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New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required. The book covers a variety of topics that thus lays a rigorous basis for geometry while at other integrals of theta functions, Eisenstein are considered central to mathematical the same time giving the student tools that will series, particular values of theta functions, the cryptography and is an ideal introduction for be useful in other courses. Rogers- Ramanujan continued fraction, other q- mathematics and computer science students to continued fractions, other integrals, and parts of the mathematical foundations of modern 2008. Approx. 410 p. 300 illus. (Universitext) Hecke’s theory of modular forms. cryptography. The book includes an extensive Softcover bibliography and index; supplementary materials ISBN 978-0-387-78240-9  approx. $49.95 2008. Approx. 430 p. 3 illus. Hardcover are available online. ISBN 978-0-387-77765-8  approx. $89.00 Surveys in Number Theory 2008. Approx. 540 p. 65 illus. (Undergraduate Texts in Mathematics) Hardcover K. Alladi, University of Florida, Gainesville, FL, Naive Lie Theory ISBN 978-0-387-77993-5  $49.95 USA (Ed.) J. Stillwell, University of San Francisco, CA, USA Number theory has a wealth of long-standing This book aims to fill a gap in the literature by Multiscale Methods problems, the study of which over the years has introducing Lie theory to junior and senior level led to major developments in many areas of undergraduates. In order to achieve this, the Averaging and Homogenization mathematics. This volume consists of seven author focuses on the so-called “classical groups,’’ G. Pavliotis, Imperial College,London, London, significant chapters on number theory and viewed as matrix groups with real, complex, or England; A. Stuart, University of Warwick, related topics. Written by distinguished quaternion entries. This allows them to be London, England mathematicians, key topics focus on multiparti- studied by elementary methods from calculus Multiscale Methods begins by setting the tions, congruences and identities (G. Andrews), and linear algebra. Each chapter is enhanced theoretical foundations of the methods and then the formulas of Koshliakov and Guinand in with numerous exercises, discussion of further moves on to develop models and prove Ramanujan’s Lost Notebook (B. C. Berndt, Y. Lee, results, and historical comments. theorems. Numerous examples show how to and J. Sohn), alternating sign matrices and the apply multiscale methods to solving a variety of 2008. Approx. 225 p. 25 illus. (Undergraduate Texts Weyl character formulas (D. M. Bressoud), theta problems. Exercises allow the reader to build in Mathematics) Hardcover functions in complex analysis (H. M. Farkas), their own skills and put them into practice. representation functions in additive number ISBN 978-0-387-78214-0  approx. $49.95 theory (M. B. Nathanson), and mock theta 2008. Approx. 330 p. (Texts in Applied Mathematics, Volume 55, Number 5, Pages 553–656, May 2008 functions, ranks, and Maass forms (K. Ono), and Volume 53) Hardcover elliptic functions (M. Waldschmidt). ISBN 978-0-387-73828-4  $49.95

2008. Approx. 200 p. (Developments in Mathematics, Volume 17) Hardcover ISBN 978-0-387-78509-7  approx. $69.95

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Patterns in factorization (see page 595)

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Communications 573 576 Interview with George Csicsery Bill Casselman 586 WHAT IS...a Toric Variety? Ezra Miller 593 Kontsevich and Witten Receive 2008 Crafoord Prize in Mathematics 594 Deligne, Griffiths, and 579 560 Mumford Receive 2008 Wolf Prize 596 Taubes Receives NAS Award in Mathematics Feature 598 2008 Award for an 560 Interview with Martin Davis Exemplary Program or Achievement in a Allyn Jackson Mathematics Department The Notices talks to the distinguished logician. 599 University of Iowa Wins Exemplary Program Award 603 Mathematics Programs that Make a Difference Featured Communications 605 2008 JPBM Communications Award 579 Visualizing the Sieve of Eratosthenes 606 MAA Prizes Presented in David Cox San Diego 609 AWM Awards Given in San Diego 588 Evansville Honors the First Black Ph.D. in Mathematics and His Family Commentary Talitha Washington 557 Opinion: Triumphs and Struggles in a Mathematics Classroom 590 Ask Professor Nescio Jesse Johnson

558 Letters to the Editor 573 Julia Robinson and Hilbert’s Tenth Problem—A Movie Review Reviewed by Carol Wood 583 Unknown Quantity—A Book Review Reviewed by Sanford Segal Notices Departments of the American Mathematical Society About the Cover...... 595 Mathematics People ...... 611 EDITOR: Andy Magid Gilbert Receives NAS Award, Feigenbaum Awarded Heineman Prize, ASSOCIATE EDITORS: Chavez Receives AAAS Mentor Award, Schedler Receives AIM Five-Year Daniel Biss, Susanne C. Brenner, Bill Casselman (Graphics Editor), Robert J. Daverman, Susan Fellowship, 2008 Clay Awards Announced, Iyama Wins ICRA Award, Friedlander, Robion Kirby, Steven G. Krantz, National Academy of Engineering Elections, Alex Rosenberg (1926– Lisette de Pillis, Peter Sarnak, Mark Saul, John Swallow, Lisa Traynor 2007). SENIOR WRITER and DEPUTY EDITOR: Mathematics Opportunities...... 614 Allyn Jackson NSF Postdoctoral Research Fellowships; NSF-CBMS Regional MANAGING EDITOR: Sandra Frost Conferences, 2008; Call for Proposals for 2009 NSF-CBMS Regional CONTRIBUTING WRITER: Elaine Kehoe Conferences; International Mathematics Competition for University PRODUCTION ASSISTANT: Muriel Toupin Students; News from the IMA; News from IPAM. PRODUCTION: Kyle Antonevich, Stephen Moye, Erin Murphy, Lori Nero, Karen Ouellette, Donna Salter, Inside the AMS...... 617 Deborah Smith, Peter Sykes Epsilon Awards for 2008, From the AMS Public Awareness Office, ADVERTISING SALES: Anne Newcomb MathSciNet Links to Genealogy Project, Deaths of AMS Members.

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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

But the result is that in class my students can explain Triumphs and not only procedurally how to solve an equation for an unknown but also why and how they are using inverse operations to do so. They can determine if three given Struggles lengths can form a triangle and also explain how the tri- angle inequality supports their reasoning. They challenge in a Mathematics each other to justify their thinking when discussing a solution, they are articulate in their presentations at the Classroom board, and their leadership and confidence has created a community in which I am just one of many resources for I first met JR two years ago in his 9th grade year when I them in a room full of teachers. My students are empow- was student teaching. He was a small kid on a skateboard, ered to come up with their own ideas, and they literally Leonardo DiCaprio’s Puerto Rican doppelganger. Funny, applaud the ideas of others. They have a good time doing manipulative, and bright, he was a serious troublemaker, mathematics—which is why those of us who love math- distracted and distracting in the classroom. In his 10th ematics do it in the first place. grade year, he doodled through his math class, chatted But also, the achievement and learning I observe in my with other students, smiled a lot and rarely did any math. classroom does not accurately predict either the success But he had brief moments of brilliance, unpredictably my students have on standardized tests, or the kinds of spouting out articulate explanations for his mental solu- choices they make in their lives outside of school. As the tions to problems. And then he got held back a grade. school year progressed, JR’s grades fell. He missed school I was a little bit terrified when I saw his name on my for court dates regarding graffiti charges, failed the first roster for 10th grade this year. Students who have been marking period, and ended up transferring to a school held back are often unsuccessful in their repeating years, in New Jersey. I hope he has found a fresh start there. I powerfully influencing the social system of their classes hope he finds success. I hope that he brings his will and with negative and disruptive attitudes. JR had been pretty imagination to his new community. I hope he is one of difficult even when he was on track. I was worried. those popular brilliant kids that make it cool to be good To my surprise, as the school year started, JR was the at school. delight of our entire class. He was outspoken, clever, and JR may still fall through the cracks. The work being done funny. He could be distracting, but he was often a model in my classroom may not yield success that can be seen in mathematics student: he worked hard, explained his ideas standardized testing. Perhaps my work is not enough, or well, participated in the class discussion every day, turned perhaps the tests are assessing something different from in his homework, and enjoyed class. He raised the bar for what I am teaching. Perhaps my students’ lack of strong intelligence, participation, and work in our classroom. His mathematics background prior to high school simply de- attitude and humor brought joy to the mathematics that mands more time to prepare them. Regardless, I intend to we explored and brought out the best in me as a teacher. enliven mathematics for my students, inspire their lead- His presence made the classroom a better place to be. ership, cultivate their problem solving, and induct them I teach algebra and geometry now at the same small into the community of mathematicians. Whatever JR does school where I first met JR. New Design High School is in his future, he has been a mathematician, excited in his a holistic college prep school on the Lower East Side of moments of discovery and brave in his leadership in the classroom. I hope he finds a way to return to it. Manhattan devoted to the success of students whose edu- cations have not heretofore prepared them for college or —Jesse Johnson life in general. Our students arrive at high school terrified New Design High School, New York City, of fractions, struggling with signed numbers, unused to Math for America Newton Fellow homework, and sometimes having forgotten the basics of multiplication and division. Nevertheless I work to promote discovery, inspire in- quiry, and cultivate a deep understanding of the whys of the mathematics we study. I ask my students to develop independence in problem-solving by working in groups and asking each other questions before they ask me. I ask them to discuss and debate their ideas, to justify their mathematical thinking, and explain the mathematical thinking of others. I ask them to be fearless about mak- ing mistakes and trying strategies they aren’t sure of. It is difficult for them; they want to know if they are right or wrong, they are uncomfortable with not knowing, they get frustrated when I don’t tell them the answer right away.

May 2008 Notices of the AMS 557 Letters to the Editor

Paying for Paid Referees broadly conceived MRC Conference Of course, the first idea does not In the May and October issues of would actually devolve into catering make a splash. It is disheartening that the Notices (vol. 54, pp. 589 and (pandering?) to a fashionable clique the AMS nowadays feels compelled, 1119), Michael Fried proposes that within the broadly-defined subject in so many things, to make a splash. mathematical journals should pay area. Whether or not scenario (b) ever referees. Of course, it would be nice arises, it seems to me that a majority —Gautam Bharali if we referees (yes, I was and also am of peridoctoral researchers will have Indian Institute of Science referee of many papers) would get to make their way into the world in [email protected] paid and good referees certainly de- the traditional style while they wait serve it. But where would the money for a “structured activity” to come (Received February 2, 2008) come from? Mathematicians have their way. been making big efforts (even leaving There is a strong undercurrent of editorial boards in protest for high passion and risk-taking inherent in My Teach for America prices), with strong support from the doing good mathematics. While most Experience AMS and its Notices, to make journals math today is collaborative in nature, John Haws recommends that young less expensive, so libraries (and in- any aspiring mathematician has to mathematicians apply to Teach For dividuals) can afford them. Clearly, learn how to independently conceive America, a national non-profit that paying referees would make journals of a research project. This necessi- places teachers in some of the highest considerably more expensive. tates a certain loneliness in which the needs school districts in the country. mathematical individuality can de- In his article, he shares his success- —Janos Aczel velop, and the risk of crashlandings ful experience in “making a differ- Distinguished Professor Emeritus as the young mathematician learns ence” in the lives and educations of University of Waterloo, Ontario to invent. The MRC would, I am sure, the students he taught, as well as [email protected] nurture a happy school of profession- emphasizing that he benefited from als, all of whom would know each “the insight, skills, and confidence” (Received December 23, 2007) other, and would be on first-name that he gained while teaching in the terms with a clutch of conspicuous Rio Grande Valley. The Mathematical Research and energetic senior mathematicians. I am following a trajectory similar Communities But are we convinced that the quan- to his: as I was finishing my under- I read the report “Building a research tum of self-reliant mathematicians graduate education, I successfully career” (Notices, Feb. 2008) with and well-conceived research projects applied to Teach For America, taught amusement and skepticism. What would be markedly smaller if the MRC in a high school in Newark, NJ, for amused me was the yuppiespeak: never existed? three years, and am now pursuing an “…provide them with structured ac- If all this did not involve public M.S. in math. tivities aimed at building social and money—and the imperative to be ef- To those who, after reading Mr. collaborative networks…” What next? ficient with it—I would not be writing Haws’ article, would apply to Teach Should a young mathematician con- this. I too have been in collaborations, For America, I would offer some sider investing in a Rolodex? Lest I in my peridoctoral years, with peri- words of warning. Nothing in my life, appear to cavil at a well-intentioned doctoral colleagues. We got together before or since, left me so physically, idea, let me clarify that facilitating because of an affinity of interests, emotionally, or spiritually drained as bonds between young researchers is and not because we were put into a any one day of teaching, let alone the a superb idea and one that is over- talented persons’ summer camp by struggle to persist week after week. due. What makes me pause is the the AMS. Yes, we would definitely Furthermore, I feel as if nothing could jamboree aspect of the Mathematical have appreciated access to funds that have prepared me for the task I took Research Communities (MRC) idea. would have enabled us to meet face- upon myself. In November of my first Firstly, consider this: “Careful to-face at crucial junctures when the year of teaching, the word at the fore- choices of conference topics over the collaboration needed it. Perhaps, if front of my mind was inadequacy; years will ensure that a wide range the MRC had recognized this type of specifically, my own inadequacy at of mathematical areas is covered.” need, it could have spread its money teaching math to the young people Really? Given that two of the three among a larger number of needy in my classes. MRC conferences in 2008 involve a cases. After all, it costs less per capita Furthermore, when I ultimately left measly 20 participants, one fears when one unit of a research group my school, I had very few illusions that either: (a) Each MRC Confer- is funded to fly, say, once a year, about the amount of change that my ence would have to be considerably to meet up with a (static) colleague presence had brought about. When I more narrowly defined in order to than to host a jamboree wherein 100 started in September of 2004, I was attain critical mass with a mere 20–25 percent of a small target group has the teacher with the least seniority participants; or (b) An ostensibly to be flown/fed/housed. (not to mention virtually no training

558 Notices of the AMS Volume 55, Number 5 Letters to the Editor in math education). Had I remained another year, in September of 2007 I would have been the math teacher 2008 Joint Meeting who had been at the high school for the third longest amount of time, out of nine teachers. Furthermore, my de- of the AMS-SBM partment chairperson was frantically searching for four math teachers for the following year. All of the above Instituto Nacional de Matemática is to suggest that the problems that Pura e Aplicada (IMPA) faced the school where I taught, and which are replicated in hundreds Rio de Janeiro, Brazil of schools across the country, can at best be alleviated, and then, only June 4–7, 2008 slightly, by any one person’s short- term commitment. If I were in a position to recom- mend a course of action to young mathematicians, I would plead with them to become involved in math SBM education. If Teach For America were the vehicle that young mathemati- Sociedade Brasileira de Matemática cians choose to begin teaching, I would support their choice because, undoubtedly, without the commit- ted participation of a sizeable part of the mathematical community, the problems faced by our youth cannot be solved. But I would also caution the young mathematicians that they should not let themselves be fooled. Plenary Speakers The problems that need solving have something to do with innovative Ruy Exel, Universidade Federal de Santa Catarina teachers and curricula, as Haws sug- Velimir Jurdjevic, University of Toronto gests, but they have much more to do with a set of institutions that Andre Nachbin, IMPA systematically direct resources away Richard M. Schoen, Stanford University from the vulnerable and towards the powerful in our society. Teach For Ivan P. Shestakov, University of Sao Paulo America never names these institu- Amie Wilkinson, Northwestern University tions, so let me do that here: insti- tutional racism, segregation, capital liberalization, the military-industrial complex. Young people who commit For accommodations, travel, and the scientific to working to ensure that schools program, go to: everywhere are going to have the www.ams.org/amsmtgs/ teachers they need ought to be aware internmtgs.html that those are the obstacles they are fighting to overcome. I don’t say this to make the reader despair that nothing can be done, but as a matter of intellectual honesty, and as an encouragement to analyze the full scope of the challenge and its implications. —Matteo Tamburini Western Washington University [email protected]

(Received February 5, 2008)

May 2008 Notices of the AMS 559 Interview with Martin Davis

artin Davis is one of the world’s outstand- latter). The unsolvability of Hilbert’s Tenth Problem ing logicians. He was born in 1928 in New follows immediately. York City, where he Davis became one of the earliest attended City College computer programmers when he and was influenced by began programming on the ORDVAC MEmil L. Post. Early on, Davis came computer at the University of Illinois under the spell of Hilbert’s Tenth in the early 1950s. His book Com- Problem: Does there exist an al- putability and Unsolvability [3] first gorithm that can, given an arbi- appeared in 1958 and has become a trary Diophantine equation, decide classic in theoretical computer sci- whether that equation is solvable? ence. After a peripatetic early career Davis’s Ph.D. dissertation, written that included stints at Bell Labs in at Princeton University under the di- the era of Claude Shannon and at the rection of Alonzo Church, contained RAND Corporation, Davis settled at a conjecture that, if true, would New York University, where he spent imply that Hilbert’s Tenth Problem thirty years on the faculty and helped is unsolvable. In rough terms, the to found the computer science de- conjecture said that any computer partment. He retired from NYU in can be simulated by a Diophantine 1996 and moved to Berkeley, Cali- equation. The implications of this fornia, where he now resides with his conjecture struck many as unbeliev- wife Virginia, who is a textile artist. able, and it was greeted with a good Davis has a strong interest in history, deal of skepticism; for example, the and in 2000 he published a popular conjecture implies that the primes book The Universal Computer [4], are the positive part of the range which follows a strand in the history Martin Davis of a Diophantine polynomial. Work of computing from Leibniz to Turing during the 1950s and 1960s by Davis, Hilary Putnam, (the book also appeared under the name Engines of and Julia Robinson made a good deal of headway to- Logic; it was reviewed by Brian Blank in the May 2001 wards proving the conjecture. The final piece of the issue of the Notices). puzzle came with work of Yuri Matiyasevich, in 1970. What follows is the edited text of an interview with The resulting theorem is usually called either DPRM or Martin Davis, conducted in September 2007 by Notices MRDP (Matiyasevich favors the former and Davis the senior writer and deputy editor Allyn Jackson.

