Ph .D. Median in Year Min Ql Median Q Max 2005 $ 1975 90 120 128 135 173 378 1980 105 155 171 185 250 355 1985 170 230 250 270 380 402 Reported Ph.D. Median in 1990 230 305 320 350 710 440 Year Min Median Q , Max 2005 $ 1995 220 320 350 382 640 426 Ql 1997" 180 340 366 400 840 430 1997 180 350 385 410 450 452 1998 140 340 370 410 700 430 1998 290 350 390 420 500 453 1999 180 360 400 430 700 458 1999 130 365 400 418 540 458 2000 250 380 415 450 650 465 2000 300 385 420 450 550 471 2001 259 400 420 461 660 460 2001 250 400 425 450 566 465 2002 230 400 450 500 840 484 2002 230 425 450 487 595 484 2003 220 415 450 510 920 475 2003 240 420 450 480 600 475 2004 285 420 450 500 1234 462 2004 300 420 450 490 625 462 2005 280 430 465 506 1002 465 2005 310 450 460 500 615 460 2001 M 259 490 430 475 660 2001 M 250 400 430 454 566 2001 F 310 390 413 443 620 2001 F 310 395 421 438 490 2002 M 230 420 450 500 840 2002 M 230 425 450 488 595 2002 F 300 400 441 498 610 2002 F 380 430 450 485 589 2003 M 220 420 450 509 855 2003 M 240 420 450 485 600 2003 F 359 414 444 512 920 2003 F 359 408 449 459 510 2004 M 285 420 450 490 850 2004 M 300 420 450 480 625 2004 F 300 421 450 500 1234 2004 F 400 440 470 500 606 Total (161 male/82 female) Total (61 male/16 female) 2005 M 300 430 465 510 710 2005 M 310 450 470 500 615 2005 F 280 430 467 501 1002 2005 F 400 437 450 471 500 One year or less experience (143 male/72 female) One year or less experience (59 male/16 female) 2005 M 300 432 470 510 710 2005 M 310 450 470 503 615 2005 F 280 431 463 500 938 2005 F 400 437 450 471 500

1500 1500

1400 1400

1300 1300 * 1200 1200 VI VI --...... !!! 1100 .!!! 1100 0 0 "0 1000 "0 1000 In * In 0 * 0 0 900 * 0 900 N * N ...... * * ...... 0 800 * * 0 800 VI * * VI "0 * "0 Cll Cll .... 700 8 * .... 700 "0 0 8 "0 8 0 c c 0 0 0 0 :::s 600 :::s 600 * 0 ..c ..c 8 c c 500 500 --....>- --....>- rei 400 rei 400 ~ rei ~ ~ 0 ~ 0 VI VI ~ 0 ~ 0 0 300 ~ 300 ~ ~ 0 1 0 ~ ~ ~ t 200 200 *

100 100 *

1998 1999 2000 2001 2002 2003 2004 2005 1998 1999 2000 2001 2002 2003 2004 2005

• Dollar amounts shown from 1997 forward include postdoctoral salaries .

AUGUST 2006 NOTICES OF THE AMS 783 2005 Annual Survey of the Mathematical Sciences in the United States

Academic Teaching/Teaching and Research Academic Research Only 1 1-12-Month Salaries 11-12-Month Salaries (in hundreds of dollars) (in hundreds of dollars) Reported Reported Ph.D. Median in Ph .D. Median in Year Min Median Max 2005 $ Year Min Median Q Max 2005 $ 1975 87 145 204 428 1975 90 119 180 351 1980 143 195 350 405 1980 120 180 321 373 1985 220 230 273 300 470 439 1985 190 295 342 400 520 550 1990 225 318 365 404 670 502 1990 180 280 300 365 546 412 1995 300 354 410 478 600 499 1995 196 280 340 370 587 414 1997 260 370 400 497 650 470 1997 190 300 350 400 600 411 1998 275 405 480 575 700 558 1998 200 333 360 428 617 418 1999 200 374 420 469 650 481 1999 270 390 440 500 720 504 2000 300 400 485 600 1170 544 2000 300 384 400 555 1000 449 2001 350 420 465 615 870 509 2001 300 367 420 625 800 460 2002 310 439 500 597 840 538 2002 270 380 440 500 700 474 2003 345 438 475 550 780 SOl 2003 300 415 470 613 900 496 2004 350 450 495 583 980 509 2004 300 384 440 543 1250 452 2005 270 450 500 615 900 500 2005 350 400 475 573 860 475 2001 M 350 420 443 498 870 2001 M 300 348 425 655 800 2001 F 380 465 588 658 750 2001 F 342 400 420 588 700 2002 M 310 420 485 595 840 2002 M 270 388 440 500 650 2002 F 400 453 500 558 700 2002 F 310 350 440 505 700 2003 M 397 440 490 555 780 2003 M 300 420 450 510 820 2003 F 345 400 440 513 620 2003 F 310 390 480 650 900 2004 M 350 448 487 533 980 2004 M 300 385 440 640 1250 2004 F 380 465 545 605 650 2004 F 350 383 440 495 820 Total (38 male/ 12 female) Total (39 male/17 female) 2005 M 270 455 490 549 900 200SM 350 410 480 640 860 2005 F 420 450 570 753 824 2005 F 350 400 470 51 5 850 One year or less experience (32 male/11 female) One year or less experience (32 male/1 7 female) 2005 M 270 450 480 535 900 2005 M 350 400 465 555 820 2005 F 420 475 620 755 824 200SF 350 400 470 515 850

1500 1500

1400 1400

1300 1300 * 1200 1200 VI.... VI.... tU 1100 tU 1100 0 0 "C 1 000 "C 1 000 Ll'l Ll'l 0 0 0 0 N 900 N 900 '+- '+- 0 800 0 800 Ill Ill 0 "C - "C ....Q) 700 ....Q) 700 "C "C s::: s::: :::s 600 :::s 600 ..s:: - ..s:: s::: - s:::

~ 500 ~ 500

400 400

300 300

200 200

100 100

1998 1999 2000 2001 2002 2003 2004 2005 1998 1999 2000 2001 2002 2003 2004 2005

784 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

Government Business and Industry 11-12-Month Salaries 11-12-Month Salaries (in hundreds of dollars) (in hundreds of dollars) Reported Reported Ph .D. Median in Ph.D. Median in Year Min Ql Median Q 3 Max 2005 $ Year Min Ql Median Q 3 Max 2005 $ 1975 78 --- 182 --- 247 537 1975 114 --- 187 --- 240 552 1980 156 --- 244 --- 501 506 1980 190 --- 284 --- 400 589 1985 263 294 325 381 440 523 1985 260 360 400 420 493 643 1990 320 345 378 430 587 519 1990 320 438 495 533 700 680 1995 370 440 494 507 650 601 1995 288 480 568 690 1250 691 1997 350 454 573 600 750 673 1997 300 483 600 658 1000 705 1998 320 475 540 736 1250 628 1998 240 550 650 750 2250 756 1999 400 495 550 651 720 630 1999 360 600 680 761 2450 779 2000 440 540 600 640 830 673 2000 200 640 720 800 1500 807 2001 400 580 644 758 920 705 2001 475 716 770 865 1850 843 2002 450 551 650 775 1005 700 2002 325 734 780 850 1400 839 2003 290 668 705 763 1008 744 2003 300 700 800 900 1250 844 2004 510 720 738 780 920 758 2004 400 728 817 900 1800 840 2005 480 610 752 848 972 752 2005 510 755 870 978 2000 870 2001 M 400 590 647 780 920 2001 M 520 717 788 875 1700 2001 F 450 550 630 670 896 2001 F 475 710 750 850 1850 2002 M 450 551 642 725 1005 2002 M 325 738 782 858 1100 2002 F 540 600 700 850 880 2002 F 600 713 768 838 1400 2003 M 290 648 710 788 830 2003 M 550 725 840 920 1250 2003 F 600 683 695 723 1008 2003 F 300 628 780 816 900 2004 M 520 700 730 740 910 2004 M 400 710 813 900 1800 2004 F 510 733 749 790 920 2004 F 480 789 850 900 1100 Total (1 0 male/11 female) Total (47 male/15 female) 2005 M 500 668 790 902 955 2005 M 510 760 930 1005 2000 2005 F 480 540 750 770 972 2005 F 600 745 860 890 1100 One year or less experience (1 0 male/6 female) One year or less experience (36 male/8 female) 2005 M 500 668 790 902 955 2005 M 510 794 940 1005 2000 2005 F 480 538 701 754 972 2005 F 650 785 860 900 950 (Note : Salaries above $1 50,000 are not shown.) 1500 1500 0 0 "' 0 0 1400 1400 0 0

1300 0 1300 0 0 1200 - 0 ~ 1200 - 0 ~ ...VI VI... 0 ~ 1100 ~ 1100 0 0 r "'C 1000 "'C L/"1 L/"1 1000 0 0 § 0 I 0 0 N 900 N 900 ...... f- f- 0 0 f- f- 800 t- VI VI 800 "'C - - "'C t- f- QJ QJ ... 700 - - ~ ... 700 "'C "'C s::: - - s::: :::s 600 0 :::s ..s::: ..s::: 600

s::: f s::: 0 500 8 L -- ~ 500 '- >- -->- 0 ...... 0 ttl ttl 0 400 400 0 iii iii VI VI 300 0 * 0 300 5- 0

0 200 200 8 100 100 •

1998 1999 2000 2001 2002 2003 2004 2005 1998 1999 2000 2001 2002 2003 2004 2005

AUGUST 2006 NOTICES OF THE AMS 785 2005 Annual Survey of the Mathematical Sciences in the United States

interquartile range (IQR) is defined as Definitions ofthe Groups Q3- Ql. Think of constructing invisible fences l.SxiQR below Ql and l.SxiQR above Q3. Whiskers As has been the case for a number of years, much of the data in are drawn from Q3 to the largest observation that these reports is presented for departments divided into groups falls below the upper invisible fence and from Ql according to several characteristics, the principal one being the to the smallest observation that falls above the highest degree offered in the mathematical sciences. Doctoral­ lower invisible fence. Think of constructing two granting departments of mathematics are further subdivided more invisible fences, each falling l.SxiQR above according to their ranking of"scholarlyquality of program faculty" or below the existing invisible fences. Any as reported in the 1995 publication Research-Doctorate Programs observation that falls between the fences on each in the United States: Continuity and Change.l These ran kings update end of the boxplots is called an outlier and is those reported in a previous study published in 1 982.2 Consequently, plotted as o in the boxplots. Any observation that the departments which now comprise Groups I, II, and Ill differ falls outside of both fences either above or below significantly from those used prior to the 1 996 survey. the box in the boxplot is called an extreme outlier The subdivision of the Group I institutions into Group I Public and is marked as * in the boxplot. and Group I Private was newforthe 1996 survey. With the increase Acknowledgments in number of the Group I departments from 39 to 48, the Data The Annual Survey attempts to provide an accurate Committeejudged that a further subdivision of public and private appraisal and analysis of various aspects of the would provide more meaningful reporting ofthe data for these academic mathematical sciences scene for the use departments. and benefit of the community and for filling the Brief descriptions of the groupings are as follows: information needs of the professional organizations. Group I is composed of 48 doctoral-granting departments with Every year, college and university departments in scores in the 3.00-5.00 range. Group I Public and Group I the United States are invited to respond. The Annual Private are Group I doctoral-granting departments at public Survey relies heavily on the conscientious efforts institutions and private institutions respectively. of the dedicated staff members of these departments Group II is composed of 56 doctoral-granting departments for the quality of its information. On behalf of the with scores in the 2.00-2.99 range. Data Committee and the Annual Survey Staff, we Group Ill contains the remaining U.S. doctoral-granting thank the many secretarial and administrative staff departments, including a number of departments not members in the mathematical sciences departments included in the 1995 ranking of program faculty. for their cooperation and assistance in responding Group IV contains U.S. doctoral-granting departments (or to the survey questionnaires. programs) of statistics, biostatistics, and biometrics reporting a doctoral program. Other Data Sources American Association of University Professors, Inequities Group V contains U.S. doctoral-granting departments (or programs) Persist for Women and Non-Tenure-Track Faculty: The of applied mathematics/applied science, operations Annual Report on the Economic Status ofthe Profession research, and management science. 2004-2005, Academe: Bull. MUP (March/ April2005), Group Va is applied mathematics/applied science doctoral­ Washington, DC. granting departments; Group Vb, which is no longer American Statistical Association, 2005-2006 Salary Re­ surveyed as of 1998-99, was operations research and port of Academic Statisticians, AmStat News (Decem­ management science. ber 2005), Alexandria, VA. Group M or Master's contains U.S. departments granting a __ , Salary Survey Results: Biostatistics and Other master's degree as the highest graduate degree. Biomedical Statistics Departments and Units, AmStat Group B or Bachelor's contains U.S. departments granting News (December 2004), Alexandria, VA. a baccalaureate degree only. Commission on Professionals in Science and Technology, Listings of the actual departments which comprise these Professional Women and Minorities, 15th ed., CPST, groups are available on the AMS website at Washington, DC. www.ams.org/outreach. __, Salaries ofScientists, Engineers, and Technicians: A Summary ofSalary Surveys, 21th ed., CPST (November 1Research-Doctorate Programs in the United States: Continuity and Change, 2005), Washington, DC, 2003. edited by Marvin L. Goldberger, Brendan A. Maher, and Pamela Ebert Flat­ tau, National Academy Press, Washington, DC, 1995. Conference Board of the Mathematical Sciences, Statistical Abstract of Undergraduate Programs in the Mathematical 2 These findings were published in An Assessment of Research-Doctorate Sciences in the United States: Fall 2000 CBMS Survey, Programs in the United States: Mathematical and Physical Sciences, edited American Mathematical Society, 2002. by Lyle V. Jones, Gardner Lindzey, and Porter E. Coggeshall, National Academy Press, Washington, DC, 1982. The information on mathematics, __, Statistical Abstract of Undergraduate Programs in statistics, and computer science was presented in digest form in the April the Mathematical Sciences in the United States: Fal/199 5 1983 issue of the Notices, pages 257-67, and an analysis of the classifi­ CBMS Survey, MMReports No. 2, 1997. cations was given in the June 1983 Notices, pages 392-3. National Opinion Research Center, Doctorate Recipients from United States Universities: Summary Report 2004, Survey of Earned Doctorates, Chicago, IL, 2005.

786 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

National Research Council, Policy Implications of CALIFORNIA International Graduate Students and Postdoctoral Scholars in the United States, National Academy Press, University of California, Irvine (8) Washington, DC,2005. __, Strengthening the Linkages between the Sciences and MATHEMATICS the Mathematical Sciences, National Academy Press, Koslover,Deborah, Quasiperiodicjacobimatrices of magnetic Washington, DC, 2000. orign. __, U.S. Research Institutes in the Mathematical Sciences: Liu, Chiung-ju, Banodo-Futakiinvariants onhypersurfaces Assessment and Perspectives, National Academy Press, and Tian-Yau-Zelditch expansions. Washington, DC, 1999. Nakamura, Remi, MLE of parameters in the drifted Brownian motion and its error. __, Research-Doctorate Programs in the United States: Rooze, Matthew, The use ofunabounded activation functions Continuity and Change, National Academy Press, in neural networks and neural network approaches to Washington, DC, 1995. nuisance parameter problems. National Science Board, Science and Engineering Indicators- Sadovsky, Alexander, A biodynamical study of epidermal 2006. Two Volumes (Volume 1, NSB 06-01; wound repair in embryos. Volume 2, NSB 06-1A), National Science Foundation, Schulteis, Melinda, Continuity of the Lyapunov exponent Arlington, VA, 2006. for quasiperiodic Jacobi matrices. National Science Foundation, Characteristics of Doctoral Sinek, John, Integrated multi-scale modeling of therapeutics Scientists and Engineers in the United States: 2001 (NSF delivery to cancerous lesions. 03-310), Detailed Statistical Tables, Arlington, VA, 2003. Xiaoming, Zheng, Adaptive finite-element/level-set methods of free boundary problems: applications to multiphase __, Graduate Students and Postdoctorates in Science and flows and reaction-diffusion models of tumor growth. Engineering: Fall 2003 (NSF 06-307), Arlington, VA, 2006. University of California, Santa Cruz __,Scienc e and Engineering Degrees: 1966-2001 (NSF (3) 04-311), Detailed Statistical Tables, Arlington, VA, 2004. __, Science and Engineering Degrees, by Race/Ethnicity MATHEMATICS of Recipients: 1992-2001 (NSF 04-318), Detailed Bass, ]amey, A Calabi-Yau analogue of the Dedekind Eta Statistical Tables, Arlington, VA, 2004. function. __ ,Science and Engineering Doctorate Awards: 2004 Raske, David, Q-curvature on closed Riemannian mani­ (NSF 06-308), Detailed Statistical Tables, Arlington, VA, folds of dimension greater than four. 2006. Moura, Francisco, Three novel clustering algorithms and their application to microarray encephalogram data. __, Women, Minorities, and Persons with Disabilities in Science and Engineering Data Update (March 2006). Stanford University (7) [http: //www.nsf.gov/statistics/wmpd/pdf/march 2006updates. pdf] MATHEMATICS Adams, Tarn, Flat chains in Banach spaces. Godin, Veronique, A category of bordered fat graphs and the mapping class group of a bordered surface. Grueneberg, Michel, The Yamabe flow on three-manifolds. Kim, Byoung-Du, The parity conjecture and algebraic functional equations for elliptic curves at primes with Doctoral Degrees supersingular reduction. Lee, Dan Archibald, Connected sums of special Lagrangian Conferred 2004-2005 submanifolds. Shi, Danzhu, Capillary surfaces at a re-entrant corner. Supplementary List Zhu, Ke, Degeneration of the moduli space of J-holomorphic The following list supplements the list of thesis titles published in discs and Legendrian contact homology. the February 2006 Notices, pages 258- 76 . CONNECTICUT ALABAMA Yale University (7) University of Alabama, Huntsville MATHEMATICS (2) Brenner, Eliot Philip, Grenier Domains for arithmetic groups and associated tilings. MATHEMATICAL SCIENCES Ershov, Mikhail V., On finite presentability of some pro-p Park, Thomas, Age structure in epidemic models of vector­ groups on related questions borne infections. Kim, Sangjib, Standard monomial theory for flag algebras. Wang, Yan, Acquisition numbers and completion­ Salmasian, Hadi, A new notion of rank for unitary acquisition numbers. representation based on KITillov's orbit method.

AUGUST 2006 NOTICES OF THE AMS 787 2005 Annual Survey of the Mathematical Sciences in the United States

Samuels, Beth Sharon, Ramanujan complexes, their non­ Tarfulea, Nicolae, Constraint preserving boundary conditions uniform quotients, and isospectrality. for hyperbolic formulations of Einstein's equations. Schul, Raanan, Subsets of rectifiable curves in Hilbert space Yenikaya, Bayram, Adapative methods for Hamilton-Jacobi and the analyst's TSP. equations. Zhang,]ian, Scattering problems in inhomogeneous scalar wave equation. MASSACHUSETTS MISSOURI Harvard University (8) University of Missouri, Columbia (6) MATHEMATICS MATHEMATICS Green, Peter, Geometricity of local p-adic representations. Batchenko, Volodymyr, On the spectraofSchrbdinger and Grigorov, Grigor, Kato's Euler system and the main conjecture. Jacobi operations with complex-valued quasi-peridoc Kaplan, jonathan, Morphlets; a multiscale representation algebra-geometric coefficients. for diffeomorphisms. Bilyk, Dmytro, Distributional estimates for multilinear Khosla, Deepak, Moduli spaces of curves with linear series operatiors. and the slope conjecture. Cramer, David, Fredholm determinants and the Evans Lef, Edward, A modular non-rigid Calabi-Yau threefold. function. Mast,]errel, Pseudoholomorphic punctured spheres in the Honzik, Petr, Maximal operators associated with Fourier symplectization of a quotient. multipliers. Mohta, Vivek, Applications of Chiral perturbation theory. Luo, Shangzhen, Filtering ofhidden weak Markov chain and Neel, Robert, The heat kernel at the cut locus. its application to finance. Mayboroda, Svitlana, The Poisson problem in Lipschitz MICHIGAN domains.

Western Michigan University (5) NEW JERSEY MATHEMATICS Rutgers University, Graduate Chaiyakarn, Archara, Structure preserving algorithms for School (6) computing the symplectic singular value decomposition. Cera, Ralucca M., Stratification and domination in graphs STATISTICS and digraphs. Ganning,Kenneth,Anexaminationofthemeanandquantiles Noh, ]ihwa, An investigation of secondary teachers' knowledge from a relational system with a fixed just unnoticeable of rate of change in the context of teaching a standard­ difference representation. based curriculum. Grothendieck, john, Tracking changes in language. Pacheenburawana, Pariwatana, Global optimality conditions Heath, Susan, A new model for wireless telephony. in mathematical programming and optimal control. Lakshminarasimhan, Ramprasa th, Statistical options-crash Shafer, Kathryn, Two high school teachers' initial use of resistant financial contracts based on robust location geometer's sketchpad: Issues of implementation. estimators. Wang, Hongwei, Selected topics in longitudinal data analysis MINNESOTA and modeling. Xia, Qi, Exact methods applied to group sequential and other University of Minnesota, stratified comparative Poisson designs. Minneapolis (10) NEW YORK MATHEMATICS Courant Institute, New York Alexandrov, Oleg, WavePropagationinopticalfibers analysis and optimization. University (14) Cho, Sungwon, Boundary behavior of solutions to second MATHEMATICS order elliptic and parabolic equation. Erban, Radek, From individual to collective behavior in Apfaltrer, Felix, Population density methods in 2 spatial biological systems. dimensions and application to neural networks with realistic synapitc kinetics. Galbraith, Michael, Geometric optics, convex functions, Carlemanestimates and interfaces in the boundary control SiefringRichard, Intersection theory of finite energy surfaces. of the wave equation. Eng, David, Scaling limits ofrandomSchrodinger equations. Hall, John, Combinatorial deformations of the full Feng, Fan-Fu, On the totally asymptotic zero range process. transformation semigroup. Kobre, Elisha, Rates of diffusion in dynamical systems with Han, Young Ae, An efficient solver for problems of scattering. random groups. Kang, Minchul, Temporal and spatial aspects of calcium Rottenstreich, Sivan, Error bounds for the weak coupling dynamics in astrocyles. Schrodinger equation.

788 NOTICES OF THE AMS VOLUME 53, NUMBER 7 2005 Annual Survey of the Mathematical Sciences in the United States

Sun, Rongfeng, Convergence of coalescingnonsimple random walks to the Brownian web. WASHINGTON Wendl, Chris, Finite energy foliations and surgery on transverse links. University ofWashington(6) Cascini, Paolo, On the cotangent bundle of a projective BIOSTATISTICS variety. Bergemann, Tracy Lee, Image analysis and signal extraction Ko, Yueh]oy, Partially regular and singular solutions to the from eDNA microarrays. Landau-Lifshits (Gilbert) equations. Buzkova, Petra, Marginal regression analysis oflongitudinal McGahagan, Helena, Some existence and uniqueness results data with irregular, biased sampling. for Schrodinger maps and Landau-Lifshitz equations. Chen, Lu, Semiparametric analysis of failure time data from case-control family studies on candidate genes. Oliveira, Roberto, Preferential attachment. Haneuse, Sebastein, Ecological studies using supplemental Zygouras, Nikolaos, Limit Theorems: for a periodically or case-control data. randomly driven semilinear equation. Liu, Hao, Semiparametric marginal mean models for Papazoglu-Statescu, Dana, Maximizing the expected utility multivariate counting processes. of final time wealth with little trading. Zhang, Zheng, Semi parametric least-squares analysis of the receiver operating characteristic curve. Polytechnic University (1) MATHEMATICS WISCONSIN Pistoia, Marco, A unifiedmathematicalmodelfor stack- and role-based authorization systems. University of Wisconsin, Madison (13) Syracuse University (1) MATHEMATICS MATHEMATICS Benesh, Bret, Counting generators in finite groups that are generated by two subgroups of prime power order. John, Thomas, Selection procedures for lognormal Taylor, Paul, Bochner-Riesz means with respect to a rough populations. distance function. Chatterjee, Rohit, On class polynomials and supersingular TEXAS j-invariants. Cossey, ]ames, Generalizations of the Fong Swan Theorem. Rice University (6) Sutherland, Jamie, Values in university mathematics placement practice. COMPUTATIONAL AND APPUED MATHEMATICS Stefansson, Narfi, The structure of sparse representations Castillo, Zenaida, A new algorithm for continuation and of images using tight frames. bifurcation analysis of large scale free surface flows. El-Guindy, Ahmad, Weierstrass point on modular curves. Nguyen, Hoang, Domain decomposition methods for linear­ Halfpap, jennifer, Contributions to the theory of the quadratic elliptic optimal control problems. holomorphic extension of CR functions. Padula, Anthony, Software design for simulation driven Laghi, Norberta, A topics in the regularity theory of fourier optimization., integral operators. Teng, Cong, Model reduction of second linear dynamical Lo, Darren, Several results onrelativized character degrees. systems. Lyall, Neil, Strongly singular integral operators on the Vincent-Finely, Rachel, A reduced basis method for molecular Heisenberg group- L2 estimates. dynamics simulation. Mukherjee, Shan tala, Representations of nilpotent lie algebras Wrightman, Jennifer, Approximation and computation of and super algebras. the solution to the magneto-ionosphere coupling equation Raich, Andrew, Heat equations in R x C. via mixed formulation.

Southern Methodist University (4) STATISTICAL SCIENCE Carmack, Patrick, Recursive partitioning in spatially correlated data. Liu, Yushan, On estimation of the number of multinomial cells from cluster sampling. Wang, Zhu, The application of the Kalman filter to nonstationary time series chirp process through exponential transformation. Shen, Shuyi, MinimumL2 estimationforPoissonrnixtures.

AUGUST 2006 NOTICES OF THE AMS 789 Mathematics People

Naur Receives Turing Award Plaskota Awarded The Association for Computing Machinery (ACM) has 2006 Information-Based named PETER NAUR of the University of Copenhagen as the winner of the 2005 A. M. Turing Award. Considered the Complexity Prize "Nobel Prize of Computing", the Turing Award was pre­ The recipient of the 2006 Information-Based Complexity sented to Naur for his pioneering work on defining the Algol Prize is LESZEK PLASKOTA of the Department of Mathemat­ 60 programming language and for his contributions to com­ ics, Informatics, and Mechanics at the University of War­ piler design and to the art and practice of computer pro­ saw, Poland. The prize consists of US $3,000 and a plaque. gramming. Naur retired in 1998. The award will be presented at the Workshop on Algorithms The Turing Award, first given in 1966 and named for and Complexity for Continuous Problems at Schloss British mathematician Alan M. Turing, carries a US$1 00,000 Dagstuhl, Germany, in September 2006. prize, with financial support provided by Intel Corpora­ This annual prize of US $3,000 is given for outstanding tion. contributions to information-based complexity.

- From an ACM announcement - joseph Traub, Columbia University Aumann Awarded Ferran Sunyer i Balaguer von Neumann Prize Prize Awarded The 2005 John von Neumann Theory Prize, the highest The Ferran Sunyer i Balaguer Prize for 2006 has been prize given in the field of operations research and man­ awarded to X!AONAN MA of the Centre de Mathematiques agement science, has been awarded to RoBERT J AUMANN of Laurent Schwartz de l'Ecole Polytechnique and GEORGE the Hebrew University of Jerusalem in recognition of his MARINEscu of the Institut fUr Analysis und Mathematische fundamental contributions to game theory and related Physik of the J W. Goethe Universitat in Frankfurt for areas. The award, which is presented by the Institute for their monograph Holomorphic Morse Inequalities and Operations Research and the Management Sciences (IN­ Bergman Kernels. The monograph presents a self­ FORMS), carries a cash award of US$5,000. contained and unified approach to the holomorphic Morse The prize citation reads in part: "Aumann has played inequalities and the asymptotic expansion of the Bergman an essential and indispensable role in game theory's de­ kernel on manifolds using the heat kernel. In addition to velopment for almost half a century. The common theme treating various applications, the book provides perspec­ in Aumann's work is a unified view of rational behav­ tives on several active areas of research in complex, Kah­ ior ... Aumann's work introduced basic concepts and prin­ ler, and symplectic geometry. ciples, created appropriate tools for their study, developed The Ferran Sunyer i Balaguer Foundation (http: I jwww. theoretic foundations for significant ideas, established crm.cat/FerranSunyerBalaguer/ffsb.htm) of the In­ important relationships, and analyzed various particular stitut d'Estudis Catalans awards this international prize applications." every year to honor the memory of Ferran Sunyer i Bala­ guer (1912-1967), a self-taught Catalan mathematician - From an INFORMS announcement who gained international recognition for his research in

790 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Mathematics People mathematical analysis despite the serious physical dis­ day meeting will include a mix of activities designed to in­ abilities with which he was born. The prize carries a cash form the next generation of students about career op­ award of 12,000 euros (approximately US$15,500); the portunities in mathematics and to provide a chance for winning monographs are published by Birkhauser Verlag. them to network with other students and with mathe­ matical scientists who play a leadership role in their com­ -From a Ferran Sunyer i Balaguer Foundation munities. announcement The members of the National Blackwell-Tapia Com­ mittee are: Douglas Arnold, Rodrigo Banuelos, Carlos Castilla-Chavez, Nathaniel Dean, David Eisenbud, Robert Massey Receives Megginson, and Arlie 0. Petters. The first three Blackwell-Tapia conferences were held Blackwell-Tapia Award at Cornell University (2000), the Mathematical Sciences Re­ search Institute (MSRI) in Berkeley (2002), and the Insti­ The National Blackwell-Tapia Committee is pleased to an­ tute for Pure and Applied Mathematics at the University nounce that the 2006 Blackwell-Tapia Prize will be awarded of California, Los Angeles (2004). The idea for the first con­ to WilliAM A MASSEY, Edwin S. Wiley Professor of Operations ference arose from discussions in the MSRI Human Re­ Research and Financial Engineering at Princeton Univer­ sources Advisory Committee. The success of that confer­ sity. ence led directly to the second in the series and the first This prize is awarded every second year in honor of the awarding of the Blackwell-Tapia Prize at MSRI in 2002, with legacy of David H. Blackwell and Richard A Tapia, two dis­ the goal of extending the honoring of these two eminent tinguished mathematical scientists who have been inspi­ mathematical scientists to those who have followed in rations to more than a generation of African American, their footsteps. Latina/Latina, and Native American students and profes­ - From an announcement of the National sionals in the mathematical sciences. It recognizes a math­ Blackwell-Tapia Committee ematical scientist who has contributed and continues to contribute significantly to research in his or her field of expertise, and who has served as a role model for mathe­ matical scientists and students from underrepresented National Academy of Sdences minority groups or contributed in other significant ways to addressing the problem of the underrepresentation of Elections minorities in mathematics. The National Academy of Sciences (NAS) has announced Massey has an outstanding record of achievement in the election of seventy-two new members and eighteen for­ both his mathematical research and his efforts to bring eign associates. The following mathematical scientists are more underrepresented minorities into the mathematical among the newly elected members: LEONARD ADELMAN , Uni­ sciences. As a mathematical scientist, he has done cutting versity of Southern California; LESLIE GREEN GARD, Courant In­ edge research in many areas, with his current interests stitute of Mathematical Sciences, New York University; being dynamical queueing systems; performance, pricing, HENRYK IWA NIEC, Rutgers University; and DAN -VIRGIL priority, and provisioning models for communication sys­ VoicULEscu, University of California, Berkeley. Elected as for­ tems and services; asymptotic analysis of stochastic net­ eign members were LENNART A E. CARLESON, University of works; and stochastic orders on posets. He has published Uppsala, Sweden; and ALOISIO PEssoA DE ARAUJO, Institute prolifically in these areas, and is a highly sought speaker of Pure and Applied Mathematics, Rio de Janeiro, Brazil. on these topics whose talks include presentations in such prestigious venues as invited hour addresses for sectional -From an NAS announcement and national meetings of the Mathematical Association of America, American Mathematical Society, and National Association of Mathematicians. His best known contribu­ American Academy Elections tion to addressing the underrepresentation of minorities in mathematics is probably his continuing work as primary Seven mathematical scientists have been elected to mem­ national organizer for the annual Conference for African bership in the American Academy of Arts and Sciences for American Researchers in the Mathematical Sciences 2006. They are: jEFF CHEEGER, Courant Institute of Mathe­ (CAARMS). However, his efforts extend well beyond that matical Sciences, New York University; DAviD D. EISENBUD, venue to chairing and contributing to many other national Mathematical Sciences Research Institute and University committees and conferences that address this problem, in of California, Berkeley; MARTIN GoLUBITSKY, University of addition to his personal mentoring of many successful mi­ Houston; ROBERT K. LAZARSFELD, University of Michigan, Ann nority mathematical scientists. Arbor; CHARLES M. NEWMAN, Courant Institute of Mathe­ The prize will be presented at the Fourth Blackwell-Tapia matical Sciences, New York University; CRAIG TRACY, Uni­ Conference, to be held at the Institute for Mathematics and versity of California, Davis; HARoLD WIDOM, University of Cal­ its Applications (IMA) in Minneapolis on November 3-4, ifornia, Santa Cruz. 2006; see http: I jwww. i rna. um n . edu/2006- 2007 I The American Academy of Arts and Sciences was SWll. 3-4.06/ for more information. The one-and-a-half founded in 1780 to foster the development of knowledge