Early Years relief” and later called welfare. I went to school Notices: I’d like to start at the beginning of your in the New York public school system, benefiting life. Could you tell me about your family? Were you from the Bronx High School of Science. Later I an only child? went to City College where the tuition was free. I was not an athletic boy at all. I was a bookish boy. Davis: I had a younger brother who died in And I got beat up a lot by more athletic boys! I got childhood. He was 8 and I was 13. interested in science quite early. I wanted to be a Notices: That must have been very hard on paleontologist, then I wanted to be a physicist, and your family. finally I fell in love with mathematics. Davis: It was devastating. My parents grew up Notices: What were your early influences as a in Poland; they were Polish Jews. They knew one child or teenager in pushing you toward math and another casually in Lodz but met again in New science? Was it teachers, or books? York and married. We were hit very hard by the Davis: It was certainly more books. I read Photography © 2007 by Peg Skorpinski. Peg by 2007 © Photography Great Depression and were really quite poor. For Bell’s Queen of the Sciences, and was delighted by a while we were on what was then called “home another book that, as a mature mathematician I

560 Notices of the AMS Volume 55, Number 5 thought rather awful, Mathematics and the Imagi- Notices: So your parents encouraged you to get nation, by Kasner and Newman. At high school I an education. met a lot of boys who had similar interests, and Davis: Oh yes, that was the given in Jewish fami- we bounced off one another. Then at City College, lies in the Bronx. They imagined I would become a there were two people who had a big influence on doctor or a lawyer, and they were at a loss to know me. One was Emil L. Post, who was a great logician what to make of the direction my interests were and a very direct influence on the direction of my taking. They simply didn’t know what it was and work, and Bennington Gill, who was really a very were worried I would starve in a garret! And of inspiring teacher, even though his mathematical course an academic career for a Jew in America was productivity pretty much ended with his disserta- a very difficult thing before the war. That changed tion. dramatically after the war. Notices: Can we go back to the Bronx High Notices: You mentioned the influence on you School of Science? What was it like to be of Emil Post. Can you tell me about a student there at that time? him and the changes that were going Davis: It was during the Second World on in logic at that time, with the work War, and that dominated the atmosphere of Church and Turing? in many ways. The principal went to Davis: Goodness, that’s a lot! You Washington and talked to various people know, I edited Post’s collected works in the government and came back with [6] and wrote an introductory article the idea of what were called “pre-induc- on his life and work. I gave a talk about tion courses”, to modify the curriculum him here at the Logic Colloquium just in the direction of subjects that would a couple of weeks ago. We could spend be useful when we were taken into the the whole interview talking about that! army, which, it was assumed, we would Briefly, Post was a bit older than Church be. So for example, light and sound and certainly older than Turing, and so were deleted as topics from the physics he came into these ideas well before curriculum, and what was thrown in to them, in the early 1920s. From one replace them was a lot more work on point of view, he really discovered all alternating current circuits and things of the main results well before them. From that sort. We were told that these were another point of view, he never got his very significant things and that a great formulations to the point where they deal of attention would be paid once we would have been acceptable for publica- were in the army due to the fact that we tion. Post’s own comment on this I find had had these courses—which of course very poignant. He was always writing was a lot of nonsense. postcards to people and sent one to The faculty adviser for the Math- Gödel shortly after they met. He apolo- ematics Club thought that we should gized for what he thought was his over- do things that were more useful, so suddenly we exuberant behavior with Gödel and then said about spent the semester talking about navigation and his own earlier contributions, “The best I can say is spherical trigonometry. that in 1921 I would have proved Gödel’s theorem if I had been Gödel.” Notices: Did you find navigation interesting? Davis: I found it boring! I remember I gave a talk Notices: So he knew of Gödel’s result but wasn’t about dead reckoning, which was the technique able to carry it through himself. that Columbus used. I was also president of the Davis: The problem was that, in effect, Post Astronomy Club for a while. bumped up against what later was called Church’s Thesis, or the Church-Turing Thesis, and didn’t Notices: You were clearly very motivated toward see how to justify it properly. His formulation education. How much education did your parents was fundamentally based on the assumption of have? the adequacy of Russell and Whitehead’s Prin- Davis: They had no formal education. They cipia Mathematica, for anything that could be went to night school courses for immigrants to done mathematically, whereas Gödel’s theorem learn English. My father was really a remarkable itself partly contradicted that. So Post decided man. His life would have been very different under that what was needed was something he called other circumstances. He worked hard to support “psychological fidelity”, which would somehow the family, but he was a very gifted artist. Recently encompass any processes that the human mind we donated thirteen of his paintings to the YIVO could develop. And then he just went totally off Institute for Jewish Research in New York; they the track, in my opinion, in how to develop such formed a cycle inspired by events in Europe dur- a thing. In effect, what he was looking for is what ing the Second World War, especially by what was Turing did to analyze the notion of a computation, happening to the Jews. but he didn’t find it. Post had other difficulties.

May 2008 Notices of the AMS 561 One was that he suffered from bipolar disease. Ginsburg, who became a computer scientist and He was a manic-depressive and had episodes that an expert on context-free languages. People who were totally debilitating. Also, he faced a climate arrived a little later included Donald Newman, of mathematical opinion that was somewhat hos- Jack Schwartz, Leon Ehrenpreis, and Bob Aumann, tile to the whole enterprise of mathematical logic. 2005 Nobel Laureate in economics. I should also For example, some of the important results in his mention John Stachel, who is now an Einstein dissertation were not accepted for publication scholar at Boston University. John was a broadly until they finally appeared a decade later, as an educated physics major with strong mathematical Annals study. interests. I learned a lot from him about various I had done calculus somewhat on my own before things. His father was an important member of coming to City College, so I started with elective the American Communist Party, which in those advanced courses right at the beginning. In my years was a tricky business. During the McCarthy sophomore year, there was a course that Post gave years, which of course came later, John was quite in real variable theory, which was quite famous isolated. One of our fellow mathematics students, among City College students. But because of the Herman Zabronsky, wrote a dissertation at Penn, war it wasn’t going to be given. So five of us went to and later got a job at a national lab, Oak Ridge or him and asked whether he would be willing to give Los Alamos. Around Christmas week he came back it as what was to New York, and a bunch of us were going to get called an hon- together somewhere, and he stipulated that John ors course, in Stachel shouldn’t be there. He said, “If John Stachel effect a read- is there I’m going to flunk the lie detector test”—to ing course. He give you an idea of the atmosphere! agreed, and At City College, there was a required course for we met once a science majors in logic and scientific method, given week for a two- in the Philosophy Department. I took that course hour period. in my freshman year, and it turned out to be a Every one of beginning course in symbolic mathematical logic. the five of us So I learned the basics of propositional calculus would tell you and quantification theory as a freshman in that that this was philosophy course. There wasn’t any meta-theory, an emotionally but still it meant I knew the basic material very wringing expe- early. I read in Bell’s Development of Mathematics rience! that Post in his dissertation had developed a many- Notices: Why? valued logic. So I knew that he worked in the area Davis: The pedagogical method was the follow- of logic. His real variable theory course certainly ing. We had a textbook, which was awful; it was just touched on topics close to logic. Also, I had heard full of mistakes. So Post had prepared about forty about Gödel, and there was a copy in the City pages of material correcting and supplementing College library—undoubtedly because Post put the text. Each week we were given an assignment it there—of the mimeographed notes that Kleene for the next week in which there was a certain and Rosser had taken of Gödel’s 1934 lectures at amount of text with accompanying notes that we the Institute for Advanced Study. The notes were had to read, absorb, and learn. Then what would published in reasonable form only much later, first happen during the two-hour period is that he in my anthology The Undecidable [5], and then would randomly call on us to go to the blackboard, in Gödel’s Collected Works. So I took it out of the with no notes, and expound parts of the text. This library and tried to make sense of it quite early, was very hard! But it was great training. and I associated all that with Post—I don’t exactly Notices: Did some of these five other than you know why or how, but somewhere along the line, go on in mathematics? I started talking with Post regularly. He gave me Davis: All of us. a batch of his reprints. John Stachel and I asked Notices: So maybe he did something right! Post if we could do a reading course with him in Davis: Well, at that time, the mathematical tal- mathematical logic. That was in my junior year. ent at City College was just incredible. Everywhere We didn’t get very far in the course, because Post you go, you find mathematicians who were gradu- had one of his breakdowns after a few weeks. He ates of City College. had just made an important discovery regarding Notices: Who do you remember in particular? incomparable degrees of unsolvability, and the Davis: In the group in that real variable class, excitement was too much for him and pitched him there was Murray Rosenblatt, who is a probabilist over into the manic phase. We didn’t see him again at La Jolla. Also Gerry Freilich, who wrote a fine for some months. dissertation and was on the faculty at Queens Col- Notices: You are mentioning Gödel and Post, lege; Julie Dwork, who was at Burlington; Seymour who had mental problems. And there are others,

562 Notices of the AMS Volume 55, Number 5 for example, Cantor. Do you think there is any as- student of Bochner’s there and was later a col- sociation between math and mental illness? league at NYU. Washnitzer, who later was on the Davis: Probably. Particularly logicians seem to faculty at Princeton, was an older student, and be prone to it! In fact, I had a joke with John Sta- to some extent acted as a mentor. Leo Goodman, chel. Post had lost an arm in a childhood accident. who is in the National Academy, is a sociologist Hans Reichenbach, who was sort of a logician and and a statistician who was part of my class. And a philosopher, came to City College for a semester of course John Nash was a fellow student when I to give some courses, and he was essentially stone was there. We didn’t get along at all. If you look deaf. Church had vision problems—he had bad at Sylvia Nasar’s biography of Nash [7], I make a cataracts, which in those days was much more of brief entrance. a problem than it is today. So the joke was that, if Notices: I read the book, but I don’t remember I’m going to be a logician, maybe I should give up what you had to say about Nash. a finger now, instead of something worse! Davis: She quotes me as saying that Nash once By the time I graduated City College, I knew I asked me whether I grew up in a slum. Serge Lang wanted to be a logician. I had written a term paper was also a fellow student in Princeton. for an advanced logic course in the Philosophy De- partment, which in a way was a first draft of part of Notices: What was he like in those days? Was he what was later my dissertation. I went to Princeton as intense and committed as he was later on? to work with Church, but I was really much more Davis: I knew him as being very eager to have influenced by Post than by Church. Emil Artin take him on as a student and very worried that that might not happen. I always had Culture Clash in Princeton friendly relations with him. Notices: How was it for you as a graduate student Notices: Was it when you were a graduate at Princeton? student that you got interested in Hilbert’s Tenth Davis: I was pretty unhappy there, all in all. Problem? Or was that earlier? Let’s say there was a very heavy culture clash. I Davis: Well, it was Post’s fault. An important grew up in a working class Jewish family in the paper of Post’s that was published in 1944 men- Bronx. At the City College cafeteria we had our tioned Hilbert’s Tenth Problem and said that it “mathematician’s table” where we argued and begged for an unsolvability proof. Most of my learned from each other. In that noisy atmosphere mathematical career I have had an ambivalent we had to speak loudly just to be heard. Besides in relationship with the problem. On the one hand, it our culture, a loud voice simply indicated excite- fascinated me and pulled me in, seduced me, and ment. I spoke at the Logic Seminar in Princeton on the other hand I felt that it was to a very large shortly after I arrived. Leon Henkin’s comment on extent a number theory problem, and I was no my talk was that it was too loud. Let me say without number theorist. When I was a graduate student I going into great detail that I certainly felt a culture kept thinking I should stay away from it, because clash. I finished my degree in two years and was I needed to write a dissertation! I had one topic very glad to leave when I was done. that I knew was going to be easy because it was Notices: Leon Henkin was a student there at the completely untouched territory—what was later same time? called the hyperarithmetic hierarchy—and that Davis: Earlier. He was a postdoc my first year. topic was one part of my dissertation. But the dissertation also included my first contribution Notices: What kind of person was Alonzo Church? to Hilbert’s Tenth Problem—what later was called Davis: Alonzo Church was a shy, retiring man, the Davis normal form. extremely pedantic, very compulsive in his hab- Notices: Post said that it needed an unsolvability its. A famous, quite true story about him is the proof. thorough way he would clean the blackboards Davis: It wasn’t hard to see. every day before his lecture. One day some of us Notices: Why was that? students cleaned the board before he came in. This Davis: Well, people have been working on Dio- had utterly no effect on his behavior; he cleaned phantine equations since Diophantus, and what it in exactly the same way. I have often thought is there to show for it? A lot of special cases. The that, when he was younger, when Kleene and idea that there should be a general algorithm that Rosser were in his classes and he was developing would tell you whether any Diophantine equation lambda calculus, he must have had a much more had a solution or not? That’s super-utopian. Once spirited lecture style. His lecture style was slow, it becomes possible to consider that problems tediously slow. of that kind could be solved negatively, Hilbert’s Notices: Who else was there among your student Tenth Problem was a natural candidate. When Post colleagues when you were at Princeton? said it begged for an unsolvability proof, he was Davis: My good friend from New York and exactly right, but that didn’t mean one knew how roommate later, Melvin Hausner, who was a to construct such a proof.

May 2008 Notices of the AMS 563 What I proposed in my a function. Yuri finally dissertation, and went a proved this hypothesis small way towards prov- ten years later by giv- ing, was a much stronger ing an explicit example. statement from which Georg Kreisel reviewed the unsolvability would our paper for Mathe- follow: That anything matical Reviews. In his that can be done by an al- review, he didn’t think it gorithmic process could was worthwhile noting also be defined by a spe- that we had shown that cific Diophantine equa- my conjecture, and con- tion. Yuri Matiyasevich sequently the unsolv- later referred to this as ability of Hilbert’s Tenth “Davis’s daring hypoth- Problem, would follow esis”. I had a reason for from the Julia Robinson thinking this might be Hypothesis, but he did true, even though the express his opinion that general opinion for years these results were likely was that it wasn’t, until not to have any con- it was proved finally by nection with Hilbert’s Yuri giving the last step. Tenth Problem. You can The experts all thought imagine why I like quot- it was false. It has to do ing that! with recursively enumer- Notices: Why did your able sets, which are sets conjecture seem hard to that can be listed by an believe? algorithm. The basic re- Davis: I can tell you sult from which unsolv- what Kreisel’s reason ability results follow is that there are recursively was. One of the things that follows from my con- enumerable sets that are not computable—for jecture-become-a-theorem is that not only is every which there is no deciding algorithm. My conjec- algorithmic process definable by a Diophantine ture was that every recursively enumerable set has equation, but it’s also definable by a Diophantine a Diophantine definition. The class of recursively equation with a bounded number of variables. enumerable sets has the key property that while In fact, later work of Julia and Yuri brought the it is closed under union and intersection, it is not number of variables down to 9. And such a bound closed under complementation: There is a recur- was thought to be totally implausible. sively enumerable set whose complement is not recursively enumerable. I could prove in a noncon- Notices: It does seem implausible, doesn’t it? It’s structive way, and it was easy, that the Diophantine really surprising. sets, the sets definable by Diophantine equations, Davis: Yes! The point is that people talked about have the same properties: They are closed under polynomial equations, but what they were thinking union and intersection but not under complemen- of was equations of degree maybe 3 or 4, and with tation. That made me think that they might be the maybe four or five unknowns. The idea of equa- very same class—which turned out to be true. tions of arbitrary degree and arbitrary number of unknowns—people had no intuition or experience Notices: But there was skepticism that this was with those. It was too hard. true. What was the reason for the skepticism? Hilary Putnam had a cute trick that turns any Davis: It seemed like a stretch that something Diophantine set into the positive part of the range as simple as polynomial equations could capture of a polynomial. When I was talking to number the full gamut of things that are algorithmic. Ten theorists before Yuri’s work, I would say, “Do you years after my dissertation there was a theorem of think the prime numbers could be the positive part me and Hilary Putnam and Julia Robinson [1] that of the range of a polynomial?” And often I would proved the analogue of that conjecture for expo- get the following answer: “No, that couldn’t be. nential Diophantine equations—that is, we proved Give me a half hour and I’ll prove it.” the conjecture under the assumption that you Notices: A half hour! That’s all they required? allow the equations to have variable exponents. Davis: Yeah! It followed from earlier work of Julia Robinson Notices: But it is counterintuitive, isn’t it? that the full conjecture would be a consequence Davis: Yes, sure it is! of what Hilary and I called “Julia Robinson’s Hy- pothesis”, that there is a polynomial Diophantine Notices: What gives Diophantine equations this equation whose solutions grow exponentially as power? What is the richness there?

564 Notices of the AMS Volume 55, Number 5 Davis: There are two pieces of richness. There to nine, that’s your result, you publish it.” He said, is the richness that reaches to exponentiation, that “No, it uses our methods, I’m not going to publish the set of triples a​, b​, and c​, such that a ​ ​b​c ​, has it unless you will be a joint author.” What finally a Diophantine definition. Logically speaking,= that happened is James Jones got permission from Yuri should have been the first thing proved, but it was to include the proof in a paper that he wrote, and the last. Way back in the 1950s, Julia started work- that’s how the proof was finally published [2]. ing on this and showed it would follow from what Notices: Can you tell me your memories of Julia Hilary Putnam and I later called the Julia Robinson Robinson, what she was like as a person? Hypothesis, which as I said wasn’t proved until Davis: Very nice, very straightforward. Broad Yuri did it in 1970. The second piece of richness in her interests, mathematical and otherwise. And is, once you have exponentiation, going all the way. great power—there is no question in my mind In the case of that first result, the richness comes that she was a much more powerful mathemati- from the power of second-degree Diophantine cian than I. We worked together on a problem on equations—Pell equations, or Fibonacci numbers. which we didn’t get anywhere. We were trying to They have the power to move up to exponentia- prove the unsolvability of the decision problem tion. for word equations. It turned out that we wouldn’t The proof in the paper the three of us wrote have been able to do that because the problem is [1] goes back to the Chinese remainder theorem. solvable. Makanin solved it positively. That had a It was Gödel who first used the Chinese remain- curious relationship to Hilbert’s Tenth Problem, der theorem as a device to code finite sequences. because some of the Russians were interested in That’s what I used in my dissertation result, but it proving it unsolvable because its unsolvability didn’t go all the way. Technically, a bounded uni- would have been a way to get the unsolvability versal quantifier stood in the way of the definition of Hilbert’s Tenth Problem, without proving my that one wanted to be entirely existential. Using conjecture, which they thought was likely false. the Chinese remainder theorem to code the effect But in fact, it turned out to be on the other side of the bounded universal quantifier needed some of the line. clever tricks, and that’s what the three of us devel- Notices: What made you think that it was un- oped. When Hilary and I first tried to prove this, solvable? our proof had the major flaw that we needed to Davis: I don’t know that we thought it was assume that there are arbitrarily long progressions unsolvable. We thought it might be unsolvable. consisting entirely of prime numbers—something When we were working on the problem, Julia and that was only proved two years ago by Ben Green I would stand at a blackboard on the campus here and Terence Tao. If we had had that theorem, our in Berkeley, and you could just feel the power. You proof would have been a perfectly good proof. could feel the power in her papers too, particularly But at the time it was Julia who showed how to do her dissertation on the definition of the integers without that then unproved assumption. in the theory of the rational numbers—it’s really Notices: So ultimately Hilbert’s Tenth Problem a powerful piece of number theory. It was also was resolved by work of you, Hilary Putnam, uncharted territory. It was the kind of number Julia Robinson, and Yuri Matiyasevich, and your theory nobody was doing. conjecture became the DPRM theorem. So often in Notices: Do you have a sense that any outstand- mathematics there are priority disputes. But that ing mathematical problems out there nowadays did not happen with you four. might be unsolvable? Davis: It’s just the opposite. We all like and Davis: In the sense of nonexistence of an al- respect one another. I guess we are nice people! gorithm? Not really. The easy stuff has all been Some people want to call the result Matiyasevich’s scooped up, I would say. One thing that is clear Theorem, and Yuri insists no, it’s DPRM. Other from many cases is that the boundary is tricky, as people say MRDP. A story I like to tell is about the is often the case with sharp mathematical bound- later collaboration of Julia and Yuri, in which the aries. Particularly in the case of Hilbert’s Entsche- number of unknowns was knocked down to nine. idungsproblem, the boundary between cases that As I said, once you had the main result, it was are solvable and the ones that are unsolvable boils clear that there was a bound. If you just took the down to the question, Are there two quantifiers, crude proof, you would get an estimate of forty or or three? I don’t think anyone would have guessed so unknowns. Julia and Yuri took on the task of to start with that three is unsolvable and two is trying to get a better bound. They published a very solvable, but that’s how it turned out. nice paper in which they got it down to thirteen. Then Yuri, basically using the same methods that Programming the ORDVAC they had developed but refining them, managed to Notices: After Princeton, in 1950, you got a job at get it down from thirteen to nine and proposed to Illinois, and that was when you started program- Julia that they publish a joint paper. She said, “No, ming. You were one of the world’s first program- I didn’t have anything to do with getting it down mers, weren’t you?

May 2008 Notices of the AMS 565 Davis: Well, let’s say an early one, anyway. I had become unreliable. We had to avoid tight inductive a research instructorship at Urbana-Champaign, loops in our code. which was basically a kind of postdoc. I taught a Notices: Did working with computers at this time logic course, and the second semester was about affect your thinking about the purely mathematical computability. I wrote a book that was published problems you were working on? years later, in 1958, called Computability and Davis: It affected the way I thought about com- Unsolvability, and the second semester was sort putability. It certainly affected my book Comput- of a first draft of that book. Part of what I was ability and Unsolvability [4]. A number of people doing was writing Turing machine programs on who became computer scientists at a time when the blackboard. Edward Moore, later known for there was no computer science told me that they his work on sequential machines, was an auditor learned programming from that book, even though of the course. He had just finished a Ph.D. and had it’s not a practical book at all, but a theoretical joined the computer project at Urbana-Champaign. one. They were building an early computer, called the ORDVAC, one of a family of early computers called The Mind and the Brain “johniacs” after John von Neumann. Moore came Notices: In 1951 you went to a lecture by Gödel in up after one of the classes to tell me that a program Providence. Can you tell me about this lecture, and I had written on the board could be improved and how it influenced you? showed me how to do it better. He said, “You really Davis: You are not getting my pure memory of ought to come across the street, we’ve got one of the lecture, because I have since read the text sev- those there!” eral times, after it was published in his collected works. The lecture was altogether remarkable. It Notices: Did you know of the existence of the was the Gibbs Lecture. Gibbs of course was an ap- computer there? plied mathematician par excellence, and here was Davis: No, I was not aware of it. I should have Gödel, coming to lecture the mathematicians on followed it up, but I didn’t. What happened instead philosophy! He said that, if you look at his incom- was that, as a result of the Korean War, I was in pleteness theorem and what it implies about math- danger of being drafted. A military project started ematics and about the human mind, you are faced up, the Control Systems Lab, and I was given the with a pair of alternatives. One is that thinking is opportunity to join it, which seemed like a good entirely mechanistic, and it’s all done by the brain, way to avoid being in the army. What they set me in which case you have to think that the brain is doing was writing programs for the ORDVAC. In just a Turing machine. Then our mathematical fact, I wrote a program that was supposed to navi- doings would be subject to the incompleteness gate 100 airplanes in real time! Of course it was a theorem, and there would be number-theoretic preposterous thing with the technology available. truths that we will never be able to prove. The But I did produce the program. My course in com- other alternative is that the human mind surpasses puter science consisted of a five-minute lecture by any mechanism, and that’s of course what Gödel Abe Taub, who said, “This is how you program.” really believed. He was a Cartesian dualist. He I was given the von Neumann-Goldstine reports, really thought the mind has an existence quite which had a lot of sample programs. separate from the physical brain. Those were the Notices: What was it like to program on this two alternatives he provided. I came out with my computer? What did you have to do? head spinning. Davis: What I had to do was to write code on Notices: Which alternative do you think is a piece of paper with a pencil. A secretary would true? type it on a teletype machine, which would produce Davis: Oh, the first one. I’m a mechanist. a piece of punched paper tape that would have Notices: Why is that so clear to you? the code on it, and that was what was fed into the Davis: I think the more research is done about computer. the human brain, particularly about people who The memory consisted of forty cathode ray suffer brain damage of one kind or another, the tubes, little TV screens. On each one, there would more we see that various aspects of what we think be a grid of 32 by 32 bits. A 0 was two dots, and a of as mind really sit in the brain. I recently read an 1 was one dot. So the data was stored as electro- article in the New Yorker by Oliver Sacks, about a static charge on the surface of the tube. This had man who had total amnesia. He simply could not the serious defect that charge doesn’t stay put, it form a memory of anything happening to him but decays. So they had what was called “read-around”, still was perfectly capable of sitting down at the a process by which the memory was constantly piano and playing at a high professional level of being read and rewritten. The programmers had to skill. People in whom the corpus calossum, the be aware of this, because if they wrote a program connection between the two halves of the brain, in such a way that the read-around didn’t get a has been severed, behave as though there were two chance to correct the memory, the data would separate people inhabiting their skull. Also, there

566 Notices of the AMS Volume 55, Number 5 is just the general historical fact that vitalism as a philosophy has been in retreat. When I was at City College, a biology professor said that he didn’t think biology would at bottom end up being physics and chemistry. But now we know about DNA and genes. And if you think the human mind is separate from the brain, what about the mind of a chimpanzee? Is that really qualitatively different? Or is it just that there are some extra little subroutines that enable us to use language? One of the strange things about this argument about mechanism and mind is that people on one side of the divide don’t even seem to be able to understand what it is that people on the other side could be thinking. My good old friend Raymond Smullyan can’t understand how a sensible person can believe what I believe! And I find it hard to Martin Davis and his wife Virginia. imagine what he thinks. logician who was at the Institute at that time as Notices: There have been books looking into this well. We had heard a rumor that Gödel had a proof question in recent years, for example, the book by of the independence of the axiom of choice from Roger Penrose [8]. the axioms of set theory and decided we should Davis: I was involved in a polemic with him make an appointment to ask him about that. I in print, in the publication Behavioral and Brain can’t remember the details of the meeting, but Science. it was awkward, and we came away without any Notices: I see. Penrose used Gödel’s ideas to argue information. that the mind must be more than the brain. One person we were very friendly with at the Institute was Julian Bigelow, the engineer who, Davis: Yes. He went a lot further than Gödel one could almost say, built the Institute johniac would have been willing to go. Gödel at least had an computer with his own soldering iron. He was alternative. Penrose is a remarkable mathematician a very interesting person. He wanted to move a and physicist, but on this subject he is simply fool- house from point A to point B in Princeton. Some ish. He won’t listen to what we logicians tell him. utility poles with wires were in the way. When he It’s simply not true, as he asserts, that we can see contacted the utility company about temporarily a truth that no machine can see. All we ever see is moving the poles so he could move the house, the that, if a particular system is consistent, then that cost was prohibitive. So what he did was take a statement is true. But your favorite machine can hand-saw and horizontally saw the house in half, see the very same implication. The tricky part is move the two pieces separately, and then screw knowing which formal systems are consistent. You them together with great big flat brackets! can find by the wayside formal systems proposed Notices: Didn’t that just ruin the house? by first-rate logicians that have turned out to be Davis: Apparently not! inconsistent, starting with Frege and continuing Notices: Did you get to know von Neumann? with Church, Quine, Rosser, and others. So the as- Davis: I met von Neumann back in Urbana, and sumption that we can somehow really tell whether that was the only time I had a conversation with a formal system is consistent is unjustified. Tur- him. I attended the inauguration of the Control ing wondered about this way back, in his famous Systems Laboratory, and there were many guests, article on whether computers can think [11]. The and von Neumann was one of them. I wanted to way he put it is that a machine has to be allowed meet him, but I was much too shy to walk up to to make mistakes just as human mathematicians him. My wife Virginia was there—we weren’t mar- make mistakes. That was his way of saying that a ried yet—and took care of the problem. She made formal system might be inconsistent, and he asked me a scotch and soda that was more scotch than for “fair play” for computers! soda, and after that von Neumann and I had a Notices: You spent 1952–1954 at the Institute for wonderful chat about sun spots and ice ages and Advanced Study in Princeton. Did you have much heaven knows what! But I never talked to him at contact with Gödel during that time? the Institute. Davis: I spoke to him twice. Once by myself, to tell him about something I was working on, in Computer Science Culture which he showed not the least interest. The sec- Notices: After the Institute you went to the Univer- ond time was with John Shepherdson, an English sity of California at Davis. You had various jobs

May 2008 Notices of the AMS 567 for a while and then eventually you ended up at theorems are stated but rarely proved, and some- New York University, where the computer science how judgments are made. But the things that are department was just getting started. claimed to be proved are not always in fact proved. Davis: Well, I came to NYU in 1965, and the And the stakes are high. People’s subsequent ca- Computer Science Department was started in 1969, reers could depend on getting papers accepted in and I was there to join it at that time. these conferences. That’s what I didn’t like. Notices: I’ve heard people say it’s unfortunate Notices: The outstanding problem in computer that computer science departments split off from science now seems to be the P versus NP problem. math departments at this time. You witnessed this Do you care to speculate on whether or how that happening at NYU. Do you think they should have will be resolved? stayed together? Davis: I have very unconventional views about Davis: No, it wouldn’t have worked. It’s really that. It is taken for granted in the field that P and a different culture. There are things about the NP are different but that it’s just much too hard culture I don’t like, but it is different. The way the for people to prove it. I think it’s 50–50! I wouldn’t theoretical and the pragmatic parts of the subject be in the least astonished to find that P equals NP. interact is very different from how applied math- I think the heuristic evidence that is given, when you look at it carefully, is just circular. I certainly agree that it’s very unlikely that there are really good algorithms for NP-com- plete problems like satisfiability. But the equating of “good” with polynomial-time computability seems to me to lack evidence. People say “polynomial”, but they mean with an exponent no higher than 3. I sort of see it as a reprise of the situation with Hilbert’s Tenth Problem, where people didn’t have any real imag- ination about what a polynomial with high degree could do. I was an invited speaker last summer at a meeting in Lisbon devoted ematics of the classical sort interacts with pure to the satisfiability problem. In my talk I said that if mathematics. At NYU, we were involved in finding I were a young person I would try to find a polyno- our way as a separate department. Of course we mial-time algorithm for satisfiability, not expecting knew very well that the mathematical power of it to be a particularly good algorithm! the people at the Courant Institute—people like Notices: Really! Nirenberg and Lax and Varadhan and so on—was Davis: Why not? I don’t see any compelling of a very different caliber than the mostly young reason there shouldn’t be one. people who we had in the computer science de- partment. But still, we had our own culture and Notices: But people aren’t working on it from needs, and we had to convince them, for example, that point of view. People seem to think that P and that it wasn’t appropriate that a Ph.D. student in NP are different. computer science be required to pass an exam in Davis: Well, there is a million-dollar prize! complex variable theory. Notices: Is the question of whether there is a Notices: What are the aspects of the computer polynomial-time algorithm the correct way of mea- science culture that you don’t like? suring the difficulty of solving problems? Davis: I am thinking of theoretical computer Davis: Well, that’s really the question. Certainly science particularly, where the field moves very theoretically the class of things for which there fast, leaving unsolved problems behind, under the are polynomial-time algorithms has nice closure assumption that, because they haven’t been able to properties. So it’s a mathematically attractive class. deal with the problems in a year or two, the prob- But the idea of identifying them with what’s com- lems are intractable. And they go on to another putationally feasible is I think the result of looking subject. Following the habits in the more applied at an analogy with Church-Turing computability, parts of computer science, the intellectual center is which is a very successful formalization of the not finished public articles, but rather conferences. intuitive notion of what is calculable in principle A conference program committee—I have been on when you don’t think about resources. But it’s just one of them—gets extended abstracts in which not a compelling analogy in my opinion.