AUGUST 2006 NOTICES OF THE AMS 791 Mathematics People as a means of promoting the public interest and social progress. The membership of the academy is elected and USA Mathematical Olympiad represents distinction and achievement in a range of in­ The thirty-fifth annual USA Mathematical Olympiad was tellectual disciplines: mathematical and physical sciences, held April 19 and 20, 2006. The students who partici­ biological sciences, social arts and sciences, and humani­ pated in the Olympiad were selected on the basis of their ties and fine arts. performances on the American High School and American Invitational Mathematics Examinations. The twelve high­ est scorers in the USAMO, listed in alphabetical order, - From an AAAS announcement were SHERRY GONG, Exeter, New Hampshire; Yr HAN, Exeter, New Hampshire; TAEHYEON Ko, Exeter, New Hampshire; YAKOV BERCHENKO KOGAN, Raleigh, North Carolina; BRIAN Cobb and D'Ambrosio Receive LAWRENCE, Silver Spring, Maryland; TEDRICK LEUNG, North Hollywood, California; RICHARD McCUTCHEN, Silver Spring, ICMIMedals Maryland; PENG Sm, Toronto, Ontario; Canada; Yr SUN , San Jose, California; ARNAV TRIP ATHY, Chapel Hill, North Carolina; The Felix Klein and Hans Freudenthal Medals were created ALEX ZHAI, Urbana, Illinois; and Yum ZHAo, Don Mills, On­ by the International Commission on Mathematical In­ tario, Canada. Lawrence achieved a perfect score. struction (ICMI) to recognize outstanding achievement in The twelve USAMO winners will attend the Mathemat­ mathematics education research. The Felix Klein Medal, ical Olympiad Summer Program (MOSP) from June 10 named for the first president of ICMI (1908-1920), hon­ through July 3, 2006. Then six of the twelve students will ors lifetime achievement. The Hans Freudenthal Medal, be selected as the United States team to compete in the named for the eighth president of ICMI (1967-1970), rec­ International Mathematical Olympiad (IMO), to be held in ognizes a major cumulative program of research. Ljubljana, Slovenia, July 10-18, 2006. The awards represent the judgment of an (anonymous) jury of distinguished scholars of international stature, -From an American Mathematics Competition chaired by Michele Artigue of the University Paris 7. ICMI is proud to announce the second awardees of the Klein and Freudenthal Medals. The Felix Klein Medal for 2005 is awarded to UBIRATAN D'AMBROSIO, emeritus professor at the University of Camp­ inas in Brazil. This distinction acknowledges the role D'Am­ City University of Hong Kong is one of eight higher education institutions directly brosio has played in the development of mathematics ed­ funded by the Government of the Hong Kong Special Administrative Region ucation as a field of research and development throughout through the University Grants Committee (Hong Kong). It aims to become one of the leading universities in the Asia-Pacific region through excellence in the world, above all in Latin America. It also recognizes professional education and applied research. In two studies, City University of Hong Kong ranks among the top 200 universities in the world, and among the his pioneering role in the development of research per­ top ten universities in the Greater China region. The mission of the University is to nurture and develop the talents of students and to create applicable spectives that are sensitive to the characteristics of social, knowledge in order to support social and economic advancement. The student cultural, and historical contexts in which the teaching and population is approximately 23,000 enrolled in over 100 programmes at the associate degree, undergraduate and postgraduate levels. The medium of learning of mathematics take place, as well as his insis­ instruction is English. tence on providing quality mathematics education to all, The University invites applications for the following posts. Candidates with not just to a privileged segment of society. applied research achievements will receive very positive consideration. Relevant experience in business and industry will be a definite asset. The Hans Freudenthal Medal for 2005 is awarded to Associate Professor/Assistant Professor PAUL CoBB, professor at Vanderbilt University in the United Department of Mathematics [Ref. A/465149] States. This distinction acknowledges his outstanding con­ Duties: Teach undergraduate and postgraduate courses, especially in Applied tribution to mathematics education: a rare combination of Mathematics and Statistics; supervise research students; conduct research in areas of Applied Mathematics; and perform other duties as assigned by Head. theoretical developments, empirical research, and practi­ Requirements : A PhD in Mathematics/Applied Mathematics/Statistics with cal applications, which has had a major influence on the an excellent research record. mathematics education community and beyond. Salary and Conditions of Service Salary offered will be highly competitive and commensurate with qualifications Full citations of the work of these medalists can be and experience. Appointment will be on a fixed-term contract with contract­ found on the ICMI website, http: I /www. mathuni on. end gratuity. Fringe benefits include annual leave, medical and dental schemes, org/ICMI/. Presentation of the medals and invited ad­ and housing benefits where applicable. Application and Information dresses of the medalists will occur at ICME-11 in Monter­ Information concerning the posts and the University is available at rey, July 2008. http://www.cityu.edu.hk or from the Human Resources Office, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong [Fax: (852) 2788 1154 Previous ICMI medalists are Guy Brousseau (2003 Felix or (852) 2788 9334/E-mail: [email protected]]. Please send an application letter enclosing a current curriculum vitae to the Human Resources Office by Klein Medal) and Celia Hayles (2003 Hans Freudenthal 30 September 2006. Please quote the reference of the post in the application and on the envelope. The University reserves the right to consider late Medal). applications and nominations, and to fill or not to fill the positions. - ICMI Announcement

792 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Mathematics Opportunities

author has made important contributions. The monograph NSF Focused Research Groups should be written in English and should be at least 150 The Focused Research Groups (FRG) activity of the Division pages long. of Mathematical Sciences (DMS) of the National Science The prize, amounting to 12,000 euros (aboutUS$15,500), Foundation (NSF) supports small groups of researchers in is provided by the Ferran Sunyer i Balaguer Foundation. the mathematical sciences. The winning monograph will be published in Birkhauser The DMS has announced deadline dates for the fiscal year Verlag's series Progress in Mathematics, subject to the 2006 competition for FRG grants. The deadline for receipt of the required letters of intent to submit FRG proposals usual regulations concerning copyright and author's is August 18, 2006. The deadline date for full proposals rights. Submissions should be sent before December 2, is September 15, 2006. The FRG solicitation may be found 2006, to: Fundaci6 Ferran Sunyer i Balaguer, Carrer on the Web at http: I /www. nsf. gov /fundi ng/pgm_summ. del Carme, 47, E-08001 Barcelona, Spain. For further jsp?pims_id=567l&org=DMS. information, visit the website http: I jwww. c rm. cat/ FerranSunyerBalaguer/ffsb.htm. -From an NSF announcement -From an Insitut d'Estudis Catalans announcement NSF Mathematical Sdences Postdoctoral Research Call for Nominations for Fellowships 2006 Information-Based The Mathematical Sciences Postdoctoral Research Fellow­ Complexity Award ship program of the Division of Mathematical Sciences of the National Science Foundation (NSF) awards fellowships The annual Information-Based Complexity Young Re­ each year for research in pure mathematics, applied searcher Award is for significant contributions to infor­ mathematics and operations research, and statistics. The mation-based complexity by a young researcher. The prize deadline for this year's applications is October 18, 2006. will consist ofUS$1,000 and a plaque and will be awarded Applications must be submitted via FastLane on the World at a suitable location. Wide Web. For more information see the website http: I I Any researcher who www.nsf.gov/funding/pgm_summ.jsp?pims_id= has not reached his or her thirty­ 5 301&o rg=DMS. fifth birthday by September 30 the year of the award is el­ igible. - From an NSF announcement The members of the award committee would appreci­ ate nominations. The members are: Josef Dick, University of New South Wales; Frances Kuo, University of New South Call for Submissions for Wales; Christiane Lemieux, University of Calgary; Friedrich Pillichshammer, University of Linz; Joseph F. Traub, Co­ Sunyer i Balaguer Prize lumbia University; and Henryk Wozniakiowski, Columbia Ferran Sunyer i Balaguer (1912-1967) was a self-taught University and University of Warsaw. However, a person Catalan mathematician who, despite a serious physical does not have to be nominated to win the award. disability, was very active in research in classical analysis, The deadline for nominations for the award is Sep­ an area in which he acquired international recognition. Each tember 30, 2006. Nominations should be sent to Joseph year, in honor of the memory of Ferran Sunyer i Balaguer, Traub. The award can be for work done in a single year or the Institut d'Estudis Catalans awards an international research prize bearing his name. a number of years. The work can be published in any jour­ The prize is awarded for a mathematical monograph of nal, number of journals, or monographs. an expository nature presenting the latest developments in an active area of research in mathematics in which the - joseph Traub, Columbia University

AUGUST 2006 NOTICES OF THE AMS 793 For Your Information

University of Missouri at Columbia; Russell Gersten, ex­ National Mathematics Advisory ecutive director, Instructional Research Group and Pro­ Panel Members Announced fessor Emeritus, College for Education, University of Ore­ gon; Nancy Ichinaga, former principal, Bennett-Kew In May 2006, U.S. Secretary of Education Margaret Spellings Elementary School, Inglewood, California; Tom Loveless, announced the seventeen expert panelists and six ex-of­ ficio members chosen to comprise the National Mathe­ director, Brown Center on Education Policy and Senior matics Advisory Panel. The panel will advise President Fellow in Governance Studies, The Brookings Institution; Bush and Secretary Spellings on the best use of scientifi­ Liping Ma, Senior Scholar for the Advancement of Teach­ cally based research to advance the teaching and learning ing, Carnegie Foundation; Valerie Reyna, professor of of mathematics. human development and professor of psychology, Cornell "To keep America competitive in the twenty-first cen­ University; Wilfried Schmid, professor of mathematics, tury, we must improve the way we teach math and we must Harvard University; Robert Siegler, Teresa Heinz Profes­ give more students the chance to take advanced math and sor of Cognitive Psychology, Carnegie Mellon University; science courses in high school," Secretary Spellings said. Jim Simons, president of Renaissance Technologies Cor­ "America's high school graduates need solid math skills, whether proceeding to college or going into the work­ poration and former professor of mathematics, Stony force." Brook University; Sandra Stotsky, independent researcher The National Mathematics Advisory Panel (NMP), mod­ and consultant in education and former Senior Associate eled after the National Reading Panel, will examine and sum­ Commissioner, Massachusetts Department of Education; marize the scientific evidence related to the teaching and Vern Williams, math teacher, Longfellow Middle School, learning of mathematics, with a specific focus on prepa­ Fairfax, Virginia; and Hung-Hsi Wu, professor of mathe­ ration for and success in learning algebra. The NMP will matics, University of California at Berkeley. issue an interim report by January 31, 2007, and a final Ex-officio members: Dan Berch, National Institute of report no later than February 28, 2008. These reports will Child Health and Human Development, National Institutes provide policy recommendations on how to improve math­ ematics achievement for all students. of Health; Diane Jones, White House Office of Science and The National Mathematics Advisory Panel will be chaired Technology Policy; Tom Luce, assistant secretary, U.S. by Larry Faulkner, president of the Houston Endowment Department of Education; Kathie Olsen, deputy director, and president emeritus of the University of Texas at Austin. National Science Foundation; Raymond Simon, deputy sec­ Other panelists: Deborah Ball, dean, School of Educa­ retary, U.S. Department of Education; and Grover (Russ) tion and Collegiate Professor, University of Michigan; Whitehurst, director, Institute of Education Sciences, U.S. Camilla Benbow, Dean of Education and Human Develop­ Department of Education. ment, Vanderbilt University, Peabody College; A. Wade All meetings of the NMP will be open to the public and Boykin, professor and director of the Developmental Psy­ will be announced in the Federal Register. chology Graduate Program in the Department of Psychol­ ogy, Howard University; Francis "Skip" Fennell, professor The NMP's website is http: I /www. ed. gov I about/ of education, McDaniel College, Maryland, and president, bdscomm/list/mathpanel/index.html. National Council of Teachers of Mathematics; David Geary, Curators' Professor, Department of Psychological Sciences, - Department of Education news release

794 NOTICES OF THE AMS VOLUME 53, NUMBER 7 For Your Information AMS SHORT COURSE Mathematics Institutes Aspects of Statistical Learning Informational Website ~ January 3-4, 2007 Two years ago, the directors of the mathematics insti­ New Orleans, Louisiana tutes funded by the National Science Foundation (NSF) ~ formed a directors' council. This council meets annually to discuss issues common to all of the institutes and also interacts by email between meetings. One outcome of the Organizers: council's work is a new website, which went online in May Cynthia Rudin 2006. The purpose of the website is to provide conve­ Center for Neural Science and Courant Institute nient, centralized access to information about the activi­ ties of the NSF-funded institutes. New York University The website offers various features, including an events Miroslav Dudik database that can be browsed or searched by institute, key­ Department of Computer Science word, or dates, giving access to all the programs at all the Princeton University institutes. A collection of research highlights describe some of the scientific outcomes from the institutes. There is also a search box that interacts with Google so that one Statistical learning is a rapidly growing area of computer can search for terms on all the institutes' websites. lscience. Its goal is to design computer algorithms that Information about six institutes is accessible through l this website: the American Institute of Mathematics, the generalize or "learn" from examples. Applications of School of Mathematics at the Institute for Advanced Study, statistical learning have been extremely wide-ranging the Institute for Mathematics and its Applications, the and include tasks in pattern and speech recognition, text Mathematical Biosciences Institute, the Mathematical Sci­ processing, portfolio management, medical diagnosis, [ ences Research Institute, and the Statistical and Applied robotics, and bioinformatics. Mathematical Sciences Institute. The mathematics institutes website is at http: I I The goal of this course is to introduce the field of statisti­ www.mathinstitutes.org. , cal learning to a wider mathematical audience. Possible 1 areas of interest to mathematicians include the design of -Allyn jackson I algorithms and analysis of their convergence, proba- bilistic guarantees of generalization performance, and beating the "curse of dimensionality". The talks will span l a variety of problem domains, techniques, and algorithm types, and touch upon many interesting applications. 1 Each talk will be tutorial-style and accessible to a broad mathematical audience.

The short course will conclude with a panel discussion on the topic "The Past and Future of Learning Theory".

A tentative list of speakers:

Peter Bartlett (University of California Berkeley) Lisa Hellerstein (Polytechnic University, Brooklyn) Lawrence Saul (University of California San Diego)

1 Robert Schapire (Princeton University)

Advance registration fees: member/ nonmember $90/120 Student/ unemployed/emeritus $40

On-site registration fees: member/nonmember $120/151 student/ unemployed/ emeritus $60

AUGUST 2006 NOTICES OF THE AMS 795 Inside the AMS

telephone 401-455-4058 (within the U.S. call 800-321- Mathematical Imagery Page 4267, ext. 4058). onAMS Website -Elaine Kehoe The AMS has added a new feature to its website, the Math­ ematical Imagery page. The page includes albums of math­ ematically inspired and mathematically generated works, which can be sent as e-postcards. Also available on the page History Volumes Now Online are links to online galleries and museums, and to other The AMS has published three volumes, edited by Peter Duren resources about mathematics and art. New works will et al, in its series "A Century of Mathematics in America". frequently be added to the collection. See all the art at These volumes include lectures, reminiscences, historical http://www.ams.org/mathimagery. surveys of mathematical culture and mathematical topics, -AMS announcement articles about the development of mathematics in American universities, and brief biographies and tributes by promi­ nent mathematicians of the twentieth century. Fan China Exchange Program These three volumes have now been made freely accessi­ ble online as PDF files that may be viewed and downloaded. Names Awardees The URis for the three volumes are: The Society's Fan China Exchange Program awards grants Part I: http://www.ams.org/online_bks//hmathl/ to support collaborations between Chinese and U.S. or Partii:http://www.ams.org/online_bks//hmath2/ Canadian researchers. Institutions in the United States or Part III: http: I /www. ams. org/onl i ne_bks/ /hmath3/ Canada apply for the funds to support a visitor from China or vice versa. This funding is made possible through a -Allyn jackson generous gift made to the AMS by Ky and Yu-Fen Fan in 1999. The awardees for 2006 follow. Purdue University was awarded a grant to support a visit from Huiyuan Li of the Chinese Academy of Sciences, Deaths of AMS Members Laboratory of Parallel Computing, Institute of Software; SIDNEY GLUSMAN, retired, from New York, NY, died on Rutgers University was awarded a grant to support a visit March 20, 2006. Born on January 31, 1912, he was a from Jiguang Bao of Beijing Normal University; and McGill member of the Society for 58 years. University was awarded a grant to support a visit from L. GAUNCE LEWIS ]R., professor, Syracuse University, died Ye Tian of the Chinese Academy of Sciences, Morningside Center, Academy of Mathematics and Systems Science. on May 17, 2006. Born on September 14, 1949, he was a For information about the Fan China Exchange Pro­ member of the Society for 34 years. gram, visit the website http: I /www. ams . o rg/ out reach/ BHALCHANDRA BALVANT PHADKE, from Brighton, Australia, chi naexchange. html, or contact the AMS Membership died on November 24, 2002. Born on january 17, 1944, he and Programs Department, email: prof-serv@ams. org, was a member of the Society for 32 years.

796 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Reference and Book List

The Reference section of the Notices www.nsf.govlpubsyslodslgetpub. August 18, 2006: Letters of intent is intended to provide the reader with cfm?nsf05 579. for NSF Focused Research Groups. See frequently sought information in July 31, 2006: Nominations for "Mathematics Opportunities" in this an easily accessible manner. New SASTRA Ramanujan Prize. See the issue. information is printed as it becomes website http: I lwww. math. ufl . September 15, 2006: Full propos­ available and is referenced after the als for NSF Focused Research Groups. edulsastra-pri zel or email: first printing. As soon as information See "Mathematics Opportunities" in [email protected] .edu. is updated or otherwise changed, it this issue. will be noted in this section. July 31, 2006: Nominations for the September 15,2006: Nominations ICTP IIMU Ramanujan Prize. See for Alfred P. Sloan Foundation Contacting the Notices http:llwww.ictp.trieste.itl Fellowships. Contact Sloan Research The preferred method for contacting -sci_info/awards/Ramanujan/ Fellowships, Alfred P. Sloan Founda­ the Notices is electronic mail. The Ramanuj an. html. tion, 630 Fifth Avenue, Suite 2550, editor is the person to whom to send articles and letters for consideration. Articles include feature articles, Where to Find It memorial articles, communications, A brief index to information that appears in this and previous issues of the Notices. opinion pieces, and book reviews. The editor is also the person to whom to AMS Bylaws-November2005, p. 1239 send news of unusual interest about AMS Email Addresses-February 2006, p. 251 other people's mathematics research. AMS Ethical Guidelines-June/July 2006, p. 701 The managing editor is the person AMS Officers 2005 and 2006 (Council, Executive Committee, to whom to send items for "Mathe­ Publications Committees, Board of Trustees)-May 2006, p. 604 matics People", "Mathematics Op­ AMS Officers and Committee Members-October 2005, p. 1073 portunities", "For Your Information", Conference Board of the Mathematical Sciences-September 2005, "Reference and Book List", and "Math­ p. 892 ematics Calendar". Requests for Information for Notices Authors-June/July 2006, p. 696 permissions, as well as all other Mathematics Research Institutes Contact Information-August 2006, inquiries, go to the managing editor. p. 798 The electronic-mail addresses are noti ces@math. ou. edu in the case of National Science Board-January 2006, p. 62 the editor and noti ces@ams. org in New Journals for 2004-June/July 2006, p. 697 the case of the managing editor. The NRC Board on Mathematical Sciences and Their Applications-March 2006, fax numbers are 405-325-7484 for p. 369 the editor and 401-331-3842 for the NRC Mathematical Sciences Education Board-April 2006, p. 488 managing editor. Postal addresses NSF Mathematical and Physical Sciences Advisory Committee-February may be found in the masthead. 2006,p. 255 Program Officers for Federal Funding Agencies-October 2005, Upcoming Deadlines p. 1069 (DoD, DoE); November 2005, p. 1223 (NSF) July 20, 2006: Proposals for NSF Stipends for Study and Travel-September 2005, p. 900 CAREER Program. See http: I I

AUGUST 2006 NOTICES OF THE AMS 797 Reference and Book List

New York, New York 10ll1-0242, or 00-956 Warszawa, Poland Centre de Recerca Matematica see the website http: I /www. Telephone: 48-22 522-82-32; (CRM) sloan.org/programs/fellowship_ 628-01-92 Apartat 50 brochure. shtml. Fax: 48-22 622-57-50; 629-39-97 E 08193 Bellaterra, Spain October 1, 2006: Nominations for email: Banach . Center. Office@ Telephone: 34 935 8ll 081 Andre Aisenstadt Mathematics Prize. i mpan. gov. p l Fax: 34 935 812 202 Contact Director, CRM, Universite Website: http: I jwww. i mpan. gov. email: crm@crm. cat de Montreal, C.P. 6128, Succursale pl/BC Website: http: I I c rm. cat Centre-ville, Montreal, QC H3C 3J7 Canada; fax: 514-343-2254; email: Banff International Research Centre for Mathematics [email protected]. Station and Its Applications October 1, 2006: Applications for c/o PIMS Central Office Building 27 AWM Travel Grants. See http: I /www. University of British Columbia Australian National University awm-math.org/travelgrants.html; 1933 West Mall Canberra ACT 0200, Australia telephone 703-934-0163; email: Vancouver, BC V6T 1Z2, Canada Telephone: 612 612 52897 awm@math. umd. edu; or contact As­ Telephone: 604-822-1649 Fax: 612 612 55549 sociation for Women in Mathematics, Fax: 604-822-0883 email:[email protected]. ll240 Waples Mill Road, Suite 200, email: bi rs-di rector@pi ms. edu.au Fairfax, VA 22030. math.ca Website: http: I /www. maths. anu. October 17, 2006: Full proposals Website: http: I /www. pi ms. math. edu.au/CMA/ for Computational Science Training ca/birs/ for Undergraduates in the Mathe­ Centre de Recherches matical Sciences (CSUMS) of the NSF. Center for Discrete Mathematics Mathematiques (CRM) See the website http: I /www. nsf. and Theoretical Computer Science Universite de Montreal gov/publications/pub_summ. (DIMACS) C.P. 6128, Succ. Centre-ville jsp?ods_key=nsf06559. CoRE Building, 4th Floor Montreal, Quebec, Canada H3C 3J7 October 18, 2006: Applications for Rutgers University Telephone: 514 343 7501 NSF Mathematical Sciences Postdoc­ 96 Frelinghuysen Road Fax: 514 343 2254 toral Research Fellowships. See "Math­ Piscataway, NJ 08854 8018 email: activites@ ematics Opportunities" in this issue. Telephone: 732 445 5930 crm.umontreal .ca November 1, 2006: Nominations Fax: 732 445 5932 Website: http: I /www. crm. for Vasil Popov Prize. Contact Pen­ email: cente r-admi n@di macs. umontreal.ca cho Petrushev, Chair, Popov Prize rutgers.edu Selection Committee, Department of Website: http: I I di macs. Centro de Investigacion en Mathematics, University of South rutgers.edu Matemciticas (CIMAT) Carolina, Columbia, SC 29208; A. P. 402, Guanajuato, Gto. email: popov@math. sc. edu. Center for Scientific Computation C.P. 36000, Mexico December 2, 2006: Submissions and Mathematical Modeling Telephone: 52 473 73 271-55/ for 2007 Sunyer i Balaguer Prize. See (CSCAMM) 73 508-00 "Mathematics Opportunities" in this University of Maryland Fax: 52 473 73 257-49 issue. 4146 CSIC Building #406 email: ci mat@ci mat. mx December 31, 2006: Entries for Paint Branch Drive Website: http: I /www. ci mat. mx Pirelli INTERNETional Award compe­ College Park, MD 20742-3289 tition. See the website http: I /www. Telephone: 301-405-0662 Chennai Mathematical Institute pirelliaward.com. Fax: 301-314-6674 Plot H1, SIPCOT IT Park Contact Information for email: i nfo@cscamm. umd. edu Padur PO, Siruseri 603103, India Mathematics Institutes Website: http: I jwww. cscamm. Telephone: 91-44-3298 3441, umd.edu/ 91-44-3298-3442 American Institute of Mathematics email: office@cmi .ac.in 360 Portage Avenue Centre International de Rencontres Website: http: I jwww. cmi . ac. in Palo Alto, CA 94306-2244 Mathematiques (CIRM) Telephone: 650-845-2071 163, avenue de Luminy Case 916 Danish National Research Founda­ Fax: 650-845-2074 F-13288 Marseille Cedex 09, France tion Network in Mathematical email: con rey@ai math. org Telephone: 33 04 91 83 30 00 Physics and Stochastics Website: http: I jwww. a i math. o rg Fax: 33 04 91 83 30 05 (MaPhySto) email: colloque@cirm. Department of Mathematical Stefan Banach International univ-mrs.fr Sciences Mathematical Center Website: http: I jwww. ci rm. University of Aarhus 8 Sniadeckich str., P.O. Box 21 univ-mrs.fr Ny Munkegade, DK-8000 Aarhus C,

798 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Reference and Book List

Denmark Institute for Advanced Study (lAS) email: i pam@ucl a. edu Telephone: 45 8942 3515; School of Mathematics Website: http: I jwww. i pam. 45 8942 3521 1 Einstein Drive ucla.edu Fax: 45 8613 1769 Princeton, NJ 08540 email: maphysto@maphysto. dk Telephone: 609 734 8100 Institute of Mathematical Sciences Website: http: I /www. maphysto. dk Fax: 609 951-4459 Chinese University of Hong Kong email: math@math. i as. edu Unit 601, 6/F The Erwin Schrodinger Website: http: I jwww. math. Academic Building No. 1 International Institute for ias.edu/ Shatin, Hong Kong Mathematical Physics Telephone: 852 2609 8038 Boltzmanngasse 9 Institute for Mathematical Sciences Fax: 852 2603 7636 A-1090 Vienna, Austria National University of Singapore email: i ms@i ms. cuhk. edu. hk Telephone 43 1 4277 28282 3 Prince George's Park Website: http: I jwww. i ms. Fax: 43 1 4277 28299 Singapore 118402, Republic cuhk.edu.hk email: secr@esi. ac. at of Singapore Website: http: I jwww. esi . ac. at/ Telephone: 65 6516 1897 Instituto Nacional de Matematica Fax: 65 6873 8292 Pura e Aplicada (IMP A) Euler International Mathematical email: i ms@nus. edu. sg Estrada Dona Castorina, 110 Institute Website: http: I jwww. i ms. nus. J ardim Botanico nab. Fontanka, 27 edu.sg CEP 22460-320 St. Petersburg 191023, Russia Rio de Janeiro, RJ. Brazil Telephone: 7 812 312-40-58 Institute for Mathematics and its Telephone: 55 21 2529 5000 Fax: 7 812 310-53-77 Applications (IMA) Fax: 55 21 2512 4115 email: admi n@eul er. pdmi. ras. ru University of Minnesota email: di retor@i mpa. br Website: http: I /www. pdmi . ras. 400 Lind Hall Website: http: I jwww. i mpa. b r ru/EIMI/index.html 207 Church Street, SE Minneapolis, MN 55455 0436 International Center The Fields Institute for Research Telephone: 612 624 6066 for Theoretical Physics (ICTP) in Mathematical Sciences Fax: 612 626 7370 Strada Costiera 11 222 College Street, 2nd Floor email: staff@i rna. umn. edu 34014 Trieste, Italy Toronto, Ontario M5T 3]1 Canada Website: http: I /www. i rna. Telephone: 39 040 2240111 Telephone: 416 348 9710 umn.edu/ Fax: 39 040 224163 Fax: 416 348 9714 email: sci_i nfo@i ctp. it email: geni nfo@fi e l ds. Institut Henri Poincare Website: http: I jwww. i ctp. it utoronto.ca 11, rue Pierre et Marie Curie Website: http: I /www. fields. 75231 Paris Cedex 05, France International Centre utoronto.ca/ Telephone : 01 44 27 67 89 for Mathematical Sciences (ICMS) Fax: 01 44 07 09 37 14 India Street Forschungsinstitut fiir Mathematik Website: http: I jwww. i hp. Edinburgh EH3 6EZ (FIM) jussieu.fr/ United Kingdom Eidgenossische Technische Telephone: 44 (0)131 220 1777 Hochschule Zentrum Fax: 44 (0)131 220 1053 Ramistrasse 101 Institut Mittag Leffler email: enquiries@ 8092 Zurich, Switzerland Auravagen 17 icms.org.uk Telephone: 41-1-632-3475 SE 182 60 Djursholm, Sweden Website: http: I jwww. rna. hw. ac. email: marcel a. kraemer@fim. Telephone: 46-8-622 05 60 uk/icms math.ethz.ch Fax: 46-8-622 05 89 Website: http: I jwww. fi m. math. email: [email protected] Isaac Newton Institute ethz.ch/ Website: http: I /www. for Mathematical Sciences mittag-leffler.se/ 20 Clarkson Road Institut des Hautes Etudes Scien­ Cambridge CB3 OEH tifiques (IHES) Institute for Pure and Applied United Kingdom Le Bois Marie 35, route de Chartres Mathematics (IP AM) Telephone: 44 1223 335999 F 91440 Bures sur Yvette, France IPAM Building Fax: 44 1223 330508 Telephone: 33 1 60 92 66 00 460 Portola Plaza email: i nfo@newton. cam. ac. uk Fax: 33 1 60 92 66 69 Box 957121 Website: http: I jwww. newton. Website: http: I jwww. i hes. fr Los Angeles, CA 90095-7121 cam.ac.uk/ Telephone: 310 825 4755 Fax: 310 825-4756

AUGUST 2006 NOTICES OF THE AMS 799 Reference and Book list

Istituto Nazionale di Alta Max Planck Institut Sobolev Institute of Mathematics Matematica "F. Severi" (INDAM) fur Mathematik in den Russian Academy of Sciences, Citta Universitaria Naturwissenschaften Siberian Branch P. le Aldo Mora 5 Inselstrasse 22 4 Acad. Koptyug Avenue 00185 Rome, Italy D-04103 Leipzig, Germany Novosibirsk, 630090 Russia Telephone: 39 06490320 Telephone: 49 (0) 341 99 59 50 Telephone: (7) 383 333 28 92 Fax: 39 064462293 Fax: 49 (0) 341 99 59 65 8 Fax: (7) 383 333 25 98 email: i ndam@a l tamatemati ca. it email: bi eli ngmi s. mpg. de email: i m@math. nsc. ru Website: http: I /www. Website: http: I jwww. mi s. mpg. de/ Website: http: I jwww. math. nsc. ru altamatematica.it Chern Institute of Mathematics Statistical and Applied Korea Institute for Advanced Nankai University Mathematical Sciences Institute Study (KIAS) Tianjin 300071, China (SAMSI) 207-43 Cheongnyangni 2-dong Telephone: 86-22-2350-8228 19 T. W. Alexander Drive Dongdaemun-gu Fax: 86-22-23 50-1532 P.O. Box 14006 Seoul130-722, Korea email: cim@nankai .edu.cn Research Triangle Park, NC Telephone: 82-2-958-3 711 Website: http: I jwww. ni m. nankai . 27709-4006 Fax: 82-2-958-3770 edu.cn/nim_e/index.htm Telephone: 919-685-9350 Website: http: I /www. ki as. re. kr Fax: 919-685-9360 New Zealand Institute email: i nfo@samsi . info Mathematical Biosciences Institute of Mathematics and Its Applica­ Website: http: I jwww. samsi. info/ The Ohio State University tions (NZIMA) 2 50 Mathematics Building University of Auckland Steklov Institute of Mathematics 231 W. 18th Avenue Private Bag 92019 Russian Academy of Sciences Columbus, Ohio 43210 Auckland, New Zealand Gubkina str. 8 Telephone: 614-292-3648 Telephone: 64 (0)9 373 7599 119991, Moscow, Russia Fax: 614-247-6643 Fax: 64 (0)9 373 7457 Telephone: 7 495 135-22-91 email: rebecca@mbi . osu. edu email: nzima-admin@nzima. Fax: 7 495 135-05-55 Website: http: I jwww. mbi . osu. edu auckland.ac.nz email: steklov@mi .ras.ru Website: http: I /www. nzi rna. Website: http: I jwww. mi . ras. ru/ Mathematical Sciences Research auckland.ac.nz index_e.html Institute (MSRI) 17 Gauss Way Pacific Institute for Steklov Institute of Mathematics Berkeley, CA 94720 5070 the Mathematical Sciences (PIMS) nab. Fontanka, 27 Telephone: 510 642 0143 University of British Columbia St. Petersburg 191023, Russia Fax: 510 642 8609 1933 West Mall, Room 200 Telephone: 7 812 312-40-58 email:msri-inquiries@msri .org Vancouver, BC, V6T 1Z2, Canada Fax: 7 812 310-53-77 Website: http: I jwww. ms ri . org/ Telephone: 604-822-3922 email: admin@pdmi .ras.ru Fax: 604-822-0883 Website: http: I /www. pdmi . ras. ru Mathematisches Forschungs email: pi ms@pi ms. math. ca Institut (Oberwolfach) Website: http: I /www. pi ms. Tata Institute of Fundamental Schwarzwaldstr. 9-11 (Lorenzenhof) math.ca Research D 77709 Oberwolfach Walke, School of Mathematics Germany Alfred Renyi Institute Dr. Homi Bhabha Road Telephone: 49 7834 979 0 of Mathematics Mumbai 400 005, India Fax: 49 7834 979 38 Hungarian Academy of Sciences Telephone: 91 22 22804545 email: admi n@mfo. de POB 127 Fax: 91 22 22804610; Website: http: I jwww. mfo. de H-1364 Budapest, Hungary 91 22 22804611 Telephone: 361-483-8302 email: regi stra@ti fr. res. in Max Planck Institut fur Fax: 361-483-8333 Website: http: I jwww. math. ti fr. Mathematik email: math@renyi .hu res. in P.O. Box 7280 Website: http: I jwww. renyi . hu D 53072 Bonn, Germany Research Institute for T. N. Thiele Centre for Applied Telephone: 49 228 402 0 Mathematical Sciences (RIMS) Mathematics in Natural Science Fax: 49 228 402277 Kyoto University University of Aarhus email: admi n@mpi m-bonn. mpg. de Kyoto, 606 8502, Japan Department of Mathematical Website: http: I /www. mpi m-bonn. Fax: 81 75 753 7272 Sciences mpg.de Website: http: I jwww. ku rims. Ny Munkegade, Building 1530 kyoto-u.ac.jp/ DK-8000 Aarhus, Denmark

800 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Reference and Book List

Telephone: 45 8942 3515 ford University Press, June 2005. ISBN Springer, September 2005 (paperback Fax: 45 8613 1769 0-198-56593-3. edition). ISBN 3-540-20100-9. email: thi e l e@i mf. au. dk Beyond Coincidence: Amazing Sto­ Euler through Time: A New Look at Website: http: I lwww. thi e l e. ries of Coincidence and the Mystery Old Themes, by V. S. Varadarajan. au.dk and Mathematics behind Them, by AMS, June 2006. ISBN 0-8218-3722-2. Martin Plimmer and Brian King. Experimentation in Mathematics: Warwick Mathematics Research Thomas Dunne Books, December Computational Paths to Discovery, by Centre 2005. ISBN 0-312-34036-2. Jonathan Borwein, David Bailey, and University of Warwick The Book of Presidents, by Susan Roland Girgensohn. A K Peters, March Coventry CV4 7AL, United Kingdom Oakes, Alan Pears, and Adrian Rice. 2004. ISBN 1-56881-136-5. (Reviewed Fax: +44 (0)24 7652 3548 London Mathematical Society, 2005. September 2005.) Phone: +44 (0)24 7652 8~17 ISBN 0-950-27341-4. The Fermat Diary, by C. J. Mozzochi. email: [email protected] Change Is Possible: Stories of Women AMS, August 2000. ISBN 0-8218- Website: http: I lwww. maths. and Minorities in Mathematics, by Pa­ 2670-0. warwick.ac.uklmrclindex.html tricia Clark Kenschaft. AMS, Septem­ The Fermat Proof, by C. J. Mozzochi. ber 2005. ISBN 0-8218-3748-6. Trafford Publishing, Inc., February Weierstrass Institute for Applied Coincidences, Chaos, and All That 2004. ISBN 1-412-02203-7. Analysis and Stochastics Math jazz: Making Light of Weighty God Created the Integers, by Stephen Mohrenstrasse 39 Ideas, by Edward B. Burger and Michael Hawking. Running Press, October 2005. lOll? Berlin, Germany Starbird. W. W. Norton, August 2005. ISBN 0-762-41922-9. Telephone: 49-30-203 720 ISBN 0-393-05945-6. G6del's Theorem: An Incomplete Fax: 49-30-2044975 The Coxeter Legacy: Reflections and Guide to Its Use and Abuse, by Torkel email: contact@wi as-berlin. de Projections, edited by Chandler Davis Franzen. A K Peters, May 2005. ISBN Website: http: I lwww. and Erich W. Ellers. AMS, March 2006. 1-56881-238-8. wias-berlin.del ISBN 0-8218-3 722-2. Hiding in the Mirror: The Mysteri­ The Curious Incident of the Dog in ous Allure of Extra Dimensions, from the Night-time, by Mark Haddon. Vin­ Plato to String Theory and Beyond, by Book List tage, May 2004. ISBN 1-400-03271-7. Lawrence M. Krauss. Viking Adult, The Book List highlights books that (Reviewed March 2006.) October 2005. ISBN 0-670-03395-2. have mathematical themes and are Dark Hero of the Information Age: Incompleteness: The Proof and aimed at a broad audience potentially In Search of Norbert Wiener, by Flo Paradox of Kurt G6del, by Rebecca including mathematicians, students, Conway and Jim Siegelman. Basic Goldstein. W. W. Norton & Company, and the general public. When a book Books, December 2004. ISBN 0-738- February 2005. ISBN 0-393-05169-2. has been reviewed in the Notices, a 20368-8. (Reviewed May 2006.) (Reviewed April 2006.) reference is given to the review. Gen­ Decoding the Universe: How the New Infinite Ascent: A Short History of erally the list will contain only books Science of Information Is Explaining Mathematics, by David Berlinski. published within the last two years, Everything in the Cosmos, from Our Modern Library, September 2005. ISBN though exceptions may be made in Brains to Black Holes, by Charles Seife. 0-679-64234-X. cases where current events (e.g., the Viking Adult, February 2006. ISBN 0- The Infinite Book: A Short Guide to death of a prominent mathematician, 670-03441-X. the Boundless, Timeless and Endless, coverage of a certain piece of mathe­ Descartes: A Biography, by Desmond by John D. Barrow. Pantheon, August matics in the news) warrant drawing Clarke. Cambridge University Press, 2005. ISBN 0-375-42227-7. readers' attention to older books. Sug­ March 2006. ISBN 0-521-82301-3. Introducing Game Theory and Its gestions for books to include on the list Divine Proportions: Rational Applications, by Elliott Mendelson. may be sent to noti ces-bookl i st@ Trigonometry to Universal Geometry, CRC Press, July 2004. ISBN 1-584- ams. org. by N.J. Wildberger. Wild Egg Books, 88300-6. ''Added to "Book List" since the September 2005. ISBN 0-9757492-0-X. It's About Time: Understanding Ein­ list's last appearance. The Equation That Couldn't Be stein's Relativity, by N. David Mermin. Solved (How Mathematical Genius Dis­ Princeton University Press, Septem­ A 3 & His Algebra: How a Boy from covered the Language of Symmetry), ber 2005. ISBN 0-691-12201-6. Chicago's West Side Became a Force in by Mario Livio. Simon and Schuster, ]tinos Bolyai, Euclid, and the Nature American Mathematics, by Nancy E. September 2005. ISBN 0-743-25820-7. of Space, by Jeremy J. Gray. MIT Press, Albert. iUniverse, Inc., January 2005. The Equations: Icons of Knowledge, May 2003. ISBN 0-262-57174-9. (Re­ ISBN 0-595-32817-2. (Reviewed De­ by Sander Bais. Harvard University viewed October 2005.) cember 2005.) Press, November 2005. ISBN 0-674- The Knot Book: An Elementary Alan Turing's Automatic Comput­ 01967-9. Introduction to the Mathematical ing Engine: The Master Codebreaker's M. C. Escher's Legacy: A Centen­ Theory ofKnots, Colin C. Adams. AMS, Struggle to Build the Modern Com­ nial Celebration, edited by Doris September 2004. ISBN 0-8218-3678-1. puter, edited by B. Jack Copeland. Ox- Schattschneider and Michele Emmer. (Reviewed September 2005.)