568 Notices of the AMS Volume 55, Number 5 At the January meeting [New Orleans Joint Math- But if you think that there is something objective ematics Meetings, January 2007] Margaret Wright about the universe of sets, then in that universe, gave a talk about linear programming. Linear pro- regardless of what we are able to do, it will have gramming was also thought to be an intractable a definite answer. problem for which there were no polynomial-time Notices: Do you think that the work of people like algorithms—until the polynomial-time algorithms Hugh Woodin and John Steel might eventually bring popped up. First there was the ellipsoid method a decision about the Continuum Hypothesis? found by the mathematician Karmarkar, then the interior-point method. Also, one of the things Davis: Yes, I am hopeful. I have to say first of Margaret Wright showed was that, in very specific all that I can’t claim I really understand in any but cases where you’re doing serious computation the vaguest way what those people are doing. I and trying to deal with hundreds of thousands admire it tremendously, but I find it very hard to of linear constraints, the old exponential-time follow in detail. But as an outsider, what comes to algorithm of Dantzig often does better than the my mind is this. Before Paul Cohen, people thought polynomial-time algorithms! So I just don’t see on of the Zermelo-Fraenkel axioms as pretty much de- what basis people measure feasibility in this way. termining the world of sets. They knew about the It’s not that I bet that P equals NP. I just can’t see Skolem-Löwenheim theorem, that there had to be any compelling evidence either way. countable models—but it seemed as though those Steve Cook once pointed out to me that the would just be weird and peculiar things. Then one separation in the field is between log-space at Paul Cohen invented the method of forcing, and the bottom end and polynomial-space at the top suddenly the Zermelo-Fraenkel axioms, instead of end. In between there are classes that theoreti- being like the axioms of, say, Euclidean geometry, cal computer scientists study: P and NP, and the became like the axioms of group theory. Suddenly whole polynomial-time hierarchy, and then PSPACE you could make models of the Zermelo-Fraenkel sits on top of all of that. But the only separation axioms every which way, with whatever properties theorem that has been proved is between the very you want. It had tremendous flexibility, and that bottom and the very top. All the other layers could was a big obstacle in trying to settle a problem like collapse, for all anybody knows. But people will the continuum problem, because you can force the publish papers that say, “If such and such is so, continuum to be 17​ or whatever you want. But ℵ then the polynomial-time hierarchy will collapse even before Woodin’s work, there was the so-called at level 2” and think that, since that’s not going to Martin’s Maximum, which is a certain axiom added happen, they have essentially proved their result. to the axioms of set theory that in effect prevents Notices: Do you think that maybe the problem forcing from working. When Martin’s Maximum is just not cast in the correct way, with the right is added to the Zermelo Fraenkel axioms, it turns viewpoint? out that the cardinality of the continuum is 2​. I ℵ Davis: I’ve thought about that and tried to think wouldn’t be a bit surprised if the true value really what the right viewpoint might be, but I haven’t turns out to be 2​. That’s certainly what some ℵ come up with anything! Maybe there is no real no- of Woodin’s work suggests, and I can be rash tion of feasibility, or maybe there is a notion, and enough to say it, because, as a bystander trying it hasn’t been found yet. to understand what’s going on, my opinion isn’t worth much! A Continuing Mystery: The Continuum One thing you have not asked me about but that Hypothesis I think is very important is the following. We know Notices: Do you think the Continuum Hypothesis as a theoretical matter that there are mathematical will ever be resolved? propositions that, formally speaking, have a very Davis: I think it has a truth value, meaning that simple form involving solvability of specific Dio- it’s a coherent statement that is either true or false. phantine equations and that require set-theoretic Whether the human race will ever be able to resolve methods for their resolution. Harvey Friedman has it or not, I have no idea. I don’t think we can do found examples of this kind with a combinatorial everything. But I don’t think it’s ill-posed, in the flavor. To me a really interesting question is: Do way Sol Feferman does. He wrote an article “Does any important unsolved problems that are really mathematics need new axioms?” [9], in which he significant to mathematicians fall into that cat- suggested that the final fate of the continuum egory? One of the things Gödel himself conjectured problem will be that it’s just regarded as incoher- ent and ill-posed. If you think that the universe of in that remarkable Gibbs Lecture was that the Rie- sets is a human creation and that there is no objec- mann Hypothesis might be of that character. And tive truth about it, then the way Sol thinks makes that wouldn’t surprise me in the least. sense. If the world of sets is a human creation Notices: So you are saying the Riemann Hypoth- in the way the play Hamlet is, then the question, esis can be reduced to a question about solvability “Was Hamlet a virgin?” might not have any answer! of a specific Diophantine equation?

May 2008 Notices of the AMS 569 Davis: Yes. The technical notion is what ​0 logicians call a Π​1​ proposition. These are statements that a certain decidable prop- erty of natural numbers is true of all natural numbers. Decidable, in the sense that there is an algorithm to tell whether a given num- ber has the property or not. By using the MRDP theorem, one easily shows that every ​0 Π​1​ proposition is equivalent to a statement asserting about a particular polynomial equation with integer coefficients that that equation has no natural number solu- tions. That’s entirely equivalent to the first

Text of letter from Paul Cohen to Martin Davis (shown at left), dated November 27, 1963:

Dear Martin,

I have thought about writing you for some time, but never quite got around to it. First, I hope you received a preprint of my work. Gödel has now submitted the paper to the PNAS [Proceedings of the National Academy of Sciences] and it comes out in Dec. and Jan. issues.

I really should thank you for the encouragement you gave me in Stockholm. You were directly responsible for my looking once more at set theory. Previously I had felt rather outplayed & even humiliated by the logicians I had spoken to. Of course, the problem I solved had little to do with my original intent. In retrospect, though, the basic ideas I developed previously played a big role when I tried to think of throwing back a proof [of] the Axiom of Choice, as I had previously thought about throwing back a proof of a contradiction.

I have received 2 letters from A. Edelson of Technical Publishing Co. I have not decided what to do about a book and so I cannot say much at this point. What do you think I should attempt to cover in a book?

How is Newman? I will be in Miami in January & then in N.Y. so I will certainly see you then.

Regards to all.

Sincerely,

Paul Cohen

570 Notices of the AMS Volume 55, Number 5 version that I stated. And the Riemann Hypothesis [7] Sylvia Nasar, A Beautiful Mind, Simon & Schuster, certainly is of that character. We worked it out in 1998. our paper [10] quite explicitly. I had the help of [8] Roger Penrose, The Emperor’s New Mind: Concerning a number theorist at NYU, Harold Shapiro, who Computers, Minds, and the Laws of Physics, Oxford University Press, 1989. pointed me in the right direction. But it was clear to [9] Solomon Feferman, Does mathematics need new everybody who thought about it that the Riemann axioms?, Amer. Math. Monthly 106 (1999), no. 2, ​0 Hypothesis had the character of being a Π​1​ propo- 99–111. sition, by thinking about the behavior of a Cauchy [10] Martin Davis, Yuri Matijasevicˇ, and Julia Robin- integral on a path around zeros and approximating son, Hilbert’s tenth problem: Diophantine equations: the integral in some way or other. positive aspects of a negative solution, in Mathemati- I am certainly no analyst, but the reason I think cal developments arising from Hilbert problems, Proc. the Riemann Hypothesis is a good candidate for Sympos. Pure Math., AMS, 1976. [11] A. M. Turing, Lecture to the London Mathematical undecidability by elementary methods is that it Society, 20 February 1947, typescript at http://www. is sitting right in the middle of classical analysis, turingarchive.org, item B/1; text in The Collected and it has been attacked by brilliant mathemati- Works of A. M. Turing: Mechanical Intelligence (D. C. cians—Paul Cohen spent a lot of time on it—and Ince, ed.), North-Holland, 1992. the existing methods just don’t seem to resolve it. It’s hard to believe it isn’t true. And why shouldn’t it be one of those propositions that require set- theoretic methods? That would be great! Suppose someone proves that the existence of a measurable cardinal implies the Riemann Hypothesis. Would mathematicians accept that as a proof of the Riemann Hypothesis? Whether there exist measurable cardinals is something that can’t be proved from the Zermelo-Fraenkel axioms. Evidence for it is like the kind of evidence that physicists come up with, not the kind of evidence that mathematicians typically want. I hope it’s clear I am presenting all of this as a wild speculation, not something that I believe is true. Notices: The Diophantine equation that you can reduce the Riemann Hypothesis to—what does that thing look like? Is it horribly complicated? Davis: Sure. Notices: So you can’t just look at it and get any information. 2008 Fall AMS Davis: No. What I say is, This is an equation that only its mother could love. Sectional Meetings October 4–5, 2008 (Saturday–Sunday) References University of British Columbia and PIMS, [1] Martin Davis, Hilary Putnam, and Julia Robinson, Vancouver, Canada The decision problem for exponential Diophantine equations, Ann. of Math. (2) 74 (1961), 425–436. (2008 Fall Western Section Meeting) [2] J. P. Jones, Universal Diophantine equation, J. Sym- **Fourth Annual Einstein Lecture** bolic Logic 47 (1982), 549–571. [3] Martin Davis, Computability and Unsolvability, October 11–12, 2008 (Saturday–Sunday) McGraw Hill, 1958; reprint edition with additional Wesleyan University, Middletown, CT appendix, Dover, 1982. (2008 Fall Eastern Section Meeting) [4] Martin Davis, The Universal Computer: The Road from Leibniz to Turing, W. W. Norton, 2000 (also October 17–19, 2008 (Friday–Sunday) issued as a paperback in 2001 under the title Engines Western Michigan University, Kalamazoo, MI of Logic). (2008 Fall Central Section Meeting) [5] Martin Davis, editor, The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and October 24–26, 2008 (Friday–Sunday) Computable Functions, Raven Press, 1965; corrected reprinted edition, Dover, 2004. University of Alabama, Huntsville, [6] Emil L. Post, Solvability, provability, definability: The Huntsville, AL collected works of Emil L. Post, edited and with an in- (2008 Fall Southeastern Meeting) troduction by Martin Davis, Contemporary Mathemati- cians, Birkhäuser Boston, Inc., Boston, MA, 1994.

May 2008 Notices of the AMS 571 THE FEATURE COLUMN monthly essays on mathematical topics www.ams.org/featurecolumn

Each month, the Feature Column provides an online in-depth look at a mathematical topic. Complete with graphics, links, and references, the columns cover a wide spectrum of mathematics and its applications, often including historical figures and their contributions. The authors—David Austin, Bill Casselman, Joe Malkevitch, and Tony Phillips—share their excitement about developments in mathematics.

Recent essays include:

How Google Finds Your Needle in the Web's Haystack Rationality and Game Theory Lorenz and Modular Flows: A Visual Introduction The Princess of Polytopia: Alicia Boole Stott and the 120-cell Finite Geometries? Voronoi Diagrams and a Day at the Beach Simple Chaos – The Hénon Map The Octosphericon and the Cretan Maze Trees: A Mathematical Tool for All Seasons Variations on Graph Minor Penrose Tilings Tied up in Ribbons Topology of Venn Diagrams

AMS members: Sign up for the AMS members-only Headlines & Deadlines service at www.ams.org/enews to receive email notifications when each new column is posted. Film Review

Julia Robinson and Hilbert’s Tenth Problem Reviewed by Carol Wood

Julia Robinson and Hilbert’s Tenth Problem Csicsery intertwines for us a human story and Zala Films a mathematical story. In Julia Robinson we find Produced and directed by George Csicsery a mathematician who was a heroine in her own time and a role model for all time. It is a story This film by George Csicsery is an hour-long of childhood, illness, love, documentary on the life and work of Julia Robin- marriage, disappointment, son, an extraordinary mathematician who played a obsession, and triumph. key role in the solution of Hilbert’s Tenth Problem. It is filled with extraordi- Csiscery is perhaps best known in the mathematical nary instances of luck both community for his documentary about Paul Erdo˝s, good and bad. The stars of N​ is a Number. The final version of Csicsery’s latest the film are the incandes- work premiered at the Joint Mathematics Meetings cent Bowman sisters, Julia in San Diego on January 7, 2008, to an appreciative Robinson and Constance audience. The setting was particularly appropriate: Reid. Julia was very for- Julia moved with her family to San Diego when she tunate to have Constance was a small girl, and she remained there through as a sister and a spokes- her early years of college. The film includes a 1920s person. Julia’s sister is view of a pristine bay, now the site of the conven- no stranger to the math- tion center and meeting hotels. ematical community, hav- The documentary was many years in the mak- ing written prize-winning ing and draws on various archival materials, both books about mathemat- ics and mathematicians, film and still shots, plus interviews of colleagues including a masterpiece and friends of the Robinsons, including the other about Hilbert. Reid’s sto- key figures involved in the solution of Hilbert’s rytelling and her presence Tenth Problem (H10): Martin Davis, Hilary Putnam, enliven the film. Her 1996 and Yuri Matijasevich. H10 asks whether there is book Julia, A Life in Math- an algorithm for determining when a polynomial ematics, published in the equation with integer coefficients has an integer MAA Spectrum series, is a solution (for details, see Bjorn Poonen’s article perfect companion to the in the April 2008 Notices). The film is narrated film. (See also Reid’s arti- sweetly by Danica McKellar, actress (Winnie in cle, “Being Julia Robinson’s The Wonder Years), math major (at the University Sister” in the December of California, Los Angeles), and author of a book 1996 Notices.) about mathematics aimed at girls (Math Doesn’t The narrative begins Suck). with Julia’s childhood, and follows her mathemati- Carol Wood is professor of mathematics at Wesleyan Uni- The Bowman sisters, Julia versity. Her email address is [email protected]. cal and personal odyssey. Robinson and Constance Reid.

May 2008 Notices of the AMS 573 single diophantine equation whose roots displayed My Julia Story exponential growth, then the full problem would be undecidable. Fulfilling the condition, called In 1968 a 22-year-old graduate student and her 25-year-old JR by others, would provide the missing piece of mathematician husband walked through the lobby of the head- the solution as envisioned by Davis, Putnam, and quarters hotel at the San Francisco AMS meeting. This was the Robinson. This was finally achieved in 1970 by first mathematics meeting for either of them. Walking in the Yuri Matiyasevich, to the delight of the other three. other direction was a distinguished-looking couple of an older An endearing aspect of the story about H10 is the generation. They stopped to speak to the young couple, say- generosity of the four main players in deflecting ing, “We live in this area and decided we should come to the credit toward each other. Once the solution of meeting and meet some new people. We are Julia and Raphael H10 was complete, recognition of Julia’s role came Robinson.” The student doesn’t remember any further detail swiftly and dramatically, a truly joyful part of the of the pleasantries that were exchanged in the lobby that day, story Csicsery tells. although perhaps she had the presence of mind to mention that she was taking a course in model theory from Abraham The film also takes us to an era when the speed Robinson. Once out of earshot she asked her husband excitedly of mathematical communication could be glacial. “Do you know who they are??!!” It is already difficult to imagine life without email, I was that student, and I had just met two of the stars in much less to recall the severe restrictions on travel my mathematical world. Nothing that thrilling has happened and correspondence due to the cold war. Com- to me at AMS meetings in the intervening 40 years, nor do I munication with many Russian colleagues was expect it ever will. extremely difficult throughout Julia’s lifetime. —C. W. Yuri Matiyasevich was not allowed to travel to the U.S. They did meet in other countries, but their collaboration was done mostly via handwritten let- ters. Yuri’s description of the challenge of mailing a letter with mathematical content to the U.S. in the 1970s is quite amazing. Julia’s life ended too early, but she will be re- membered as she wished to be, for the mathemat- ics that she did. Her work has a modern quality, with its emphasis on definability and on the con- nections between number theory and logic. Her collected works, edited by Solomon Feferman, were published by the AMS in 1996. The film is made all the more timely by current activity related to H10, Left to right: Martin Davis, Julia Robinson, Yuri Matiyasevich. e.g., by Poonen’s recent improvement of Julia’s thesis. Poonen’s result Opportunities for young women in mathematics reduces the complexity were severely constrained in her day. Nonethe- of the formula needed to less, in the late 1930s she found her mathematical select the integers from milieu in Berkeley. Two figures stand out in her among the rationals, mathematical development. Raphael Robinson bringing us closer to the was one of her first teachers at Berkeley. He desired analogue of H10 then became her mentor and soon thereafter her for the rational numbers; husband. Her thesis advisor, Alfred Tarski, ar- how close remains to be rived at Berkeley during her graduate study. Both seen. Robinsons benefited from Tarski’s presence. One I cannot resist a word of Tarski’s great strengths was his ability to pose here about Raphael Rob- powerful, insightful questions. As the story goes, inson, something I be- many of these were communicated at the men’s lieve Julia would want faculty club, some to Raphael. Fortunately, Raphael said. “Hillary Clinton is passed them along to Julia. a politician in her own The main result of Julia’s 1948 thesis, easily right!” sounds quaint in in my top ten list of favorite theorems, answered 2008. But surely Julia, in one of Tarski’s questions. She proved the defin- her role as the wife of a ability of the integers in the rationals, a result Berkeley professor, was that transported Gödel’s undecidability phenom- regularly referred to as enon from the integers to the rational numbers. “a mathematician in her Shortly thereafter she began to work on H10 and own right”, up to and in- produced an inspired sufficient condition for a Julia and Raphael cluding the time of her negative solution, showing that if one could find a Robinson. election to the National

574 Notices of the AMS Volume 55, Number 5 sponsor of the film’s production, as were Margaret and Will Hearst. George Csicsery, Constance Reid, and Martin Davis were present at the showing, add- ing to the celebratory atmosphere. Even without principal figures in attendance, this film is worth a viewing by readers of the Notices. It is equally suitable for an undergraduate math club and for a mathematics colloquium audience. I have not yet had the opportunity to show it to nonmathemati- cians, but I can imagine that a general audience, such as viewers of the NOVA series on PBS, would also be captivated by the story. However, this is a film about mathematics and mathematicians, and it will be most deeply appreciated by mathemati- cians and our students.

Academy. My point is that one should not over- compensate, while celebrating the achievements of Julia, by overlooking the related work of her husband. As luck would have it, his fame does Photo credits for this article: not match hers, nor is he the subject of this film, Page 575—top and bottom photos by Ralph Bow- although his crucial role in Julia’s mathematical man, courtesy of Constance Reid. Page 576—left, development is acknowledged. However, this kind photo by Louise Guy; right/top, photo by Raphael and quiet man was very much a “mathematician in Robinson, courtesy of Constance Reid; right/bot- his own right”, with many beautiful results to his tom, courtesy of Constance Reid, photographer credit, including undecidability results for certain unknown. Page 577—top, photo by Ralph Bow- function fields, together with an impressive record man, courtesy of Constance Reid; middle, photo as a problem solver. He was a key figure in early courtesy of George Csicsery from Julia Robinson work on tiling of the plane and the author of un- and Hilbert’s Tenth Problem; bottom, photo by decidability results for certain fields. One account Constance Reid. of Raphael’s work is found in the article by Leon Henkin in the Bulletin of Symbolic Logic, Volume 1, No. 3 (1995). The AMS film premier was hosted by the Clay Math- ematics Institute, which was a major

Top of page: Julia and Constance at the beach. Below: Constance Reid and Julia Robinson.

May 2008 Notices of the AMS 575 Interview with George Csicsery

George Csicsery is the producer and director of the film Julia Robinson and Hilbert’s Tenth Problem (see movie review, pages 573–575, this issue). The following is an interview with Csicsery, conducted on February 19, 2008, by Notices graphics editor Bill Casselman, University of British Columbia.

Notices: How did you come to make this film? you consider that she had already written, or co- Csicsery: The idea for this film came in 1998. written, Julia Robinson’s autobiography, Julia: A Charlie Silver, a logician and a friend, sent me an Life in Mathematics. email in which he summarized the idea of the film My main conceptual contribution was to tell for me in a few enthusiastic paragraphs, beginning the mathematical story inside the biography of with “While waking up this morning, I had a flash Julia Robinson. And this proved to be the most of a math film … .” In the rest of his email he out- difficult part—making the two parts move forward lined much of what eventually went into the film. in tandem so that neither would subtract from Charlie had helped me a great deal while I was the other. making N is a Number: A Portrait of Paul Erd˝so , Notices: How did you get interested in making mathematics films in general? Csicsery: That’s a question I get often, since I’m not a mathematician and my understanding of mathematical ideas is rather primitive. Just as often, my official answer is that I’m a refugee from the social sciences looking for terra firma. And this is only half a joke, because in my lifetime there has been terrific erosion in the quality of work being done in what used to be called the social sciences, and more precisely the fields in which I was best trained—anthropology, sociology, comparative religions, and history. My interest in mathemati- cians, rather than mathematics itself, was sparked by hearing and reading about individuals who had

Photograph courtesy of George Csicsery. George of courtesy Photograph a passionate dedication to finding out things that George Csicsery filming in 1977. might actually be close to truth. There’s a second part to this. My films about mathematicians are also films about people who found ways to over- and he’s worked extensively on the films of Errol come the less pleasant aspects of life. Paul Erdo˝s Morris. He had been a student of Julia Robinson and Julia Robinson are both interesting exemplars at Berkeley, and knew her. As he explained it, the of the life of the mind prevailing over the daily story of how Hilbert’s Tenth Problem was solved travails that consume most people. came to life for me. Constance Reid was already a legend in math- When I agreed that the story was compelling, ematics, being the pre-eminent biographer she Charlie flew out to California and we went to visit is. I always felt that she is an important part of two people together. One was Constance Reid, the the story in her own right, independently of Julia other Martin Davis. Both of them embraced the Robinson. Constance also had a wonderful col- idea for a film and agreed to participate. In a sense, lection of photographs taken by their father. She Constance, being Julia Robinson’s sister, became made these and countless other artifacts available her surrogate in the film. This is not so strange if to the project.

576 Notices of the AMS Volume 55, Number 5 Photograph by Helen Moore, courtesy of George Csicsery. George of courtesy Moore, Helen by Photograph Some of the people involved in the making of the Julia Robinson film, including Kirsten Eisentraeger, Yuri Matiyasevich, Alexandra Shlapentokh (top row, first, fourth, and seventh from left), George Csicsery (front row, third from left), Bjorn Poonen (to the right of Csicsery), and Martin Davis (standing, third from right). All of those named appeared in the film, with the exception of Csicsery.

Martin Davis is one of the four people cred- an audience, or in the case of a film like this one, ited with solving Hilbert’s Tenth Problem. He creating an audience. The third is actually making had worked with Hilary Putnam, then with Julia the film. Of course, these three things are inti- Robinson, and then later, with Yuri Matiyasevich. mately connected. His descriptions of the other participants and of I started working on the film with no funding be- events turned out to be key parts of the narrative, cause Constance Reid was flying to St. Petersburg, shedding light not only on an important piece of Russia, in January 1999 to celebrate her birthday mathematical history, but adding color and nuance and the anniversary of the solution of H10 with to the characters. Yuri Matiyasevich, and I thought this should be About a year into the process I was able to meet covered. It was frustrating to say the least; I paid a Yuri Matiyasevich at a Hilbert’s Tenth Problem Russian crew to follow them around, but in the end meeting in Gent, Belgium. Here was the man who could not afford to go myself. Talk about remote had actually succeeded in solving the problem in directing. Well, as you can imagine, there is very 1970, and then, overcoming the immense politi- little footage from that adventure in the finished cal barriers between the U.S. and the USSR at the film. Then I was committed. I kept shooting from time, went on to forge a creative partnership with 1999 through about 2005 with no resources. There Julia Robinson and Martin Davis. Is there anything were two or three times when I was working on more dramatic? Matiyasevich proved invaluable to projects for MSRI [Mathematical Sciences Research the film. The deep sincerity and intense emotion Institute] and would be shooting an interview with with which he addressed every one of my ques- someone who figured in Julia Robinson’s story as tions reveals a great deal about him. He brought well. I asked David Eisenbud, the former director another gift to the project—his own 8mm films of MSRI, if I could shoot an extra roll or two for from 1970 and 1971. His first presentations of his the Julia Robinson film. Fortunately, he always said yes. Finally, in 2005 I got a decent grant from the solution to Hilbert’s Tenth Problem were filmed, Clay Mathematics Institute, followed by two more. and he had the footage, which you see in our film. And in 2007 we got a generous grant from the Mar- In 1971 he also filmed about one minute of scenes garet & Will Hearst Foundation. As a result we were with Julia and Raphael Robinson at the Bucharest able to schedule the final shoots and complete the mathematics meeting where they first met. As far editing. The film premiered at the Joint Mathemat- as I know, this is the only existing piece of film ics Meetings in San Diego in January 2008. with Julia Robinson in it. The challenge of finding an audience for the film Notices: What were the trials and tribulations seems mitigated by the terrific outpouring of inter- involved in making this film? est from mathematicians and teachers. I can only Csicsery: The biggest challenge for most docu- hope that this will lead to some television broad- mentary films is funding. The second is finding casts. It’s hard to be optimistic about TV though;

May 2008 Notices of the AMS 577 even the best science series have been dumbed time it’s impossible to explain to people why you down to accommodate the fleeting attention spans have chosen such an arcane subject. People seem of viewers. If you’ve seen the film you can appreci- to question your grip on reality, and sometimes ate that it takes more than five seconds to grasp you start suspecting they may be right and that some of the concepts. you’re wasting your time on a futile effort that Finally, there was the challenge of actually was doomed from the outset. Then you show the making the film. The film has three threads: the film, and people with no interest in mathematics biography of Julia Robinson, the history of how come up and say they got something out of it. And Hilbert’s Tenth Problem was solved, and some when you ask what that might be, they tell you the quite demanding mathematics. Weav- exact thing that you had in mind when you set out ing these together into a single narra- to make the film. That is rewarding. tive without sacrificing any of the bits Notices: Can you tell us a bit about your own was possibly the hardest task I’ve ever background? attempted. To be honest, I’m still not Csicsery: I was born in Germany in 1948. My sure how well we succeeded. I worked parents were refugees from Hungary, and we came with a superb editing crew consisting to the United States in 1951. They sent me to a six- of film editor Tal Skloot, and assistant year boarding school in Buffalo, New York, that had editor/animator Andrea Hale. We also been founded by Hungarian refugee priests who had the best available mathematical had run some of the best high schools in Hungary consultants, many of whom are in the before the war. From there I went to Berkeley in film, and had worked—or still work—on 1965, and got to experience the full blast of the some of the ideas we had to find ways 1960s. While I did earn a B.A. in Comparative Re- of presenting on screen. It’s an impres- ligions four years later, the Berkeley-in-the-Sixties sive list of names: Martin Davis, Yuri experience probably accounts for how I kept up Matiyasevich, Solomon Feferman, Hilary my careers in journalism and film. I’ve been mak- Putnam, Lenore Blum, Bjorn Poonen, ing films since 1968, most of them documentary. Steve Givant, and several others. And There are so many themes that it’s hard to detect Charlie Silver was always there in the a thread, but with N is a Number: A Portrait of background, making sure that I would Paul Erd˝so (1993) I got typecast as a biographer of keep the balance between making a mathematicians. It’s a terrific niche; there’s not a coherent film and maintaining some lot of competition. fidelity to the mathematical ideas. Notices: Do you have any future projects planned Notices: What did you enjoy most involving mathematicians? about this film and the earlier one about Csicsery: We just finished a feature-length doc- Erd˝s?o umentary about the 2006 U.S. International Math Csicsery: With Paul Erdo˝s I got the Olympiad team. Hard Problems: The Road to the feeling that I was in the presence of World’s Toughest Math Contest also premiered in a rare and wonderful human being San Diego at the JMM in January 2008. It’s available who happened to be one of the great- from the MAA on DVD. This was really a different est mathematicians of the twentieth kind of project for me, and I really enjoyed it. It’s century. The people around him are a great experience to work with the very brightest impressive enough, but he had a special high school students, and to watch them stop and Above: Still shots quality that inspired. I actually felt that think before they answer a question. I think the from the Julia he was not eccentric at all; that his ap- film provides a glimmer of hope about the next Robinson movie. Top proach to life made absolute sense. generation. to bottom: Julia at 3, Julia Robinson died in 1985, interest- During 2008 I hope to finish a small piece about as a young woman, ingly, at a hospital less than 100 yards Paul Halmos for the MAA that I started in 1999, and shortly before her from my home and office. We never and there are a few other projects in the planning death. met, and this posed another challenge stages that I’d rather not discuss. Somewhere for the film. I had to get a sense of her down the road I would love to make a film about from Constance Reid and from her Coincidence. colleagues and students. In the end, I think we succeed in presenting not only the facts, but also a flesh and blood human being. I hope that her voice, her writings, the dozens of photographs, Yuri’s footage from Bucharest, and the stories in the film about her, do bring her to life. Photos courtesy of Zala Films. Zala of courtesy Photos In both cases, however, I was never quite sure until very near the end that the films worked. You spend years on a project, and during that whole

578 Notices of the AMS Volume 55, Number 5 Visualizing the Sieve of Eratosthenes David N. Cox

Every so often new technology is applied to an age- the next remaining number in the sequence) by old problem to produce unexpected results. This crossing off every third number. When done, the article re-examines the Sieve of Eratosthenes. The next number remaining in the sequence will be 5. Sieve is a one-dimensional device for finding prime Repeat the process for every fifth number in the numbers. The numbers from 2 to n​ are written as sequence. Continue with this process until you a single, long sequence. Then the multiples of 2 reach the end of the sequence. At the end of the are crossed out but leaving 2. Then the multiples process the numbers remaining in the sequence of 3 are crossed out but leaving 3. And so on until will be the primes. the only numbers remaining are the primes. This This simple technique has been used for more paper explores what happens if the procedure is than 2,000 years to find prime numbers. One converted from one dimension to two. Rather than would think that everything there is to know a single sequence, a matrix is constructed such that about the method has long since been discov- in the first row every column is marked with a dot. ered. Indeed, there are advanced sieve methods In the second row, every other column is marked and optimization methods. However, these are with a dot. In the third row, every third column is significant variations of the original method and marked with a dot. In general, in the n​t​h​ row, every do not provide any additional characterization of nt​h​ column is marked with a dot. In this fashion a the original method itself. After 2,000 years what two-dimensional image is built for all n​2​ cells. Re- more could be said? sults of this procedure as generated by computer This article explores the use of computerized software are presented in this article. Despite the visualization to further characterize the Sieve of simplicity of this method, when enough dots are Eratosthenes. After all, Eratosthenes didn’t have a generated, the resulting image turns out to be computer and computer graphics and visualization stunning. This article demonstrates well that com- have only been widely available for the past 20 of puterized visualization can shed new light on old those 2,000 years. With a simple extension of the subjects—even those more than 2,000 years old. Sieve we arrive at a novel result. According to [1] Eratosthenes lived from 276 to The Method 194 BC. Only fragments of Eratosthenes’s original documents have survived. However, a description The method extends the Sieve of Eratosthenes from a one-dimensional sequence to a two- of his sieve method for finding prime numbers dimensional matrix. The method constructs a ma- was described in “Introduction to Arithmetic” by trix of dots that can be easily viewed on a computer Nicomedes written sometime prior to 210 BC [2]. screen. The method is as follows. In the first row To use the method imagine a written sequence of the matrix every column contains a dot. This of numbers from 2 to n. Starting at 2 cross off ​ would correspond to crossing off every number every other number in the sequence except for in Eratosthenes’s original sequence. In the original 2 itself. When done, repeat for 3 (which will be method this is not done. However, in two dimen- David N. Cox is a Ph.D. student in the Computer Science sions it proves useful. Department, North Carolina State University. For freely In the second row of the matrix, every other available software to accompany the article and contact column contains a dot starting with the second col- information, visit http://www.guffy.net/sieve. umn. This corresponds to crossing off every other

May 2008 Notices of the AMS 579 number in the original sequence. In the third row, every third column contains a dot starting with the third column. Again, this corresponds to crossing off every third number in the original sequence. In general, in the n​t​h​ row, every n​t​h​ column contains a dot starting with the n​t​h column. Aside from extending the one-dimensional sequence of length n to a two-dimensional matrix of size n ​​n​, the process of crossing off numbers (using dots)× remains faithful to the original method with two differences. In the first row every number is marked with a dot. In the remaining rows every n​t​h number is marked with a dot including n itself. Consequently, even though 2 is not crossed off in Figure 1. Eratosthenes’s original sequence, it is marked with a dot in row 2. The same holds for rows 3, 5, 7, etc. The implication of this is that a prime number corresponds to a column containing two dots—one in the first row (division by 1) and one in the n​t​h row (division by the number itself). Using this method a computer program was created to generate a matrix containing 1 million columns and the first 1,000 rows. The matrix is easily converted into a binary bitmap for viewing. Because it is not possible to view the entire matrix on a computer screen, a scrolling facility was pro- vided to traverse through the columns and rows. The computer algorithm builds the image of the matrix with the first row at the top of the screen and the first column at the left. The only reason for doing this is because most computers address pixels beginning with (0,0) at the top left. Other orientations would also work. As will be shown, the resulting image has several interesting features.