AUGUST 2006 NOTICES OF THE AMS 801 Reference and Book List

g % # The Lifebox, the Seashell, and the 0-349-11721-7. (Reviewed November Soul: What Gnarly Computation 2005.) Taught Me about Ultimate Reality, the The Pea and the Sun: A Mathe­ Meaning of Life, and How to be Happy, matical Paradox, by Leonard M. by Rudy Rucker. Thunder's Mouth Wapner. A K Peters, April2005. ISBN Press, October 2005. ISBN 1-560- 1-56881-213-2. 25722-9. Piero della Francesca: A Mathe­ t'~..----b-f&i~·-····-····~·+•••1!~ ..~· - Saunders Mac Lane: A Mathemati­ matician's Art, by]. V. Field. Yale cal Autobiography, by Saunders University Press, August 2005. ISBN Mac Lane. A K Peters, May 2005. ISBN 0-300-10342-5. 1-56881-150-0. (Reviewed December PopCo, by Scarlett Thomas. Har­ 2005.) vest Books, October 2005. ISBN 0-156- The Man Who Knew Too Much: Alan 03137-X. (Reviewed February 2006.) Turing and the Invention of the Com­ Probability Theory: The Logic of puter, by David Leavitt. Great Science, by E. T. Jaynes. Edited by G. Discoveries series, W. W. Norton, Larry Bretthorst. Cambridge Univer­ c;' : $;-. December 2005. ISBN 0-393-05236-2. sity Press, April 2003. ISBN 0-521- The Math Instinct: Why You're a Math­ 592 71-2. (Reviewed January 2006.) ematical Genius (Along with Lobsters, Reality Conditions: Short Mathe­ Birds, Cats, and Dogs), by Keith Devlin. matical Fiction, by Alex Kasman. Math­ Thunder's Mouth Press, March 2005. ematical Association of America, May ISBN 1-56025-672-9. 2005. ISBN 0-88385-552-6. (Reviewed Mathematical Adventures for Stu­ in this issue.) dents and Amateurs, David F. Hayes Ref1ections: V. I. Arnold's Reminis­ and Tatiana Shubin, editors. Mathe­ cences, by V. I. Arnold. Springer, April matical Association of America, 2004. 2006. ISBN 3-540-28734-5. ISBN 0-88385-548-8. The Road to Reality: A Complete Mathematical Musings: A Collection Guide to the Laws of the Universe, ofQuotes, edited by Dan Sonnenschein. by Roger Penrose. Knopf, February Clarium Press, November 2005. ISBN 2005. ISBN 0-679-45443-8. (Reviewed 0-9697688-8-5. June/ July 2006.) Mathematics by Experiment: Plau­ Science in the Looking Glass, by sible Reasoning in the 21st Century, by E. Brian Davies. Oxford University Jonathan Borwein and David Bailey. Press, August 2003. ISBN 0-198- A K Peters, December 2003. ISBN 52543-5. (Reviewed December 2005.) 1-56881-211-6. (Reviewed September *The Secret Life of Numbers: 50 2005.) Easy Pieces on How Mathematicians Meta Math! The Quest for Omega, by Work And Think, by George G. Szpiro. Gregory Chaitin. Pantheon, October Joseph Henry Press, March 2006. ISBN 2005. ISBN 0- 375-42313-3. 0-309-09658-8. More Mathematical Astronomy Shadows of Reality: The Fourth Di­ Morsels, by Jean Meeus. Willmann­ mension in Relativity, Cubism, an,d Bell, 2002. ISBN 0-943396-743. Modern Thought, by Tony Robbin. ".~-~ Mystic, Geometer, and Intuitionist: Yale University Press, March 2006. ----~---==~~---~·· The Life of L. E.]. Brouwer. Volume 2: ISBN 0-300-11039-1. . Hope and Disillusion, by Dirk van Symmetry and the Monster: The Dalen. Oxford University Press, Oc­ Story of One of the Greatest ~uests, of tober 2005. ISBN 0-198-51620-7. Mathematics, by Mark Ronari. Oxford New Mexico Mathematics Contest University Press, May 2006: ISBN·. 0- Problem Book, by Liong-shin Hahn. 192-80722-6. University of New Mexico Press, No­ The Three Body Problem, by Cather­ vember 2005. ISBN 0-8263-3534-9. ine Shaw. Allison and Busby, March The Newtonian Moment: Isaac New­ 2005. ISBN 0-749-08347-6. ton and the Making ofModem Culture, Using the Mathematics Literature, by Mordechai Feingold. New York by Kristine K. Fowler. Marcel Dekker, Library and Oxford University Press, June 2004. ISBN 0-824-75035-7. December 2004. ISBN 0-195-17735-5. The Visual Mind II, edited by The Oxford Murders, by Guillermo Michele Emmer. MIT Press, May 2005. Martinez. Abacus, January 2005. ISBN ISBN 0-262-05076-5.

802 NOTICES OF THE AMS VOLUME 53, N UMBER 7 FROM THE AMS SECRETARY ATTENTION ALL AMS MEMBERS VOTING INFORMATION ®AMS AMERICAN MATHEMATICAL SOCIETY FOR 2006 AMS ELECTION I www.ams.org I

AMS members who have chosen to vote online will receive an email message on or shortly after August 21, 2006, from the "AMS Election Coordinator". The sender will be [email protected], and the subject will be "AMS 2006 Election-login information below". The body of the message J will provide your unique voting login information and the address (URL) of the voting website. If you use a spam filter you may want to use the above address or subject informa­ tion to configure your spam filter to ensure this email will be delivered to you.

AMS members who have chosen to vote by paper should expect to receive their ballot by the middle of September. Unique voting login information will be printed on the ballot, should you wish to vote online.

At midnight (U.S. Eastern Standard Time) on November 3, 2006, tl1e website will stop accepting votes. Paper ballots received after this date will not be counted.

Additional information regarding the 2006 AMS Election is · I available on the AMS website: www.ams.orgjsecretary/

1 election-info.html; or by contacting the AMS: ; [email protected], 800-321-4267 (U.S. & Canada), I 401-455-4000 (worldwide).

Thank you and please remember to vote.

Robert J. Daverman

AMERICAN MATHEMATICAL SOCIETY WWW.AMS.ORG From the AMS Secretary

3.5% of the AMS Operating Revenue (2005) Report of the Executive total. In fact, we Director, State of AMS, 2006 deliberately Mise keep meetings 13% My annual report to the Council each year views the Soci­ revenue low be­ Invest inc ety from a particular perspective, focusing on a special pro­ cause of the 6% gram or merely concen- long-standing AMS Membership (2005) trating on a particular philosophy of Meetings 3% Affiliate aspect. This year, I'd like the Society not 10% to view the AMS in the to make money Dues 6% simplest possible way­ on meetings. Publications as an organization that The major 72% makes money and portion of our spends it. revenue (72%) comes from publishing- books, journals, and This can be mislead­ Mathematical Reviews. ing, of course. Societies • The book program (13% of revenue) competes well with are not merely busi­ programs of other well-known publishers of high-level nesses and their success mathematics. The number of new titles published was cannot (and should not!) slightly higher in 2005 (89), and so be measured by their were the actual number of books revenue alone. But understanding the ways in which an or­ sold. Revenue was slightly down. We ganization derives its revenue, as well as the ways it spends work hard to keep our prices low, it, allows one to understand the organization's values and which helps to keep prices of other goals. publishers lower as well. We make a II I'll organize my report into three parts-the money we commitment to keep every mono­ make, the money we spend, and the money we save. graph in print (we have a new print­ on-demand program), and we now show more than 3,000 The Money We Make titles in print. When members think of the Society's revenue, the first • Journals (18% of revenue) have played a key role in thing they think about is dues. That's natural because publications of the AMS from its founding. The Society pub­ members are always aware that they pay dues. Individual lishes twelve in all, including translation and e-only jour­ dues, however, make up less than 6% of the Society's rev­ nals. While there had been slow attrition in subscriptions enue each year. Institutional dues make up another 3.5%, for many years, in the past several we have seen that trend but the total is still very small (and institutional dues are reverse, and the number of subscriptions has actually less than the subscription discounts given to member in­ risen slightly. As we do for books, we have tried to keep stitutions). Dues are an important source of revenue, but journal prices low. As a consequence, the fraction of the not a large one. Members will also think about revenue from the Soci­ ety's meetings, for which the AMS charges registration fees. But revenue from meetings amounts to less than

804 NOTICES OF THE AMS VOLUME 53, NUMBER 7 From the AMS Secretary

Society's revenue from journals has steadily decreased, The Money We Spend from 24% in 2000 to 18% last year. Journals remain an es­ It is likely not surprising that most of the money the AMS sential part of our scholarly heritage, however. spends each year goes to the publication program- it is a • Mathematical Reviews (nearly 39% of revenue) is re­ large enterprise involving most of the 210 staff of the So­ ally many products rather than one. The essential part con­ ciety. Mathematical Reviews alone has more than 70 peo­ sists of several databases- one made up of nearly two mil­ ple working in our Ann Arbor office. We maintain our own lion items, one of all authors (uniquely identified for each warehouse and printing plant; we engage in marketing item), one of all journals, and a new one of more than a and promotion for journals and books; we engage in reg­ million references, providing citation data that gives new ular development cycles to update our publications web­ insight into the mathematical literature. These have been site. Publishing is our largest expense category by a wide painstakingly assembled over the past margin. sixty-five years. The data is offered in We also spend a lot of money on our meetings, which several formats, although the most include the Joint Meetings each January (about 5,000 peo­ popular (and by far the most used) is ple), eight sectional meetings, one joint international meet­ MathSciNet. For more than ten years ing, and various the Society has charged for access Join Us out West for the workshops and to Math Reviews using a novel conferences. As model: Institutions pay a "data ac­ previously men­ cess fee" (DAF), which is their con­ tioned, the AMS tribution to assembling the database, and tries to balance rev­ then pay a separate fee for access to each par­ enues and direct ticular product. The DAF is the largest portion of the cost expenses for meet­ (in 2006, US$7,320 1 list and$ 5,856 for institutional mem­ ings as closely as bers). By grouping institutions into consortia, we allow sub­ possible. We have scribers to share the cost of the DAF. This scheme has had been successful in some important consequences for the AMS: the number doing this. of institutions with access to Math Reviews has more than Most scientific societies would doubled over the past ten years, and revenue from the DAF divide their other expenses into and products has risen steadily, while the "average" cost two categories, those directed at of access per institution has dropped dramatically. members and those directed at the A member recently wrote to me arguing that the Soci­ scientific community as a whole. ety should divest itself of its publishing activities because That division is hard to accom­ he claimed they represent a conflict of interest: The AMS plish for the AMS, because we often depends on publishing revenue for its existence, and hence blur the lines between member ser­ cannot take the necessary steps to change the way schol­ vice and professional outreach. For arly books and journals are published. I argue the oppo­ example, our two member jour­ site is true: Because we depend so much on publishing for nals, the Bulletin and Notices, are our revenue, we must take steps to change scholarly pub­ major member benefits, but both journals lishing. And by being a major publisher, the AMS has in­ are freely accessible to all mathematicians online. fluenced the publishing of mathematics in many ways­ The AMS website has become a cen- lower prices, forward-thinking policies, and higher quality. tral way to communicate informa­ Publishing is far more than making money for the tion to members, but almost all the Leading a Mathematics Department in AMS ... but making money is important. information is made available to all the 21st Century There are a number of additional sources of revenue mathematicians at no cost (to them). (contributions, advertising, sale of service, short-term in­ Employment services are accessi­ vestments, etc.), but each is relatively modest when com­ ble to everyone (because restrict­ pared to our publications revenue. Our total revenue for ing them to members, either indi­ 2005 was a little more than twenty-three million dollars. viduals or institutions, seems unthinkable). Even discounts on meetings registrations are extended to people beyond our membership (because our meetings are joint), Ttwo Amorican.aothomatloai Soclety l askForc..,nExc.l'-c. When paying dues, our members sometimes ask what they get in return, and this blurring of member benefits and professional outreach makes it hard to give a direct answer. A list of activities on which we spend our money there­ 1 All dollar figures appearing on the following pages in the Report fore looks like a list of outreach, that is, things we do for of the Executive Director; as well as the Report of the Treasurer, the entire mathematics community and not just for our are expressed in terms of U.S. dollars.

AUGUST 2006 NOTICES OF THE AMS 805 From the AMS Secretary members. It's important to keep in mind that almost every Employment Center. The Employment Center takes place one of these things benefits members, either directly or at the Joint Meetings each year and used to be called the indirectly, and hence a part of every activity is a "member "employment register". It is now a centralized site for em­ benefit" as well as outreach. ployers and job appli- Here is a list of some of that outreach, divided into cat­ cants tO meet while at EmploymentServicesforPh.D. Mathematicians ElMS Job Ustings (post or browse) egories that reflect the part of the Society most directly the January meetings. Employment Center (Interviewing Program) .1\MS Coversheet responsible for the activity. A sophisticated mes­ Matb]obs (automated system) sage center and op­ Advice for new Ph.D.'s Programs for graduate students and new Ph.D.'s Membership and Programs tional scheduling sys­ This is the part of the AMS one usually thinks of when tem help with appointments, but employers use it in a thinking about outreach. Its activities are variety of ways. This project is jointly "sponsored" by the ..._ About as varied as any at the AMS, and reach American Mathematical Society, the Mathematical Asso­ ' the nearly every part of the mathematical ciation of America, and the Society for Industrial and Ap­ I community. Here is a sample. plied Mathematics, but it is carried out entirely by AMS Annual Survey. The AMS surveys over staff. AMS 1,500 mathematics, applied mathemat- http://www.ams.org/emp-reg/ ics, and statistics departments each year to gather information on everything from Ph.D.'s to salaries. Mathjobs. This is a new service provided by the AMS in Results are reported in the Notices and on the AMS web­ cooperation with Duke University. It is a Web service that site. This is a large effort, costing more than $100,000 each connects job applicants, year, but it provides invaluable information to mathe­ employers, and reference maticians, especially young ones. The Annual Survey is writers in a flexible way that cosponsored with the American Statistical Association, makes the application the Institute for Mathematical Statistics, and the Mathe­ process easier for all. The matical Association of America. service is free to applicants, but costs a modest fee for em­ ployers. We now have 62 employers and about 2,700 ap­ http://www.ams.org/employment/surveyreports. plicants using the system, with more than 100,000 logins html to the system during the current recruitment season. CBMS Survey. This detailed investigation of undergradu­ http://www.mathjobs.org/jobs ate programs in the mathematical sciences in the U.S. has been conducted every five years since 1965 under the aus­ Young Scholars Program. Summer programs for talented pices of the Conference Board on the Mathematical Sciences high school students played an important role in the ca­ (CBMS), with funding provided by the NSF. The AMS be­ reers of many current mathematicians. For the past seven came a partner in the actual conduct of this survey in 1990, years, the AMS held the NSF grant and provided survey infrastructure ...... has provided support for the 199 5 survey, and is doing the same for the LI_ lb • . LD. L Sll sm~ll grants to- 2005 survey. .I A .. 1liili "'.. . talmg about $80,000 each http://www.ams.org/cbms/ year to h elp Assistantships and Graduate Fellowships in the Mathe­ such programs. Part of the money is used as scholarships, matical Sciences. This annual publication contains infor­ but the modest awards are largely used as seed money to mation on the graduate programs of mathematics and obtain further funding. The Society has established the Ep­ statistics departments in the U.S. Its purpose is to provide silon Fund in order to endow this activity, with a goal of prospective graduate students with a current and reliable reaching two million dollars. We are about three-quarters source of basic information on graduate programs as a first of the way to meeting that goal. step in their exploration of programs to which they might http://www.ams.org/employment/epsilon.html apply. A copy is provided free to every department listed in the AMS Professional Directory and is provided free to REU Conference. The Society conducted a workshop on AMS members upon request. It is also available on the AMS undergraduate research in 1999 with funding from the Na­ website. tional Security Agency. This year, we will repeat that work­ shop, although with a broader focus (to include a variety http://www.ams.org/employment/asst.pdf of undergraduate research experiences). The AMS main­ Employment Information in the Mathematical Sciences tains a central list of all REU programs on its website at (ElMS). ElMS has become a standard location for advertising http://www.ams.org/employment/reu.html academic, and some industrial, positions in mathematics. While the traditional yellow print publication still exists, Math in Moscow Semester for Undergraduates. For the most job seekers access the ads over the Web. The ads are past five years, the Society has carried out this program heavily browsed by mathematicians from all over the with support from the National Science Foundation. Un­ world. dergraduates (and a few graduate students) apply to spend a semester at the Independent University in Moscow, work­ http://www.ams.org/eims/ ing in an intensive mathematical program designed for the

806 NOTICES OF THE AMS VOLUME 53, NUMBER 7 From the AMS Secretary

very best students. It is a unique op­ Stroock Family Foundation, the AMS matches individual portunity to work with some of the donations of mathematics books and journals with li­ best mathematicians in Russia. Re­ braries and mathematics departments at educational in­ turning students have praised the pro­ stitutions around the world, and reimburses donors for the gram and commented about the pro­ cost of shipping. Work is currently underway to expand found effect on their careers. this program. http://www. ams.org/employment/bookdonation. http://www.ams.org/ html employment/mimoscow.html Affiliate Membership. For nearly twenty years, the Soci­ Early Careers. What good is a major in mathematics? We ety has offered special memberships to all mathemati­ all hear that question asked every day and to find an an­ cians in lower-income countries (as classified by the World swer the AMS has recruited a group of mathematics de­ Bank). This is now referred to as "affiliate membership" partments to survey their recent graduates in order to pro­ (it used to be called "Category-S"), and it provides such file their jobs after graduation. The profiles will accumulate members with full benefits, except that they must choose over time, but the first batch is already posted. between the Notices and Bulletin as a (print) member jour­ http://www.ams.org/early-careers/ nal. The dues rate is $16, which can be paid using AMS ICM Travel Grants. Since 1990, the AMS has administered points-the equivalent of two mathematical reviews. There NSF funding for travel support of U.S. mathematicians at­ are more than 3,000 affiliate members. The cost of sus­ tending the International Congress of Mathematicians taining affiliate memberships is substantially more than (ICM). Approximately $250,000 in travel grants have been the dues, but the Society gains a great deal from this pro­ awarded each time through the program. The same effort gram, and so does the community of mathematicians. is planned for ICM 2006 in Madrid, Spain. Approximately Public Awareness 125-150 awards are administered, with a portion going to The AMS created its public awareness office five years recent Ph.D.'s. ago, and it continues to refine its operations. A large part http://www.ams.org/employment/icmapp.html of the work of the public awareness office is providing day­ to-day publicity-cultivating contacts with the press, post­ SACNAS Annual Meeting. The Society for the Advancement ing announcements (including posts to EureakAlert), of Chicanos and Native Americans in Science (SACNAS) preparing releases about events at meetings and work­ holds lively meetings shops. A sample of other activities includes the following. each year in which the AMS participates. The Mathematical Moments. Mathematicians have always had central goal of these a tough time convincing the pub­ meetings is to encourage lic of the value of mathematics. outstanding undergradu­ "Moments" are one-page, brief de­ ates who show an interest scriptions of applications, each in pursuing advanced de­ with a graphic to draw attention. grees in science and They have a common message: mathematics. The AMS Mathematical research is ongoing provides financial support for the meeting and staffs an and important to our lives. They exhibit with materials of interest to the undergraduates have been especially popular in attending the meeting. high school classrooms and un­ http://www.ams.org/ams/sacnas2005-mtg.html dergraduate departments. We have now produced more than fifty Mo­ Ky Fan China Program. Funded by a gift from Ky and Yu­ ments, and we plan to translate Fen Fan, the AMS carries out a program to them into multiple languages for wider distribution. facilitate collaboration between Chinese and http://www.ams.org/ams/mathmoments.html American researchers. The program pro­ vides grants for Chinese mathematicians Math in the Media/Feature Columns. The AMS website in­ (especially young ones) to visit departments cludes two wonderful features that are unknown to many in the U.S. and Canada, and for American mathematicians. One is Tony Phillips' commentary on mathematicians to visit departments in mathematics in the media, which contains insightful analy­ China. sis and concise essays on mathematics of every kind. The other is a monthly column written for "those who have al­ http://www.ams.org/employment/chinaexchange. ready discovered the joys of mathematics as well as for html those who may be uncomfortable with mathematics." Col­ Book & Journal Donation Program. Mathematicians often umn editors have included David Austin, Bill Casselman, ask about donating books and journals to departments in ~4"'"'""'~ currency-weak countries. The largest impediment is the ~~TH in 'the MEDIA cost of shipping materials. Using funds donated by the '"' ,_, J ,., A Mtmthlv Maxazme from the Amencan Miltltemallcal Soctety ,

AUGUST 2006 NOTICES OF THE AMS 807 From the AMS Secretary

Joe Malkevitch, Tony Phillips, and Steve Weintraub. The col­ societies. Providing a visible presence for mathematics in lection extends back to 1997, and they all make wonder­ these communities is critically important. But the Office ful reading. It's a spectacular resource and a wonderful also carries out a number of specific projects each year. place to browse, for experts and novices alike. Here is a sample of just a few. http://www.ams.org/mathmedia/ Science Policy Forums. The annual meetings of the Com­ Who Wants to Be a Mathematician? The popular Who mittee on Science Policy and the Committee on Education Wants to Be a Mathematician game show has now traveled take place in Washington and involve representatives from around the country, held in high schools, college depart- many different organizations in Washington. Mathemat­ ments, and soci­ ics department chairs are invited and frequently out­ ety meetings. number the committee members themselves. The give and Created by pub­ take between mathematicians and the Washington repre­ lic awareness of­ sentatives is good for both sides. ficer Mike Breen, http://www.ams.org/government the game is pat­ terned (loosely) Congressional Luncheons. For the past eight years, the on Who Wants to Society has held an annual Be a Millionaire, luncheon for congres­ and sparks the sional staff (and others). interest of large groups of students, who often cheer for Each luncheon features a their team mates. The game attracts students because it's mathematician who de­ light-hearted and humorous, but at the same time it re­ scribes in simple terms an minds them that there are research mathematicians (30,000 important application of at the AMS) who want them as future colleagues. mathematics, emphasiz­ http://www.ams.org/wwtbam/ ing the connections of What's Happening in the Mathematical Sciences. Every mathematics to all science How Mathematics Helps Predict and technology. These Storm Surges two years or so, a new volume of What's Happening high­ Joannes Westerin, Congresswoman lights some of the latest mathematical research in short have been popular and ef­ Eddie Bernice Johnson (D·TX), and essays focused on selected topics. These books are aimed fective, highlighting both Clint Dawson. at scientifically and mathematically literate audiences, but mathematics and the So- not experts. They have been popular among scientists in ciety. other disciplines. http://www.ams.org/government/ http://ww.ams.org/featurecolumn/archive/ congress-briefing-novOS.html happening.html Congressional Fellows. Beginning last year, the AMS now Mathematics Awareness Month. Every year since 1986, the participates in the AAAS Congressional Fellows program, Joint Policy Board for Mathematics (which includes four supporting a mathematician who serves for one year in a societies, including the AMS) has produced an annual cel­ Congressional office. While the fellows do not specifically ebration of mathematics centered on a particular theme. represent the interests of mathematics (or the AMS), they The theme for 2006 is Internet Security. The Mathematics provide a special perspective for Congress about science Awareness website contains both posters and essays for and research. Fellows usually return to the mathematical use by mathematicians. community, providing a future resource of mathemati­ http://www.mathaware.org cians knowledgeable about science policy. Headlines and Deadlines. The public awareness office http://www.ams.org/government/ gathers information of interest to the community and e­ congressfellowann.html mails it regularly to AMS members who subscribe to Mass Media Fellows. For a number years, the AMS has par­ the service. This is a simple ticipated in the AAAS mass media fellows program by Headlines way to keep mathemati­ supporting one or two fellows each summer. Fellows are &: Deadlines cians informed about news typically graduate students who work for a summer at some and to remind them of im­ media outlet (a newspaper, magazine, or television station), portant deadlines for meetings, proposals, and applica­ learning about the public presentation of science. The col­ tions. lection of fellows is a great asset to the mathematics com­ http://www.ams.org/enews munity, and the AMS has made good use of their talents. Washington Office http: I /www. ams. o rg/gove rnment/ The most important goal of the Washington Office is to massmediaann.html network with various groups in Washington, including Congress, the agencies, and (especially) the other scientific

808 NOTICES OF THE AMS VOLUME 53, NUMBER 7 From the AMS Secretary

Department Chairs Workshops. Each year, the AMS con­ Moore, David P. Robbins, and Al­ ducts a day-long workshop for present or prospective de­ bert Leon Whiteman prizes). These partment chairs. The em­ are all funded using annual in­ phasis is on practical come, which is computed as 5% problems- dealing with bud­ of the gifts and its appreciated gets, deans, and personnel, value. for example-and partici­ The AMS does other things pants spend much of the through its endowments. We time in open conversation award approximately eight sharing ideas. The workshops are always led by a small Trjitzinsky Fellowships of $3,000 group of experienced chairs, who set the agenda and con­ to mathematics majors each year. duct the meeting itself. We give Menger awards to out- Joseph L. Doob http: //www .ams.org/government / standing mathematics-related pro- chrsworkshop06report.html jects at the annual Intel Science Fair and help fund the judg­ ing. We award Centennial Fellowships to young Coalition for National Science Funding. The CNSF is an mathematicians, providing full support for a year at crit­ alliance of over 100 scientific and professional societies ical points in their careers. (The Centennial Fellowships are and universities, united by only partially endowed and are largely funded through an­ a concern for the future of nual gifts from our members.) the nation's science, math­ Not all gifts to the endowment have a specific purpose. ematics, and engineering. Income from these unrestricted gifts is used for special This coalition is chaired by projects each year, as designated by the Board. Samuel Rankin, the director The reserves of the Society represent another kind of of the AMS Washington of­ savings- the kind that a family sets aside in case of an fice, and its primary goal is emergency. In the early 1980s, the AMS faced such an congressman vernon Ehlers (R·MI) to increase the federal in­ emergency when revenue from subscriptions suddenly and Robert lipton. vestment in the National plummeted. In just a few years, the Society used up all its Science Foundation. The reserves and contemplated taking out large loans. After AMS always participates in the annual CNSF Exhibition, that experi­ which showcases the crucial role the NSF plays in meet­ Endowment & Reserves ence, the ing the nation's research and education needs. The exhi­ Board began to bition provides an opportunity for university researchers (restricted) build reserves 5% and educators to describe their work to leaders on Capi­ that would tol Hill. This past year, Robert Lipton of Louisiana State '""'"''"''•d> sustain the So- University represented the AMS at the exhibition, high­ 10% ciety through lighting his recent work on "Mathematics for Advanced 85% future emer­ Composites Technology". gencies, and it This is a sample of the ways in which the AMS spends set a goal of its money, on programs that bring in less money than reaching they cost. There are many more that often go unnoticed three-fourths because they are so common. The Notices and Bulletin are of a year's operating budget. To reach that goal, funds were both member journals that people expect as a member ben­ set aside at regular intervals from operations, and be­ efit. The Combined Membership List and Professional Di­ cause the investments did well during this period, the rectory are used by mathematicians every day. Periodically AMS reached its target ahead of schedule. updating the Mathematical Sciences Classification (MSC), Now that reserves have grown beyond their original maintaining the Journals Price Survey (a ten-year history purpose (as an emergency fund), the Society has begun to of prices and page counts for roughly 300 journals), pro­ use them as a new source of revenue. Since 2002 a por­ viding T};X fonts and tools-all these services we do for the tion of the reserves has been used to generate income for community, and they are ways in which we spend our operations each year, by computing income as 5% of the money. value (like the endowment). This new revenue provides more than $600,000 annually. While this is only 2.5% of The Money We Save our present revenue, it will likely become more and more important in future years. It represents a new source of The AMS has two types of savings, the endowment and the income for the Society, much like income from a family's reserves. Both are crucial to the Society's operations, but savings that has been invested wisely. in different ways. The endowment is made up of gifts to the Society, many of which were given for a specific purpose, such as a prize. Conclusion The Society has added six new prizes in the past six years Viewing the operations of the Society through its finances (the Levi Conant, Joseph L. Doob, Leonard Eisenbud, E. H. can be misleading, of course; the AMS does more than

AUGUST 2006 NOTICES OF THE AMS 809 From the AMS Secretary merely earn money, spend it, and save it. But taking note Unrestricted net assets are those that have no requirements of which programs produce revenue and which consume as to their use placed on them by donors outside the So­ it can be a useful exercise. It helps the So­ ciety. A substantial majority of the Society's net assets and ciety's members and leaders to recognize activities are in this category. Temporarily restricted net the scope and breadth of our activi­ assets are those with donor-imposed restrictions or con­ ties. ditions that will lapse upon the passage of time or the ac­ It also helps to complishment of a specified purpose. Examples of the So­ remind us that ciety's temporarily restricted net assets and related our activities are activities include grant awards and the spendable income interdependent. from prize and other income-restricted endowment funds. Members of the So­ Permanently restricted net assets are those that must be ciety are sometimes invested in perpetuity and are commonly referred to as en­ passionate about dowment funds. The accompanying financial information one particular aspect principally relates to the unrestricted net assets, as this of the AMS, for ex­ category includes the operating activities of the Society. ample, meetings, pub­ Unrestricted revenues in excess of unrestricted ex­ lications, or advocacy. penses for the year ended December 31, 2005, resulted in They sometimes view their own an increase in unrestricted net assets of approximately interest as the most impor­ $4,393,000. Of this amount, net income on the unrestricted tant - as something that should be portion of the long-term investment portfolio totaled ap­ supported by (but not support!) the rest of proximately $2,482,000 and net income from operations the Society's programs. But the AMS would not exist totaled approximately $1,911,000. The recovery in the do­ for long if everything it did lost money. mestic and international financial markets that contin­ A healthy society consists of many parts, all of them ued in 2005 resulted in a return on the long-term portfo­ woven together, all supporting one another-and all of lio of approximately 6.4%. These and other matters are them important. discussed in more detail in the following sections. The Society's net assets totaled $65,037,000 at De­ - john Ewing cember 31, 2005. $3,474,000 is permanently restricted, con­ Executive Director sisting of the original amount of donor restricted gifts and bequests received by the Society. $1,794,000 is temporarily restricted by donor-imposed limitations that will lapse Report of the Treasurer (2005) upon the passage of time or the use of the asset for its in­ tended purpose. $59,769,000 is unrestricted, of which $50,85 3,000 has been designated by the Board of Trustees I. Introduction as reserved for future expenditure, principally in the form One of the most important duties of the Treasurer is to of the Economic Stabilization Fund (ESF). The ESF's pur­ lead the Board of Trustees in the oversight of financial ac­ pose is to provide a source of cash in the event of a financial tivities of the Society. This is done through close contact crisis. The fund consists of two sub-funds, known as the with the executive staff of the Society, review of internally base and supplemental portions of the ESF. The Society's generated financial reports, review of audited financial Board of Trustees set the minimum level at which to main­ statements, and direct contact with the Society's inde­ tain the base portion of the ESF at the sum of 75% of an­ pendent auditors. Through these and other means, the nual operating expenses plus the current estimate of the Trustees gain an understanding of the finances of the So­ post-retirement health benefit obligation. As of the end of ciety and the important issues surrounding its financial 2005, the value of the base portion of the ESF exceeds the reporting. The Report of the Treasurer is presented an­ established minimum level. The supplemental portion of nually and discusses the financial condition of the Soci­ the ESF is used to provide operating income to the Soci­ ety as of the immediately preceding fiscal year end, and ety via the use of a 5% spending rate. The remaining un­ the results of its operations for the year then ended. It con­ restricted net assets consist of $3,828,000 invested in tains summary information regarding the operating results fixed assets and undesignated net assets of $5,088,000. and financial condition of the Society for 2005; a review of 2005 operations, containing more detailed information II. Review of 2005 Operations regarding the Society's operations; and a discussion of the As indicated in the graph below, the past five years have assets and liabilities of the Society. Finally, in the last part been very good years, financially, for the Society, apart from of the report, there are financial statements derived prin­ investment losses incurred in the first two of these years. cipally from the Society's audited financial statements, Although the Society experienced investment losses which present the balance sheet, statement of activities from 2000-2002, a significant portion of those losses had (akin to an income statement in a for-profit organization) and information regarding the Society's invested funds. 1 All dollar figures appearing in charts and graphs on the follow­ The Society segregates its net assets, and the activities ing pages in the Report of the Treasurer are expressed in terms of that increase or decrease net assets, into three types. thousands of dollars.