Results Figure 1 shows several hundred columns and rows beginning with column 1 on the left. The most striking feature is the set of diagonals. Close inspection of these diagonals reveals a pattern. Figure 2. The main diagonal has a slope of 1 and consists of contiguous dots. The adjacent diagonal has a slope of 2 and has a dot in every other column. The third diagonal has a slope of 3 and has a dot in every third column. And so on. Remarkably, these diagonals are constructed in exactly the same manner as the rows from which the image was constructed. Figure 2 shows a portion of the matrix begin- ning at number 17918. Diagonals are apparent at the bottom of the image. Towards the top the dots merge into other patterns. From row 1 there are smaller diagonals radiating out from the top row. Several rows below appear parabolic-like structures. Some of the diagonals radiating out from the first row will be very prominent. An example is 327600 as shown in Figure 3. This prominence is related to the number of dots in the central Figure 3. column. The more dots, the more prominent the

580 Notices of the AMS Volume 55, Number 5 diagonals. This is easy to understand by consider- ing that a dot represents that column c​ is evenly divisible by row r​. Consider two rows, r 1​ and r 2​, that both evenly divide column c​. Clearly, if c​ is divisible by r​, then so is c ​​r​. Similarly, c ​​r​ is 1 + 1 + 2 divisible by r 2​. Consequently a dot will be plotted at (r​, ​c ​​r​) and another dot will be plotted at 1 + 1 (r 2​, ​c ​​r 2​). These points lie on a line with a slope of 1. The+ same reasoning can be extended to a dot at (r 1​, ​c ​​2r 1​) and another at (r 2​, ​c ​​2r 2​) which both lie +on a line with a slope of 2. + Thus, while it is not immediately obvious, every column of points will have corresponding diago- nals. What about the diagonals in Figure 1? What central column of points do they correspond to? Figure 4. If the procedure used to construct the matrix is extended to the left, we arrive at a result that is 1 1 1 1 1 1 1 1 1 1 1 illustrated in Figure 4. There is a central column where every row contains a dot. The image to the 0 1 0 1 0 1 0 1 0 1 0 left of this column is the mirror image of that to the right. Furthermore, the central column corre- 0 0 1 0 0 1 0 0 1 0 0 sponds to the number 0. 0 0 0 1 0 0 0 1 0 0 0 Any binary image is easily represented numeri- cally using 1’s and 0’s. Consequently, Figure 1 can 0 0 0 0 1 0 0 0 0 1 0 be represented as in Figure 5. Carrying this idea further, these numbers can be 0 0 0 0 0 1 0 0 0 0 0 replaced by remainders. In other words, each cell 0 0 0 0 0 0 1 0 0 0 0 will contain the value c​ mod r​ where c​ and r​ are the column and row respectively. Doing so gives 0 0 0 0 0 0 0 1 0 0 0 the result in Figure 6. The central column of red numbers are the re- 0 0 0 0 0 0 0 0 1 0 0 mainders of 15 divided by 1, ​2, ​3, ​. ​. ​. ​, ​15. Notice that these same remainders appear in the diagonals that 0 0 0 0 0 0 0 0 0 1 0 are highlighted in red, yellow, and blue for easier 0 0 0 0 0 0 0 0 0 0 1 reading. What is interesting is that every number will have a column of divisors that will be repeated in corresponding diagonals radiating out from the Figure 5. first row. This simple method for visualizing the Sieve of The cells of the matrix can also be filled with re- Eratosthenes has resulted in surprisingly complex mainders found by dividing each column by each patterns. The set of dots in each column represents row. Doing so reveals copies of each number’s divi- a set of divisors for that column. Extending out sors along diagonals extending out from the first from each column is a set of diagonals with slopes row. These diagonals have slopes of 1, 2, 3, etc. of 1, 2, 3, etc. containing sets of dots that map These images are instructive in that they reveal 1-to-1 to the divisors in the corresponding column. that the divisors are not distributed randomly. This is true for every column. There is repetition of each number’s divisors along Every column except for column 0 has a finite set of dots. Clearly every integer has a finite set of the diagonals that radiate from each number. Al- divisors while 0 is divisible by everything. Hence, though a number’s divisors radiate diagonally and column 0 contains an infinite set of dots. are intertwined with those of other numbers, they The original Sieve is used to find prime num- do not interfere with another number’s divisors. bers. In this method, the prime numbers are Interestingly, the spacing of the divisors along represented in the image as columns containing these diagonals mirrors the spacing of dots used exactly two dots. Column c​ corresponds to a prime to create the initial images. number if it contains a dot in row 1 and row c and Finally, there are other parabolic-like patterns nowhere else. that emerge in these images. The points of several Alternatively, these images can be represented of these patterns have been checked and verified numerically using a matrix whose cells are filled that they do indeed lie on a true parabola. For ex- with 1’s and 0’s. However, it is not necessary to ample, the point corresponding to column 17956 limit the numerical representation to 1’s and 0’s. and row 134 is a vertex of a left-opening parabola.

May 2008 Notices of the AMS 581 Figure 6.

The vertex of another left-opening parabola is References nearby at column 18050 and row 95. In all cases [1] J. Gullberg, Mathematics From the Birth of Numbers, up to number 1,000,000 the observed parabolas W. W. Norton & Company, New York, NY, 1997. have all been left-opening. It remains to be proven [2] A. Cojocaru and M. R. Murty, An Introduction to that the points on all of these parabolic-like pat- Sieve Methods and Their Applications, Cambridge terns do, in fact, lie on true parabolas and why. University Press, 2005. Furthermore, it remains to be proven if all such [3] C. S. Ogilvy and J. T. Anderson, Excursions in Num- ber Theory, Dover Publications, Inc., New York, NY, parabolas are left-opening and why. 1966. Clearly, these images illustrate the wonderful [4] R. Kaplan and E. Kaplan, The Art of the Infinite: The nature of the integers. Moreover, these images il- Pleasures of Mathematics, Oxford University Press, lustrate that even with a method more than 2,000 New York, NY, 2003. years old, a surprising new way of viewing the results can be found through the use of computer- ized visualization.

582 Notices of the AMS Volume 55, Number 5 Book Review Unknown Quantity Reviewed by Sanford L. Segal

The second primer is on cubic and quartic equa- Unknown Quantity: A Real and Imaginary History of Algebra tions (which, in fact, is where complex numbers John Derbyshire made their necessary appearance—previously, in 2007, Plume quadratic equations, complex solutions had been US$16.00 (paperback), 416 pages neglected under the assumption that “the solu- ISBN 978-0452288539 tion does not exist”). This primer deals with the reduced cubic (called by the old term “depressed” by the author) and graphs (Derbyshire nowhere This is not a book to give to anyone mathemati- mentions that graphs did not exist for a long time, cally knowledgeable. It is appropriate for someone e.g., as late as Omar Khayyam). He explains the who knows precious little about mathematics and “irreducible case” and comments (in an endnote) would like to find out more. As the author says how this is inappropriate terminology. A solution in the first sentence of his introduction: “This to the general cubic is given. Then comes the book is a history of algebra, written for the curi- quartic solution (as in fact it did historically). ous non-mathematician.” The book is divided into The primer on roots of unity includes Gauss’s three sections: The Unknown Quantity, Universal solution of the constructibility of the hep- Arithmetic, Levels of Abstraction. tadecagon (but not a geometric construction of it, However, one has to know some mathemat- ics to read such a history. Consequently, the nor a mention of Gauss’s diary entry). And there is a misprint: at the bottom of page 112, k 6 author’s fifteen chapters are interspersed with = should be k 5. “Math Primers”. The first of these precedes the = first chapter of the book. It is perhaps good, first The primer on Vector Spaces and Algebras is of all, to say what these “Math Primers” contain, “an entirely modern treatment—using ideas and since they are the mathematical substance of Der- terms that began to be current around 1920”. Ad- byshire’s book, before proceeding to his history dition of vectors is defined, as is linear dependence of algebra. The first one, which opens the book is (and independence), and also dimension and ba- on Numbers and Polynomials and begins with the sis. It is emphasized that the concept of vector “five Russian dolls” N, Z, Q, R, and C. There is an space is purely algebraic. Linear transformations explanation of why we need to extend the natural are defined, as are the notions of projection and numbers and others of the “Russian dolls”, so embedding. The dual of a vector space is defined, N Z Q R C. What it means for Q to be as is inner product. An algebra is defined as a ⊂ ⊂ ⊂ ⊂ dense is explained. The appearance of complex vector space with a multiplication. numbers in the sixteenth century is mentioned The last two math primers are Field Theory and (1 i)/√2 is demonstrated to be √i (the and Algebraic Geometry. Field Theory precedes + distinction between i and i is not mentioned). A the first chapter of Levels of Abstraction, Part III − sequence of definitions explains polynomials. of the text. It mentions finite fields (with an ex- ample) and extension fields, pointing out that an Sanford L. Segal is professor of mathematics at extension field, say of R, is a vector space over the University of Rochester. His email address is R. Galois groups are defined (the ensuing chapter [email protected]. will talk further about Galois).

May 2008 Notices of the AMS 583 The final math primer is on algebraic geom- or that Eduard Lucas is responsible for the term etry and begins first with conic sections and Fibonacci Sequence. Derbyshire quotes Fibonac- the eccentricity of an ellipse, to introduce the ci’s real root of x3 2x2 10x 20, but does idea of invariant. All conic sections (including not show (as Leonardo+ did)+ that= it could not be degenerate ones) are discussed. Points at infinity rational (which is surely not beyond his intended and projective geometry with its line at infini- audience). ty and homogeneous coordinates are introduced. In explaining that Khayyam spent his life under The topological distinction between the Euclidean 1 the rule of Seljuk Turks (2 2 pages that are mathe- plane, the projective plane, and the surface of a matically irrelevant), Derbyshire manages to insert sphere is discussed. Also, the fact that the lines his version of the origin of the Crusades in 1095 and points are in a certain sense interchangeable as a throwaway remark. is discussed. Derbyshire, in discussing Bombelli (who was Derbyshire’s book is written in a light informal the first to give rules for multiplying complex style. Included in this style is a sort of potted histo- numbers), talks about his solution of x3 15x 4. ry with random remarks by Derbyshire reflecting Using Cardano’s method for solving the= cubic,+ he his historical prejudices. For example, on the gets Rubaiyat of Omar Khayyam, he says that Edward 3 3 Fitzgerald’s “translation” “was a great favorite all x q2 √ 121 q2 √ 121 . over the English-speaking world up to World War I” = + − + − − Then according to Derbyshire, “By some ingenious and is a “sort of death-haunted hedonism with an arithmetic he works out the cube roots to be alcoholic threat somewhat prefiguring A. E. Hous- 2 √ 1 and 2 √ 1, respectively.” Adding of man.” I do not know of an “alcoholic threat” in course+ − produces− 4. But− he never produces the “in- Housman, andFitzgeraldwas readlong after World genious arithmetic”. Of course inspection shows War I. In fact, one disadvantage for Derbyshire’s that 4 is a solution. I do not know what Bombelli readers is that he has no bibliography. This, of did, but cubing a ib and asking that a be 2 (since course, allows his potted history of mathemati- ± cal irrelevancies “to give the atmosphere” while 4 was a solution) would give the required solution. remaining uncheckable. Derbyshire is not above presenting the usual Furthermore, Derbyshire does not take a great idea of algebra as confusing, e.g., on page 90 or deal of effort to explain the mathematics not in page 119. Similarly (endnote 30) he avoids giv- his primers. For example, Omar Khayyam’s use ing the solution in general to Archimedes’ cubic, of the intersection of two quadratic curves to though he does give the easy solution to one case. solve a cubic is noted on page 55. All he says, in In discussing analytic geometry, Derbyshire discussing the cubic equation 2x3 2x2 2x 1, omits Fermat. In fact, while Descartes and Fermat which he says has solution .647798871…but− + does− both, in 1637, connected algebra and geometry, it not say where this comes from, is “Khayyam took was Fermat who took what seems today to be the an indirect approach, ending up with a slightly more “modern approach” making the algebraic different cubic which he solved numerically via equation central. the intersection of two classic geometric curves.” Descartes brings us to the conclusion of Part I. But he does not present this approach, nor even Part II, entitled Universal Arithmetic, begins with mention what the curves are. Thus we are left to Newton. Derbyshire’s description of Newton, the marvel at Khayyam’s ingenuity in solving some- person, leaves something to be desired. For exam- how (not given) the geometric problem leading to ple, it seems a bit much to call Newton’s disputes a cubic equation (approximately, but not exactly with Hooke or Flamsteed “petty squabbles”, and (!) the one discussed). This sort of throwaway filler his persecution of Leibniz even beyond the grave litters the book. Often where Derbyshire could does not sit well with the description of Newton say something intelligibly concrete to anyone, he as a “cold fish”; nor does his friendship with avoids saying anything at all. He could, after all, John Locke, nor his nervous breakdown in 1693, say what Khayyam did instead of wasting sen- which followed frequent explosions of anger and tences on what he did not do. This sort of remark depressions. extends itself to the copywriter of the dust jacket Chapter 7, entitled “The Assault on the Quintic” blurb who says: “Moving deftly from Abel’s proof deals fairly with Ruffini, Lagrange, Vandermonde, to the higher levels of abstraction developed mil- and Abel. It ends with the declaration that the lenia later by Galois….” (!) (As though Abel were strictly chronological approach followed up to in the Garden of Eden.) this point in the book will be dispensed with in the Sometimes Derbyshire’s “atmospheric” potted next few chapters. The chapter that follows deals history leads him astray, e.g., he knows that Fi- reasonably with Hamilton and Grassman, though bonacci means “filius Bonacci”, but he does not it does not mention the attraction that quaternions mention that this name was first stuck on Leonar- had for Maxwell, Tait, and their physics colleagues do of Pisa some six centuries after he lived (!), (though Maxwell is credited with using vectors to

584 Notices of the AMS Volume 55, Number 5 “fill out the math” for Faraday’s lines of force). The next chapter is cutely titled “Lady of the The fact that Faraday knew no mathematics is not Rings” who is, of course, Emmy Noether, though mentioned. she only occupies the last two of nine sections After this, we swing back to the origins of ma- of this chapter, which is mostly spent appropri- trices in ancient China. Derbyshire’s comments at ately on Fermat’s Last Theorem, Kummer, and the end of 9.6 (page 174) are typical of his “light Dedekind. Incidentally, on page 253 there is not a writing”: “Matrices are, in short, the bee’s knees. picture of a Klein bottle (which is not explained) They are tremendously useful, and any modern in a mathematical exhibit (since a Klein bottle algebra course quite rightly begins with a good requires four dimensions); but only a model of a comprehensive introduction to matrices.” While Klein bottle. We are then led through “Geometry anyone would agree that matrices are important, Makes a Comeback” (which consists of brief men- apparently Derbyshire has never heard of the late tions of classical algebraic geometry, projective Paul Halmos’ Finite Dimensional Vector Spaces. geometry, varieties, the Nullstellensatz, Riemann, In talking about Sylvester (page 175), Derbyshire the Erlangen Program, Lie). hints at homoeroticism. Hirst, who is cited in- The next chapter: “Algebraic This, Algebraic nocently here, was more than a “mathematical That” points out that the Möbius strip should be hanger-on” (among other things he was a pres- named for Listing (who first used the word Topolo- ident of the London Mathematical Society). This gie, though Analysis Situs was popular for quite a sort of hint, or sexual remark, occupies Derbyshire while). This chapter also mentions intuitionism (à elsewhere. For example, we learn that Henri III of la Brouwer, though I do not know what that has to France, though married, was “flamboyantly gay” do with the history of algebra), algebraic number and assassinated “while sitting on his commode” theory and p-adic numbers (which are explained), (whatever that has to do with the history of and ends with Lefschetz and Zariski. André Weil’s algebra). situation in World War II is mentioned but not On page 206, nearly one hundred pages after Bourbaki (strangely for a book about algebra). the quintic, which was addressed on page 115 ff., The last chapter “From Universal Arithmetic we reach Galois. Derbyshire mentions the novel to Universal Algebra” ends essentially with about Galois by Tom Petsinis (who teaches math- Grothendieck. This is preceded by a description of ematics in Australia), and, of course, E. T. Bell, category theory (where forming a field of fractions whose fictionalization is dismissed, and the web- from an integral domain is described in terms of site by Tony Rothman, which updates his 1982 functors). For Grothendieck, Derbyshire gives one American Mathematical Monthly article (unmen- of the sources he rarely acknowledges, namely tioned). He does not mention Mario Livio’s The Allyn Jackson’s superb “As If Summoned from the Equation that Couldn’t be Solved, also written for Void”, Notices, October 2004 and November 2004. the general reader, which covers some of the same While there are no mathematical errors visible ground as Derbyshire’s book. Livio’s book also has in Derbyshire’s book, as this review makes clear, a bibliography (so that the interested reader can there is not much mathematical substance either. pursue matters further). The treatment of most individuals is fair and accu- Derbyshire puts a question mark after Ernest rate, with the occasional shock. Derbyshire’s book (page 210) to query Ernest Armand Duchatelet’s will be found excellent by those for whom it is name, Galois’ supposed opponent in the fatal written. They are not, however, mathematicians. duel. As the opponent is identified in a newspaper article in Lyon, a good distance from Paris, as “L. D.”, he wants the first name to begin with L, as is clear on page 211. This is more potted history—if you don’t like the facts, change them. Derbyshire makes it clear in an endnote that Liouville’s journal was founded many years before it published Galois’ papers. On page 218, the First Sylow Theorem is (half) mentioned, since the idea of normal subgroups is not mentioned until later. The last sentence on page 218 is another example of Derbyshire’s “light” writing: “...and it is infalli- bly the case, at any point in time that somewhere in the world is a university math department with a rock band calling themselves ‘Sylow and his p-subgroup’. ” I suppose this made-up irrelevancy assures the reader that Derbyshire is a “regular guy”. On page 222, the size of the Fischer-Griess “monster” is given (presumablyto horrify readers).