810 NOTICES OF THE AMS VOLUME 53, NUMBER 7 From the AMS Secretary been recouped by the end of 2005. Fur- ther, in spite of these losses, long-term investments have generated high returns over a long period (an average annual re­ turn of 8.34% over the last 10 years), and that income has helped the endowment funds (and the income they produce) to keep pace with inflation. Since 2002, the Board of Trustees has appropriated investment income from those endowment funds with income whose use is unrestricted and from a portion of the Economic Stabilization Fund to support operations. The amounts of such appropriations that have been in­ cluded in operating revenue totaled $847,225 in 2005, $792 ,870 in 2004, $865,696 in 2003, and $760,811 in 2002. (10.000) j______Net I .ong-tcm1 When reflecting on years with good op­ Operating Revenues Operating Expenses Operating Income Investment Income Net Income erating results, it is instructive to review the Society's record for a somewhat longer period. The chart at right shows Operating Income As % of Revenue operating income as a percentage of op­ 20.0% ------. erating revenues. Over this 26-year pe­ 14.2% riod, the average operating income as a 1 % percentage of revenue is 3.8%, with sig­ 11 .0% 10.0% +------10-.1'_V, ------"'""-4'....___--+.ll,.,_-'8"'-.7'"-Vo ___8_ 5_.%'-"""1 nificant variation. For the most recent 15- year period the average rises to 6.5% with 5.9% 6.7% 6.9% 6.6%~ less variation. Since 199 7, the margin achieved is consistently higher than ei­ ther of these averages and shows even -0.1% -2.8% less variation. Taken together, these are -1.8% positive financial indicators. If the Board of Trustees had not ap­ -10.0% +------i propriated investment income to sup­ -11.9% port operations in 2002-2005, the oper­ -14.1% -14.4% ating income margin percentage above -20.0% L______j would have been approximately 5.5% in 2002 , 7.1% in 2003, 5.2% in 2004, and 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 4.9% in 2005. These results are both above the average for the entire period shown above, and in this time period. This is indicative of the productivity gains remain consistent for the period from 1991 forward. experienced by the Society. At the same time, the average annual growth in revenue was 2.02%. While the revenue Sales Trends growth did not keep up with inflation during this period, The graphs on the following page show sales trends from it was almost 50 basis points better than that of the ex­ 1995 through 2005, first in historical dollars and second pense growth rate. This positive differential was achieved in constant dollars (using 2005 as the base year and ad­ during the same period of time when price increases on justing other years for inflation). journals and MR products were lowered (the DAF had no The trends shown in historical dollars are in general price increase for one year), sectional meeting fees were mildly upward, and this is partly due to pricing strategies held constant and individual dues were frozen for a year. that counter the effects of inflation and attrition. When If the Board had not appropriated investment income to shown in constant dollars, most sources of revenue are flat support operations (commencing in 2002), there would or slightly decreasing. have been a positive difference between the growth of ex­ During the nine-year period from 1996 through 2005, the penses and revenues of only 0.07% annually during the pe­ average annual inflation was 2.43% (1996 was selected as riod 1996-2005. the base year as it was the first year after the loss of the Mathematical Reviews. Total revenue from MR in its var­ four Russian translation journals). During this same pe­ ious forms increased in 2005. This is due to price in­ riod, the Society's average annual expense growth was 1.53%, creases effective in 2005, net of attrition (which was minor). indicating that the Society was able to keep its expense The Society continues to concentrate its marketing efforts growth almost 1% below the rate of inflation for each year on working with consortia, where costs can be spread

AUGUST 2006 NOTICES OF THE AMS 811 From the AMS Secretary

Sales Trends - Historical Dollars to meet its obligations to subscribers and 10.000 ,------, publishers. Ultimately, it is the choice of the subscriber to use a subscription agent, but the scholarly publishers pay the highest price should any further financial difficulties arise. There continue to be financial pressures on libraries everywhere in the world, as their budgets lag behind the cost of obtaining n. C>I>£ > ...... - ...... _ ...... ___...... - ...... - ..- .... - ... .. scholarly journals and books. This has been the case for many years now, and is not likely to change. Accordingly, scholarly publishers are fighting over an ever dwindling slice of pie. The decline in the value of the dollar compared to many other currencies during 2.1100 2001-2004 helped the Society's retention ef­ forts with respect to non-U.S. subscribers. 1. 011~ r--- -;~;-·····;:( The dollar started to get stronger against other currencies in 2005, which may hamper 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 ,------~ retention efforts for 2006 and subsequent ~ & re lated - Joumal s - Books individual dues - lnstitutiotJal dues ~ All other lv1R years. The domestic economy continued to improve slowly in 2005, despite a higher rate Sales Trends - Constant Dollars of inflation, soaring fuel costs, and the over­ 12,000 .------___;,:_____;,:__=._~------, all economic effects of natural disasters. The drop in 1996 resulted from decisions made by those in control of four Russian journals (Izvestiya, Sbornik, Steklov, and Dok­ lady) to use sources other than the AMS for 8,000 , ... ,,,_,__ ,,_,,,...... ,_,,,...... translation into English and distribution of the resulting translation journals. Books. Book revenues increased in 2005 in 6.000 historical dollars and slightly in constant dollars, despite a shortfall of new titles pro­ duced (87 titles were published in 2005 ver­ sus a budget of 103). Sales of new and back­ list titles remained strong throughout 2005. 2,ooo ------··························································· ------The Society continues to work with distrib- ~:1<-I E-~l:E(---""J:E----"Jl~E -~l:E;.----'l~E-~l:

_.,_ MR & rela(ed _._ J\)urnals -.- Bonks Individual dues - Institutional dues -e- All ol.b t:r Dues. Dues, the sum of individual and in­ stitutional, have shown a slight upward slope on the historical dollars chart and a flat or over a larger number of institutions. This has the effect slightly decreasing line in constant dollars. A flat con­ of providing the MR product line to a much wider audi­ stant dollar line is expected for institutional dues, as the ence than could afford it as individual institutions, as well number of members varies little from year to year and the as protecting the current revenue stream for future years. dues rates have been set so that dues will increase at MR is currently financially healthy; however, it is proba­ about the same level as inflation. There has been a slight bly unrealistic to expect significant increases in sales rev­ decline in individual dues from their high in 1998. enue from additional subscribers. Journals. Journal revenues are doing well with im­ Major Expense Categories provement seen in the last four years, as attrition of sub­ The table at the top of the following page shows the major scribers has been less than expected. The strength of the expenses for 2003, 2004, and 2005, in thousands of dol­ Society's journal program is further illustrated by the fact lars. There has not been much change from year to year that substantially all of the subscribers granted gratis sub­ in the types of expenses incurred by the Society. scriptions in 2003 due to the bankruptcy of a subscription Operating expenses can also be associated with the var­ agent renewed their subscriptions with the Society in 2004 ious activities of the Society, and this is how our audited and 2005. The financial solvency of subscription agents con­ financial statements are presented (see Section N). The So­ tinues to be a worry to scholarly publishers, as in 2004 a ciety has accounting systems in place to capture the iden­ subscription agent with significant market share required tifiable direct costs of its publishing and member and the infusion of additional capital from investors in order professional services activities, as well as indirect costs

812 NOTICES OF THE AMS VOLUME 53, NUMBER 7 From the AMS Secretary

Major Expense Categories 2003 2004 2005 Personnel Costs $13 ,388 67% $13 ,881 66% $1 4,608 66% Building and equipment related 1,387 7% 1,391 7% 1, 389 6% Postage 815 4% 799 4% 865 4% Outside printing and binding 691 3% 669 3% 806 4% Travel: staff, volunteers, grant support 778 4% 796 4% 972 4% All other expenses 3,050 15% 3,294 16% 3,557 16% TOTAL $2 0,109 100% $20,8 30 100% $22 ,197 100% associated with these two major functions. General and endowment funds, and the margin from publishing administrative costs are those that cannot be directly as­ activities. While the various activities in this functional area sociated with either of its two main functions or any ac­ do have revenue streams, such as fees, grant support, tivity therein. Below is a summary presentation that prize fund spendable income, etc., the costs incurred by matches the revenue and costs of the major activities of these activities are significantly greater than the revenues the Society, derived directly from its audited financial generated. statements. Some points worth noting in the above presentation are Ill. Assets and Liabilities that the Mathematical Reviews activities and the Providence So far, this report has dealt with revenues and expendi­ publications produce about the same margin (in dollars) tures that affect unrestricted net assets. Another aspect after identifiable direct costs associated with these prod­ of the Society's finances is what it owns and owes, or its ucts. The indirect costs associated with the overall pub­ assets and liabilities, which are reported below in the Bal­ lishing activities of the Society (taking orders, shipping and ance Sheets. As discussed previously, the Society's net as­ storing goods, marketing and sales efforts, etc.) reduces sets and activities that increase or decrease net assets are this margin by 35%. If general and administrative were al­ classified as unrestricted, temporarily restricted, or per­ located to the publishing activities, this margin would be manently restricted. A majority of the assets and liabili­ reduced even further. But there would still be a margin from ties detailed on the accompanying Balance Sheets consti­ publications, available to spend on services and outreach tute the unrestricted net assets. The permanently restricted activities. net assets are supported by investments in the long-term The member and professional services activities use re­ investment portfolio and the temporarily restricted net as­ sources of the Society, which are then supported, or "paid sets are supported by investments in the long-term and for" by member dues, spendable income from reserve and short-term investment portfolios. The Market Value of

2005 Operating Revenue and Expenses by Major Activity, in Thousands of Dollars Revenue Expense Net Publications: Mathematical Reviews $ 9,294 $ 5,920 $ 3,374 Providence publications (books, journals, etc.) 7,885 4,206 3,679 Publications indirect (customer services, marketing, distribution and warehousing, etc.) 2,45 3 (2,453) Total publications 17,179 12,579 4,600

Member and professional services: Services and outreach programs 1,246 3,114 (1,868) Grants, prizes and awards 977 1,278 (301) Meetings 822 736 86 Divisional indirect 500 (500) Governance 420 (420) Spendable income from investments 727 727 Dues 2,186 2,186 Total member and professional services 5,958 6,048 (90)

Other 641 97 544 General and administrative 3,143 (3,143)

Total $23,778 $21,867 $ 1,911

AUGUST 2006 NOTICES OF THE AMS 813 From the AMS Secretary

Invested Funds shows the market value of each endowment BALANCE SHEETS and Board designated (quasi-endowment) fund, including December 3 7, 2005, and 2004 any reinvested earnings. The Society's fiscal year is the calendar year and thus Assets 2005 2004 coincides with the period covered by subscriptions and dues. Since dues and subscriptions are generally received Cash and cash equivalents $ 674,624 $ 360,398 in advance, the Society reports a large balance of cash and Short-term investments 16,145,544 16,384,598 short-term investments on its financial statements at year­ Receivables, less allowances of $230,000 and $185,089 end. This amounted to approximately $16,820,000 and respectively 1,135,742 800, 123 $16,745,000 at December 31, 2005, and 2004, respec­ Deferred prepublication costs 609,877 575,040 tively. The corresponding liability for the revenues re­ Completed books 972,114 986,303 ceived in advance was approximately $11,971,000 and Prepaid expenses and $11,633,000 at December 31, 2005, and 2004, respec­ deposits 1 ,079,528 1,021,248 tively. Land , bldgs., and equipment, less The Society's property and equipment include land, accumulated depreciation 3,828,1 56 4,027,381 buildings and improvements, office furniture and equip­ Long·term investments 60,258,660 54,740,077 ment, and software. The Society also owns a small amount Total assets $84,704,245 $78,895,168 of transportation equipment. The land, buildings, and im­ provements include the Society's Rhode Island headquar­ Liabilities and Net Assets ters, with buildings in Providence and Pawtucket, and the Liabilities: Mathematical Reviews offices in Ann Arbor. The largest part Accounts payable $ 1 ,545,820 $ 1 ' 198,389 of the Society's office equipment is its investment in com­ Accrued expenses: puter facilities. Severance and study The Society's endowment is managed under the "total leave pay 1 ,058,971 1 ,093,480 return concept". Under this management policy, income Payroll, benefits, and other 1,092,225 974,527 in excess of a reasonable amount (set by the Board of Deferred revenue 11 ,971,02 1 11 ,633,462 Postretirement benefit Trustees) is reinvested and increases the value of the fund. obligation 3,998,645 3,538,947 This allows for growth in income over time. As discussed Total liabilities 19,666,682 18,438,805 previously, in 2002 the Board of Trustees established a pol­ icy of annually appropriating investment income from Net assets : those true endowment funds whose use of income is un­ Unrestricted 59,769,368 55,375,894 restricted and from the supplemental portion of the Eco­ Temporarily restricted 1,794,484 1,794,111 nomic Stabilization Fund to support operations. The Permanently restricted 3,473,711 3,286,358 amount of such appropriations included in operating rev­ enue is $847,225 and $792,870 in 2005 and 2004, re­ Total net assets 65,037,563 60,456,363 spectively. Total liabilities and net assets $84,704,245 $78,895,168 IV. Summary Financial Information The following Balance Sheets and Statements of Activities are from the audited annual financial statements of the Society, and the Statement of Invested Funds is from the internal financial records of the Society. Each year, the Audit Committee of the Board of Trustees meets with the Soci­ ety's auditors to review the conduct of the audit, the So­ ciety's financial statements, and the auditors' report on the financial statements. Pursuant to the recommendation of the Audit Committee, the Board of Trustees has accepted the audited financial statements. A copy of the Society's audited financial statements, as submitted to the Trustees and the Council, will be sent from the Providence Office to any member who requests it from the treasurer. The trea­ surer will be happy to answer any questions members may have regarding the financial affairs of the Society.

-Respectfully submitted,

John M. Franks Treasurer

814 NOTICES OF THE AMS VOLUME 53, NUMBER 7 From the AMS Secretary

STATEMENTS OF ACTIVITIES 2005 2004 Years Ended December 3 7, 2005, and 2004

Changes in unrestricted net assets: Changes in temporarily restricted net assets: Operating Revenue 2005 2004 Contributions and grants 153,455 148,873 Long-term investment Publication: income (loss) Mathematical Reviews and 191,766 301,818 Net assets released from related activities $ 9,294,428 $ 8,935,727 restrictions (344,848) (247,580) Journals (excluding MR) 4,288,978 4,199,508 Change in temporarily Books 3,081,012 3,047,302 restricted net assets Sale of services 379,114 341 ,789 373 203,111 Other 135,675 142,114 Change in permanently Total publication revenue 17,1 79,207 16,666,440 restricted net assets- Contributions 187,353 130,186 Membership and professional services: Dues, services, and outreach 3,431,224 3,299,211 Change in net assets 4,581 ,200 6,635,166 Grants, prizes, and awards 977,253 669,036 Net assets, beginning of year 60,456,363 53,821,197 Investment earnings available for spending 727,225 754,116 Net assets, end of year $65,037,563 $60,456,363 Meetings 822,188 938,409 Total membership and professional services revenue 5,957,890 5,660,772 STATEMENTS OF INVESTED FUNDS As of December 3 7, 2005 and 2004 Short-term investment income 503,262 331,610 Other 137,844 108,758 Dec. 31, 2005 Dec. 31, 2004 Original Market Market Total operating revenue $23,778,203 $22,767,580 Gift(s) Value Value Endowment Funds:

Operating Expenses Prize Funds : Steele $145,009 $ 593,039 $ 581,243 Publication: Birkhoff 10,076 35,876 35,163 Mathematical Reviews and Veblen 2,000 12,116 11 ,875 related activities $ 5,919,533 $ 5,635,138 Wiener 2,000 12,116 11,875 Journals (excluding MR) 1,276,304 1,323,861 Bacher 1 ,450 8,812 8,636 Books 2,604,319 2,533,093 Conant 9,477 39,550 38,764 Publication-divisional indirect 666,448 808,173 Cole 5,550 20,808 20,394 Warehousing and distribution 791,142 716,452 Satter 15,000 31,499 30,872 Customer services 776,448 675,595 Morgan 25,000 43,041 42,185 Marketing and sales 219,230 229,373 Whiteman 48,796 50,493 43,257 Sale of services 325,321 226,930 Doob Book Prize 45,000 48,059 Total publication expense 12 ,578,655 12,148,615 Robbins Prize 40,000 43,678 Arnold Ross Membership and professional services: Lectures 60,000 63,202 61,945 Dues , services, and outreach 311 5,145 2,940,084 Trjitzinsky Grants, prizes, and awards 1 ,278,042 732,548 Scholarships 196,030 476,817 467,333 Meetings 735,513 896,816 C. V. Newsom 100,000 221,885 217,472 Governance 419,659 464,003 Centennial Divisional indirect 500,038 488,888 Fellowship 56,100 11 3,768 111 ,505 Total membership and professional Menger 9,250 11,134 10,913 services expense 6,048,397 5,522,339 Ky Fan (China) 366,757 366,75 7 366,757 Epsilon 771,316 812,237 700,003 Other 97,118 9,395 Total Income General and administrative 3,142,371 3,149,791 Restricted Total operating expenses $21,866,541 $20,830,140 Funds $1,908,811 $3,004,887 $2,760,192

Excess of operating revenue (continued) over operating expenses $1,911,662 $1,937,440 Long-term investment return in excess of investment earnings available for spending 2,481,812 4,364,429 Change in unrestricted net assets 4,393,474 6,301,869

AUGUST 2006 NOTICES OF THE AMS 815 From the AMS Secretary NEW from A K PETERS STATEMENTS OF INVESTED FUNDS (contined)

Dec. 31, 2005 Dec. 31, 2004 l Yearning for the Impossible The Surprising Truths of Mathematics Original Market Market Gift(s) Value Value John Stillwell $29.95; Hardcover; 250 pp. Endowment 100,000 730,870 71 3,905 Morita 100,000 130,422 127,395 "With wonderful clarity, Yearning for the Impossible brings you right Henderson 548,223 3,91 7,891 3,826,949 Schoenfeld/ into the midst of the mind's play Mitchell 573,447 735,034 717,973 with number and shape, where the Laha 189,309 247,907 242,153 imaginary makes sense of the real Ritt 51,347 233,422 228,004 and the infinite of our constricted, Moore 2,575 22,003 21 ,492 finite world." Total Income - Robert and Ellen Kaplan, The Math Circle Unrestricted Funds 1,564,901 6,017,549 5,877,871 Save 20% on these titles discount code AMS Total Endowment Funds $3,473,712 $9,022,436 $8,638,063 j Once Upon Einstein Board-Restricted Funds: Thibault Damour Friends of Math 123,572 $24.95; Paperback; 199 pp. Russian Royalties 17,829 journal Archive 487,182 41 5,607 "Once Upon Einstein takes the Economic Stabilization reader on a novel and enjoyable (total) 49,791,023 44,277,514 stroll through the well-trodden by­ Young Scholars 574,912 539,561 ways of Einstein's revolutionary Total Board-Restricted breakthroughs. Both novice and Funds 50,853,117 45,374,083 expert alike will be entertained Total Funds $59,875,553 $54,012,146 and enlightened by Damour's masterful insights." -Brian Greene, author of The Fabric of the Cosmos and The Elegant Universe Pursuit of Genius Flexner, Einstein, and the Early Faculty at the Institute for Advanced Study Steve Batterson $39.00; Hardcover; 314 pp. "Batterson has mined the Institute's Pursuit of archives to provide a detailed and Genius unvarnished account of the back­ stage conflicts and intrigue that attended the Institute's growth and determined its future." -John W. Dawson, Jr., author of Logical Dilemmas: The Life and Work of Kurt Godel

"An engrossing tale about the development of advanced mathematical research in the twentieth century." -Paul Sally, Jr., The University of Chicago

; www.akpeters.com

816 NOTICES OF THE AMS VOLUME 53, NUMBER 7 This prize was established in 2005 in memory of David P. Robbins by members of his family. Robbins, who died in 2003, received his Ph.D. in 1970 from MIT. He was a long-time member of the Institute for Defense Analysis Center for Communications Research and a prolific mathematician whose work (much of it classified) was in discrete mathematics. The prize is for a paper with the following characteristics: it shall report on novel research in algebra, combinatorics or discrete mathematics and shall have a significant experimental component; and it shall be on a topic which is broadly accessible and shall provide a simple statement of the problem and clear expositi-on of the work. The US$5,000 prize will be awarded every three years. It is expected that the first award will be made in January 2007.

Nominations should be submitted to the AMS Secretary, Robert J. Daverman, American Mathematical Society, 312D Ayres Hall, University of Tennessee, Knoxville, TN 37996-1330. Include a complete bibliographic citation for the work that is the basis of the nomination, supplemented with brief remarks explaining what aspects of the work make it particularly suited for this prize. The nominations will be forwarded by the Secretary to the Prize Selection Committee, which will make the final decision on the award.

Deadline for nominations: August 15, 2006 ®AMSMATHllMATICAL SOCIETY AMERICAN I www.ams.org I AMERICAN MATHEMATICAL SOCIETY

Math in the Media is a great way to keep The Feature Column is a series of essays on abreast of math news as reported in news, various mathematical topics-such as voting, papers and general science magazines. The Penrose tiles, cosmology, and networks­ collection-Tony Phillips' Take on Math in written by David Austin, Bill Casselman, the Media, Math Digest, and Reviews of books, Joe Malkevitch, and Tony Phillips. plays, and films with mathematical themes-is a centralized repository of articles in the media about mathematics.

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THE FISKE SOCIETY The Thomas S. Fiske Society honors individuals who provide for a gift to the American Mathematical Society in their estate plans. They use planned giving to include the AMS in their wills, life insurance policies, or retirement plans. Such gifts ensure that the AMS will continue to fulfill its mission to promote mathematical research, advance the mathematics profession, support mathematics e'ducation at all levels, and foster awareness and appreciation of mathematics well into the future. Thomas S. Fiske founded the American Mathematical Society in 1888 to foster comradeship and share research through meetings and publications. Fiske Society members hold an honored place in the annals of the Society and in the mathematical community for building on the foundation started by Fiske. For more information see www.ams.org/giving-to-ams or contact the Development Office, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA; telephone: 800-321-4267 (U.S. and Canada), 401-455-4000 (worldwide); fax: 401-331-3842; email: [email protected]. Mathematics Calendar

The most comprehensive and up-to-date Mathematics Calendar information is available one-MATH at http ://www.ams.org/mathcal/.

August2006 International Conference on Automated Reasoning (August 17-20), IEEE Symposium on Logic in Computer Science (August 12-15), '' 5-7 7th International Pure Mathematics Conference 2006, Is­ Conference on Rewriting Techniques and Applications (August lamabad, Pakistan. 12-14), International Conference on Theory and Applications of Description: It is a thematic conference on Algebra, Geometry, SatisfiabilityTesting (August 12-15). The six major conferences will Analysis held under the auspices of the Pakistan Mathematical be accompanied by 41 workshops, held on August 10-ll, 15-16, SoCiety. The entire conference is organized under one roof at a and 21-22. four-star hotel in the modern, peaceful and beautiful federal capital Speakers: The FLoC'06 program includes a keynote session to of Pakistan located at the footsteps of the scenic Margalla Hills. There will be free housing and lodging for foreign participants. commemorate the Goede! Centenary, with John Dawson and Dana Scott as speakers, a keynote talk by David Harel, plenary talks by Several recreational trips will be organized in and around Islamabad Randy Bryant and David Dill, and invited talks by F. Bacchus, A. introducing the unique local and multi-ethnic culture. Blass, B. Buchberger, A. Darwiche, M. Das, ]. Esparza, ]. Giesl, A. Information and registration: Please fill in the on-line registration Gordon, T. Hoare, 0 . Kupferman, M. Lam, D. Miller, K. Sakallah, ]. format http : I /www . pmc. org. pkandfindmoreinformation therein. Stay, and C. Welty. The conference is convened by Qaiser Mushtaq in collaboration with Mathematics Division, Institute of Basic Research (Florida, Funding: FLoC has received an NSF grant to provide funds for USA), Higher Education Cbmmission, Pakistan Telecommunication travel grants of up to $750 for student attendees of FLoC'06. We Ltd, and Quaid-i-Azam University, Islamabad. expect to award about 50 grants. See application information on the website. * 7-11 Recent Developments in Arrangements and Configura­ Registration: Online registration for FLoC is now open at: http :, tion Spaces, Mathematical Sciences Research Institute, Berkeley, //www.easychair . org/FLoC-06/. · California. Organizers: Michael Falk (Northern Arizona University), Eva-Maria * 1 4-1 8 The Teachers Circle, Mathematical Sciences Research Feichtner (University of Stuttgart), Hiroaki Terao (Tokyo Metropoli­ Institute, Berkeley, California. tan University). Organizers: Tom Davis, Mary Fay-Zenk, Tatiana Shubm, Sam Information: http : I /www. msri. org/ calendar /workshops/ Vandervelde, Paul Zeitz, joshua Zucker. Workshoplnfo/389/show_workshop/. Information: http : I /www. msri . org/ calendar /workshops/ Workshoplnfo/397/show_workshop/. * 1 0-2 2 The 2006 Federated logic Conference, Seattle, Washington. Program: The following conferences will participate in FLoC'06: * 31 - September 1 Connections for Women: Computational Appli­ Conference on Computer Aided Verification (August 17-20), In­ cations of Algebraic Topology, Mathematical Sciences Research ternational Conference on Logic Programming (August 17-20), Institute, Berkeley, California.

respect to participation in the meeting, this fact should be noted. This section contains announcements of meetings and conferences All communications on meetings and conferences in the mathematical of interest to some segment of the mathematical public, including ad sciences should be sent to the Editor of the Notices in care of the American hoc, local, or regional meetings, and meetings and symposia devoted Mathematical Society in Providence or electronically to notices@ams .=org to specialized topics, as well as announcements of regularly scheduled or mathcal@ams. org. meetings of national or international mathematical organizations. A In order to allow participants to arrange their travel plans, organizers of complete list of meetings of the Society can be found on the last page of meetings are urged to submit information for these listings early enough each issue. to allow them to appear. in more than one issue of the Not'ices prior to An announcement will be published in the Notices if it contains a call for pa:->ers and specifies the place, date, subject (when applicable), and the meeting ~n question. To achieve this, listings should b1 received in ProVIdence e1ght months prior to the scheduled date of the meeting. the sp··akers; a second announcement will be published only if there The complete listing of the Mathematics Calendar will e published are c!1 ;mges or necessary additional information. Once an announcement only in the September issue of the Notices. The March, jUne/July, and has appeared, the event will be briefly noted in every third issue until December issues will include, along with new announcements, references it has been held and a reference will be given in parentheses to the to any previously announced meetings and conferences occurring within month, year, and page of the issue in which the complete information the twelve-month period following. the month of those issues. New appeared. Asterisks (*) mark those announcements containing new or information about meetings and conferences that will occur later than revised information. the twelve-month period will be announced once in full and will not be In general, announcements of meetings and conferences held in North repeated until the date of the conference or meeting falls within the America carry only the date, title of meeting, place of meeting, names of twelve-month period. ·speakers (or sometimes a general statement on the program), deadlines The Mathematics Calendar, as well as Meetings and! Conferences of for abstracts or contributed papers, and source of further information. the AMS, is now available-electronically through the AMS website on the Meetings held outside the North American area may carry more detailed World Wide Web. To access the AMS website, use the URL: http: 1/www. information. In any case, if there is any application deadline with ams.org/. . .

820 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Mathematics Calendar

Organizer: Susan Holmes. Topics: General theory of univalent and multivalent functions; Information: http : I /www. rnsri. org/ calendar /workshops/ Extremal problems for conformal and quasiconformal mappings; Workshoplnfo/377/show_workshop/. Bloch functions, normal functions, normal families; Covering theo­ rems in conformal mapping theory; Finely holomorphic functions September 2006 and topological function theory; Quasiconformal methods and Teichmuller theory; Fuchsian and Kleinian groups as dynamical '' 3-8 CR Geometry and POE's, Grand Hotel Bellavista, Levi co Terme, systems; Potentials and capacity, harmonic measure, extremal Trento, Italy. length; Pluripotential theory; Bergman spaces; Potential theory on Topic: CR Geometry and Partial Differential Equations present a Riemannian manifolds; Biharmonic and polyharmonic equations field of interaction with a wide range of mathematical areas such and functions; Discrete potential theory; Equations of mathematical as Real and Complex Symplectic Geometry, Differential Geometry, physics and other areas of application; Holomorphic mappings and Complex Dynamics, Jet Theory, Microlocal Analysis. The aim of correspondences; Nonlinear potential theory; Related topics. the conference is to bring together both active senior researchers Organizing Committee: Tahir Aliyev Azeroglu (Gebze Institute of and young mathematicians vvith interest in CR Geometry and technology, chair), Promarz Tarnrazov (Institute of Mathematics Partial Differential Equations and to foster exchange of ideas and of the NAS of Ukraine), Alinur Buyukaksoy (Gebze Institute of interaction between these fields. Technology), Mithat Idemen (Yeditepe University, Turkey), Aydin Scientific Organizers: Dmitri Zaitsev (Dublin) and Giuseppe Aytuna (Sabanci University, Turkey), Faik Mikailov (Gebze Institute Zampieri (Padova). of Technology). Confirmed Participants: M. Agranovsky (Ramat Gan), L. Baracco Information: http: I / www. gyte . edu . tr/iccapt/. (Padova), F. Bracci (Roma II), A. Cap (Wien), P.D. Cordaro (Sao Paulo), M. Derridj (Rouen), P. Dolbeault (Paris), M. Eastwood (Adelaide), '' 11-1 5 Arithmetic Algebraic Geometry, Research Institute for P.F. Eb enfelt (La Jolla), N. Eisen (Poitiers), C. Epstein (Philadelphia), Mathematical Sciences, Kyoto University, Kyoto, Japan. G. Fels (Tuebingen), F. Forstneric (Ljubljana), S. Fu (Camden), L. Organizer: KATO, Kazuya (Dept. of Math., Kyoto Univ). Geatti (Roma II), ]. Globevnik (Ljubljana), X. Gong (Madison), K. Information: http: I /www. kurirns. kyoto-u. ac. jp;-kyodo/ Hirachi (Tokyo), X. Huang (Piscataway), A. Isaev (Canberra), W. prograrn18-en.htrn. Kaup (Tuebingen), B. Lame! (Wien), C. Laurent-Thiebaut (Grenoble), H.-M. Maire (Geneve), N. Mir (Rouen), M. Nacinovich (Roma II), M. '' 11 - 1 5 Introductory Workshop on Geometric Flows And Function Peloso (Torino), A. Perotti (Trento), F. Ricci (SNS Pisa), G. Schmalz Theory in Real and Complex Geometry, Mathematical Sciences (Armidale), Y.-T. Siu (Harvard), L. Stolovitch (Toulouse), G. Tomassini Research Institute, Berkeley, California. (S NS Pisa), V. Vajaitu (Bucharest), S.S.-T. Yau (Chicago), L. Zalcman Organizers: Bennett Chow, Peter Li and Gang Tian. (Ramat Gan). Information: http: I /www. rnsri. org/ calendar /workshops/ Deadline for registration: July 31, 2006. Workshoplnfo/380/show_workshop/. Information: Augusto Micheletti, Secretary of CIRM, Istituto '' 11-1 5 Stochastic Analysis and Applications, Research Institute Trentino di Cultura, Via Sommarive 14, I-38050 Povo (Trento), Italy; for Mathematical Sciences, Kyoto University, Kyoto, Japan. Tel. +39-0461-881628; Fax +39-0461-810629; email: rnichelet@ Organizers: SHIGEKAWA, Ichiro (Dept. of Mathematics, Kyoto science.unitn.it; http://www.science.unitn.it/ Univ.). cirrn/AnnCR2006.htrnl. Information: http: I /www. kurirns. kyoto-u. ac . jp;-kyodo/ ''5-6 Digitization of Mathematical Journals and Related Topics, prograrn18-en.htrn. Research Institute for Mathematical Sciences, Kyoto University, '' 1 3- 1 5 Combinatorics and its application to Information Sci­ Kyoto, Japan. ences, Research Institute for Mathematical Sciences, Kyoto Univer­ Organizer: TOSE, Nobuyuki (Faculty of Economics, Keio Univ.). sity, Kyoto, Japan. Information: http: I /www. kurirns. kyoto-u. ac. jp;-kyodo/ Organizers: FUJI-HARA, Ryoh (System Information and Engineer­ prograrn18-en.htrn. ing, Univ. of Tsukuba). Information: http: I /www. kurirns. kyoto-u. ac . j p;-kyodo/ '' 5-8 Workshop on Computational Applications of Algebraic prograrn18-en.htrn. Topology, Mathematical Sciences Research Institute, Berkeley, California. '' 14- 1 ?The Second International Symposium on Banach and Func· Organizers: G. Carlsson, P. Diaconis, G. M. Ziegler. tion Spaces: 2006, Kyushu Institute of Technology, Kitakyushu, Information: http: I /www. rnsri. org/ calendar/workshops/ Japan. Workshoplnfo/378/show_workshop/. Support: KlT and the Mathematical Society of J;:,pan. Subjects: The main subjects are Banach spaces and function spaces '' 6-8 Development of operator algebra, Research Institute for vvith related topics. Twelve invited lectures and an appropriate Mathematical Sciences, Kyoto University, Kyoto, japan. number of short communications of 20-30 minutes will be planned. Organizer: KAJIWARA, Tsuyoshi (Graduate School of Environmen­ We are also planning to organize a special lecture of 30 minutes tal Science, Okayama Univ.). devoted to the memory of the Japanese mathematician Professor Information: http: I /www. kurirns. kyoto-u. ac . jp;-kyodo/ Tosio Aoki at the beginning of the conference by Professor Lech prograrn18-en.htrn. Maligranda. Organizing and Scientific Committee: Mikio Kato (Kyushu In­ '' 8-9 Connections for Women: Geometric Analysis and Nonlinear stitute of Technology, Chair), Lech Maligranda (LuleaUniversity Partial Differential Equations, Mathematical Sciences Research of Technology-Sweden), Yoshiaki Okazaki (Kyushu Institute of Institute, Berkeley, California. Technology), Kichi-Suke Saito (Niigata University), Wataru Taka­ Organizers: Christine Guenther and Panagiota Daskalopoulos. hashi (Tokyo Institute of Technology), Yasuji Takahashi (Okayama Information: http: I /www. rnsri. org/ calendar /workshops/ Prefectural University). Workshopinfo/379/show_workshop/. Invited Speakers: Francesco Altomare (Bari, Italy), Joan Cerda (Barcelona, Spain), Ka zimierz Geobel (Lublin, Poland), Anna Karnin­ * 8-14 International Conference on Complex Analysis and Poten­ ska (Memphis, USA), Lech Maligranda (Lulea, Sweden), Toshihiko tial Theory. Satellite Conference of ICM06, Gebze Institute of Nishishiraho (Okinawa, Japan), Lars Erik Persson (Luleaand Upp­ Technology, Istanbul Area, Turkey. sala, Sweden), Gord Sinnamon (London, Canada), Yasuji Takahashi

AUGUST 2006 NOTICES OF THE AMS 821 Mathematics Calendar

(Okayama, Japan), Wataru Takahashi (Tokyo, Japan), Yuwen Wang '' 16-1 8 The interplay between set theory of the reals and (Harbin, P. R. China), Witold Wnuk (Poznan, Poland). iterated forcing, Research Institute for Mathematical Sciences, Information: http: I /www. kyutech. ac. jp/english/index .html Kyoto University, Kyoto, Japan. and http: I /isbfs .mns. kyutech. ac. jp/. Organizers: BRENDLE, ]org (Graduate School of Science and Tech­ nology, Kobe Univ.). * 1 8-22 Workshop on Application of Topology in Science and Information: http: I /www. kurims. kyoto-u. ac. jp;-kyodo/ Engineering, Mathematical Sciences Research Institute, Berkeley, program18-en.htm. California. Organizers: G. Carlsson, P. Diaconis, and S. Holmes. '' 1 8-20 General Topology, Geometric Topology and their Ap­ Information: http: I /www. msri. org/ calendar /workshops/ plications, Research Institute for Mathematical Sciences, Kyoto Workshop!nfo/381/show_workshop/. University, Kyoto, Japan. Organizers: YAMAZAKI, Kaori (Institute of Mathematics, Univ. of '' 25-27 Information and mathematics of non-additivity and non­ Tsukuba). extensivity: from the viewpoint of functional analysis, Research Information: http: I /www .kurims . kyoto-u. ac. jp;-kyodo/ Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan. program18-en.htm. Organizers: MUROFUSHI, Toshiaki (Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technol­ '' 1 8-20 Mathematical Models of Phenomena and Evolution Equa­ ogy). tions, Research Institute for Mathematical Sciences, Kyoto Univer­ Information: http: I /www. kurims . kyoto-u . ac. jp;-kyodo/ sity, Kyoto, Japan. program18-en.htm. Organizers: YAMADA, Naoki (Fukuoka Univ.). Information: http: I /www .kurims .kyoto-u. ac. jp;-kyodo/ '' 25-29 Joint research-trees on graphs, Research Institute for program18-en.htm. Mathematical Sciences, Kyoto University, Kyoto, Japan. Organizers: ODA, Yoshiaki (Dept. of Mathematics, Keio Univ.). '' 23-27 Analytic and Computational Aspects of Elliptic and Parabolic Equations, Mathematical Sciences Research Institute, Information: http: I /www. kurims. kyoto-u. ac. jp;-kyodo/ Berkeley, California. program18-en.htm. Organizers: Panagiota Daskalopoulos, Peter Li and Lei Ni. '' 28-30 Conference Mtisd2006, Procida, Naples, Italy. Information: http: I /www .msri . org/calendar/workshops/ Information: http: I /www .mtisd06. unior. it/; email: squill an© Workshop!nfo/383/show_workshop/. unisannio . it. '' 23-27 Arithmetic Galois Theory and Related Moduli Spaces, Research Institute for Mathematical Sciences, Kyoto University, October 2006 Kyoto, Japan. '' 2-6 Complex Dynamics and its Related Topics, Research Institute Organizer: NAKAMURA, Hiroaki (Graduate School of Natural Sci­ for Mathematical Sciences, Kyoto University, Kyoto, Japan. ence, Okayhama Univ.). Organizers: SHISHIKURA, Mitsuhiro (Dept. of Mathematics, Kyoto Information: http: I /www . kurims. kyoto-u. ac. jp;-kyodo/ Univ.). program18-en.htm. Information: http: I /www. kurims. kyoto-u. ac . jp;-kyodo/ '' 24-2 7 Combinatorics, Representation Theory and Related Top­ program18-en.htm. ics, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan. * 2-6 Workshop on Topological Methods in Combinatorics, Com­ Organizers: SUZUKI, Takeshi (RIMS, Kyoto Univ.). putational Geometry, and the Study of Algorithms, Mathematical Sciences Research Institute, Berkeley, California. Information: http: I /www. kurims. kyoto-u. ac . jp;-kyodo/ program18-en.htm. Organizers: G. Carlsson, P. Diaconis, R. Jardine, and G. M. Ziegler. Information: http: I /www .msri. org/ calendar /workshops/ * 2 5-26 Modern Mathematics: An Introduction to 2007-08 Pro­ Workshop!nfo/382/show_workshop/. grams at MSRI, Mathematical Sciences Research Institute, Berkeley, California. '' 11-1 3 Analytic Number Theory, Research Institute for Mathemat­ Organizers: Ricardo Cortez, Hugo Rossi, Ivelisse Rubio. ical Sciences, Kyoto University, Kyoto, Japan. Information: http: I /www. msri. org/ calendar /workshops/ Organizers: EGAMI, Shigeki (Toyama Univ.). Workshop!nfo/394/show_workshop/. Information: http: I /www. kurims. kyoto-u. ac. jp;-kyodo/ program18-en.htm. '' 2 ?-November 1 International Conference of Computational Methods in Sciences and Engineering 2006 (ICCMSE 2006), '' 11-1 3 Recent Developments in Theory of Linear Operators and Hotel Panorama, Chania, Crete. its Applications, Research Institute for Mathematical Sciences, Special Lecture: Rudolph A. Marcus, Nobel Prize in Chemistry 1992, Kyoto University, Kyoto, Japan. Arthur Amos Noyes Professor of Chemistry, (California Institute Organizers: NAKAZATO, Hiroshi (Faculty of Sci. & Tech., Hirosaki of Technology). Univ.). Highlighted Lectures: A. D. Buckingham, University of Cambridge, Information: http: I /www. kurims . kyoto-u. ac . jp;-kyodo/ UK; Bjorn 0. Roos, University of Lund, Sweden; Werner Kutzelnigg, program18-en.htm. University of Bochum, Germany. Invited Speakers: Tadeusz Bancewicz (Poland), Sylvio Canuto * 16-18 Pattern formation problems in dissipative systems, (Brazil), Minhaeng Cho (Korea), James R. Chelikowsky (USA), C. Research Institute for Mathematical Sciences, Kyoto University, Cramer (USA), M. Heaven (USA), Hans Herrmann (Germany), A. Kyoto, Japan. Hinchliffe (UK), K. Hirao (Japan), K.A. Jackson (USA), P. Jorgensen Organizers: KUWAMURA, Masataka (Faculty of Human Develop­ (Denmark), Ilya Kaplan (Mexico), ]. Leszczynski (USA), Paul G. ment, Kobe Univ.). Mezey (Canada), M. Nakano (Japan), P. Pyykko (Finland), ]. Sauer Information: http: I /www. kurims. kyoto-u. ac. jp;-kyodo/ (Germany), H.F. Schaefer (USA), N. S. Scott (UK), M. Urban (Slovakia), program18-en.htm. K. Yamaguchi (Japan).

822 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Mathematics Calendar

Highlighted Symposium: The multiconfigurational method for all and engineering. The interplay connects to other subjects and the periodic table. A theoretical chemistry Symposium in honour applications. of Bjorn Roos. Organizer: Laura Gagliardi, Department of Physical Organizers: Ola Bratteli (University of Oslo), Palle Jorgensen Chemistry, Sciences II University of Geneva. (The University of Iowa), David Kribs (University of Guelph), Contact Information: Secretary ICCMSE 2006 (Mrs Eleni Ralli­ Gestur Olafsson (Louisiana State University), Sergei Silvestrov Simou); email: iccmse©uop. gr and tsimos©mail. ariadne-t. gr, (Lund University). 10 Konitsis Street, Amfithea Paleon Faliron, GR-175 64, Athens, Information: http: I /www. pims. math. ca/birs/birspages. php? Greece; fax: +3 0210 94 20 091 or+ 30 2710 237397. task=displayevent&event_id.

'' 30-November 1 Mathematical Aspects and Applications of Wave January 2007 Phenomena, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan. '' 11 -1 2 Connections for Women: Dynamical Systems, Mathemat­ Organizers: TANAKA, Mitsuhiro (Faculty of Engineering, Gifu ical Sciences Research Institute, Berkeley, California. Univ.). Information: http: I /www . msri. org/ calendar /workshops/ Information: http : I /www. kurims. kyoto-u. ac. jp;-kyodo/ Workshopinfo/384/show_workshop/. program18-en.htm. '' 1 5-19 Computational Commutative Algebra and Computational November 2006 Algebraic Geometry, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan. '' 6- 1 0 Development of Computational Algebraic Statistics, Re­ Organizer: HIBI, Taka yuki (Graduate School of Information Science search Institute for Mathematical Sciences, Kyoto University, Kyoto, and Technology, Osaka Univ.). Japan. Information: http : I /www. kurims. kyoto-u. ac. jp;-kyodo/ Organizer: TAKEMURA, Akimichi (Graduate School of Information program18-en.htm. Science and Technology, Univ. of Tokyo. Information: http: I /www. kurims. kyoto-u. ac. jp;-kyodo/ '' 1 5-19 Introductory Workshop on Dynamical Systems with program18-en.htm. Emphasis on Extended Systems, Mathematical Sciences Research Institute, Berkeley, California. '' 6-11 International Conference on Harmonic Analysis and Ap­ Organizers: Chris Jones (Univ. North Carolina), Edgar Knobloch plications, El-Kantaoui, Sousse, Tunisia. (Univ. Calif., Berkeley-Physics), Nancy Kopell (Boston Univ.), Lai-Sang Description: The activities will focus on commutative and non­ Young (chair, Courant). commutative harmonic analysis, analysis on homogeneous spaces, Information: http: I /www. msri. org/ calendar /workshops/ representation theory, hypergroups, special functions and the Workshopinfo/385/show_workshop/. interplay between these fields. It is planned as a forum for scientific and fruitful exchange of new ideas in these different areas. Young '' 22-26 Local Holomorphic Dynamics, Pisa, Italy. researchers are particularly invited to attend the event and even Main Speakers: Dominique Cerveau (Univ. de Rennes I), Jean Ecalle encouraged to present their recent works and to discuss their (Univ. de Paris-Sud), Todor Gramtchev (Univ. di Cagliari), Mattias subjects with experts. We shall organize some twenty minutes Jonsson (Royal Inst. of Tech. Stockholm), Frank Loray (Univ. de contributed talks especially for that purpose. Rennes I), Stefano Marmi (Scuola Normale Superiore Pisa), Jean­ Information: Please contact: Mohamed Sifi: Faculte des Sciences Francais Mattei (Univ. P. Sabatier de Toulouse), Robert Moussu de Tunis, Departement de Mathematiques, 2092 El-Manar, Tunis, (Univ. de Bourgogne Dijon), Jorge V. Pereira (IMP A), Ricardo Perez­ Tunisie. Mobile: (216) 97 672 349, Fax: (216) 71 885 350, email: Marco (UCLA), Julio Rebelo (Univ. de Paris-Sud), Bruno Scardua mohamed. sifi©fst. rnu. tn. Ali Baklouti: Faculte des Sciences de (IMPA), Tetsuo Ueda (Kyoto Univ.), Jean-Cristophe Yoccoz (College Sfax, Departement de Mathematiques, 3038 Sfax, Tunisie. Mobile: de France), Nguyen Tien Zung (Univ. P. Sabatier de Toulouse). (216) 98 641 600, Fax: (216) 74 274 4437, email: ali.baklouti© Program: The aim of this workshop is to bring together researchers fss. rnu. tn. interested in local holomorphic dynamics, from both the continuous and the discrete side of the subject, with the goals of presenting the '' 20-22 P-adic Arithmetic Geometry, Research Institute for Mathe­ more recent results, comparing the techniques used, and possibly matical Sciences, Kyoto University, Kyoto, Japan. to spark new collaborations and researches. Every morning there Organizer: KATO, Kazuya (Dept. of Mathematics, Kyoto Univ.). will be three plenary lectures given by some of the main researchers Information: http: I /www. kurims .kyoto-u. ac. jp;-kyodo/ in the area. The afternoons will instead be devoted to talks given program18-en.htm. by junior researchers from all over the world. '' 30-December 2 SIGEF'06: First Announcement: XIII Congress Registration: To register, go to the address http : I /www. crm. of International Association for Fuzzy-Set Management and sns. it/index_02 . html and follow the links scientific activities­ Economy: Optimization techniques: Fuzziness and nonlinearity workshops-future-Local holomorphic dynamics-Registration. The for management and economy, Hammamet, Tunisia. deadline for registration is: September 30, 2006. Information: For any information please contact conference secre­ Contacts: Dr. Haria Gabbani, Dr. Antonella Gregorace, Centro tary by mail or e-mail: SIGEF'06, Institut Superieur de Gestion, 41 di Ricerca Matematica "Ennio De Giorgi", crm©crm. sns. it, Fax: rue de la liberte, 2000 Le Bardo, Tunisie, Tel: (+216) 98 409 533, Fax: +39/050/509178. (+216) 71 703 652, email: foued.benabdelaz©isg.rnu.tn; http: I /www. isg. rnu. tn/SIGEFXIII. (under construction) March 2007 '' 4-7 3rd International Conference on 21st Century Mathematics December 2006 2007, School of Mathematical Sciences, Lahore, Pakistan. '' 2-7 Operator methods in fractal analysis, wavelets and dynam­ Organizers: Convener: A. D. R. Choudary, SMS, Lahore, Pakistan ical systems, BIRS, Banff, Canada. (choudary©cwu. edu); Conference Chairman: Faqir Mm Bhatti, LUMS, Aim: This workshop is aimed at developing new approaches and Pakistan (fmbhatti©lums. edu . pk). mathematical foundations for wavelet analysis, dynamical and Keynote Speakers: C. G. Gibson (University of Liverpool, UK); iterated function systems, spectral and tiling duality, fractal itera­ T. Zamfirescu (University of Dortmund, Germay); D. Popescu tion processes and non-commutative dynamical systems. Operator (University of Bucharest, Romania); A. Laptev (Royal Institute of theory, harmonic analysis and representation theory. Mathematics Technology KTH), Stockholm); D. A. Leites (Max-Planck-Institute

AUGUST 2006 NOTICES OF THE AMS 823 Mathematics Calendar

for Mathematics, Germany); ]. Seade (UNAM, Mexico) ; Edy Tri all areas of AI, PR and related topics. The conference will be held Baskoro (Institut Teknologi Bandung, Indonesia); D. K. Arrowsmith at the same time and location where three other major events will (University of London, UK) . be taking place. Information: http: I /wc2007 . lums. edu. pk. Information: Visit http: I /www. promoteresearch. org/; email: j eedward©gmail . com. '' 1 2-16 Geometric Evolution Equations, Mathematical Sciences Research Institute, Berkeley, California. ,., 9-12 International Conference on Enterprise Information Sys­ Organizers: Bennett Chow, Gerhard Huisken, Chuu-Lian Terng, tems and Web Technologies, Orlando, Florida. and Gang Tian. Description: EISWT is an important event in the areas of Enterprise Information: http : I /www .msri. org/ calendar/worksh ops/ Information Systems as well as Web Technologies. The conference Workshoplnfo/386/show_workshop/. will be held at the same time and location where three other major events will be taking place. '' 19-23 Stochastic Dynamical Systems and Control, Mathematical Information: Visit http: I /www. promoteresearch. or g/; Sciences Research Institute, Berkeley, California. email: j eedward©gmail. com. Organizers: Jonathan Mattingly (Duke), Igor Mezic (UCSB-Chair), Andrew Stuart (Warwick). '' 9-121nternational Conference on High Performance Computing, Information: http: I /www. msri. org/ cal endar /workshops/ Networking and Communication Systems, Orlando, Florida. Workshopinfo/387/show_workshop/. Description: HPCNCS is an important event in the areas of computer networks, high performance computing, communication systems, '' 26 World Congress on Computational Finance: The First Decade, signal processing and related areas. The conference will be held at London, England. the same time and location where three other major events will be Organizers: Jesper Andraesen, Myron Scholes, Domingo Tavella. taking place. Information: http: I /www. msri. org/ special s/ compf inance/ Information: Visit http : I /www. promoteresearch. org/; index_html. email: j eedward©gmail . com.

April 2007 '' 9- 1 2 International Conference on Software Engineering Theory and Practice (SETP-07), Orlando, Florida. * 28- May 5 Advances in Algebra and Geometry, Mathematical Description: The conference will be held simultaneously at the Sciences Research Institute, Berkeley, California. same place where three other major events in computer science Organizers: Joe Harris, Craig Huneke, Hugo Rossi, Frank-Olaf are taking place. Schreyer, Bernd Sturmfels. Information: Visit http: I /www . promoteresearch. org/; Information: http : I /www. msri. org/ calendar /workshops/ email: j eedward©gmail . com. Workshoplnfo/390/sh ow_workshop/.

May 2007 The following new announcements will not be repeated until '' 21-2 5 Mathematical Issues in Stochast ic Approaches for Multi­ the criteria in the next to the last paragraph at the bottom of scale Modeling, Mathematical Sciences Research Institute, Berkeley, the first page of this section are met. California. Organizers: Roberto Camassa (Univ. North Carolina, Chapel Hill), September 2007 ]inqiao Duan (Illinois Institute of Technology, Chicago), Peter E. '' 1 0-1 4 High-order methods for computational wave propaga­ Kloeden (Univ. of Frankfurt, Germany), Jonathan Mattingly (Duke tion and scattering, AIM Research Conference Center, Palo Alto, Univ.), Richard McLaughlin (Univ. North Carolina, Chapel Hill). California. Information: http: I /www. msri . org/ cal endar /workshops/ Description: This workshop, sponsored by AIM and the NSF, will Workshoplnfo/398/show_wor kshop/. address numerical methods for wave propagation with a focus on '' 22-26 Extremal problems in complex and real analysis, Peoples high-order convergence for general scattering configurations. The Friendship University of Russia, Moscow, Russia. workshop will have an emphasis on spectral methods concerning the following topics: High frequency approximations, Geometric Topics: The list of covered topics includes (but is not limited to): singularities, and Generalized impedance boundary conditions. approximation theory, theory of spaces of analytic and harmonic Organizers: Oscar P. Bruno and Rainer Kress. functions, optimal recovery, geometric function theory in one and Deadline: June l, 2007. several variables, function related operator theory. Information: Visit http: I I aimath. org/ ARCC/workshops/ Information: Visit http: I /www. albany. edu;-pb6916/; wavescattering. html. email: kosipenko©yahoo. com, stessin©math. albany . edu, amontes©us. es.

'' 28-June 2 Workshop on Finsler Geomertry and its Applications, Hotel Jogar, Balatonfoldvar, Hungary. Organizers: S. Bacsu, L. Kozma and ]. Szilai, Department of Geometry, Univ. of Debrecen, Hungary. Honorary chairman: L. Tamasssy, Univ. of Debrecen, Debrecen, Hungary. Information: Visit http : I /www .math . kl te . hu/finsler2007 /; email: kozma©math. kl te . hu; http: I /www. hotelj ogar. hu.

July 2007 '' 9-12 International Co nference on Artificial Intelligence and Pattern Recognition, Orlando, Florida. Description: AIPR is an important event in the areas of Artificial Intelligence (AI) as well as Pattern Recognition (PR) and focuses on

824 NOTICES OF THE AMS VOLUME 53, NUMBER 7 New Publications Offered by the AMS

Selfinjective algebras: Finite and tame type; 0. Solberg, Algebra and Algebraic Support varieties for modules and complexes. Geometry Contemporary Mathematics, Volume 406 August 2006, 270 pages, Softcover, ISBN-10: 0-8218-3818-0, ISBN-13: 978-0-8218-3818-1, LC 2006040706, 2000 ------Mathematics Subject Classification: 16G10, 16G20, 16G50, CONTEMPORARY Trends in 16G60, 16G70, 18E30, 16D90, 18G40, 16S99, All AMS MATHEMATICS members US$63, List US$79, Order code CONM/406 ------..- .------Representation Trends in Theory of Algebras Representation Theory of Algebras and Related Topics Pseudo Limits, and Related Topics MEM9IRS American Mathematical Socldy Jose de Ia Pet'la Jose A. de la Pe:fia and Biadjoints, and A. Raymundo Bautista Editors Raymundo Bautista, Editors Pseudo Limits. Pseudo Algebras: Biadjoints, and Pseudo This book is based on lectures given Algebras: Categorical Categorical ------Foundations of Amorlcan Ma100matlcal Sode.ty during a Workshop on Representations of Algebras and Conformal Field Theory Foundations of Related Topics. Some additional Thomas M. Flore articles are included in order to complete a panoramic view of Conformal Field the main trends of the subject. The volume contains original Theory presentations by leading algebraists addressed to specialists Atner!eanMatl>omutkalSodety as well as to a broader mathematical audience. The articles Thomas M. Fiore include new proofs, examples, and detailed arguments. Topics Contents: Introduction; Some comments on conformal field under discussion include moduli spaces associated to quivers, theory; Weighted pseudo limits in a 2-category; Weighted canonical basis of quantum algebras, categorifications and pseudo colimits in the 2-category of small categories; derived categories, A -infinity algebras and functor categories, Weighted pseudo limits in the 2-category of small categories; cluster algebras, support varieties for modules and complexes, Theories and algebras; Pseudo T-algebras; Weighted pseudo the Gabriel-Roiter measure for modules, and selfinjective limits in the 2-category of pseudo T-algebras; Biuniversal algebras. arrows and biadjoints; Forgetful 2-functors for pseudo Contents: A. Bakke Buan and R. Marsh, Cluster-tilting theory; algebras; Weighted bicolomits of pseudo T-algebras; Stacks; 2- C. GeiR, Introduction to moduli spaces associated to quivers Theories, algebras, and weighted pseudo limits; Bibliography; (With an appendix by Lieven Le Bruyn and Markus Reineke); Index. A. Hubery, From triangulated categories to Lie algebras: A Memoirs of the American Mathematical Society, Volume 182, theorem of Peng and Xiao; B. Keller, A-infinity algebras, Number 860 modules and functor categories; H. Krause and D. Kussin, Rouquier's theorem on representation dimension; June 2006, 171 pages, Softcover, ISBN-10: 0-8218-3914-4, lSBN- C. M. Ringel, Foundation of the representation theory of Artin 13 : 978-0-8218-3914-0, LC 2006042824, 2000 Mathematics algebras, using the Gabriel-Roiter measure.; R. Rouquier, Subject Classification: 18C10, 18C20; 81T40, 18A30, Individual Categorification of .sl2 and braid groups; A. Skowronski, member US$39, List US$65, Institutional member US$ 52, Order code MEM0/182/ 860

AUGUST 2006 NOTICES OF THE AMS 825 New Publications Offered by the AMS

L q (0, d11); Returning to Carnot groups; The Neumann Analysis problem; The case of Lipschitz vector fields; Bibliography. Memoirs of the American Mathematical Society, Volume 182, Number 857 Carleson Measures June 2006, 119 pages, Softcover, ISBN-10: 0-8218-3911-X,

MEMOIRSof t he AmerlcanMathematlea\Soclety ISBN-13: 978-0-8218-3911-9, LC 2006042821, 2000 and Interpolating Mathematics Subject Classification: 43A85, 46E35; 35H20, Ca rleson Measures Sequences for Besov Individual member US$36, List US $60, Institutional member and Interpolating US$48, Order code MEM0/ 182/857 Sequences for Besov Spaces Spaces on Complex on Complex Balls Balls N. Arcoz7.1. R. Rochberg. and E. Sawyer ------N. Arcozzi, Universita di CONTEMPORARY Integral Geometry Bologna, Italy, R. Rochberg, ------MATHEMATICS and Tomography American Mo. t hem~Ucal Society 1 Washington University, St. Integral Geometry Andrew Markoe, Rider Louis, MO, and E. Sawyer, University, Lawrenceville, N], McMaster University, Hamilton, ON, Canada and Tomography Andrew Markee and Eric Todd Quinto, Tufts Eric Todd Quinto Contents: Introduction; A tree structure for the unit ball lffin in Editors University, Medford, MA,

826 NOTICES OF THE AMS VOLUME 53, NUMBER 7 New Publications Offered by the AMS

August 2006, 155 pages, Softcover, ISBN-10: 0-8218-3755-9, accessible research articles. This is the first and so far only ISBN-13: 978-0-8218-3755-9, LC 2006040669, 2000 book that covers all the fundamental facts about chaotic Mathematics Subject Classification: 44A12, 92C55; 35B05, billiards in a complete and systematic manner. The book 35L05, 35R30, 42B20, 42C40, 43A85, 52A22, 94Cl2, All AMS contains all the necessary definitions, full proofs of all the members US$47, List US$ 59, Order code CONM/ 405 main theorems, and many examples and illustrations that help the reader to understand the material. Hundreds of carefully designed exercises allow the reader not only to become Flat Level Set familiar with chaotic billiards but to master the subject. ME~91RS The book addresses graduate students and young researchers AmcrlcanMathematlcalSoo!cty Regularity of in physics and mathematics. Prerequisites include standard graduate courses in measure theory, probability, Riemannian Flat Level p-Laplace Phase Set Regularity geometry, topology, and complex analysis. Some of this of p -Laplace Transitions material is summarized in the appendices to the book. Phase Transitions Enrico Valdinocl Contents: Simple examples; Basic constructions; Lyapunov Berardino Sclunzl Enrico Valdinoci, Universita di Vasil e Ovldiu Savin Roma Tor Vertaga, Rome, exponents and hyperbolicity; Dispersing billiards; Dynamics of unstable manifolds; Ergodic properties; Statistical properties; Italy, Berardino Sciunzi, Bunimovich billiards; General focusing chaotic billiards; Universita di Roma Tor Afterword; Measure theory; Probability theory; Ergodic theory; Vergata, Rome, Italy, and Bibliography; Index. Vasile Ovidiu Savin, Mathematical Surveys and Monographs, Volume 127 University of California, Berkeley, CA August 2006, 316 pages, Hardcover, ISBN-10: 0-8218-4096-7, Contents: Introduction; Modifications of the potential and of ISBN-13: 978-0-8218-4096-2, LC 2006042819, 2000 one-dimensional solutions; Geometry of the touching points; Mathematics Subject Classification: 37D50; 37D25, 37A25, Measure theoretic results; Estimates on the measure of the 37N05, 82B99, All AMS members US$68, List US$85, Order projection of the contact set; Proof of Theorem 1.1; Proof of code SURV / 127 Theorem 1.2; Proof of Theorem 1.3; Proof of Theorem 1.4; Appendix A. Proof of the measure theoretic results; Appendix B. Summary of elementary lemmata; Bibliography. Painleve Memoirs of the American Mathematical Society, Volume 182, Number 858 Painleve Transcendents June 2006, 144 pages, Softcover, ISBN-10: 0-8218-3910-1, ISBN- Transcendents The Riemann-Hilbert The Riemann-Hilbert 13: 978-0-8218-3910-2, LC 2006042822, 2000 Mathematics Approach Approach Subject Classification: 35]70, 35B65, Individual member Athanassios S. Fokas US$37, List US $62, Institutional member US$ 50, Order code Alexander R. Its Athanassios S. Fokas, MEM0/ 182/ 858 Andrei A. Kapaev Victor Yu. Novokshenov Cambridge University, United Kingdom, Alexander R. Its, Indiana State University, Indianapolis, IN, Andrei A. Differential Equations Kapaev, Steklov Mathematical Institute, St. Petersburg, Russia, and Victor Yu . ..~. COURSE Novokshenov, Russian Academy of Sciences, Ufa, ~ A DOPTI O N Russia Chaotic Billiards At the turn of the twentieth century, the French Nikolai Chernov, University of mathematician Paul Painleve and his students classified Chaotic . Alabama at Birmingham, AL, second order nonlinear ordinary differential equations with Billiards the property that the location of possible branch points and and Roberto Markarian, essential singularities of their solutions does not depend on Nikolai Chernov Universidad de la Republica, initial conditions. It turned out that there are only six such Roberto Markarian Montevideo, Uruguay equations (up to natural equivalence), which later became known as Painleve I-VI. This book covers one of the most exciting but most difficult topics in Although these equations were initially obtained answering a the modern theory of dynamical strictly mathematical question, they appeared later in an systems: chaotic billiards. In physics, astonishing (and growing) range of applications, including, billiard models describe various e.g., statistical physics, fluid mechanics, random matrices, and mechanical processes, molecular dynamics, and optical orthogonal polynomials. Actually, it is now becoming clear phenomena. that the Painleve transcendents (i.e., the solutions of the Painleve equations) play the same role in nonlinear The theory of chaotic billiards has made remarkable progress mathematical physics that the classical special functions, such in the past thirty-five years, but it remains notoriously as Airy and Bessel functions, play in linear physics. difficult for the beginner, with main results scattered in hardly

AUGUST 2006 NOTICES OF THE AMS 827 New Publications Offered by the AMS

The explicit formulas relating the asymptotic behaviour of the classical special functions at different critical points, play a Discrete Mathematics and crucial role in the applications of these functions. It is shown in this book, that even though the six Painleve equations are Combinatorics nonlinear, it is still possible, using a new technique called the Riemann-Hilbert formalism, to obtain analogous explicit ~+..~ COURSE formulas for the Painleve transcendents. This striking fact, • ADOPTION apparently unknown to Painleve and his contemporaries, is '"""'"""""'""'.... the key ingredient for the remarkable applicability of these •<>·•·"''''"''"""" .'"'""'"" Lectures in "nonlinear special functions". Lectures in Geometric Geometric The book describes in detail the Riemann-Hilbert method and emphasizes its close connection to classical monodromy Combinatorics theory of linear equations as well as to modern theory of Rekha R. Thomas, University integrable systems. In addition, the book contains an ample of Washington, Seattle, WA collection of material concerning the asymptotics of the Painleve functions and their various applications, which makes This book presents a course in the it a good reference source for everyone working in the theory geometry of convex polytopes in and applications of Painleve equations and related areas. arbitrary dimension, suitable for an Contents: Introduction. Painleve transcendents as nonlinear advanced undergraduate or beginning special functions; Part 1. Riemannian-Hilbert problem, graduate student. The book starts isomonodromy method and special functions: Systems of linear with the basics of polytope theory. ordinary differential equations with rational coefficients. Schlegel and Gale diagrams are introduced as geometric tools Elements of the general theory; Monodromy theory and special to visualize polytopes in high dimension and to unearth functions; Inverse monodromy problem and Riemann-Hilbert bizarre phenomena in polytopes. The heart of the book is a factorization; Isomonodromy deformations. The Painleve treatment of the secondary polytope of a point configuration equations; The isomonodromy method; Backlund and its connections to the state polytope of the toric ideal transformations; Part 2. Asymptotics of the Pain/eve II defined by the configuration. These polytopes are relatively transcendent. A case study: Asymptotic solutions of the recent constructs with numerous connections to discrete second Painleve equation in the complex plane. Direct geometry, classical algebraic geometry, symplectic geometry, monodromy problem approach; Asymptotic solutions of the and combinatorics. The connections rely on Grabner bases of second Painleve equation in the complex plane. Inverse toric ideals and other methods from commutative algebra. monodromy problem approach; PII asymptotics on the The book is self-contained and does not require any canonical six-rays. The purely imaginary case; PII asymptotics background beyond basic linear algebra. With numerous on the canonical six-rays. Real-valued case; PII quasi-linear figures and exercises, it can be used as a textbook for courses Stokes phenomenon; Part 3. Asymptotics of the third Pain/eve on geometric, combinatorial, and computational aspects of the transcendent: PHI equation, an overview; Sine-Gordon theory of polytopes. reduction of PIII; Canonical four-rays. Real-valued solutions of SG-PIII; Canonical four-rays. Singular solutions of the SG-PIII; Contents: Abstract algebra: Groups, rings and fields; Convex Asymptotics in the complex plane of the SG-PIII transcendent; polytopes: Definitions and examples; Faces of polytopes; Proof of Theorem 3.4; The Birkhoff-Grothendieck theorem Schlegel diagrams; Gale diagrams; Bizarre polytopes; with a parameter; Bibliography; Subject index. Triangulations of point configurations; The secondary polytope; The permutahedron; Abstract algebra: Polynomial Mathematical Surveys and Monographs, Volume 128 rings; Grabner bases I; Grabner bases II; Initial complexes of August 2006, approximately 560 pages, Hardcover, ISBN-10: 0- toric ideals; State polytopes of toric ideals; Bibliography; 8218-3651-X, ISBN-13: 978-0-8218-3651-4, LC 2006042772, Index. 2000 Mathematics Subject Classification: 34M55, All AMS Student Mathematical Library, Volume 33 members US$87, List US$109, Order code SURV/ 128 July 2006, 143 pages, Softcover, ISBN-10: 0-8218-4140-8, ISBN- 13: 978-0-8218-4140-2, LC 2006042841, 2000 Mathematics Subject Classification: 52-01; 13-01, All AMS members US$23, List US$29, Order code STML/ 33

828 NOTICES OF THE AMS VOLUME 53, NUMBER 7 New Publications Offered by the AMS

Geometry and Topology Perspectives in c CRM R PROCEEDINGS & Riemannian M LECTIJRE NOTES Geometry ------CONTEMPORARY Recent Perspectives Vestislav Apostolov, ' MATHEMATICS Developments in in Riemannian Universite du Quebec ------Geometry a VestlslavApostolov Montreal, QC, Canada, Algebraic Topology Andrew Dancer Recent Developments NlgelHJtchtn McKenzie Wang Andrew Dancer and Nigel in Algebraic Topology Alejandro Adem, Jesus Editors Alejandro Adem Hitchin, Mathematical JesUs Gonz61ez Gonzalez, and Guillermo Guillermo Pastor Institute, Oxford, England, and Editors Pastor, Editors McKenzie Wang, McMaster This book is an excellent illustration University, Hamilton, ON, Canada, Editors ------of the versatility of Algebraic 1 ,. Amerloon Malhemat!C<11 Society Topology interacting with other areas Special geometries as well as the relation between curvature in Mathematics and Physics. Topics and topology have always been of interest to differential discussed in this volume range from classical Differential geometers. More recently, these topics have turned out to be Topology and Homotopy Theory (Kervaire invariant one of use in physical problems related to string theory as well. problem) to more recent lines of research such as Topological This volume provides a unique and thorough survey on the Quantum Field Theory (string theory). Likewise, alternative latest developments on Riemannian geometry, special viewpoints on classical problems in Global Analysis and geometrical structures on manifolds, and their interactions Dynamical Systems are developed (a spectral sequence with other fields such as mathematical physics, complex approach to normal form theory). analysis, and algebraic geometry. This collection of papers is based on talks at the conference This volume presents ten papers written by participants of the on the occasion of Sam Gitler's 70th birthday (December, "Short Program on Riemannian Geometry," a workshop held at 2003). The variety of topics covered in this book reflects the the CRM in Montreal in 2004. It will be a valuable reference for many areas where Sam Gitler's contributions have had an graduate students and research mathematicians alike. impact. Titles in this series are copublished with the Centre de Recherches Mathematiques. Contents: D. M. Davis, The mathematical work of Sam Gitler, 1960-2003; N. A. Baas, R. L. Cohen, and A. Ramirez, The Contents: M. T. Anderson, Topics in comformally compact topology of the category of open and closed strings; Einstein metrics; 0. Biquard, Cauchy-Riemann 3-manifolds and M. Bendersky and R. C. Churchill, A spectral sequence Einstein fillings; C. P. Boyer and K. Galicki, Sasakian geometry approach to normal forms; F. R. Cohen and I. johnson, On the and Einstein metrics on spheres; R. L. Bryant, Second order degree 2 map for a sphere; C. L. Douglas, On the fibrewise families of special Lagrangian 3-folds; A. Dancer and Poincare-Hopf theorem; T. de Fernex, E. Lupercio, T. Nevins, M. Y. Wang, Einstein equations, superpotentials and convex and B. Uribe, A localization principle for orbifold theories; polytopes; L. David and P. Gauduchon, The Bochner-flat D. juan-Pineda and I. j. Leary, On classifying spaces for the geometry of weighted projective spaces; K. Grove, Aspects of family of virtually cyclic subgroups; S. Kallel and P. Salvatore, comparison geometry; N. Hitchin, Low-dimensional Symmetric products of two dimensional complexes; K. Y. Lam geometry-A variational approach; C. LeBrun, Twistors, and D. Randall, Block bundle obstruction to Kervaire invariant holomorphic disks, and Riemann surfaces with boundary; one; P. Sankaran and P. Zvengrowski, Upper bounds for the A. Nabutovsky, Combinatorics of the spaces of Riemannian span of projective Stiefel manifolds; M. A. Xicotencatl, On 71. 2- structures and logic phenomena of Euclidean quantum gravity. equivariant loop spaces. CRM Proceedings & Lecture Notes, Volume 40 Contemporary Mathematics, Volume 407 july 2006, 248 pages, Softcover, ISBN-10: 0-8218-3852-0, ISBN- August 2006, 191 pages, Softcover, ISBN-10: 0-8218-3676-5, 13: 978-0-8218-3852-5, LC 2006042818, 2000 Mathematics ISBN-13 : 978-0-8218-3676-7, LC 2006044458, 2000 Subject Classification: 53Cxx, 53Bxx, 53C26; 53Dxx, 32Qxx, All Mathematics Subject Classification: 55-06, All AMS members AMS members US$68, List US$85, Order code CRMP/40 US$47, List US$ 59, Order code CONM/407