May 2008 Notices of the AMS 585 WHAT IS... ? a Toric Variety? Ezra Miller

A toric variety XP is a certain algebraic variety—or, over the real or complex numbers, a differen- tiable manifold with some singularities allowed— moment map modeled on a convex polyhedron P. Examples include all (products of) projective spaces, which are modeled on (products of) standard simplices. Algebraically, toric geometry is the study of sparse polynomials, whose nonzero coefficients are at- tached to specified monomials. In general, toric XP P varieties admit equivalent descriptions arising naturally in many mathematical areas, including Example 2. If P is the positive orthant in Rn then n symplectic geometry, algebraic geometry, theoret- XP is the complex vector space C . The moment ical physics, and commutative algebra, as we shall map squashes each of the n copies of C to a ray by see. These perspectives, combined with intimate collapsing the concentric circles around the origin connections to pure and applied topics as wide- to points. The decomposition of XP as a disjoint n I ranging as integer programming, representation union over the faces of P is C (C×) , where = SI theory, geometric modeling, number theory, alge- C× is the group of nonzero complex numbers, and I braic topology, and enumerative combinatorics, (C×) is the algebraic torus indexed by the subset lend toric varieties their importance, especially in I 1,...,n . view of their concreteness as examples. ⊆{ } As in the figure, the projection XP P is called In the symplectic setting [2], the space XP is → constructed by specifying a surjection to the poly- the moment map. It is an instance of a general hedron P Rn. The faces of P are all assumed construction wherein a particularly well-behaved to possess⊆ normal vectors with rational numbers group action on a symplectic manifold X induces a for coordinates. (Thus P could be a regular cube map from X to the dual of the group’s Lie algebra. but not a regular icosahedron.) The fiber over When the vertices of P have integer coordinates, any point p P is declared to be a real compact XP is a disjoint union of algebraic tori, one for each ∈ n torus T d —a product of d circles. The dimension face of P, as is C . If P has dimension n, then XP n of this torus equals that of the smallest face of P carries a global action of the algebraic torus (C×) . containing p. As p moves to the boundary of this Restricting to the piece of XP corresponding to n face, a certain subtorus of the fiber is required to the interior P ◦ yields the regular action of (C×) shrink and, at the boundary, collapse. Set theoret- on itself. This description is definitive [3]: a toric ically, then, XP is a disjoint union, over all faces variety over C is a complex algebraic variety with dim(F) n F of P, of products F ◦ T , where F ◦ is the an action of (C×) and a dense open subset iso- × n relative interior of F. morphic to (C×) carrying the regular action. That is, a toric variety is an algebraic torus orbit closure. Example 1. If P is an interval of length ℓ then The same works for fields other than C, such as X is a sphere of diameter ℓ. The moment map P the real numbers R or algebraically closed fields collapses the circles of latitude, which shrink to- of positive characteristic. With this definition, the ward the north and south poles as their collapsed connection to polyhedra is a fundamental theo- images move to the endpoints of P; see the figure. rem: the quotient of a complex toric variety XP by n n the global action of the compact torus T (C×) Ezra Miller is associate professor of mathematics at the ⊆ University of Minnesota, Twin Cities. His email address is is the moment map to P in the dual Rn to the Lie [email protected]. algebra of T n.

586 Notices of the AMS Volume 55, Number 5 The term variety indicates a relation to polyno- elegant expression for the sum of the monomi- mials, which occurs in this integer-vertex case. Any als corresponding to the lattice points in P. The n d subgroup of (C×) isomorphic to (C×) has an or- underlying geometry is that global sections of n bit closure in C through the point (1,..., 1). This holomorphic line bundles on XP correspond to affine toric variety is parametrized by monomi- lattice points in polytopes related to P. Brion’s d n -als: the inclusion (C×) ֓ C takes (τ1,...,τd) to formula is the key to A. Barvinok’s polynomial a a a1 an ai i1 id (τ ,...,τ ), where τ τ1 τd is a mono- time algorithms for enumerating lattice points in mial for each i. For example,= the· · · parabola in the polytopes. Concrete cohomological computations plane C2 is the curve parametrized by t ֏ (t,t2). also form the basis for R. Stanley’s approach to Every toric variety has a finite open cover by affine the enumerative combinatorics of polytopes. The toric varieties; hence torus orbit closures in Cn question is how to count faces of convex polytopes. are, in a toric sense, locally universal. Translating into the toric world, Morse theory in- The parametrized view of (not necessarily dicates an efficient way to encode the numbers affine) toric varieties is key in applications to of faces, and the Hard Lefschetz theorem from geometric modeling, because every polynomial algebraic geometry implies unimodality for the parametrization of a space is the projection of a encoded face numbers. monomial one. Thus projections of toric varieties In theoretical physics, toric varieties arise in the over the real numbers generalize Bézier curves, context of gauged linear sigma models. Quantum which come from rational normal curves XP , where field theory considers maps from a Riemann sur- P is an interval of integer length. Geometrically, face into Cn, which carries an action of a compact the moment map carries the positive real part of d-torus T d . Ground states for this theory, obtained a toric variety XP homeomorphically to P itself, by setting the potential energy to zero, constitute n and the wavy polyhedral patch XP+(R) can be a certain fiber of the moment map of C ; modulo used for modeling purposes. When P is a lattice gauge equivalence—the T d -action—this results in triangle, for instance, X+(R) is a Bézier triangle in a toric variety XP . (When n 2 and XP is the P = a Veronese embedding of the projective plane. complex projective line, gauge equivalence is the Incommutative algebra, monomialparametriza- Hopf fibration S3 S2.) Duality for polytopes in → tions give rise to simple implicit equations. As this setting gives rise to the phenomenon known with any variety in Cn, an affine toric variety can be as mirror symmetry. expressed as the set of points in Cn where a family A huge amount of active research has ties to f1,...,fr of polynomials in variables x1,...,xn all toric methods. The symplectic setting has seen simultaneously vanish. The crucial observation increasingly deep Euler–Maclaurin type summa- is that in the toric case, one can always choose tion formulas. Generalizations of toric spaces are u v all of the fj to be binomials, of the form x x ubiquitous, including log schemes, which are toric for some nonnegative integer vectors u and− v étale locally; quasitoric manifolds and torus mani- of length n. The binomials can be interpreted folds, which are more flexible topological versions as linear equations on the exponent vectors of of toric varieties; and toric stacks, which take geo- the parametrizing monomials. In the parabola metric account of extra arithmetic data beyond example, the parametrized curve (x, y) (t,t2) is the polyhedron P. For the purpose of pushing implicitly defined as the set of points= where the Stanley’s enumerative combinatorics to the set- binomial y x2 vanishes; this binomial says that ting of nonrational polytopes, there has even been the exponent− on the second t-monomial is twice success in abstracting toric cohomological com- the exponent on the first one. In this way, the putations polyhedrally, without constructing any binomials for XP encode crucial information about sort of toric space at all! The future will surely see the lattice points in P, and the integer vectors other types of developments, as well. joining them. Aside from endowing the vanishing ideal of XP with particularly rich algebraic and References combinatorial structure, the binomials thereby [1] Victor M. Buchstaber and Taras E. Panov, Torus convert toric varieties into vehicles for investi- actions and their applications in topology and com- gating integer programming, where the goal is to binatorics, University Lecture Series, vol. 24, Amer. find a (path to a) vertex of P that maximizes some Math. Soc., Providence, RI, 2002. Ana Cannas da Silva given linear cost function. [2] , Lectures on symplectic ge- ometry, Lecture Notes in Mathematics, vol. 1764, The combinatorial structure of toric varieties Springer–Verlag, Berlin, 2001. makes various flavors of cohomology explicitly [3] David Cox, What is a toric variety?, Topics in computable. These computations have surprising- algebraic geometry and geometric modeling, 203– ly wide applications, the overarching idea being 223, Contemp. Math., vol. 334, Amer. Math. Soc., that the topology of XP usefully distills the com- Providence, RI, 2003. binatorics of P itself, and vice-versa. For instance, Brion’s formula interprets a statement in equi- variant K-theory of toric varieties as a shockingly

May 2008 Notices of the AMS 587 Evansville Honors the First Black Ph.D. in Mathematics and His Family Talitha M. Washington

About four years ago I came across the Mathema- the value of an education which then led him to ticians of the African Diaspora website and dis- encourage his son, Elbert, to succeed. covered that the first Black in the world to earn a In 1913 Elbert graduated from Clark High School Ph.D. in mathematics was from my neighborhood and enrolled at Indiana University. In 1915 Cox in Evansville, Indiana. While growing up, no one joined Kappa Alpha Psi, which is a Black fraternity talked to me about Elbert Frank Cox, who is the that emphasizes achievement. When Cox received first Black in the world to earn a Ph.D. in mathemat- his transcript from IU, it had “Colored Student” ics. After stumbling upon Elbert, excitement came printed across the top. At that time it was common over me and then I became curious about who he for colleges and universities to distinguish race on was and what motivated him to be successful in an academic transcript. By doing so, employers would immediately know if the person was Black mathematics. so that they could grant or deny a position based In 2001 I became the second African American on race. from Evansville to earn a Ph.D. in mathematics. After graduation, Cox taught for a year at Alves Thus, I felt a personal responsibility and an ob- Street School in Henderson, Kentucky. Later he en- ligation to give Evansville and the world an op- tered the U.S. Army and taught at Shaw University. portunity to thank Elbert for his accomplishments He had enrolled in summer graduate classes at as they opened doors for me and many other Cornell University as early as 1920 to learn more mathematicians. about science. After a couple of years Cox left Shaw In 1895 Elbert Frank Cox was born to Johnson to study mathematics at Cornell University. Under and Eugenia Cox at 715 Oak Street in Evansville, the supervision of William Lloyd Garrison Williams, Indiana (which is located less than one mile from Cox completed and successfully defended his where I grew up). Elbert’s father, Johnson D. Cox, dissertation “Polynomial Solutions of Difference was principal and teacher for over forty years at Equations”. In 1925 he became the first African Third Avenue School. In those days the Evansville schools were segregated and Third Avenue School was an elementary school for African Americans. There is no confirmation that J. D. had an advanced degree but it was common to not have a college degree before entering the teaching profession. However, J. D. did further his education by taking courses at Indiana University in the summer of 1927 and the summer and fall of 1928. He con- tinued his studies by completing four summer courses from 1930 to 1939 at Evansville College, which is now my place of employment, the Uni-

versity of Evansville. J. D. Cox must have known author. the of courtesy Photograph

Talitha M. Washington is assistant professor of mathemat- The author and the plaque dedicated to J. D. ics at the University of Evansville. Her email address is Cox and his son Elbert Frank Cox in Evansville, [email protected]. Indiana.

588 Notices of the AMS Volume 55, Number 5 American to receive a Ph.D. in mathematics and the first graduate of an Evansville high school to receive a Ph.D. degree. Ironically and sadly, during the year that Elbert joined an elite group of only twenty-eight men who were awarded Ph.D.’s in mathematics in the country, thirty-one Black men were lynched. After leaving Cornell he went on to become the head of the Math and Physics Departments at West Virginia State University. In the summers he would visit his brother, Avalon, in Princeton, Indi- ana. At Avalon’s church, Bethel African Methodist Episcopal Church, he met Beulah Kaufman and married her after a six-year courtship. In 1929 he joined the faculty at Howard University. In those days many Black scholars migrated to Howard University. In 1929 Cox joined the faculty, and by 1943, Howard University employed five of the eight Black math Ph.D.’s. Cox retired in 1965 and passed on in 1969. Sometimes I wonder if J. D. Cox knew that his

passion for education would encourage his son to Church. Baptist Missionary Liberty of courtesy Photograph become a trailblazer for so many. On November 18, 2006, Evansville welcomed J. D. Cox’s grandson Photograph which hangs in the hallway of the Liberty and great-grandchildren to a dedication ceremony Baptist Church. J. D. Cox is in the middle row, second from of a plaque at Liberty Baptist Church. In the main the left. hallway of the Liberty, one can still find J. D. Cox’s child will realize that “if Elbert could earn such picture hanging on the wall. a high degree in mathematics, then I can do any- The ceremony stirred up various emotions of thing.” Behind the child, a parent will follow, and thanks and gratitude from the Cox family for their after reading the plaque, the parent will gaze at forefathers. J. D.’s great-grandson, Elbert Lucien the nearby tulip tree and know that her child has Cox Jr., spoke about how the educational legacy no limitations in this world. The parent will know of his family contributed to his accomplishments. that J. D.’s passion for education helped his son He now serves as a program manager for NASA succeed, and will become encouraged to value her (National Aeronautics and Space Administration). own child’s education. When the child becomes J. D.’s grandson was touched by the presence of frustrated in mathematics, the parent will provide the brothers of the Kappa Alpha Psi Fraternity a kind reminder about the man named Cox who who proudly wore the red blazers in their sup- broke through racial barriers and stereotypes to port of their Kappa brother, Elbert. At the end of become the first African American to earn the Ph.D. the ceremony the Cox family was moved by J. D.’s in mathematics. students as they stood up and gave testimonials about how he encouraged and inspired all children to do better. On that day, the Evansville-Vanderburgh School Corporation, University of Evansville, University of Southern Indiana, and Ivy Tech Community College joined together to support the plaque that reads: HOME OF JOHNSON DUNCAN COX J. D. COX (1873–1952) WAS A TEACHER AND PRINCIPAL AT THIRD AVENUE SCHOOL FOR 40 YEARS. IN 1925, HIS SON, ELBERT FRANK COX, BECAME THE FIRST GRADUATE OF AN EVANSVILLE HIGH SCHOOL TO RECEIVE A Ph.D. DEGREE AND THE FIRST AFRICAN AMERICAN TO EARN A Ph.D. IN MATHEMATICS My hope is that a child will stroll by the plaque, pause, and then read it and become amazed. The

May 2008 Notices of the AMS 589 Ask Professor Nescio

Editor’s Note: Graduate students, early career faculty, and other mathematicians may have pro- fessional questions that they are reluctant to pose to colleagues, junior or senior. The Notices advice column, “Ask Professor Nescio”, is a place to address such queries. Nomen Nescio is the pseudonym of a distinguished mathematician with wide experience in mathematics teaching, research, and service. Letters to Professor Nescio are redacted to eliminate any details which might identify the questioner. They are also edited, in some cases, to recast questions to be of more general interest and so that all questions are first person. Some letters may be edited composites of several submitted questions. Query letters should be sent to [email protected] with the phrase “A question for Professor Nescio” in the subject line. —Andy Magid

Dear Professor Nescio, entire spectrum of feelings about their advisor. If I’m wrapping up my Ph.D. thesis and will gradu- you really like him/her, then I would suggest the ate the end of this semester. My advisor just told two of you sit down and have a friendly conversa- me that he thinks we should submit my thesis tion where you express your concerns. So let’s as- results as a joint paper. Some of my fellow grad sume your feelings are somewhere between indif- students tell me that this is a good idea because my ference and dislike and you don’t feel comfortable advisor is so famous, but others say it’s a bad idea approaching this directly. because it will look like the thesis work is his, not Understand that advising a Ph.D. student is mine. Of course I don’t want to make my advisor hard work. In many cases, even when the thesis is mad at me at this stage. What should I tell him? published only by the student, there is a lot of the advisor’s energy and creativity in the work. This —Troubled is hard to measure but is certainly a reason why some advisors want their name on the student’s Dear Troubled, work. Some have even told me that each doctoral Understand that the answer to this question is student is one less paper in their bibliography. tricky. A correct answer, if it exists, would depend Thus the request is neither unique nor entirely on a lot of additional information not contained unreasonable. I think the assumption of most in your query. Even with additional information, mathematicians is that the advisor has helped the I can almost guarantee the solution is not unique student with the dissertation. In some cases that and you have to try for a solution that optimizes may be an unfair assumption. Having both names some set of criteria. on the paper reinforces the perception. Neverthe- The fact that your advisor is “famous” says that less understand a fundamental fact. When you talk he/she really doesn’t need to pad his/her publica- about the thesis at a conference or in a colloquium, tion list; therefore the motive for putting his/her one of two things is going to happen. Either you name on the paper lies elsewhere. (Unless, that will dispel that notion and affirm your dominance is, the advisor is an insecure egomaniac. It’s not or equality as a contributor, or you will convince impossible for a famous person to have an uncon- the audience that your advisor’s input was even trollable desire to plaster their name everywhere more significant than originally thought. In other but the walls of a public toilet. If that’s the case, words, having a joint paper with your advisor is grin and bear it. Contesting this is likely to lead to unlikely to affect the mathematics community’s a confrontation.) pre-conceived view of the work, and only you can If, on the other hand, all is normal, there is a convince them you were the driver. spectrum of responses, and I would ask you some Incidentally, some of your friends are correct. additional questions if we were talking over a glass Given that your advisor is famous, there could be of wine (or beverage of your choice). The first ques- a benefit to shared authorship: people are more tion is the obvious one: Did your advisor prove any likely to look at the paper seriously. Yes, the con- of your theorems? I am going to assume the answer tent will ultimately determine whether the research to this one is “No,” since the opposite indicates a is judged meritorious, but name recognition draws clear answer. Maybe the next question I would ask quick attention. you is, “Do you like your advisor?” If that strikes I have had several doctoral students and have you as an odd question in these circumstances, let contributed to their theses in different ways—oc- me say that I have met mathematicians having the casionally with a good idea, sometimes just as a