AUGUST 2006 NOTICES OF THE AMS 829 New AMS-Distributed Publications

Mathematical Physics New AMS-Distributed Publications Randomly Forced Nonlinear PDEs and Statistical Geometry and Topology Hydrodynamics in 2 Space Dimensions Sergei B. Kuksin, Heriot-Watt Lectures on Un iversity, Edinburgh, Scotland Algebraic Topology This book gives an account of recent Sergey V. Matveev, achievements in the mathematical Chelyabinsk State University, theory of two-dimensional turbulence, described by the 2D Navier-Stokes equation, perturbed by a random force. The Russia main results presented here were obtained during the last five Algebraic topology is the study of the to ten years and, up to now, have been available only in global properties of spaces by means papers in the primary literature. Their summary and synthesis of algebra. It is an important branch here, beginning with some preliminaries on partial differential of modern mathematics with a wide equations and stochastics, make this book a self-contained degree of applicability to other fields, account that will appeal to readers with a general background including geometric topology, in analysis. differential geometry, functional analysis, differential After laying the groundwork, the author goes on to recent equations, algebraic geometry, number theory, and theoretical results on ergodicity of random dynamical systems, which the physics. randomly forced Navier-Stokes equation defines in the This book provides an introduction to the basic concepts and function space of divergence-free vector fields, including a methods of algebraic topology for the beginner. It presents Central Limit Theorem. The physical meaning of these results elements of both homology theory and homotopy theory, and is discussed as well as their relations with the theory of includes various applications. attractors. Next, the author studies the behaviour of solutions when the viscosity goes to zero. In the final section these The author's intention is to rely on the geometric approach by dynamical methods are used to derive the so-called balance appealing to the reader's own intuition to help understanding. relations-the infinitely many algebraical relations satisfied by The numerous illustrations in the text also serve this purpose. the solutions. Two features make the text different from the standard literature: first, special attention is given to providing explicit Th is item will also be of interest to those working in differential algorithms for calculating the homology groups and for equations. manipulating the fundamental groups. Second, the book A publication of the European Mathematical Society (EMS). Distributed contains many exercises, all of which are supplied with hints within the Americas by the American Mathematical Society. or solutions. This makes the book suitable for both classroom Contents: Function spaces; The deterministic 2D Navier-Stokes use and for independent study. Equation; Random kick-forces; White-forced equations; A publication of the European Mathematical Society (EMS). Distributed Preliminaries from measure theory; Uniqueness of a stationary within the Americas by the American Mathematical Society. measure: kick-forces; Uniqueness of a stationary measure: Contents: Elements of homology theory; Elements of white-forces; Ergodicity and the strong law of large numbers; homotopy theory; Answers, hints, solutions; Bibliography; The martingale approximation and CLT; The Eulerian limit; Index. Balance relations for the white-forced NSE; Comments; Bibliography; Index. EMS Series of Lectures in Mathematics Zurich Lectures in Advanced Mathematics April 2006, 108 pages, Softcover, ISBN-10: 3-03719-023-X, ISBN-13 : 978-3-03719-0 23 -4, 2000 Mathematics Subject April 2006, 104 pages, Softcover, ISBN-10: 3-0 3719-021-3, Classification: 55 -01 , All AMS members US$27, List US$34, ISBN-13: 978-3-03719-021-0, 2000 Mathematics Subject Order code EMSSERLEC/3 Classification: 35Q30, 76F05, All AMS members US$27, List US$34, Order code EMSZLEC/3

830 NOTICES OF THE AMS VOLUME 53, N UMBER 7 AMERICAN MATHEMATICAL SOCIETY

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available: July 1, 2007. Deadline: Hard­ CALIFORNIA copy application materials and reference NEW YORK letters must be postmarked by November UNIVERSITY OF CALIFORNIA, SANTA D. E. SHAW & CO., L.P. 10, 2006. Applicants must submit hard CRUZ Quantitative Analyst copies of a Curriculum Vitae, a research Mathematics Department statement, a teaching statement, and four Quants at the D. E. Shaw group apply so­ The Mathematics Department at the Uni­ letters of recommendation (at least one let­ phisticated numerical techniques and write versity of California, Santa Cruz, expects ter must address teaching experience and software to develop and analyze statistical to have one tenure-track Assistant Pro­ ability). Letters of recommendation will models for our computerized financial trading strategies. Their work involves ex­ fessor position available in the area of be treated as confidential documents Mathematical Aspects of String Theory (in­ amining trading data to determine ways of (Please direct your letter writers to the increasing profitability, decreasing risk, cluding Gromov-Witten invariants and Mir­ UCSC Confidentiality Statement at ror symmetry); subject to availability of and lowering transaction costs. In addition, funding. Candidates in other areas of Math­ http://www2.ucsc.edu/ahr/policies/ quants research financial literature to iden­ ematical Physics may also be considered. confstm. htm). tify new trading ideas and create simula­ Appointees will be expected to teach, pur­ All applications should be sent to: Fac­ tions to test them. Quants with the D. E. ulty Recruitment Committee, Mathematics Shaw group have traditionally been the sue their research, and perform depart­ top students in their respective math, ment and university service. The teaching Department, University of California, 1156 physics, engineering, and computer sci­ load is four one-quarter courses per year. High Street, Santa Cruz, CA 95064. Please ence programs; a considerable number of We invite applications from qualified math­ refer to position #718-07 in your reply. In­ them have also competed successfully in ematicians. The campus is especially in­ quiries (not applications) can be sent to the United States and International Math terested in candidates who can contribute [email protected]. UCSC is an EEO/AA Olympiads as well as the Putnam Compe­ to the diversity and excellence of the aca­ tition. To apply, email your resume and a demic community through their research, employer. See http: I jwww . math. ucsc. edu /about/jobs. html for complete job cover letter to AMS-NMoseley@career. teaching, and/or service. Rank: Assistant des haw. com. EOE. description. Professor (9 month basis, step and salary 000239 commensurate with qualifications and ex­ 000241 perience). Minimum qualifications: Ph.D. or equivalent by 6/30/07 in Mathematics or Physics; demonstrated achievements or potential for excellence in research, teach­ ing, and professional service. Position

Suggested uses for classified advertising are positions available, books issue-August 28, 2006; December 2006 issue-September 28, 2006; January or lecture notes for sale, books being sought, exchange or rental of houses, 2007 issue-October 27, 2006; February 2007 issue-November 28, 2006. and typing services. U.S. laws prohibit discrinlination in employment on the basis of color, age, The 2006 rate is $100 per inch or fraction thereof on a single column (one­ sex, race, religion, or national origin. "Positions Available" advertisements inch minimum), calculated from top of headline. Any fractional text of 1/ 2 from institutions outside the U.S. cannot be published unless they are inch or more will be charged at the next inch rate. No discounts for multi­ accompanied by a statement that the institution does not discriminate on ple ads or the same ad in consecutive issues. For an additional $10 charge, these grounds whether or not it is subject to U.S. laws. Details and spe­ announcements can be placed anonymously. Correspondence will be cific wording may be found on page 1373 (vol. 44). forwarded. Situations wanted advertisements from involuntarily unemployed math­ Advertisements in the "Positions Available" classified section will be set ematicians are accepted under certain conditions for free publication. Call with a minimum one-line headline, consisting of the institution name above toll-free 800-321-4AMS (321-4267) in the U.S . and Canada or 401-455-4084 body copy, unless additional headline copy is specified by the advertiser. worldwide for further information. Headlines will be centered in boldface at no extra charge. Ads will appear Submission: Promotions Department, AMS, P.O. Box 6248, Providence, in the language in which they are submitted. Rhode Island 02940; or via fax: 401-331-3842; or send email to There are no member discounts for classified ads. Dictation over the cl assads@ams. or g. AMS location for express delivery packages is telephone will not be accepted for classified ads. 201 Charles Street, Providence, Rhode Island 20904. Advertisers will be Upcoming deadlines for classified advertising are as follows: September billed upon publication. 2006 issue-June 27, 2006, October 2006 issue-July 31, 2006; November 2006

832 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Classified Advertisements

and teaching in algorithmic discrete math­ CANADA ematics, especially discrete optimization and its application in the design of ultra­ UNIVERSITY OF BRITISH COLUMBIA complex chips and microprocessors. In Department of Mathematics this connection the Institute has a very University Faculty Awards (UFA) successful record of long-term cooperation with industry. The Mathematics Department at the Uni­ Applications are invited for the follow­ versity of British Columbia is seeking to ing posts: nominate at least one woman and/ or Abo­ W2-Chair of Discrete Mathematics: riginal candidate for an NSERC University The Research Institute seeks to appoint Faculty Award in the Fall2006 competition. an outstanding researcher and teacher in A departmental nominee will have a strong research record in a field that fits in with the field of algorithmic discrete mathe­ the research interests of the Department, matics and the applications of discrete as well as strong teaching qualifications. optimization. It is expected that the can­ didate has an active interest in applications A successful nominee would assume a tenure-track faculty position at the ap­ to chip design. propriate rank to begin July 1, 2007, with Junior (W1) Professorships in Discrete a reduced teaching load for the duration Mathematics: of the award. The University Faculty Award These posts are addressed to young re­ was created by the Natural Science and search scientists in the field of discrete op­ Engineering Research Council to encour­ timization and with an active interest in ap­ age Canadian universities to appoint very plications to chip design. promising women and/ or Aboriginal re­ Women with equivalent qualifications searchers to tenure-track positions in sci­ will, in accordance with the State Equal ence and engineering. Opportunities Law, be preferentially con­ Further information on the program can sidered. Handicapped applicants with be found at the NSERC web page: equivalent qualifications will be given pri­ http://www.nserc.ca/sf_e.asp?nav=sfn ority. av&lbi=c7. Further information on the above posts In accordance with the NSERC regula­ and the research interests of the Institute tions for the awards, an applicant must be are available from the Research Institute female and/ or Aboriginal and must be a for Discrete Mathematics, Tel. +49-228-73 Canadian citizen or a permanent resident 87 70, email: [email protected]. of Canada. An applicant must either hold Applications, together with a CV and a a doctorate degree, or have completed all list of publications, should be sent to the the requirements for such a degree by the following address by August 31, 2006: proposed appointment date. Applicants Rektorat der Rheinischen Friedrich­ are strongly encouraged to apply online as Wilhelms-Universitat, Regina-Pacis-Weg 3, described at: http: I jwww. math. ubc. 53113 Bonn, Germany. ca/Dept/jobs.htm#Apply. 000 242 Alternatively, applicants may send a cur­ rent CV including a list of publications, preprints, reprints, statement of research PUBLICATIONS AVAILABLE ---IIIRiii~ and teaching interests, and should arrange for three letters of recommendation to be NEW ADVANCED UNDERGRADUATE sent directly to: Chair, Departmental Com­ MATHEMATICS TEXT mittee on Appointments, Department of Mathematics, # 121-1984 Mathematics The self-published advanced undergradu­ Road, University of British Columbia, Van­ ate mathematics textbook "Introductory couver, BC, Canada, V6T 1Z2. Algebra, Topology, and Category Theory" Applications and supporting material, in­ may be ordered at http: I jwww. cluding letters of recommendation, must hyperon soft. com. It provides compre­ be received by September 8, 2006. hensive introductions to many basic top­ 000243 ics, and is ideal preparation for first year graduate school. It is also ideal for further education for various other students, and as a supplementary text as early as sopho­ GERMANY more year. 000240 RHEINISCHE FRIEDRICH-WILHELMS­ UNIVERSITAT BONN Research Institute for Discrete Mathematics The Research Institute for Discrete Math­ ematics wishes to make an appointment to a W2-Chair (tenured) as well as ap­ pointments to Junior (W1) Professorships in Discrete Mathematics. The Research In­ stitute is a central scientific institution of the University of Bonn. It pursues research

AUGUST 2006 NOTICES OF THE AMS 833 Meetings & Conferences oftheAMS

IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS SectionalMeetingprograms do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links totheabstractforeach talkcanbefoundon theAMSwebsite.See http: I /www. ams. org/meeti ngs/.Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting.

Special Sessions Salt Lake City, Utah Commutative Algebra (Code: SS 3A), Paul Roberts, Anurag University of Utah K. Singh, and Oana Veliche, University of Utah. Complex Geometry, Kaehler Groups, and Related Topics October 7-8,2006 (Code: SS 9A), Terrence Napier, Lehigh University, Mohan Saturday - Sunday Ramachandran, State University of New York at Buffalo, and Domingo Toledo, University of Utah. Meeting #1 019 Western Section Floer Methods in Low-dimensional Topology (Code: SS 8A), Associate secretary: Michel L. Lapidus Alexander Felshtyn and Uwe Kaiser, Boise State Univer­ Announcement issue of Notices: August 2006 sity. Program first available on AMS website: August 24, 2006 Harmonic Analysis: Trends and Perspectives (Code: SS lA), Program issue of electronic Notices: October 2006 Alex Iosevich, University of Missouri, and Michael T. Issue of Abstracts: Volume 27, Issue 3 Lacey, Georgia Institute of Technology. Deadlines Interface of Stochastic Partial Differential Equations and Gaussian Analysis (Code: SS 7A), Davar Khoshnevisan, Uni­ For organizers: Expired versity of Utah, and Eulalia Nualart, University of Paris XIII. For consideration of contributed papers in Special Sessions: Expired Low Dimensional Topology and Geometry (Code: SS 4A), For abstracts: August 15, 2006 Mladen Bestvina and Kenneth W. Bromberg, University of Utah. Invited Addresses Mathematics Motivated by Physics (Code: SS SA), Aaron J. William Arveson, University of California Berkeley, Title Bertram, Yuan-Pin Lee, and Eric R. Sharpe, University of to be announced. Utah. Alexei Borodin, California Institute of Technology, Title Multi-variable Operator Theory (Code: SS 13A), William B. to be announced. Arveson, University of California Berkeley, Scott A. Mc­ Izabella Joanna Laba, University of British Columbia, Title Cullough, University of Florida, and Geoffrey L. Price, US to be announced. Naval Academy. Darren Long, University of California Santa Barbara, Title Noncommutative Dynamical Systems (Code: SS 12A), to be announced. William B. Arveson, University of California Berkeley,

834 NOTICES OF THE AMS VOLUME 53 NUMBER 7 Meetings & Conferences

Scott A. McCullough, University of Florida, and Geoffrey able only at the meeting. Complimentary coffee will be L. Price, US Naval Academy. served courtesy of AMS Membership Services. Nonconvex Variational Problems: Recent Advances and Ap­ AMS Editorial Activity: An acquisitions editor from plications (Code: SS lOA), Marian Bocea, North Dakota the AMS book program will be present to speak with State University and University of Utah, and Andrej prospective authors. If you have a book project that you Cherkaev, University of Utah. would like to discuss with the AMS, please stop by the book exhibit. Nonlinear Differential Equations: Methods and Applica­ tions (Code: SS 2A), David G. Costa, University of Nevada, Parking and Zhi-Qiang Wang, Utah State University. Parking restrictions are not enforced on weekends (except Number Theory (Code: SS 14A), jasbir Singh Cllahal, in the obvious do not park zones and special reserved Brigham Young University, and Machiel van Frankenhui­ spots) and participants can park in any of the posted lots jsen, Utah Valley State College. free of charge. (See map at http: I lwww. map. utah. edul). Random Motion in Random Media (Code: SS llA), Firas Ras­ soul-Agha, University of Utah, and Tom Schmitz, Swiss Fed­ Registration and Meeting Information eral Institute of Technology (ETH), Zurich. The registration desk will be located in the Leroy Cowles Building, and will be open 8:00a.m. to 4:30p.m. on Sat­ Theory and Applications of Infinite Dimensional Dynami­ urday, and 8:00 a.m. to noon on Sunday. Talks will take cal Systems (Code: SS 6A), Peter W. Bates, Michigan State place in the following buildings: Leroy Cowles Building University, and Kening Lu, Brigham Young University. (LCB), Alfred Emery Building (AEB), James Widtsoe Build­ Accommodations ing (JWB), and the James Fletcher Building (JFB). Registration fees: (payable on-site only) US$401AMS When making a reservation, participants should state that members; US$60inonmembers; US$5Iemeritus members, they are with the American Mathematical Society (AMS) students, or unemployed mathematicians. Fees are payable Meeting at the University of Utah group. Rates quoted by cash, check, VISA, Mastercard, Discover, or American do not include tax of 12.46%. Cancellation and early Express. checkout policies vary; be sure to check when you make your reservation. The AMS is not responsible for rate Travel changes or for the quality of the accommodations. By Air: The Salt Lake City International Airport is served ChaseSuites, 765 East 400 South, Salt Lake City, 801- by most major airlines and is located ten minutes from 532-5511; for information email: j cl ark@woodfi nsui tes. downtown Salt Lake City. Taxi fare is approximately com; US$ 7 4 single or double. Deadline for reservations is US$20-US$25. September 6, 2006. Be sure to check cancellation and Driving: From the Salt Lake City International Airport: early checkout policies. Take I-80 East approximately 1.5 miles to the North Tem­ Hilton, 255 South West Temple, SaltLake City; 801-328- ple exit. Follow North Temple approximately 3 miles to 2000 or 877-776-4936 toll-free; US$103 single or double. State Street (one block beyond the Mormon Temple). Turn Deadline for reservations is September 22, 2006. Be sure right on State Street and go south three blocks to 200 South. to check cancellation and early checkout policies. Turn left proceeding east on 200 South for approximately University Guest House 110 South Fort Douglas Blvd., 2 miles until you reach University Street (1400 East). Salt Lake City; 801-587-1000 or 888-416-4075 toll-free; From I-15 Northbound: Take the eastbound 600 South i nfo@guesthouse. utah. edu; or http: I lwww . exit. At State Street turn left proceeding 4 blocks north until guesthouse. utah. edu; US$72 single or double. Dead­ you reach 200 South. Turn right proceeding east on 200 line for reservations is September 22, 2006. Be sure to South for approximately 2 miles until you reach Univer­ check cancellation and early checkout policies. sity Street (1400 East). From I-15 Southbound: Take the eastbound 600 South Food Service exit. At 300 West turn right proceeding approximately 1.5 There are a number of restaurants adjacent to the cam­ miles south until you reach 200 South. Turn left pro­ pus. A list of restaurants will be available at the registra­ ceeding east on 200 South for approximately 2 miles until tion desk. you reach University Street (1400 East). Once you get to University Street you will be facing Local Information "President's Circle". This is a one-way street that you enter Please visit the website maintained by the Department of on the south. Drive of the way around the circle to the Math­ Mathematics at http: I lwww. math. utah. edu, the Uni­ ematics Complex. versity of Utah website http: I lwww. utah. edu, or Salt Car rental: Special rates have been negotiated with Avis Lake Convention and Visitors Bureau site at Rent A Car for the period September 30-0ctober 15, 2006, http:llwww.visitsaltlake.com. and begin at US$24.99Iday (weekend rate). All rates include unlimited free mileage; the weekend rates quoted are avail­ Other Activities able from noon Thursday until Monday at 11:59 p.m. Rates Book Sales: Examine the newest titles from the AMS! Many do not include state or local surcharges, tax, optional cov­ of the AMS books will be available at special discounts avail- erages, or gas refueling charges. Renter must meet Avis'

AUGUST 2006 NOTICES OF THE AMS 835 Meetings & Conferences age, driver, and credit requirements. Make reservations by calling 800-331-1600 or online at www.avis.com. Non­ Cincinnati, Ohio weekend and weekly rates are also available. Please quote Avis Discount Number B159266 when making reserva­ University of Cincinnati tions October 21-22, 2006 Information for International Participants Saturday - Sunday Visa regulations are continually changing for travel to Meeting #1 020 the United States. Visa applications may take from three to four months to process and require a personal inter­ Central Section view, as well as specific personal information. Interna­ Associate secretary: Susan ]. Friedlander tional participants should view the important informa­ Announcement issue of Notices: August 2006 tion about traveling to the U.S. found at http: I /www7. Program first available onAMS website: September 7, 2006 nationalacademies.org/visas/Traveling_to_US. Program issue of electronic Notices: October 2006 html and http: I It ravel . state. gov /visa/index. html. Issue of Abstracts: Volume 27, Issue 3 If you need a preliminary conference invitation in order Deadlines to secure a visa, please send your request to dl s@ams. org. For organizers: Expired If you discover you do need a visa, the National Acad­ For consideration of contributed papers in Special Sessions: emies website (see above) provides these tips for suc­ Expired cessful visa applications: For abstracts: August 29, 2006 '' Visa applicants are expected to provide evidence that they are intending to return to their country of residence. Invited Addresses Therefore, applicants should provide proof of "binding" or sufficient ties to their home country or permanent res­ Suncica Canic, University of Houston, Title to be an­ idence abroad. This may include documentation of the fol­ nounced. lowing: Bryna R. Kra, Northwestern University, Title to be an­ • family ties in home country or country of legal per- nounced. manent residence Ezra N. Miller, University of Minnesota, Title to be an­ • property ownership nounced. • bank accounts Jon G. Wolfson, Michigan State University, Title to be an­ • employment contract or statement from employer stat­ nounced. ing that the position will continue when the employee re­ turns; Special Sessions '' Visa applications are more likely to be successful if done in a visitor's home country than in a third country; Algebraic Coding Theory-Honoring the Retirement of '' Applicants should present their entire trip itinerary, Vera Pless (Code: SS 8A), William Cary Huffman, Loyola including travel to any countries other than the United University, and Jon-Lark Kim, University of Louisville. States, at the time of their visa application; Analysis and Potential Theory on Metric Spaces (Code: SS '' Include a letter of invitation from the meeting orga­ 4A), Thomas Bieske, University of South Florida, and Zair nizer or the U.S. host, specifying the subject, location, and Ibragimov and Nageswari Shanmugalingam, University dates of the activity, and how travel and local expenses will of Cincinnati. be covered; Applied Algebraic Geometry and Cryptography (Code: SS ,., If travel plans will depend on early approval of the visa 3A), Jintai Ding, Jason Eric Gower, and Timothy]. Hodges, application, specify this at the time of the application; University of Cincinnati, Lei Hu, Chinese Academy of Sci­ ,., Provide proof of professional scientific and/or edu­ ences, and Dieter S. Schmidt, University of Cincinnati. cational status (students should provide a university tran­ Birational Geometry(Code: SS 2A), Mirel Constantin Caibar script). and Gary P. Kennedy, Ohio State University. This list is not to be considered complete. Please visit Boundary Value Problems for Differential Equations with the websites above for the most up-to-date information. Applications (Code: SS 11A), Xiaojie Hou, Philip L. Korman, Weather and Bingyu Zhang, University of Cincinnati. Temperatures vary from 70°F to 50°F in October. Fall is Ergodic Theory(Code: SS 1A), Nikos Frantzikinakis, Penn­ the favorite season of many who visit and live in Utah. Vi­ sylvania State University, Bryna R. Kra, Northwestern Uni­ brant colors splash across the mountains and canyons as versity, and Mate Wierdl, University of Memphis. the cooler temperatures turn the leaves all shades of gold, Financial and Actuarial Mathematics (Code: SS 12A), purple, red, green, and brown. For up- to-date forecasts visit Srdjan D. Stojanovic and Ning Zhong, University of Cincin­ http://www.visitsaltlake.com. nati.

836 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

Geometric Combinatorics (Code: SS 6A), Ezra N. Miller, local Information University of Minnesota, and Igor Pak, Massachusetts In­ Please visit the websites maintained by the Department of stitute of Technology. Mathematical Sciences, http: I /math. uc. edu/; the Uni­ Limit Theorems ofProbability Theory(Code: SS 9A), Wlodz­ versity of Cincinnati, http: I jwww. uc . edu; and for a cam­ imierz Bryc and Magda Peligrad, University of Cincin­ pusmap:http://www.uc.edu/architect/documents/ nati. Logistics/logisticsbw.pdf. Mathematical Modeling of Biological Systems (Code: SS Other Activities lSA), Edward W. Swim, Air Force Institute of Technology, AMS Book Sale: Examine the newest titles from AMS! Com­ and Richard Schugart, Ohio State University. plimentary coffee will be served, courtesy of AMS Mem­ Nonlinear Functional Analysis and Applications (Code: SS bership Services. The AMS Book Sale will operate during SA), S. P. Singh and Bruce Watson, Memorial University the same hours as registration. The Book Sale is in Room of Newfoundland. 736, Old Chemistry Building on West Campus. This atrium Nonlinear Partial Differential and Its Applications (Code: is also known as the Max Kade German Cultural Center. SS 7A), Changyou Wang, University of Kentucky, and Guan AMS Editorial Activity: An acquisitions editor from the AMS Book program will be present to speak with Bo, Ohio State University. prospective authors. If you have a book project that you Optimal Controls and Stochastic Differential Games (Code: would like to discuss with the AMS please stop by the book SS 14A), Michael J. McAsey and Libin Mou, Bradley Uni­ exhibit. versity. Physical Knotting and Linking (Code: SS 13A), Eric J. Raw­ Parking don, University of St. Thomas, Kenneth C. Millett, Uni­ Parking on campus is US$6 per day on Saturdays and Sun­ versity of California Santa Barbara, and Jonathan Simon, days. The Clifton Court Garage is the most convenient park­ University of Iowa. ing for the meeting. Please visit http: I /www. uc. edu/ parking/visit. htm for more details on parking. Recent Results on Operator Algebras (Code: SS lOA), Her­ bert Halpern, Gary Weiss, Cos tel Peligrad, Shuang Zhang, Registration and Meeting Information and Victor G. Kaftal, University of Cincinnati. The registration desk will be open 7:30 a.m. to 4:00 p.m. on Saturday, and 8:00 a.m. to noon on Sunday in Room 736, Accommodations Old Chemistry Building on West Campus. This atrium is Participants should make their own arrangements directly also known as the Max Kade German Cultural Center. with the hotel of their choice and state that they will be at­ Talks will take place in Swift and Braunstein Halls. tending the AMS meeting and use group code AMSAMSA. Registration fees: (payable on-site only) US$40/AMS The AMS is not responsible for rate changes or for the qual­ members; US$60/nonrnembers; US$5/emeritus members, ity of the accommodations. Rates quoted do not include students, or unemployed mathematicians. Fees are payable taxes of 17.5%. Hotels have varying cancellation or early by cash, check, VISA, Mastercard, Discover, or American checkout penalties; be sure to ask for details when mak­ Express. ing your reservation. Kingsgate Marriott Conference Hotel (located on UC's Social Event Campus); 151 Goodman Drive, Cincinnati, Ohio 45219; The Department of Mathematical Sciences will host a re­ 513-487-3800, Toll-Free: 888-720-1299, Fax: 513-487-3810; ception for all conference participants Saturday evening, US$109/night, US$12/night parking (US$15/night for valet October 21, 2006, from 6:30p.m. to 8:30p.m., at Mick & parking). For more information please visit http: I I Mack's, located on the third level of TUC (Tangeman Uni­ marriott.com/property/propertypage/CVGKG. Dead­ versity Center). line for reservations is September 21, 2006. Travel Vernon Manor Hotel 400 Oak Street, Cincinnati, OH By air: The Cincinnati/Northern Kentucky International 45219; email: reservati ons@vernonmanorhotel. com; Airport (CVG) is served by most major airlines and is lo­ Tel: 513-281-3300, Toll Free: 800-543-3999, Fax: 513-281- cated approximately 15 miles from the campus. For more 8933; US$99, complimentary parking in a secured lot (com­ information please visit http: I /www. cvgai rport. com. plimentary valet parking 7 a.m.-11:00 p.m.). The hotel is By Car: Most persons driving to the campus will come located a short distance from UC Campus and offers shut­ by way of one of the routes below. Should you be corning tle service to surrounding areas. For more information by a different route please check MapQuest. please visit http: I /www. vernon-manor. com/index. html. From the north or south via 1-75: From I-75, take the Deadline for reservations is September 21, 2006. Hopple Street exit (exit 3). (If you are traveling north, Hop­ ple Street exits from the left lane). Turn left off the exit Food Service on to Hopple Street. As you cross the first intersection (Cen­ A list of restaurants will be available at the registration tral Parkway), Hopple Street becomes Martin Luther King desk. Drive. Follow Martin Luther King Drive up the hill to Clifton

AUGUST 2006 NOTICES OF THE AMS 837 Meetings & Conferences

Avenue. To West Campus: ML King Drive borders the by calling 800-331-1600 or online at http: I jwww. avis. north edge of the West Campus. Clifton Avenue borders com. Meeting Avis Discount Number Bl59266. the west edge of the West Campus. To East Campus (Med­ ical Center): To get to the East Campus, follow King to Vine Weather Street. Turn left onto Vine, then turn right at Goodman Av­ Weather in Greater Cincinnati is moderate with tempera­ enue. tures averaging 3JOF in winter, and 76°F in summer. The From the west via 1-74: Take I-74 east to I-75 south. Take annual average temperature is 54°F; average annual rain­ the Hopple Street exit (Exit 3). Turn left off the exit on to fall is 40 inches- averaging 11.7 inches in the summer Hopple Street. As you cross the first intersection (Central months. For current and future weather conditions in Parkway), Hopple Street becomes Martin Luther King Drive. Cincinnati please visit http: jwww. wunde rg round. com/ Follow Martin Luther King Drive up the hill to Clifton Av­ I enue. To West Campus: ML King Drive King borders the US/OH/Cincinnati .html. north edge of West Campus. Clifton Avenue borders the west edge of West Campus. To East Campus (Medical Center): To get to the East campus, follow King to Vine Storrs, Connecticut Street. Turn left onto Vine, then turn right at Goodman Av­ enue. University of Connecticut From the north via 1-71 From I-71 south, take the Taft Road exit (exit 3). The exit places you on Taft Road, a one­ October28-29,2006 way street heading west. Taft Road becomes Calhoun Saturday - Sunday Street as you near campus. To East Campus (Medical Cen­ ter): Turn right on Jefferson Avenue. Follow Jefferson until Meeting#l021 it crosses Martin Luther King Drive. At MLK Drive, Jeffer­ Eastern Section son Avenue becomes Vine Street. From Vine, turn right on Associate secretary: Lesley M. Sibner Goodman Avenue. To West Campus; Stay on Calhoun Announcement issue of Notices: August 2006 until it ends at Clifton Avenue. Turn right on Clifton Av­ Program first available on AMS website: September 14, enue. 2006 From the south via 1-71: Take I-71 north until it merges Program issue of electronic Notices: October 2006 with I-75 just south of Florence, Ky. Stay on I-75 after you Issue of Abstracts: Volume 27, Issue 4 cross the Ohio River. From the left lane on I-75, take the Hopple Street exit (Exit 3). Turn left off the exit on to Hop­ Deadlines ple Street. As you cross the first intersection (Central Park­ way), Hopple Street becomes Martin Luther King Drive. Fol­ For organizers: Expired low Martin Luther King Drive up the hill to Clifton Avenue. For consideration of contributed papers in Special Sessions: To West Campus: ML King Drive borders the north edge Expired of the West Campus. Clifton Avenue borders the west For abstracts: September 6, 2006 edge of the West Campus. To East Campus (Medical Cen­ ter): To get to the East Campus, follow King to Vine Street. Invited Addresses Turn left onto Vine, then turn right at Goodman Avenue. Changfeng Gui, University of Connecticut, Storrs, Title to From the east via US 50: From US 50 west, turn right be announced. on Taft Road. Taft is a one-way street heading west. Taft becomes Calhoun Street as you near campus. To West Niranjan Ramachandran, University of Maryland, College Campus: Stay on Calhoun until it ends at Clifton Avenue. Park, Zeta! Turn right on Clifton Avenue. To East Campus (Medical Karman Soundararajan, University of Michigan, Title to be Center): Turn right on Jefferson Avenue. Follow Jefferson announced. until it crosses Martin Luther King Drive. At ML King Drive, Katrin Wehrheim, Massachusetts Institute of Technology, Jefferson Avenue becomes Vine Street. From Vine, turn Floer theories in symplectic topology and gauge theory. right on Goodman Avenue. Car Rental: Avis is the official car rental company for Special Sessions the sectional meeting in Cincinnati, Ohio. All rates include unlimited free mileage. Weekend daily rates are available Algebraic Geometry and Moduli Spaces (Code: SS 12A), from noon Thursday-Monday at 11:59 p.m and start at Dan Abramovich, Brown University, and Ralph M. Kauf­ US$24.99 per day. Rates for this meeting are effective Oc­ mann, University of Connecticut, Storrs. tober 14, 2006-0ctober 29, 2006. Should a lower qualify­ Algebraic and Analytic Combinatorics (Code: SS 11A), ing rate become available at the time of booking, Avis is Richard Ehrenberg and Margaret A. Readdy, University pleased to offer a 5% discount off the lower qualifying rate of Kentucky and MIT. or the meeting rate, whichever is lowest. Rates do not in­ clude any state or local surcharges, tax, optional coverages Analysis and Probability on Fractals (Code: SS 3A), Robert or gas refueling charges. Renters must meet Avis' age, S. Strichartz, Cornell University, and Alexander Teplyaev, driver, and credit requirements. Reservations can be made University of Connecticut, Storrs.

838 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

Combinatorial Methods in Equivariant Topology (Code: SS AMS Sectional meeting has been reduced to US$5. Dead­ lA), Tara Holm, University of Connecticut, Storrs, and line for reservations is September 27, 2006. There are a Tom C. Braden, University of Massachusetts, Amherst. number of restaurants within walking distance. Be sure to Computability Theory in Honor of Manuel Lerman's Re­ check cancellation and early checkout policies. tirement (Code: SS 4A), Joseph S. Miller and David Reed The Best Western Regent Inn, 123 Storrs Road (Route Solomon, University of Connecticut, Storrs. 195) Mansfield Center, Connecticut 06250; phone: 860-423- Geometric Analysis (Code: SS 9A), Jesse Ratzkin, Univer­ 8451, fax: 860-423-8451; approximately six (6) miles sity of Connecticut, and Rob Kusner, University of Mass­ from the university campus; US$86.80/single/double. achusetts. Complimentary continental breakfast, high speed Internet Geometric Structures Related to Quantum Field Theory access, indoor pool, exercise facility, and free parking. (Code: SS 14A), Roman Fedorov and Ivan Mirkovic, Uni­ Deadline for reservations is September 27, 2006. There versity of Massachusetts, Amherst. are a number of restaurants within walking distance: Harmonic Analysis and Integral Geometry (Code: SS 7A), McDonald's, Applebee's restaurant, Angelino's Italian William 0. Bray, University of Maine, and Wolodymyr R. restaurant. Be sure to check cancellation and early check­ Madych, University of Connecticut, Storrs. out policies. For other accommodations check out the UConn visi­ Homotopy Theory of Compactified Moduli Spaces (Code: SS lSA), Thomas J. Lada, North Carrolina State University, and tor site: http: I /visitors. uconn. edu/accommos. htm. Jim Stasheff, University of North Carolina, Chapel Hill. Food Service Nonlinear Elliptic and Parabolic Equations (Code: SS SA), There is a food court in the Student Union which is located Yung-Sze Choi, Changfeng Gui, and Joseph McKenna, about one hundred meters from the meeting areas. It is University of Connecticut, Storrs. suitable for lunch, but groups of people should make NonlinearGeometricPDEs(Code: SS lOA), WenxiongChen, reservations at area restaurants for Friday and Saturday Yeshiva University, and Zheng-Chao Han, Rutgers Uni­ nights. Those are normally the most crowded nights of the versity. week, especially at this time of the year. Number Theory (Code: SS 2A), Keith Conrad, University There are a number of restaurants within walking of Connecticut, Storrs, David Pollack, Wesleyan University, distance of campus. See http: I /visitors. uconn. edu/ and Thomas A. Weston, University of Massachusetts, dining. htm. Amherst. Teichmuller Theory and Hyperbolic Geometry (Code: SS Local Information 13A), Martin Bridgeman, Boston College, Jeffrey F. Brock, The university's website is http: I /www. uconn. edu/; the Brown University, Linda Keen, Lehman College, CUNY, Department of Mathematics is at http: I /www. math. and Kasra Rafi, University of Connecticut, Storrs. uconn. edu/contact/contact. php. A general website Topology and Computing (Code: SS 6A), Thomas J. Pe­ about visiting Storrs and the University of Connecticut area ters, University of Connecticut, Storrs. ~http://visitors.uconn.edu/visiting.htm. Undergraduate Mathematics Education (Code: SS 8A), Tom Also see the link maintained by the local organizers at: Roby, University of Connecticut, Storrs. http: I /www. math. uconn. edu/ AMSmeeti ng, featuring links to lists of restaurants, transportation, etc. Accommodations Participants should make their own arrangements directly Other Activities with a hotel of their choice as early as possible. Special rates Book Sale: Examine the newest titles from the AMS! Many have been negotiated with the hotels listed below. Rates of the AMS books will be available at a special 50% discount quoted do not include the sales and tourist tax of 12%. The available only at the meeting. Complimentary coffee will AMS is not responsible for rate changes or for the quality be served courtesy of AMS Membership Services. of the accommodations. When making a reservation, par­ AMS Editorial Activity: An acquisitions editor from ticipants should state that they are with the American the AMS book program will be present to speak with Mathematical Society (AMS) Meeting at the University of prospective authors. If you have a book project that you Connecticut. Cancellation and early checkout policies would like to discuss with the AMS, please stop by the book vary; be sure to check when you make your reservation. This is prime tourist season in New England and exhibit. participants are encouraged to book a hotel room early Parking as rooms may sell out. The Nathan Hale Inn and Conference Center, 855 Unless otherwise indicated, parking in university lots is free Bolton Road, Storrs, CT 06268; phone: 860-427-7888, fax: and unrestricted starting in the late afternoon on Friday, 860-427-7850; on the university campus; US$99/ overnight, and on weekends. There is a modest-cost park­ single/double. Amenities include a full service restaurant ing structure across the street from the Business School. and lounge on the premises, Internet access, fitness cen­ There is a US$5 parking fee for those staying at the Nathan ter, indoor heated pool and spa. The parking fee for the Hale Inn when they use the Inn's lot.

AUGUST 2006 NOTICES OF THE AMS 839 Meetings & Conferences

Registration and Meeting Information • Always affordable-Realize up to 50% savings on every­ The meeting is on the campus of the University of day fares in the contiguous 48 states Connecticut, Storrs. Meeting registration and the Invited • Lower change fees-reduced from US$100 to US$ 50 to Addresses will take place in the Information Technologies change travel plans Engineering (ITE) Building. Sessions will be held in the • Just eight fares-less guessing and easier planning Business (BUSN) School building. See the map at http: I I To make immediate reservations call Delta Air Lines at visitors.uconn.edu/mapsdirs.htm. 1-800-221-1212. Be sure to reference US738367060 or The registration desk will be in the foyer of the ITE visit http: I /www. delta. com and enter SkyBonus account building and will be open Saturday, October 28, 7:30 a.m. number US738367060 in your passenger information to 4:00 p.m., and Sunday, October 29, 8:00 a.m. to noon. screen to be recognized as a participant. Your benefits Fees are US$40 for AMS or CMS members, US$60 for non­ include: members; and US$5 for students, unemployed mathe­ • No service fees maticians, and emeritus members. Fees are payable on site • 1,000 sky miles for Delta members by cash, check, or credit card. • Skip the airport lines; check in online Car Rental: Avis is the official car rental company for Social Event the sectional meeting in Storrs, Connecticut. All rates in­ The University of Connecticut, Storrs, Mathematics De­ clude unlimited free mileage. Weekend daily rates are partment will host a reception for participants. It will be available from noon Thursday-Monday at 11:59 p.m. and held at the Nathan Hale Inn on Saturday from 5:30 p.m. start at US$35.99 per day. Rates for this meeting are ef­ to 7 p.m. Appetizers will be served and there will be a cash fective October 21, 2006-November 5, 2006. Should a bar. The AMS thanks the university and the Department lower qualifying rate become available at the time of book­ of Mathematics for its generous hospitality. ing, Avis is pleased to offer a 5% discount off the lower qualifying rate or the meeting rate, whichever is lowest. Travel and Campus Map Rates do not include any state or local surcharges, tax, op­ The University of Connecticut, Storrs Campus, is located tional coverages, or gas refueling charges. Renters must 40 minutes from Hartford in tranquil Northeastern Con­ meet Avis' age, driver, and credit requirements. Reserva­ necticut. tions can be made by calling 1-800-331-1600 or online at Getting to the University by Car: Driving directions and http: I /www. avis. com. Meeting Avis Discount Number campus maps can be found at the following link B159265. http://visitors.uconn.edu/mapsdirs.htm. Information for International Participants: Visa The UConn visitor center page (http: I /visitors. regulations are continually changing for travel to the uconn. edu/) contains many useful links including maps, United States. Visa applications may take from three to directions, accommodations, (mostly fast food) restau­ four months to process and require a personal interview, rants, etc. The accommodations list includes some rea­ as well as specific personal information. International sonably priced hotels in Vernon, CT, about twenty minutes participants should view the important information from the campus. There are downloadable maps of the about traveling to the U.S. found at http: I /www7. campus and parking, along with driving directions to the nationalacademies.org/visas/Traveling_to_US. campusathttp://www.uconn.edu/campuses/storrs. html and http: I /travel . state. gov /visa/index. html. php. If you need a preliminary conference invitation in order There is bus service, provided by Bonanza, from Boston, to secure a visa, please send your request to dl s@ams . o rg. Providence, and Hartford. Public transportation between If you discover you do need a visa, the National Acad­ the airport and the campus is either by taxi or a bus to emies website (see above) provides these tips for suc­ Hartford and then another to Storrs. The bus stops at the cessful visa applications: Student Union (see http: I /www. bonanzabus. com or *Visa applicants are expected to provide evidence that the links from the above-mentioned departmental infor­ they are intending to return to their country of residence. mation site). Therefore, applicants should provide proof of "binding" The nearest airport is Bradley (BDL) serving the Hart­ or sufficient ties to their home country or permanent ford-Springfield area. It is about 30 miles away. From residence abroad. This may include documentation of the Bradley International Airport, Windsor Locks, CT, to the following: University of Connecticut, Storrs, the estimated driving time • family ties in home country or country of legal perma- is an hour or less. The airport's home page is located at: nent residence http://www.bradleyairport.com/home/home.php.At • property ownership the time that this is published, the one-way taxi fare from • bank accounts Bradley Airport is US$ 72 to anywhere in Storrs. • employment contract or statement from employer stat­ The official airline for the meeting is Delta Airlines. ing that the position will continue when the employee Take advantage of Delta's new SimpliFares™ and enjoy the returns; following benefits: '' Visa applications are more likely to be successful if • No Saturday-night stay required-more flexibility done in a visitor's home country than in a third country;

840 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

1' Applicants should present their entire trip itinerary, Andras Vasy, Massachusetts Institute of Technology, Scat­ including travel to any countries other than the United tering theory on symmetric spaces and N-body scattering. States, at the time of their visa application; Special Sessions 1' Include a letter of invitation from the meeting orga­ nizer or the U.S. host, specifying the subject, location, and Algebraic Combinatorics (Code: SS 6A), Marcelo Aguiar, dates of the activity, and how travel and local expenses will University of Texas A&M, and Claudia Malvenuto, Uni­ be covered; versity of Rome "La Sapienza". ,., If travel plans will depend on early approval of the visa Analytic Number Theory and Modular Forms (Code: SS application, specify this at the time of the application; 2A), Matthew Boylan and Gang Yu, University of South Car­ '' Provide proof of professional scientific and/or olina. educational status (students should provide a university transcript). Boundary Operators in Real and Complex Domains (Code: This list is not to be considered complete. Please visit SS 3A), Loredana Lanzani, University of Arkansas, Fayet­ the websites above for the most up-to-date information. teville, and David E. Barrett, University of Michigan, Ann Arbor. Weather Combinatorial Representation Theory (Code: SS SA), Arun In this region of Connecticut, the averages for the month Ram, University of Wisconsin-Madison, and Frank Sottile, of October are a high of 64°F and a low of 41 °F. Precipi­ University of Texas A&M. tation in October averages 3.5 inches and snow is not ex­ Dirac Operators in Analysis and Geometry (Code: SS lA), pected (but you never know!). John Ryan, University of Arkansas, Marius Mitrea, Uni­ New England weather varies considerably. It would be versity of Missouri, and Mircea Martin, Baker University. wise to consult the weather forecast on the Web (e.g. Evolution Equations in Physics and Mechanics (Code: SS 4A), http: jwww. weather. com) for Storrs, CT, just before I John P. Albert, University of Oklahoma, Jerry L. Bona, Uni­ coming to the meeting. versity of Illinois at Chicago, and Jiahong Wu, Oklahoma State University. Extremal and Probabilistic Combinatorics (Code: SS 9A), Jer­ Fayetteville, rold R. Griggs, University of South Carolina, and Peter Keevash, California Institute of Technology. Arkansas Progress on Problems in Mathematical Fluid Dynamics University of Arkansas (Code: SS SA), Ning Ju and Jiahong Wu, Oklahoma State University. November 3-4, 2006 Scattering Theory and Wave Propagation (Code: SS 7A), Friday - Saturday Tanya ]. Christiansen, University of Missouri, Columbia, and Andras Vasy, Stanford University. Meeting #1 022 Subelliptic PDEs and Sub-Reimannian Geometry (Code: SS Southeastern Section lOA), Luca Capogna, University of Arkansas, Scott Pauls, Associate secretary: Matthew Miller Dartmouth College, and Jeremy T. Tyson, University of Announcement issue of Notices: September 2006 Illinois, Urbana-Champaign. Program first available on AMS website: September 21, 2006 Program issue of electronic Notices: November 2006 Issue of Abstracts: Volume 27, Issue 4 New Orleans, Deadlines Louisiana For organizers: Expired New Orleans Marriott and Sheraton New For consideration of contributed papers in Special Sessions: July 18, 2006 Orleans Hotel For abstracts: September 12, 2006 january 5-8, 2007 Invited Addresses Friday - Monday R. P. Anstee, UBC, Vancouver, Canada, Forbidden config­ Meeting #1 023 urations, a survey. ]oint Mathematics Meetings, including the 113th Annual Arun Ram, University of Wisconsin, Space walks: Combi­ Meeting of the AMS, 90th Annual Meeting of the Mathe­ natorics, representations, spherical functions, and matical Association ofAmerica (MAA), annual meetings of p-compact groups. the Association for Women in Mathematics (A WM) and the Donald G. Saari, University of California Irvine, Mathematics National Association of Mathematicians (NAM), and the of voting. winter meeting of the Association for Symbolic Logic (ASL),

AUGUST 2006 NOTICES OF THE AMS 841 Meetings & Conferences with sessions contributed by the Society for Industrial and Commutative Algebra and Algebraic Geometry (Code: SS Applied Mathematics (SIAM). SA), Paul C. Roberts, Anurag K. Singh, and Oana Veliche, Associate secretary: Susan]. Friedlander University of Utah. Announcement issue of Notices: October 2006 Continuous and Discrete Integrable Systems and Their Ap­ Program first available on AMS website: November 1, 2006 plications (Code: SS 6A), Wen-Xiu Ma, University of South Program issue of electronic Notices: January 2007 Florida, Taixi Xu, Southern Polytechnic State University, Issue of Abstracts: Volume 28, Issue 1 and Bao-Feng Feng and Zhijun Qiao, University of Texas­ Pan American. Deadlines Dynamic Programming (Code: SS 7A), Gerald C. Kobylski For organizers: Expired and Randal Hickman, United States Military Academy. For consideration of contributed papers in Special Sessions: Experimental Mathematics in Action (Code: SS 8A), Victor August 1, 2006 H. Moll and Tewodros Amdeberhan, Tulane University. For abstracts: September 26, 2006 Financial Mathematics (Code: SS 9A), Jean-Pierre Fouque, Joint Invited Addresses University of California Santa Barbara, Craig A. Nolder, Florida State University, Knut Solna, University of California Bryna R. Kra, Northwestern University, Title to be an­ Irvine, and Thaleia Zariphopoulou, University 6f Texas nounced (AMS-MAA Invited Address). Austin. AMS Invited Addresses Fixed Point Theory, Dynamics, and Group Theory (Code: SS lOA), Michael R. Kelly, Loyola University, and Peter N. Peter D. Lax, New York University-Courant Institute, Title Wong, Bates College. to be announced (AMS Josiah Willard Gibbs Lecture). Frames and Wavelets in Harmonic Analysis, Geometry, and Andrei Okounkov, Princeton University, Title to be an­ Applications (Code: SS llA), Palle E. T. Jorgensen, Uni­ nounced (AMS Colloquium Lectures). versity of Iowa, David R. Larson, Texas A&M University, Bjorn Poonen, University of California Berkeley, Title to be Peter R. Massopust, Institute of Biomathematics and Bio­ announced. metry, Neuherberg, and Technical University of Munich, and Gestur Olafsson, Louisiana State University. Victor S. Reiner, University of Minnesota, Minneapolis, Title to be announced. Free Discontinuity Problems: From Image Processing to Ma­ terials Science (Code: SS 12A), Blaise Bourdin, Louisiana Andras Vasy, Stanford University, Title to be announced. State University, and Christopher J. Larsen, Worcester Margaret H. Wright, New York University-Courant Insti­ Polytechnic Institute. tute, Title to be announced. Geometric Group Theory(Code: SS 13A), RuthM. Charney, Brandeis University, and Karen Vogtmann, Cornell Uni­ AMS Special Sessions versity (AMS-AWM). Some sessions are cosponsored with other organiza­ Group Representations, Ergodic Theory, and Mathematical tions. These are noted within the parenthesis at the end Physics: Honoring the Memory of George W. Mackey (Code: of each listing, where applicable. SS 14A), Robert S. Doran, Texas Christian University, Arithmetic Geometry (Code: SS 38A), Matthew H. Baker, Calvin C. Moore, University of California Berkeley, and Georgia Institute of Technology, and Bjorn Poonen, Uni­ Robert J. Zimmer, The University of Chicago. versity of California Berkeley. HistoryofMathematics(Code: SS 15A), Joseph W. Dauben, Arithmetic of Function Fields (Code: SS 33A), Allison M. Lehman College, Patti Hunter, Westmont College, Victor Pacelli, Williams College, and Michael J. Rosen, Brown J. Katz, University of the District of Columbia, and Karen H. Parshall, University of Virginia (AMS-MAA). University. Infinite Dimensional Analysis Honoring H.-H. Kuo (Code: SS Arrangements and Related Topics (Code: SS lA), Daniel C. 16A), Ambar N. Sengupta and P. Sundar, Louisiana State Cohen, Louisiana State University, and Anne V. Shepler, University. University of North Texas. Initial- and Boundary-Value Problems, Solvability, and Sta­ Calculus of Variations and Nonlinear PDEs: Theory and Ap­ bility for Some Nonlinear PDEs: Theorem, Computation, plications (Code: SS 2A), Marian Bocea and Cristina M. and Application (Code: SS 17A), Jerry L. Bona, University Popovici, North Dakota State University. of Illinois at Chicago, and Laihan Luo, Stockton College of Coding Theory and Its Applications (Code: SS 3A), Roxana New Jersey. N. Smarandache, University of Notre Dame and San Diego Invariant Theory (Code: SS 18A), Mara D. Neusel, Texas State University, and Pascal 0. Vontobel, Massachusetts Tech University, and Frank D. Grosshans, West Chester Institute of Technology. University. Cohomology and Representation Theory(Code: SS 4A), Jon Knots, 3-manifolds, and Their Invariants (Code: SS 19A), F. Carlson and Daniel K. Nakano, University of Georgia, Oliver T. Dasbach, Louisiana State University, and Xiao­ and Julia Pevtsova, University of Washington. Song Lin, University of California Riverside.

842 NoTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

Logical Methods in Computational Mathematics (Code: SS Structure Theory for Matroids and Graphs (Code: SS 32A), 20A), Saugata Basu, Georgia Institute of Technology, and Joseph P. Kung, University of North Texas, and Bogdan Charles N. Delzell, Louisiana State University (AMS-ASL). S. Oporowski and James G. Oxley, Louisiana State Uni­ Mapping Class Groups and Handlebodies (Code: SS 21A), versity. Tara E. Brendle, Louisiana State University, and William Time Scales: Dynamic Equations with Applications (Code: R. Vautaw, Southeastern Louisiana University. SS 34A), Martin J. Bohner, University of Missouri-Rolla, and Math Circles and Similar Programs for Students and Teach­ Allan C. Peterson, University of Nebraska-Lincoln. ers (Code: SS 22A), Morris Kalka, Tulane University, Hugo Universal Algebra and Order (Code: SS 35A), John W. Rossi, Mathematical Sciences Research Institute, Tatiana Snow, Sam Houston State University, and Japheth Wood, Shubin, San Jose State University, Zvezdelina E. Stankova, Chatham College. Mills College, Daniel H. Ullman, George Washington Uni­ versity, and Paul A. Zeitz, University of San Francisco. Call for MAA Contributed Papers Mathematical Techniques in Musical Analysis (Code: SS The MAA Committee on Contributed Paper Sessions so­ 23A), Robert W. Peck, Louisiana State University, Julian licits contributed papers pertinent to the sessions listed Hook, Indiana University-Bloomington, and Rachel W. below. Contributed paper session organizers generally Hall, Saint Joseph's University. limit presentations to ten or fifteen minutes. Each session room contains an overhead projector and screen; black­ Mathematics and Education Reform (Code: SS 3 7A), William boards will not be available. Speakers needing additional H. Barker, Bowdoin College, Dale R. Oliver, Humboldt audiovisual equipment should contact, as soon as possi­ State University, Bonnie S. Saunders, University of Illinois ble, but prior to October 1, 2006, the session organizer at Chicago, and Michael Starbird, University of Texas, whose name is followed by an asterisk ("). Organizers have Austin (AMS-MAA-MER). been advised that the majority of speakers in a session Microlocal Analysis and Singular Spaces (Code: SS 36A), Paul must require the use of additional audiovisual equipment A. Loya, Binghamton University, and Andras Vasy, Mass­ in order to justify the expenditure. Please note that the days achusetts Institute of Technology. and times scheduled for these sessions remain tentative. Nonlinear Variational Inclusion Problems and Optimization Applications ofDiscrete Mathematics (MM CP D 1 ), Mon­ Theory(Code: SS 24A), Ram U. Verma, University of Toledo, day morning; Thomas Koshy'' (tkoshy@frc. mass. edu), and International Publications. Framingham State College, and Thomas Moore, Bridge­ Nonsmooth Analysis in Inverse and Variational Problems water State College. The advent of modern digital com­ (Code: SS 25A), M. Zuhair Nashed, University of Central puters has increased the need for a better understanding Florida, and Otmar Scherzer, University of Innsbruck. of discrete mathematics. The tools and techniques of dis­ crete mathematics enable us to appreciate the power and Numerical Relativity (Code: SS 26A), Alexander M. Alek­ beauty of mathematics in designing problem-solving strate­ seenko, California State University Northridge, and Arup gies in everyday life, especially in computer science, and Mukherjee, Montclair State University. to communicate with ease in the language of discrete Radon Transforms, Convex Geometry, and Geometric Analy­ mathematics. Discrete mathematics has a wealth of in­ sis (Code: SS 27 A), Eric L. Grinberg, University of New triguillg applications to a variety of areas, including abstract Hampshire, Peter Kuchment, Texas A&M University, Ges­ algebra, casino games, coding theory, computer science, tur Olafsson, Louisiana State University, Eric Todd Quinto, cryptography, decision theory, electronics, genetics, graph Tufts University, and Boris S. Rubin, Louisiana State Uni­ theory, organic chemistry, management science, number versity. theory, sports, and the theory of scheduling, to name a few. Recent Advances in Mathematical Biology, Ecology, and They are well within reach of undergraduate and gradu­ Epidemiology (Code: SS 28A), Lih-Ing Roeger and Linda J. ate students, as well as advanced high school students. Allen, Texas Tech University, and Sophia Jang, University They are a powerful way to manifest both the power and of Louisiana at Lafayette. the beauty of discrete mathematics, and to provide new opportunities for experimentation and exploration, and for Recent Developments in Analysis and Numerics of Geo­ advancing the frontiers of mathematical knowledge. Ac­ physical Fluid Dynamics Problems (Code: SS 29A), Jie Shen, cordingly, this session focuses on the rich and fascinat­ Purdue University, and Shouhong Wang, Indiana Univer­ ing applications of discrete mathematics to numerous sity. fields of human endeavor. Recent Developments in Floer Homology (Code: SS 30A), Assessment ofStudent Learning in Undergraduate Math­ Scott J. Baldridge, Louisiana State University, Ronald A. ematics (MAA CP DS), Monday morning; William Martin''' Fintushel, Michigan State University, Thomas E. Mark, (william. marti n@ndsu. edu), North Dakota State Uni­ Southeastern Louisiana University, and Brendan E. Owens, versity, and Bernard L. Madison, University of Arkansas. Louisiana State University. Project SAUM (Supporting Assessment in Undergraduate Representation Theory and the Theta Correspondence Mathematics) has organized four workshop series for (Code: SS 31A), Wee Teck Gan, University of California San teams of faculty from a wide variety of mathematics de­ Diego, Hongyu He, Louisiana State University, and An­ partments across the country since 2002. This session in­ negret Paul, Western Michigan University. vites contributed papers that (a) describe assessment pro-

AUGUST 2006 NOTICES OF THE AMS 843 Meetings & Conferences jects in undergraduate mathematics programs, (b) report tracking data in both traditional and new versions of these findings of those projects, and (c) describe faculty and de­ courses and in follow-up courses; discuss the needs of partmental responses to those findings. Papers are so­ other disciplines and the workplace from courses at this licited from any individuals or groups actively involved in level; and discuss connections to the changing high school assessment and are not restricted to the participants of curricula and implications for teacher education. This ses­ Project SAUM workshops. sion is cosponsored by CRAFTY and the Committee on Two­ Building Diversity in Advanced Mathematics: Models Year Colleges. that Work (MAA CP El ), Sunday morning; Patricia Hale" Communication Theory in Undergraduate Courses (MAA (ph a l e@csupomona. edu), California State Polytechnic Uni­ CP FS), Saturday afternoon; Tim McDevitt1' (McDevi ttT@ versity, Pomona, and Abbe H. Herzig, University at Albany, etown. edu), Elizabethtown College. Effective communi­ SUNY. Papers presented at this session give models of cation is a cornerstone of our modern society, and math­ programs that have been successful at supporting diverse ematics is fundamentally important for rapid, economical, groups of people (women of all races, African Americans, error-free, and private communication. Mathematical com­ Latinos and Chicanos, and Native Americans) in their pur­ munication theory is a very broad and deep subject that suit of advanced mathematics study and careers. Presen­ involves mathematics at all levels of difficulty, and this ses­ tations will span the educational pathway, since issues of sion invites papers describing effective ways of enhanc­ diversity need to be addressed at every educational and ing existing courses (like calculus, linear algebra, differ­ professional juncture. Proposals are sought that describe ential equations, number theory, or abstract algebra) with successful programs for post-doctoral (faculty), graduate, topics from communication theory at an appropriate level. undergraduate or pre-college students. We interpret "suc­ Areas of interest include, but are not limited to, image, cess" broadly, and are looking for ideas that should be sound, or data compression, signal processing, error cor­ shared with others in the mathematics community as mod­ recting codes, cryptology, and Fourier or wavelet analysis. els for promoting diversity across the educational spec­ Content Courses for the Mathematical Education ofMid­ trum. These might be academic or extracurricular pro­ dle School Teachers (MAA CP G1 ), Friday morning; Laurie grams, which have targeted any group of people Burton''' (burton l @wou. edu), Maria G. Fung, and Klay traditionally underrepresented in the mathematical sci­ Kruczek, Western Oregon University. In 2001 the CBMS ences. Historical perspectives are also welcome. MET document proposed a series of recommendations Chaos and Fractals (MAA CP ES), Friday afternoon; for the mathematics curriculum and instruction of prospec­ Denny Gulick* (dng@math. umd. edu), University of Mary­ tive middle school teachers. This session invites papers de­ land, and Jon W. Scott, Montgomery College. Chaotic dy­ scribing how institutions are designing courses toward namics and fractal geometry have gained prominence in mathematics and applications. Because of the varied na­ meeting these goals for the mathematical education of pre­ ture both of the mathematical insights and the applications, service middle school teachers. Papers should describe the the goal of this special session is to make such results avail­ content and structure of the courses at your institution able to a larger mathematical audience. We invite papers that are specifically designed and offered for preservice on topics related to either chaotic dynamics or fractal middle school teachers. Additionally these papers should geometry. The papers need to have an expository flavor. describe how the courses fit into your institutional pro­ College Algebra: Concepts, Data, and Models (MM CP Fl ), gram and should describe how the courses address the MET recommendations. We also ask that papers describe course Monday morning; Florence S. Gordon1' (fgordon@ nyi t. edu), New York Institute of Technology, Mary prerequisites, teaching strategies and pedagogical ap­ Robinson, University of New Mexico Valencia Campus, proaches. Presenters are encouraged to share sample ac­ Norma Agras, Miami Dade Community College, and tivities and/or course syllabi and to share curriculum Laurette Foster, Prairie View A&M University. The MAA un­ sources and resources. Courses offered for future ele­ der the leadership of CRAFTY is conducting a national ini­ mentary teachers covering content beyond the Mathe­ tiative to refocus the courses below calculus to better matics for Elementary Teachers foundational series will also serve the majority of students taking these courses. The be considered. This session is sponsored by COMET (Com­ goal is to encourage courses that place much greater em­ mittee on the Mathematical Education of Teachers). phasis on conceptual understanding and realistic appli­ Countering "I Can't Do Math": Strategies For Teaching cations compared to traditional courses that too often are Under-Prepared, Math-Anxious Students (MAA CP G5), Sun­ designed to develop algebraic skills needed for calculus. day afternoon; Winston Crawley'' (jwc raw@shi p. edu) and We seek to address all the college level courses below cal­ Kim Presser, Shippensburg University. How can we create culus, with particular emphasis on offerings in college al­ a comfortable learning environment for under-prepared or gebra and precalculus that focus on conceptual under­ math-anxious students and, in particular, how can we con­ standing, the use of real-world data, and mathematical structively assess student learning? What classroom prac­ modeling. We seek presentations that present new visions tices are especially effective with such students and how for such courses; discuss experiences teaching such courses; does research on student learning inform those practices? discuss implementation issues (such as faculty training, How might the recommendations of the 2004 CUPM Cur­ placement tests, introduction of alternative tracks for dif­ riculum Guide influence our approach in teaching devel­ ferent groups of students, transferability problems, etc.); opmental or introductory courses to better reach these stu­ present results of studies on student performance and dents? This session invites papers on all aspects of "what

844 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences works" in teaching under-prepared, math-anxious stu­ mand for quantitative skills needed in the financial in­ dents. dustry, and this ushered in a "new mathematics" that is Entertaining with Math (MAA CP H 1 ), Friday afternoon; now known as financial mathematics. Leading research in­ TimothyP. Chartier1' (ti charti er@davi dson. edu), David­ stitutions have developed graduate level programs in this son College. Performing arts such as juggling, music, area, and as a result of the increasing demand and the prac­ dance, magic, and drama can enrich the classroom. Beyond ticality of the subject, undergraduate institutions have entertaining students, such demonstrations can offer new started offering programs in financial mathematics at var­ and novel perspectives on mathematical content and en­ ious levels, from a single course to a major concentration gage a class in a fun, educational, and interactive activity. track. Nationwide website searches in 2005 revealed that This session seeks to provide a forum in which presenters over sixty institutions are offering formal undergraduate may demonstrate and discuss creative ways of teaching majors in financial mathematics. These programs have and presenting mathematics using techniques generally as­ been established in three ways: as a subsidiary of existing sociated with entertainment and the performing arts. Pro­ graduate programs, as an extension of existing actuarial posals should clearly delineate the mathematical subject programs, and as an independent program on its own. that will be covered. When a short performance or portion Innovative and Effective Ways to Teach Linear Algebra of a performance is included, a presenter should also in­ (MAA CP J1 ), Saturday morning; David Strong'' (David. corporate a clear discussion of how a presenter's meth­ Strong@pepperdi ne. edu), Pepperdine University, and ods can be adapted for general classroom use. Descriptions Gilbert Strang, Massachusetts Institute of Technology. of classroom activities that are suitable for use by teach­ Linear algebra is one of the most interesting and useful ers and professors without a performance background areas of mathematics, because of its beautiful and multi­ are also strongly encouraged. faceted theory, as well as the enormous importance it Euler in the Classroom (MAA CP HS), Friday morning; plays in understanding and solving many real world prob­ Robert E. Bradley''' (b radl ey@ade l phi . edu), Adelphi Uni­ lems. Consequently, many valuable and creative ways to versity, and Amy Shell-Gellasch, Grafenwoer, Germany. teach its rich theory and its many applications are con­ This session solicits talks that describe ways to incorpo­ tinually being developed and refined. This session will rate the mathematics of Leonard Euler into the classroom. serve as a forum in which to share and discuss new or im­ We are looking for papers that describe ways to use his proved teaching ideas and approaches. These innovative mathematics, science, or the history of his life and times and effective ways to teach linear algebra include, but are in the secondary and undergraduate mathematics cur­ not necessarily limited to: (1) hands-on, in-class demos; (2) riculum. This session is sponsored by the History of Math­ effective use of technology, such as Matlab, Maple, Math­ ematics Special Interest Group of the MAA (HOMSIGMAA). ematica, Java Applets or Flash; (3) interesting and en­ Getting Students to Discuss and to Write about Mathe­ lightening connections between ideas that arise in linear matics (MAA CP 11 ), Saturday morning and afternoon; algebra and ideas in other mathematical branches; (4) in­ Martha Ellen (Murphy) Waggoner'' (waggoner@simpson. teresting and compelling examples and problems involv­ edu), Simpson College, Charlotte Knotts-Zides, Wofford ing particular ideas being taught; (5) comparing and con­ College, and Harrison W. Straley, Wheaton College. This trasting visual (geometric) and more abstract (algebraic) session invites papers about assignments and projects explanations of specific ideas; (6) other novel and useful that require students to communicate mathematics through approaches or pedagogical tools. Presenters should discuss oral presentations, classroom discussions, and writing. their own experience in using their presented idea or ap­ These assignments/projects can come from any area of proach in their own teaching. The purpose of this session mathematics including courses for mathematics or re­ is to share the experience of establishing undergraduate lated majors, mathematics service courses, or mathemat­ level financial mathematics programs and to discuss fur­ ics education courses. Each presenter is encouraged to ther outreach, such as a partnership between academia and discuss how the use of the assignment/project helped the financial industry. Of principal interest are presenta­ students to improve their understanding of mathematics, tions that discuss establishing financial mathematics pro­ their communication of mathematics, and their attitude grams as a major concentration track and reports on the toward mathematics. Of particular interest are innovative outcomes. Also welcome are papers that describe plans and implementations of such assignments/projects including objectives of starting new ones. peer review of student writing or presentations, using Innovative Examples of Using Graphs in Statistics (MAA mathematical writing or presentations as part of service CP JS), Sunday afternoon; Christopher J. Lacke"' (l acke@ learning, rubrics for assessing student writing and pre­ rowan. edu), Rowan University, and Ginger Holmes Row­ sentations, using student writing or oral presentations as ell, Middle Tennessee State University. The Guidelines for part of program assessment, and programs to help stu­ Assessment and Instruction in Statistics Education (GAISE) dents improve written and oral communication of math­ College Report state that a statistically educated student ematics. should understand "how to graph the data as a first step How to Start and Develop Undergraduate Level Finan­ in analyzing data, and how to know when that's enough cial Mathematics Programs (MAA CP 15), Sunday morning; to answer the question of interest" and "how to inter­ Youngna Choi'' (choi y@mai l . mantel air. edu), Montclair pret ...graphical displays of data-both to answer questions State University. The proliferation of complex financial and to check conditions (in order to use statistical proce­ products over the last two decades has increased the de- dures correctly)." Unfortunately most introductory ap-

AUGUST 2006 NOTICES OF THE AMS 845 Meetings & Conferences plied statistics courses introduce graphical displays in dience, and/or assessment of impact of interdisciplinary the first two weeks of a semester and rarely return to experience on students. these important tools later on. With the ease in creating Mathematics Experiences in Business, Industry, and Gov­ such displays with today's technology, this should not be ernment (MAA CP L 1 ), Sunday afternoon; Philip E. the case. This session looks for innovative examples of Gustafson'' (pgustafs@mesastate. edu), Mesa State Col­ using graphical displays for exploratory data analysis and lege, and Michael Monticino, University of North Texas. checking assumptions of traditional inference. It also seeks This session will provide a forum for mathematicians with creative examples of graphical inference. Furthermore, it experience in Business, Industry and Government (BIG) to desires examples of developing and critiquing graphical present papers or discuss projects involving the applica­ displays for presentation. In order to be considered for this tion of mathematics to BIG problems. BIG mathematicians session, applicants should submit a one-page summary of as well as faculty and students in academia who are in­ the presentation to Christopher Lacke at [email protected] terested in learning more about BIG practitioners, pro­ along with the abstract to the AMS. Presenters in the ses­ jects, and issues, will find this session of interest. This ses­ sion will be considered for the SIGMAA on Statistics Edu­ sion is sponsored by the MAA Business, Industry and cation's Best Contributed Paper Award. Government Special Interest Group (BIG SIGMAA). Integrating Mathematics and Biology in Undergraduate Mathematics of Chemistry (MAA CP LS), Monday morn­ Education (MAA CP K 1 ), Friday morning; Glenn W. Ledder''' ing; George Rublein''' (gt rub l @math. wm. edu), The Col­ (g l edde r@math. un l . edu), University of Nebraska-Lincoln, lege of William and Mary. Mathematics makes its appear­ Yajun Yang, Farmingdale State University of New York, ance early on in college-level chemistry courses. Physical Jack Bookman, Duke University, and James P. Fulton, chemistry, which is heavily laced with mathematical mod­ Suffolk County Community College. The MAA published els, has a reputation as the most difficult course in the un­ a report in 2005 called "Math and Bio 2010: Linking Un­ dergraduate chemistry curriculum. The treatment of math­ dergraduate Disciplines" that outlined a number of issues ematics in chemistry textbooks often bears little and approaches in mathematics curriculum development resemblance to the approaches that students see in math­ for life science students. A number of new initiatives in ematics courses. This session solicits contributions that this area sprung up between the collection of articles for show examples of models drawn from chemistry that this report and its appearance in print. More are at vari­ might comfortably appear in the calculus, differential ous stages of development. Other initiatives focus on the equations, or linear algebra courses in which chemistry stu­ dents are commonly enrolled. Chemical thermodynam­ incorporation of mathematical content into biology courses. ics, stoichiometry, and chemical kinetics are good sources This session provides a forum for mathematicians to share for such models. ideas about how to connect mathematics and biology in The Mathematics of Sudoku and Other Puzzles (MAA CP the undergraduate curriculum. We seek presenters who will M1 ), Sunday morning; Laura A. Taalman'' (taal@math. discuss the content and format of math courses designed jmu. edu), James Madison University. Sudoku puzzles and to meet the needs of students in the biological sciences, their variants are linked to many mathematical problems ways to incorporate the application of mathematics to bi­ involving combinatorics, Latin squares, magic squares, ology in existing undergraduate mathematics courses, and polyominos, symmetries, computer algorithms, the rook ways to incorporate mathematics in existing undergradu­ problem, knight tours, graph colorings, and permutation ate biology courses. Examples of desirable topics include group theory. Many other puzzles also have underlying innovative mathematics courses and curricula for biolog­ mathematical content that can be a source of open prob­ ical science students, exemplary course modules (appli­ lems, undergraduate research projects, and new results. cations modules for mathematics courses and mathe­ In this session we will explore the mathematics involved matics modules for biology), and student projects. in solving, contructing, and analyzing Sudoku and other Presentations from teams of mathematicians and biologists puzzles. We invite the submission of presentations con­ are especially welcome. cerning the mathematics of Sudoku, its variants, and other Mathematics and Biology 2010: Building Connections puzzles. Examples of presentations might include pre­ (MAA CP KS), Saturday morning; G. Elton Graves'' (graves@ sentations of new mathematical results or computational rose-hul man. edu), Rose-Hulman Institute of Technol­ techniques, survey talks describing known results and ogy, and Catherine M. Murphy, Purdue University. The open problems, and discussions on using Sudoku and CUPM Subcommittee on Mathematics Across the Disci­ other puzzles as learning tools in the classroom or as the plines requests proposals for papers on interdisciplinary basis for undergraduate research projects. Speakers are course/programs jointly developed by mathematicians encouraged to provide puzzle handouts for attendees if and biologists for undergraduate students. We especially possible and relevant. solicit proposals from interdisciplinary teams (bring your Mathlets for Teaching and Learning Mathematics (MAA biology colleague to JMM as a guest. We would like to hear CP M 5). Friday afternoon; David Strong''' (David. Strong@ the biologist's perspective too). Preference will be given to pepperdi ne. edu), Pepperdine University, Thomas collaborations which have been in effect for two or more Leathrum, Jacksonville State University, and joe Yanik, Em­ years. Your proposal should address such nuts and bolts poria State University. This session seeks to provide a issues as: how you got started, roadblocks to either start­ forum in which presenters may demonstrate mathlets and ing or sustaining your collaboration, intended student au- related materials that they have created or further devel-

846 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences oped. Mathlets are small computer-based (but ideally plat­ encouraged to organize and run special events for their form-independent) interactive tools for teaching math, students. Descriptions of activities could include, but are frequently developed as World Wide Web materials such not limited to, special lectures, workshops for students, as scripts or Java applets, but there may be many other Math Days/Fairs, student conferences, recreational math­ innovative variations. Mathlets allow students to experi­ ematics activities, problem-solving activities and contests, ment with and visualize a variety of mathematical concepts, general community-building activities, and student con­ and they can be easily shared by mathematics instructors sulting projects. We especially encourage information around the world. about student research projects and programs, including Philosophy ofMathematics (MAA CP N 1), Saturday morn­ program logistics and project ideas. Information on how ing and afternoon; Bonnie Gold'' (bgo l d@ monmouth. edu), such activities are organized and carried out, what activ­ Monmouth University, and Charles R. Hampton, The Col­ ities especially grab students' interests, how students are lege of Wooster. This session, sponsored by the SIGMAA contacted and encouraged to participate, and how the for the Philosophy of Mathematics, invites papers on any events are funded will be especially helpful. This session topic in the philosophy of mathematics except logic and is organized by the CUPM Subcommittee on Undergradu­ set theory. Possible topics include the nature of mathe­ ate Research. matics, the nature of mathematical objects, the nature of Research on the Teaching and Learning of Undergrad­ mathematical knowledge, the relation between mathe­ uate Mathematics (MAA CP PS), Saturday morning; David matics and the physical world, the role of esthetics in the E. Meel" (mee l @bgsu. edu), Bowling Green State University, development of mathematics. Papers that stem from some Michael Oehrtman, Arizona State University, and Chris specific problems are encouraged, and so are those cut­ Rasmussen, San Diego State University. Research papers ting across disciplines. that address issues concerning the teaching and learning Reconceptualizing Content Courses for Prospective High of undergraduate mathematics are invited. Appropriate for School Mathematics Teachers (MAA CP NS), Saturday af­ this session are theoretical or empirical investigations ternoon; Jean McGivney-Burelle" (bu re ll e@hartfo rd. conducted within clearly defined theoretical frameworks, edu), University of Hartford, and Neil Portnoy, Stony Brook using either qualitative or quantitative methodologies. Of University. Today, most preservice secondary mathemat­ highest priority are proposals that report on completed ics teacher (PSMT) education programs require mathe­ studies that further existing work in the field. matics coursework similar to that of mathematics majors Teaching Innovations in Real Analysis (MAA CP Q 1 ), and education coursework that emphasizes teaching and Sunday afternoon; Robert W. Vallin'' (robert. vall in@ learning. However, there is widespread concern that to­ s ru. edu), Slippery Rock University, and Erik 0. Talvila, gether these courses do not provide prospective teachers University College of the Fraser Valley. Everyone agrees that with the depth and breadth of knowledge needed to teach undergraduate math majors should take at least one course high school mathematics well (CBMS, 2001). PSMTs often in real analysis. As we have all seen, though, this tends to fail to see the connections between advanced mathemat­ strike fear into the heart of even strong students. This ses­ ics content they are required to study and the high school sion is about how we show analysis to be the exciting and mathematics they will soon teach. Further, PSMTs have dif­ interesting discipline we know it to be. How do you ease ficulty translating general theories of epistemology, psy­ the stress for your students? What are your favorite ex­ chology, and pedagogy learned in their education courses amples/counterexamples? Do you use Java applets, Maple into effective strategies for teaching mathematics. This ses­ or Mathematica to illustrate concepts? Have you used writ­ sion invites papers on promising practices in mathemat­ ing or group projects in your class? How does your ver­ ics courses which help PSMTs to develop mathematical sion of Moore Method work? Are there different topics or knowledge that is organized for teaching- knowledge techniques you favor such as nonstandard analysis or which is characterized by a deep understanding of the Henstock-Kurzweil integration? Your colleagues want you mathematics PSMTs will teach; a sound grasp of content­ to share your successes with them. specific pedagogy; an awareness of conceptual barriers to Teaching Mathematics Courses Online (MAA CP QS), Fri­ learning mathematics; and an understanding of the his­ daymorning; Cheryl Olsen''' (cl ol se@shi p. edu) and Kate torical, cultural, and scientific roots of mathematical ideas McGivney, Shippensburg University. In recent years there and processes. has been an increasing trend for undergraduate institutions Research and Other Mathematical Experiences for Stu­ to offer mathematics courses online. This session will dents Outside the Classroom (MAA CP P1 ), Friday afternoon; focus both on presenting successful strategies for teach­ Sarah Spence Adams''' (sarah. adams@o lin. edu), Franklin ing such courses as well as describing shortcomings in de­ W. Olin College of Engineering, James A. Davis, University livering mathematics online. Consideration will be given of Richmond, and Susan E. Morey, Texas State University, to courses where at least 50% of the content is communi­ San Marcos. Mathematics "happens" both inside and out­ cated via the web. Proposals that address issues includ­ side the classroom and, in fact, many mathematics majors ing, but not limited to, designing effective means of com­ are drawn to the subject through a special event sponsored munication between students and the instructor, managing by a Student Chapter or Math Club or through special re­ group projects and assignments, incorporating various search projects and programs. This session seeks pre­ technologies into the course, and implementing success­ sentations by academic, industrial, business, and/or stu­ ful assessment strategies are welcome. Papers that ad­ dent mathematicians so that the audience will be dress how to design an online course that meet the same

AUGUST 2006 NOTICES OF THE AMS 847 Meetings & Conferences course goals as a traditionally taught course are of par­ by other instructors are of particular interest. After the ses­ ticular interest. Finally, data based on student experiences sion is over, we plan to collect such materials and make from learning in an online environment are welcome. them available at a website upon speakers' approval, aim­ Teaching Operations Research in the Undergraduate ing to serve as a clearinghouse for teachers who are in­ Classroom (MAA CP R 1 ), Sunday morning; Gerald Kobyl­ terested in trying similar experiments in undergraduate ski" ([email protected]) and Steve Horton, courses as well as undergraduate research. United States Military Academy, Christopher j. Lacke, General Session (MAA CP Z1 ), Friday, Saturday, Sunday, Rowan University, and William Fox, Francis Marion Uni­ and Monday mornings and afternoons; Eric S. Marland1' versity. This session solicits papers highlighting innova­ (marl andes@appstate. edu), Appalachian State Univer­ tive instructional strategies and assessment methods in sity, and jay A. Malmstrom, Oklahoma City Community the introductory undergraduate operations research se­ College. Papers may be presented on any mathematical quence. Suggested topics include, but are not limited to, topic. course projects, case studies, technology demonstrations, cooperative learning activities, and writing assignments. Papers may focus on original teaching materials or the cre­ Davidson, North ative use of previously existing ones, but all papers should provide specific learning objectives addressed by the use of such materials. Each submission must focus on opera­ Carolina tions research topics at the undergraduate level, includ­ Davidson College ing those in the introductory undergraduate operations re­ search sequence or undergraduate courses in stochastic March 3-4, 2007 processes, queuing theory, network optimization, etc., Saturday - Sunday and should be accompanied by a course syllabus. The Scholarship of Teaching and Learning in Mathe­ Meeting #1 024 matics (MAA CP RS), Saturday afternoon; Curtis D. Bennett1' Southeastern Section (cbennett@l mu. edu) and Jacqueline M. Dewar, Loyola Associate secretary: Matthew Miller Marymount University. The Scholarship of Teaching and Announcement issue of Notices: To be announced Learning is an international movement where faculty bring Program first available on AMS website: To be announced disciplinary knowledge to bear on questions of teaching Program issue of electronic Notices: To be announced and learning and use student-based evidence to support Issue of Abstracts: To be announced their conclusions. Work in this area can range from small investigations around teaching innovations or the pro­ Deadlines duction of course portfolios to more formal investiga­ For organizers: August 3, 2006 tions of student learning. Goals of this session are to: (1) For consideration of contributed papers in Special Sessions: Feature scholarly work focused on teaching; (2) Provide a To be announced venue for mathematicians to make their scholarly work on For abstracts: To be announced teaching public; and (3) Highlight evidence-based argu­ ments for the value of teaching innovations. Reports that Invited Addresses address issues concerning the teaching and learning of un­ dergraduate mathematics are invited. Appropriate for this Chaim Goodman-Strauss, University of Arkansas at Fayet­ session are reports of classroom-based investigations of teville, Title to be announced. teaching methods, student learning difficulties, or curric­ Andrew J. Granville, University of Montreal, Title to be an­ ular assessment. Papers should discuss more than anec­ nounced (Erdos Memorial Lecture). dotal evidence. For example, papers might reference the Alex Iosevich, University of Missouri-Columbia, Analysis, following types of qualitative or quantitative evidence: combinatorics, and arithmetic of incidence theory. student work, interviews, surveys, pre/post tests, etc. Shrawan Kumar, University of North Carolina, Eigenvalue Use of Technology in Abstract Algebra and Number problem for Hermitian matrices and its generalization to Theory (MAA CP S 1 ), Friday morning; Byungchul Cha1' arbitrary reductive groups. (cha@hendri x. edu), Hendrix College, and Bo-Hae Im, Uni­ versity of Utah. This session concerns the use of computer, Special Sessions such as Computer Algebra Systems and programming lan­ guages, in abstract algebra and number theory. These Between Harmonic Analysis, Number Theory, and Combi­ technologies can provide students with highly computa­ natorics (Code: SS lA), Alex Iosevich, University of Mis­ tional examples that would be inaccessible by hand, assist souri-Columbia, Michael T. Lacey, Georgia Institute of in doing symbolic computations and developing algo­ Technology, and Konstantin Oskolkov, University of South rithms, and help conceptual understanding. We invite pa­ Carolina. pers that address novel ways and various issues regard­ Computational Group Theory (Code: SS 3A), Arturo ing the computational tools in teaching courses in the Magidin, University of Louisiana at Lafayette, Luise Char­ abstract algebra and number theory. Examples of lab ses­ lotte Kappe, Binghamton University, and Robert F. Morse, sions/modules and computer exercises that can be shared University of Evansville.

848 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

Geometric and Combinatorial Methods in Representation Announcement issue of Notices: To be announced Theory (Code: SS 2A), Brian Boe and William A. Graham, Program first available on AMS website: To be announced University of Georgia, and Kailash C. Misra, North Carolina Program issue of electronic Notices: To be announced State University. Issue of Abstracts: To be announced

Deadlines Oxford, Ohio For organizers: September 14, 2006 For consideration of contributed papers in Special Sessions: Miami University To be announced For abstracts: To be announced March 16-1 7, 2007 Friday - Saturday Invited Addresses Meeting #1 025 Neal Koblitz, University of Washington, Title to be an­ Central Section nounced. Associate secretary: Susan J. Friedlander Florian Luca, Universidad Nacional Aut6noma de Mexico, Announcement issue of Notices: To be announced Title to be announced. Program first available on AMS website: To be announced Natasa Pavlovic, Princeton University, Title to be an­ Program issue of electronic Notices: To be announced nounced. Issue of Abstracts: To be announced Elisabeth Werner, Case Western Reserve University, Title Deadlines to be announced. For organizers: To be announced Special Sessions For consideration of contributed papers in Special Sessions: To be announced Affine Invariants, Randomness, and Approximation in Con­ For abstracts: To be announced vex Geometry(Code: SS 2A), Elisabeth Werner, Case West­ ern Reserve University, and Artem Zvavitch, Kent State Uni­ Invited Addresses versity. Sergey Fomin, University of Michigan, Title to be an­ Automorphic Forms and Arithmetic Geometry (Code: SS SA), nounced. Guatam Chinta, City College of New York, and Paul E. Naichung Conan Leung, University of Minnesota, Title to Gunnells, University of Massachusetts, Amherst. be announced. Convex Sets (Code: SS lA), David Larman, University Col­ Emil J. Straube, Texas A & M University, Title to be an­ lege London, and Valeriu Soltan, George Mason University. nounced. Differential Algebra (Code: SS 4A), Phyllis J. Cassidy, Shouhong Wang, Indiana University, Title to be announced. Smith College and The City College of CUNY; Richard C. Churchill, Hunter College and The Graduate Center of Special Sessions CUNY; Li Guo and William F. Keigher, Rutgers University Finite Geometry and Combinatorics (Code: SS 3A), Mark A. at Newark; and Jerald]. Kovacic and William Sit, The City Miller, Marietta College. College of CUNY. Geometric Topology (Code: SS 2A), Jean-Francois LaFont, Fourier Analysis and Convexity (Code: SS 3A), Alexander SUNY Binghamton and Ohio State University, and Ivonne Koldobsky, University of Missouri, Columbia, and Dmitry J. Ortiz, Miami University. Ryabogin, Kansas State University. Large Cardinals in Set Theory (Code: SS lA), Paul B. Lar­ son, Miami University, Justin Tatch Moore, Boise State Uni­ versity, and Ernest Schimmerling, Carnegie Mellon Uni­ Tucson, Arizona versity. University of Arizona April21-22, 2007 Hoboken, New Jersey Saturday - Sunday Stevens Institute of Technology Meeting #1 027 April14-1 5, 2007 Western Section Saturday - Sunday Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced Meeting #1 026 Program first available on AMS website: To be announced Eastern Section Program issue of electronic Notices: To be announced Associate secretary: Lesley M. Sibner Issue of Abstracts: To be announced

AUGUST 2006 NOTICES OF THE AMS 849 Meetings & Conferences

Deadlines For organizers: September 21, 2006 Chicago, Illinois For consideration of contributed papers in Special Sessions: To be announced DePaul University For abstracts: To be announced October 5-6,2007 Invited Addresses Saturday - Sunday Central Section Liliana Borcea, Rice University, Title to be announced. Associate secretary: Susan ]. Friedlander James Cushing, University of Arizona, Tucson, Title to be Announcement issue of Notices: To be announced announced. Program first available on AMS website: To be announced Hans Lindblad, University of California, San Diego, Title Program issue of electronic Notices: To be announced to be announced. Issue of Abstracts: To be announced Vinayak Vatsal, University of British Columbia, Vancou­ ver, Title to be announced. Deadlines For organizers: To be announced Special Sessions For consideration of contributed papers in Special Sessions: Inverse Problems for Wave Propagation (Code: SS 2A), Lil­ To be announced iana Borcea, Rice University. For abstracts: To be announced Representations of Algebras (Code: SS lA), Frauke Maria Bleher, University of Iowa, Birge K. Huisgen-Zimmer­ mann, University of California Santa Barbara, and Dan New Brunswick, New Zacharia, Syracuse University. Jersey Warsaw, Poland Rutgers University-New Brunswick, Busch Campus University of Warsaw October 6-7, 2007 July 31 -August 3, 2007 Saturday - Sunday Tuesday - Friday Eastern Section Meeting #1 028 Associate secretary: Lesley M. Sibner First ]oint International Meeting between the AMS and the Announcement issue of Notices: To be announced Polish Mathematical Society Program first available on AMS website: To be announced Associate secretary: Susan]. Friedlander Program issue of electronic Notices: To be announced Announcement issue of Notices: To be announced Issue of Abstracts: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Deadlines Issue of Abstracts: To be announced For organizers: March 6, 2007 For consideration of contributed papers in Special Sessions: Deadlines To be announced For organizers: To be announced For abstracts: To be announced For consideration of contributed papers in Special Sessions: To be announced For abstracts: To be announced Albuquerque, New Invited Addresses Henryk Iwaniec, Rutgers University, Title to be announced. Mexico Tomasz J Luczak, Adam Mickiewicz University, Title to be University of New Mexico announced. October 1 3-14, 2007 Tomasz Mrowka, Massachusetts Institute of Technology, Title to be announced. Saturday - Sunday Western Section Ludomir Newelski, University of Wroclaw, Title to be an­ Associate secretary: Michel L. Lapidus nounced. Announcement issue of Notices: To be announced Madhu Sudan, Massachusetts Institute of Technology, Program first available on AMS website: To be announced Title to be announced. Program issue of electronic Notices: To be announced Anna Zdunik, Warsaw University, Title to be announced. Issue of Abstracts: To be announced

850 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

Deadlines For organizers: To be announced San Diego, California For consideration of contributed papers in Special Sessions: To be announced San Diego Convention Center For abstracts: To be announced january 6-9, 2008 Sunday - Wednesday ]oint Mathematics Meetings, including the 114th Annual Murfreesboro, Meeting of the AMS, 9lst Annual Meeting of the Mathe­ matical Association of America (MAA), annual meetings of Tennessee the Association for Women in Mathematics (A WM) and the Middle Tennessee State University National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL}, November 3-4, 2007 with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Saturday - Sunday Associate secretary: Michel L. Lapidus Southeastern Section Announcement issue of Notices: October 2007 Associate secretary: Matthew Miller Program first available on AMS website: November Announcement issue of Notices: To be announced 1, 2007 Program first available on AMS website: To be announced Program issue of electronic Notices: January 2008 Issue of Abstracts: Program issue of electronic Notices: To be announced Volume 29, Issue 1 Issue of Abstracts: To be announced Deadlines Deadlines For organizers: April1, 2007 For organizers: April 4, 2007 For consideration of contributed papers in Special Sessions: For consideration of contributed papers in Special Sessions: To be announced To be announced For abstracts: To be announced For abstracts: To be announced Invited Addresses New York, New York Daniel K. Nakano, University of Georgia, Title to be an­ Courant Institute of New York University nounced. Carla D. Savage, North Carolina State University, Title to March 22-23,2008 be announced. Saturday - Sunday Sergei Tabachnikov, Pennsylvania State University, Title Eastern Section to be announced. Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Wellington, New Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Zealand Deadlines To be announced For organizers: August 22, 2007 For consideration of contributed papers in Special Sessions: December 12-1 5, 2007 To be announced Wednesday - Saturday For abstracts: To be announced First ]oint International Meeting between the AMS and the New Zealand Mathematical Society (NZMS). Associate secretary: Matthew Miller Baton Rouge, Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Louisiana Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Louisiana State University, Baton Rouge Deadlines March 28-30, 2008 For organizers: To be announced Friday - Sunday For consideration of contributed papers in Special Sessions: Southeastern Section To be announced Associate secretary: Matthew Miller For abstracts: To be announced Announcement issue of Notices: To be announced

AUGUST 2006 NOTICES OF THE AMS 851 Meetings & Conferences

Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Rio de Janeiro, Brazil Issue of Abstracts: To be announced Instituto Nacional de Matematica Pura e Deadlines Aplicada (IMPA) For organizers: August 28, 2007 june 4-7,2008 For consideration of contributed papers in Special Sessions: Wednesday - Saturday To be announced First ]oint International Meeting between the AMS and the For abstracts: To be announced Sociedade Brasileira de Matematica. Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced Bloomington, Indiana Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Indiana University Issue of Abstracts: Not applicable

April4-6, 2008 Deadlines Friday - Sunday For organizers: To be announced Central Section For consideration of contributed papers in Special Sessions: Associate secretary: Susan]. Friedlander To be announced Announcement issue of Notices: To be announced For abstracts: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Vancouver, Canada University of British Columbia and the Pa­ Deadlines For organizers: September 4, 2007 cific Institute of Mathematical Sciences For consideration of contributed papers in Special Sessions: (PIMS) To be announced October4-5, 2008 For abstracts: To be announced Saturday - Sunday Western Section Associate secretary: Michel L. Lapidus Claremont, California Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Claremont McKenna College Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced May 3-4, 2008 Saturday - Sunday Deadlines Southeastern Section For organizers: March 9, 2008 Associate secretary: Michel L. Lapidus For consideration of contributed papers in Special Sessions: Announcement issue of Notices: To be announced To be announced Program first available on AMS website: To be announced For abstracts: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Huntsville, Alabama Deadlines University of Alabama, Huntsville For organizers: October 4, 2007 For consideration of contributed papers in Special Sessions: October 24-26, 2008 To be announced Friday - Sunday For abstracts: To be announced Southeastern Section Associate secretary: Matthew Miller Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced

852 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings & Conferences

Deadlines For organizers: March 24, 2008 Urbana, Illinois For consideration of contributed papers in Special Sessions: To be announced University of Illinois at Urbana-Champaign For abstracts: To be announced March 27-29, 2009 Friday - Sunday Shanghai, People's Southeastern Section Associate secretary: Susan]. Friedlander Republic of China Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Fudan University Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced December 17-21,2008 Wednesday - Sunday Deadlines First ]oint Interntional Meeting Between the AMS and the For organizers: August 29, 2008 Shanghai Mathematical Society Associate secretary: Susan]. Friedlander For consideration of contributed papers in Special Sessions: Announcement issue of Notices: To be announced To be announced Program first available on AMS website: Not applicable For abstracts: To be announced Program issue of electronic Notices: Not applicable Issue of Abstracts: Not applicable San Francisco, Deadlines For organizers: To be announced For consideration of contributed papers in Special Sessions: California To be announced Moscone Center West and the San Fran­ For abstracts: To be announced cisco Marriott

January 6-9, 201 0 Washington, District Wednesday - Saturday ]oint Mathematics Meetings, including the 116th Annual of Columbia Meeting of the AMS, 93rd Annual Meeting of the Mathe­ Marriott Wardman Park Hotel and Omni matical Association of America (MAA), annual meetings of Shoreham Hotel the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM), and the January 7-10, 2009 winter meeting of the Association for Symbolic Logic (ASL), Wednesday - Saturday with sessions contributed by the Society of Industrial and ]oint Mathematics Meetings, including the llSth Annual Applied Mathematics (SIAM). Meeting of the AMS, 92nd Annual Meeting of the Mathe­ Associate secretary: Matthew Miller matical Association of America (MAA), annual meetings of Announcement issue of Notices: October 2009 the Association for Women in Mathematics (A WM) and the Program first available on AMS website: November 1, 2009 National Association of Mathematicians (NAM), and the Program issue of electronic Notices: January 2010 winter meeting of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and Issue of Abstracts: Volume 31, Issue 1 Applied Mathematics (SIAM). Deadlines Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2008 For organizers: April1, 2009 Program first available on AMS website: November 1, 2008 For consideration of contributed papers in Special Sessions: Program issue of electronic Notices: January 2009 To be announced Issue of Abstracts: Volume 30, Issue 1 For abstracts: To be announced Deadlines For organizers: April1, 2008 For consideration of contributed papers in Special Sessions: To be announced For abstracts: To be announced

AUGUST 2006 NOTICES OF THE AMS 853 Meetings & Conferences

For consideration of contributed papers in Special Sessions: New Orleans, To be announced Louisiana For abstracts: To be announced New Orleans Marriott and Sheraton New San Diego, California Orleans Hotel San Diego Convention Center and San January 5-8,2011 Diego Marriott Hotel and Marina Wednesday - Saturday January 9-12,2013 ]oint Mathematics Meetings, including the 117th Annual Meeting of the AMS, 94th Annual Meeting of the Mathe­ Wednesday - Saturday ]oint Mathematics Meetings, including the 119th Annual matical Association ofAmerica, annual meetings of the As­ Meeting of the AMS, 96th Annual meeting of the Mathe­ sociation for Women in Mathematics (Alt'M) and the National matical Association ofAmerica, annual meetings of the As­ Association ofMathematicians (NAM), and the winter meet­ sociation for Women in Mathematics (A Tt'M) and the National ing of the Association for Symbolic Logic (ASL), with sessions Association ofMathematicians (NAM), and the winter meet­ contributed by the Society for Industrial and Applied Math­ ing of the Association for Symbolic Logic (ASL), with sessions ematics (SIAM). contributed by the Society for Industrial and Applied Math­ Associate secretary: Susan ]. Friedlander ematics (SIAM). Announcement issue of Notices: October 2010 Associate secretary: Lesley M. Sibner Program first available on AMS website: November 1, 2010 Announcement issue of Notices: To be announced Program issue of electronic Notices: January 2011 Program first available on AMS website: To be announced Issue of Abstracts: Volume 32, Issue 1 Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Deadlines For organizers: April1, 2010 Deadlines For consideration of contributed papers in Special Sessions: For organizers: April1, 2012 To be announced For consideration of contributed papers in Special Sessions: For a:bstracts: To be announced To be announced For abstracts: To be announced Boston, Massachusetts john B. Hynes Veterans Memorial Conven­ tion Center, Boston Marriott Hotel, and Boston Sheraton Hotel January 4-7,2012 Wednesday - Saturday ]oint Mathematics Meetings, including the 118th Annual Meeting of the AMS, 95th Annual Meeting of the Mathe­ matical Association ofAmerica, annual meetings of the As­ sociation for Women in Mathematics (A Jii!M) and the National Association ofMathematicians (NAM), and the winter meet­ ing of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and Applied Math­ ematics (SIAM). Associate secretary: Michel L. Lapidus Announcement issue of Notices: October 2011 Program first available on AMS website: November 1, 2011 Program issue of electronic Notices: January 2012 Issue of Abstracts: Volume 33, Issue 1

Deadlines For organizers: April1, 2011

854 NOTICES OF THE AMS VOLUME 53, NUMBER 7 Meetings and Conferences of the AMS

Associate Secretaries of the AMS 249), Chicago, IL 60607-7045; e-mail: susan@math. nwu. edu; tele­ Western Section: MichelL. Lapidus, Department of Math­ phone: 312-996-3041. ematics, University of California, Sproul Hall, Riverside, CA Eastern Section: Lesley M. Sibner, Department of Mathe­ 92521-0135; e-mail: l api dus@math. ucr. edu; telephone: 951- matics, Polytechnic University, Brooklyn, NY 11201-2990; 827-5910. e-mail: lsi bner@duke. poly. edu; telephone: 718-260-3505. Central Section: Susan J. Friedlander, Department of Math­ Southeastern Section: Matthew Miller, Department of Math­ ematics, University of Illinois at Chicago, 851 S. Morgan (M/C ematics, University of South Carolina, Columbia, SC 29208- 0001, e-mail: mill er@math. sc. edu; telephone: 803-777-3690.

The Meetings and Conferences section of the Notices June 4-7 Rio de Janeiro, Brazil p.852 gives information on all AMS meetings and conferences October 4-5 Vancouver, Canada p.852 approved by press time for this issue. Please refer to the page October 24-26 Huntsville, Alabama p.852 numbers cited in the table of contents on this page for more December 17-21 Shanghai, People's detailed information on each event. Invited Speakers and Republic of China p.853 Special Sessions are listed as soon as they are approved by the cognizant program committee; the codes listed are needed 2009 for electronic abstract submission. For some meetings the list January 7-10 Washington, DC p. 853 may be incomplete. Information in this issue may be dated. Annual Meeting Up-to-date meeting and conference information can be March 27-29 Urbana, Illinois p.853 found at www. ams. org/meeti ngs/. 2010 Meetings: January 6-9 San Franciso, California p.853 2006 Annual Meeting October 7-8 Salt Lake City, Utah p.834 2011 October 21-22 Cincinnati, Ohio p.836 January 5-8 New Orleans, Louisiana p.854 October 28-29 Storrs, Connecticut p.838 Annual Meeting November 3-4 Fayetteville, Arkansas p.841 2012 January 4-7 Boston, Massachusetts p.854 2007 Annual Meeting January 5-8 New Orleans, Louisiana p. 841 2013 Annual Meeting January 9-12 San Diego, California p. 854 March 3-4 Davidson, North Carolina p. 848 Annual Meeting March 16-17 Oxford, Ohio p.849 Important Information Regarding AMS Meetings April14-15 Hoboken, New Jersey p.849 April21-22 Tucson, Arizona p. 849 Potential organizers, speakers, and hosts should refer to page 296 in the February 2006 issue of the Notices for gen­ July 31-August 3 Warsaw, Poland p.850 eral information regarding participation in AMS meetings and October 5-6 Chicago, Illinois p.850 conferences. October 6-7 New Brunswick, New Jersey p.850 October 13-14 Albuquerque, New Mexico p.850 Abstracts November 3-4 Murfreesboro, Tennessee p.851 Speakers should submit abstracts on the easy-to-use interactive December 12-15 Wellington, New Zealand p. 851 Web form. No knowledge of m_pc is necessary to submit an electronic form, although those who use LAI_EX may submit 2008 abstracts with such coding, and all math displays and simi­ January 6-9 San Diego, California p.851 larily coded material (such as accent marks in text) must Annual Meeting be typeset in m_pc. Visit http://www.ams.org/cgi-bin/ abstracts/abstract. pl. Questions about abstracts maybe March 22-23 New York, NY p.851 sent to abs-i nfo@ams. org. Close attention should be paid March 28-30 Baton Rouge, Louisiana p.851 to specified deadlines in this issue. Unfortunately, late ab­ April4-6 Bloomington, Indiana p.852 stracts cannot be accommodated. May 3-4 Claremont, California p.852

AUGUST 2006 NOTICES OF THE AMS 855 CAMBRIDGE

Music: Lectures on the Ricci Flow Principles A Mathematical Peter Topping of Statistical Offering The Ricci flow, introduced by Hamilton Inference David J. Benson in 1982, has attracted considerable interest D.R.Cox Since the time of the via the work of Perelman and his work In this definitive book, Ancient Greeks, much on the Poincare conjecture and Thurston's D. R. Cox gives a compre­ has been written about geometrization conjecture; this book hensive and balanced the relation between provides an introduction to the subject appraisal of statistical mathematics and music; following Perelman's approach. inference. He develops here, Benson provides London Mathematical Society Lecture Note Series the key concepts, describ­ a wealth of information to enable the teacher, $39.99*: Paperback: 0-521-68947-3: 140pp ing the main ideas and controversies over the student, or the interested amateur to under­ foundational issues that have been keenly stand, at varying levels of technicality, the real argued for more than two hundred years. interplay between these two ancient disciplines. Elliptic Functions $80.00*: Hardback: 0-521 -86673-1: 250pp $90.00*: Hardback: 0-521-85387-7 : 400pp $34.99*: Paperback: 0-521 -68567-2 $42.99*: Paperback: 0-521 -61999-8 V.Armitage In its first six chapters, this text presents the basic ideas and properties of the Jacobi The Coordinate-Free Approach Additive Combinatorics elliptic functions as a historical essay, exploring to Linear Models Terence Tao and Van H. Vu what the treatment of ell iptic functions would Michael J. Wichura Additive combinatorics is the theory of counting have been like if Abel, rather than Jacobi, had This book is about the coordinate-free, or additive structures in sets. This graduate-level developed the ideas. The later chapters present geometric, approach to the theory of linear textbook will allow students and researchers a more conventional approach to the Weierstrass models; more precisely, Modell AN OVA and easy entry into this fascinating field. functions and to elliptic integrals, and then the reader is introduced to the richly varied linear regression models with non-random Cambridge Studies in Advanced Mathematics predictors in a finite-dimensional setting. $11 0.00*: Hardback: 0-521-85386-9: 570pp applications of the elliptic and related functions. London Mathematical Society Student Texts This approach is more insightful, more elegant, $90.00*: Hardback: 0-521-78078-0: 420pp and more direct than the more common matrix $42.99*: Paperback: 0-521-78563-4 Combinatorial Matrix Classes approach to linear regression, analysis of variance, and analysis of covariance models Richard A. Brualdi in statistics. This is the first book devoted exclusively to Third Edition! Cambridge Series in Statistical and Probabilistic existence questions, constructive algorithms, Mathematics enumeration questions, and other properties The Cambridge $50.00*: Hardback: 0-521-86842-4: 216pp concerning classes of matrices of combinatorial Dictionary of significance. Statistics Encyclopedia ofMathematics and its Applications Second Edition! $110.00: Hardback: 0-521-86565-4: 560pp B. S. Everitt Praise for the Weather Prediction by Second Edition: Numerical Process Lectures on the Combinatorics "This is already the lewis Fry Richardson of Free Probability most useful book on my The idea of forecasting the weather by Alexandru Nica and Roland Speicher shelf... [it is an] excellent calculation was first realized by Lewis Fry value and it is highly This book gives a self-contained and compre­ Richardson. The first edition of this book, recommended as a reference text for anyone hensive introduction to free probability theory, published in 1922, set out a detailed algorithm who is even mildly interested in statistics." focusing on the combinatorial aspects. The for systematic numerical weather prediction. volume can be used as a text for an introductory -The Statistician This edition contains a new foreword by Peter course (on an advanced undergraduate or $95.00*: Hardback: 0-521-86039-3: 450pp Lynch that sets the original book in context. $45.00*: Paperback: 0-521 -69027-7 beginning graduate level), and is also well-suited Cambridge Mathematical Library for the individual study of free probability. $55.00*: Paperback: 0-521 -68044-1 : 250pp London Mathematical Society Lecture Note Series $75.00*: Pa perback: 0-521 -85852-6: 335pp '*prices subject to change

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The Asian Journal of Mathematics, Volume 10, Number 2 (June 2006): A Complete Proof of the Poincare and Geometrization Conjectures -Application of the Hamilton-Perelman Theory of Ricci Flow by H.-D. Cao and X. Zhu

The Poincare conjecture is one hundred years old, and one of the seven "Millennium Prize Problems" in mathematics. In the past two decades, Ricci flow and in particular, Richard Hamilton's work therein, has received much attention as both having a profound influence on geometric evolution equations and as a possible approach to studying Thurston's Geometrization Conjecture. Editors-in-Chief: Raymond Chan In this paper, Huai-Dong Cao (Lehigh University) and Xiping Zhu (Sun Yat-Sen Shing-Tung Yau University, China) provide an essentially self-contained description of both the ISSN: 1093-6106 fundamental works of Hamilton and Perelman's recent breakthrough, as well as the Issues: 4/year important contributions by many others to the subject of Ricci flow and its application US$398 annually to the geometrization of three-manifolds. US$69.00 for issue The paper offers a complete proof of the famous Poincare conjecture and the Thurston E t.\0\fll\ geometrization conjecture based on the Hamilton-Perelman theory ofRicci flow. p..'Jf:lo.\\-f:lo.S\-

Also Available: Collected Papers on Ricci Flow Editors: H.-D. Cao, B. Chow, S.C. Chu and S.-T. Yau This collection of papers makes readily available in one book the works of Hamilton and others on Ricci flow. Graduate students or researchers unfamiliar with Ricci flow may use this book as an introduction to the topic which quickly leads readers to current research topics and open problems, and geometers already familiar with Ricci flow may use it as a handy reference containing almost all of Richard Hamilton's papers on the subject to date. 2003 I 545 pp. I Hardcover I $64.00 I ISBN 1-5 7146-110-8 I 978-1-57146-110-0

Collected Papers on Ricci Flow, Volume II - Forthcoming!

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