590 Notices of the AMS Volume 55, Number 5 cheerleader, and sometimes as the person who for publication. I received an email from a math- plants a kick in an appropriate place at the ap- ematician who said that he and a co-author were propriate time. Some students probably thought I working on some of the same problems treated in contributed less than I think I did, some thought my papers. Although their work is not available as the opposite. I generally avoided trying to be a co- a preprint, he said they had lectured on this subject author and sometimes I had to insist to the student and suggested that I acknowledge their work in my that they should publish solo. So if your advisor papers. They have now sent me a preprint. Do I were asking me, I’d advise letting you publish need to acknowledge their work in my papers? under your name alone. —Confused In summary, this is one of those questions that have many possible correct answers. I hope that even if I haven’t answered your question, I have Dear Confused, provided a bit of perspective so you can come to This is an innocuous request. Strictly speaking, your own conclusion. there is no necessity to acknowledge their work, —Respectfully, but what will you lose if you do? Since you now Professor N. N. have their preprint, a footnote along the following lines might be good: “Upon seeing my paper on the arXiv, Professor X kindly informed me of his Dear Professor Nescio, work with Professor Y [here cite the preprint] that I’m up for tenure along with three other assis- tant professors. The tenure committee has asked is related to the present work.” This does three me, and not the others, to meet with them to talk things. First it informs the interested reader of ad- about my research. All our dossiers are pretty ditional information on the subject, thus further- similar. Should I be worried about this “special” ing the advance of mathematics. Second it extends treatment? a professional courtesy to Professors X and Y, who, —Flummoxed given that they are working in your area, may be of assistance in the future. Finally it firmly proclaims that you did not have access to their ideas when Dear Flummoxed, you were doing your research. Then you should Professor Nescio is shocked! Shocked that in inform Professor X about what you are doing and this day and age a tenure committee does not un- urge him/her to post his preprint on the arXiv. It derstand that all candidates must be approached may well be that at some point in the future you and treated the same. Whether you should be too will ask for such a professional courtesy. worried or not is unclear, but I cannot imagine a So, gentle supplicant, understand, as you begin reason for such a singular meeting. your voyage across that wide sea of discovery that I would hope that after the time you have spent we call a career, that even though this voyage is at your university you have made a good friend in fraught with peril, every swell in that sea is not a the tenured ranks—a mentor, a confidant, a senior portent of an approaching storm. researcher in your area who values your work. (If —Respectfully, you haven’t, this may be a cause for greater con- Professor N. N. cern than your singular treatment.) Approach this person or the department chair and mention this turn of events. If you can do this casually during an Dear Professor Nescio, encounter in the hallway, all the better since this The referee report for a recent paper of mine will seem to say the request is not a major event in suggested that I add citations to several papers your life. (Sometimes a trace of naiveté is useful.) by a certain author, which are only peripherally It’s likely they will be surprised and can, perhaps, related to my paper. I suspect that the author is get to the bottom of this matter. In the meantime, the referee and that he is simply trying to promote agree to the meeting. his own work. And yet, in order for the paper to be Frankly, if you were denied tenure and the oth- accepted, I am supposed to revise it in accordance ers were not, you might have grounds for a law- with the referee’s comments. How can I handle suit. I am not a lawyer, but it is my understanding this situation? that most of the lawsuits that concern tenure or —Baffled promotion are based on procedural issues, not the final decision. Dear Baffled, —Respectfully, Your suspicion sounds realistic and Professor Professor N. N. Nescio understands your reluctance to comply. He understands pride, having enough of this trait that Dear Professor Nescio, some humble folks of a religious bent might accuse I am working on my thesis and have written two him of possessing this one of the seven deadly sins. papers, which I posted on the arXiv and submitted No one likes to be asked for such a revision that

May 2008 Notices of the AMS 591 08CIQ05_E_3.25x9.5_E.qxd 2/18/08 6:03 PM Page 1

seems to be pandering to an anonymous force. Nevertheless let us ask, “How accurate is your use NATIONAL SECURITY AGENCY of the word ‘peripherally’?” This will be difficult, but try to objectively assess the relation of the NSA references to your work. Then ask, “Does including the reference damage my work?” With the added detachment that time brings, you might be able to address these issues correctly, and the answers to the questions should indicate your response. Your situation reminds me of a pair of referee reports I received at an early stage of my career. In one of these cases my paper solved a problem If you want to raised in another mathematician’s work. I included make a career out a different proof of one of his results, and I said of solving complex in the paper that my proof was easier. The referee, mathematical who I strongly suspect was the original author, said he didn’t see that my proof was easier. Professor challenges, join Nescio was proud of his proof. Nevertheless, he NSA as a removed the offending word, kept the proof in Mathematician. his paper, and said, “The following is an alternate proof.” This satisfied the referee, though to this day I think my proof was easier. In the other case I was more forceful because At NSA you can bring the power of Mathematics the referee was off base. After having held onto to bear on today's most distinctive challenges and my paper for about 18 months, he returned a problems. We identify structure within the chaotic, report only after I had prompted the editor to and discover patterns among the arbitrary. You prod this negligent mathematician. In the report will work with the finest minds and the most he said that the proof of my main theorem could powerful technology. be shortened by using a result that appeared in a standard reference. In fact the referenced result was connected to mine only by the fact that they Make the move both belonged to the same area of mathematics; that puts your there was no connection between the hypotheses math intelligence and conclusions of the two. Even at this tender age to work. Apply Professor Nescio was quite disturbed by such a to NSA. lack of professionalism. After making some other, minor changes called for by the referee, I sent the manuscript back to the editor with the following statement in my cover letter. “I fail to see the WHERE INTELLIGENCE GOES TO WORK ® relevance of the referee’s comment number 6.” I was notified in about three weeks that the paper DISCIPLINES was accepted. > Number Theory > Finite Field Theory I have included these two tales from my past to > Probability Theory > Combinatorics indicate that there is a wide spectrum of possible responses to a referee’s report and to illustrate > Group Theory > Linear Algebra that such a report need not be slavishly heeded. > Mathematical Statistics > and More You are a professional mathematician, and your opinion is valid. Your opinion of your own paper Visit our Web site for a complete list of current career opportunities. is not objective, but it has merit. Returning to your situation, it sounds like it is closer to the first of my two experiences. Neverthe- Your perspective. Your culture. Your intelligence. less, if you truly find including the references to be offensive, tell the editor that this is the case, state your reasons, and ask for his/her advice U.S. citizenship is required. and/or intervention. Remember that an editor is NSA is an Equal Opportunity Employer and abides by not supposed to be a mere paper processor but to applicable employment laws and regulations. exercise judgment. Rubik’s Cube® is used —Respectfully, by permission of Seven Towns Ltd. www.rubiks.com www.NSA.gov/Careers Professor N. N.

592 Notices of the AMS Volume 55, Number 5 Kontsevich and Witten Receive 2008 Crafoord Prize in Mathematics

The Royal Swedish Academy of Sciences has an- nounced the recipients of the Crafoord Prize in Mathematics and Astronomy 2008. The mathematics portion of the prize is awarded jointly to Maxim Kontsevich, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France, and Edward Witten, Institute for Advanced Study, Princeton, NJ. The two were cited “for their im- portant contributions to mathematics inspired by modern theoretical physics”. The laureates in mathematics have used the methodology of physics to develop a revolutionary new mathematics intended for the study of various types of geometrical objects. Their work is not only Maxim Kontsevich Edward Witten of great interest in the discipline of mathematics but may also find applications in totally different The amount of this year’s Crafoord Prize is areas. Its results are of considerable value for US$500,000. Kontsevich and Witten are awarded physics and research into the fundamental laws one half, and the other half is awarded to Rashid of nature. According to string theory, which is an Sunyaev, an astrophysicist who is receiving the ambitious attempt to formulate a theory for all astronomy prize. The prize-awarding ceremony the natural forces, the smallest particles of which will take place at the Academy in Stockholm on the universe is composed are vibrating strings. April 23, 2008, in the presence of His Majesty the This theory predicts the existence of additional King. dimensions and requires very advanced mathemat- The Royal Swedish Academy of Sciences, ics. The laureates have resolved several important founded in 1739, is an independent organization mathematical problems related to string theory whose overall objective is to promote the sciences and have in this way paved the way for its further and strengthen their influence in society. Tradi- development. tionally, the Academy takes special responsibility Maxim Kontsevich was born in 1964 in Khimki, for the natural sciences and mathematics. Russia. He received his Ph.D. in mathematics in —From a news release of the Royal Swedish 1992 at the University of Bonn. He is a professor Academy of Sciences at the Institut des Hautes Études Scientifiques. He received the Fields Medal in 1998. Edward Witten was born in 1951 in Baltimore, MD. He received his Ph.D. in physics in 1976 from Princeton University. He is the Charles Simonyi Professor in the School of Natural Sciences at the Institute for Advanced Study in Princeton. He re- ceived the Fields Medal in 1990.

May 2008 Notices of the AMS 593 Deligne, Griffiths, and Mumford Receive 2008 Wolf Prize

Prize in Mathematics is available on the website of the Wolf Foundation, http://www.wolffund.org.il.

Description of Prizewinners’ Work The following description of the work of Deligne, Griffiths, and Mum- ford was prepared by the Wolf Foun- Pierre R. Deligne Phillip A. Griffiths David B. Mumford dation. Central to modern algebraic ge- The 2008 Wolf Prize in Mathematics has been ometry is the theory of moduli, i.e., variation of awarded jointly to three individuals: algebraic or analytic structure. This theory was traditionally mysterious and problematic. In criti- Pierre R. Deligne, Institute for Ad- cal special cases, i.e., curves, it made sense, i.e., vanced Study, Princeton, “for his work the set of curves of genus greater than one had a on mixed Hodge theory; the Weil con- natural algebraic structure. In dimensions greater jectures; the Riemann-Hilbert corre- than one, there was some sort of structure locally, spondence; and for his contributions but globally everything remained mysterious. to arithmetic”; The two main (and closely related) approaches to moduli were invariant theory on the one hand and Phillip A. Griffiths, Institute for Ad- periods of abelian integrals on the other. This key vanced Study, Princeton, “for his work problem was tackled and greatly elucidated by on variations of Hodge structures, the Deligne, Griffiths, and Mumford. theory of periods of abelian integrals, David B. Mumford revolutionized the algebraic and for his contributions to complex approach through invariant theory, which he re- differential geometry”; and named “geometric invariant theory”. With this ap- proach, he provided a complicated prescription for David B. Mumford, Brown University, the construction of moduli in the algebraic case. “for his work on algebraic surfaces; As one application he proved that there is a set of on geometric invariant theory; and for equations defining the space of curves, with inte- laying the foundations of the modern ger coefficients. Most important, Mumford showed that moduli spaces, though often very complicated, algebraic theory of moduli of curves exist except for what, after his work, are well- and theta functions.” understood exceptions. This framework is critical The US$100,000 prize will be presented by the for the work by Griffiths and Deligne. Classically, president of the State of Israel in a ceremony at the moduli space of curves was parameterized by the Knesset (parliament) in Jerusalem on May 25, using periods of the abelian integrals on them. 2008. The list of previous recipients of the Wolf Mathematicians, e.g., the Wolf Prize winner André

594 Notices of the AMS Volume 55, Number 5 Weil, have unsuccessfully tried to generalize the periods to higher dimensions. About the Cover Phillip A. Griffiths had the fundamental insight Patterns of factorization that the Hodge filtration measured against the integer homology generalizes the classical periods This month’s cover is derived from David N. of integrals. Moreover, he realized that the period Cox’s article on the arithmetic sieve. The pix- mapping had a natural generalization as a map els in the column above n are at heights equal into a classifying space for variations of Hodge to the divisors of n. The primes are character- structure, with a new non-classical restriction ized in this figure by yellow columns. imposed by the Kodaira-Spencer class action. This Clues in the cover image ought to help in led to a great deal of work in complex differential figuring out the origin of the parabolas Cox geometry, e.g., his basic work with Deligne, John observes. Various other views of Cox’s fac- Morgan, and Dennis Sullivan on rational homotopy torization images will bring to light other in- theory of compact Kähler manifolds. teresting patterns, but none seem to involve Building on Mumford’s and Griffiths’ work, deep number theory. What’s astonishing is Pierre R. Deligne demonstrated how to extend the how good the human eye is at perceiving variation of Hodge theory to singular varieties. regular patterns in a noisy background. This advance, called mixed Hodge theory, allowed —Bill Casselman, Graphics Editor explicit calculation on the singular compactifica- ([email protected]) tion of moduli spaces that came up in Mumford’s geometric invariant theory, which is called the Deligne-Mumford compactification. These ideas assisted Deligne in proving several other major results, e.g., the Riemann-Hilbert correspondence and the Weil conjectures.

Biographical Sketches Pierre R. Deligne was born in 1944 in Belgium. Starting in 1967, he was a visitor at the Institut des Hautes Études Scientifiques, where he worked with Alexander Grothendieck. Deligne received his doc- torat en mathématiques in 1968 and his doctorat d’état des sciences in 1972, from the Université de Paris-Sud. He was a professor at the IHÉS from 1970 until 1984, when he took his current position as a professor at the Institute for Advanced Study in Princeton. Deligne received the Fields Medal in 1978, the Crafoord Prize in 1988, and the Balzan Prize in 2004. Phillip A. Griffiths was born in the United States in 1938. He received his Ph.D. from Princeton University in 1962 under the direction of Donald Spencer. Griffiths has held positions at Univer- sity of California, Berkeley (1962–1967), Prince­ ton University (1967–1972), Harvard University (1972–1983), Duke University (1983–1991), and the Institute for Advanced Study (1991 to the present), where he was director until 2003. He received the AMS Steele Prize in 1971. David Mumford was born in England in 1937 but grew up in the United States from 1940 on. He was an undergraduate and graduate student at Harvard University, where he received his Ph.D. in 1961, under the direction of Oscar Zariski. Mumford was on the faculty at Harvard until 1996, when he moved to Division of Applied Mathematics at Brown University. He received the Fields Medal in 1974 and the AMS Steele Prize in 2007.

—Allyn Jackson

May 2008 Notices of the AMS 595 Taubes Receives NAS Award in Mathematics

Clifford H. Taubes has re- four-manifolds. The latter was, of course, crucial in ceived the 2008 NAS Award Donaldson’s celebrated application of gauge theory in Mathematics from the Na- to four-dimensional differential topology. Taubes tional Academy of Sciences. himself proved the existence of uncountably many He was honored “for ground- exotic differentiable structures on R​4​; he reinter- breaking work relating to preted Casson’s invariant in terms of gauge theory Seiberg-Witten and Gromov- and proved a homotopy approximation theorem Witten invariants of symplec- for Yang-Mills moduli spaces. Taubes also proved tic 4-manifolds, and his proof a powerful existence theorem for anti-self-dual of the Weinstein conjecture conformal structures on four-manifolds. for all contact 3-manifolds.” “When Witten proposed the study of the so- The NAS Award in Math- called Seiberg-Witten equations in 1994, Cliff ematics was established by Taubes was one of the handful of mathematicians the AMS in commemora- who quickly worked out the basics of the theory Clifford H. Taubes tion of its centennial, which and launched it on its meteoric path. From an was celebrated in 1988. The analyst’s point of view, the quasi-linear Seiberg- award is presented every four Witten equations may seem rather mundane, at years in recognition of excellence in research in least when compared to the challenges offered up the mathematical sciences published within the by the Yang-Mills equations. True to this spirit, past ten years. The award carries a cash prize of Taubes announced at the time that he would never US$5,000. Previous recipients are Robert P. Lang- again write a paper more than twenty pages long. lands (1988), Robert MacPherson (1992), Andrew Of course, this resolution lasted only for about six J. Wiles (1996), Ingrid Daubechies (2000), and Dan months! After that, Taubes wrote a whole series of Virgil Voiculescu (2004). deep, technical, and very long papers that became known by the slogan ‘Seiberg-Witten = Gromov’. The Work of Clifford Taubes These papers establish the most profound results The Notices asked D. Kotschick, Ludwig- known to this day about the Seiberg-Witten equa- Maximilians-Universität München, and T. S. Mrowka, tions, linking their solutions on symplectic four- Massachusetts Institute of Technology, to com- manifolds to Gromov’s pseudo-holomorphic curve ment on the work of Taubes. They responded: theory in a very precise way. “By his own account, Cliff Taubes would like “Taubes’s work on the Seiberg-Witten equations to be considered a topologist. Ignoring this wish, remains one of the cornerstones underpinning the most of his colleagues see him as a great geometric current very productive symbiosis between sym- analyst, whose work has had a profound impact on plectic geometry and low-dimensional topology. geometry, topology and mathematical physics. Nevertheless, it was a shock to many when Taubes “Starting out in mathematics with a phys- knocked off one of the holy grails of symplectic ics background, Taubes did some of the early topology last year. The Weinstein conjecture pre- foundational work in mathematical gauge theory dicts the existence of periodic orbits for the Reeb studying vortices and Bogomolny monopoles and flows of arbitrary contact forms on closed three- building up a substantial existence theory for the manifolds. Many special cases had been proved by self-dual Yang-Mills, or instanton, equations on a variety of methods from symplectic geometry,

596 Notices of the AMS Volume 55, Number 5 and a proof of the full conjecture was one of the AMERICAN MATHEMATICAL SOCIETY ultimate goals of symplectic field theory. However, Taubes’s proof follows a rather different line, using gauge theory and deploying a strategy similar to his work on ‘Seiberg-Witten = Gromov’. The proof also hinges on a novel estimate for the spectral flow of a family of Dirac-type operators. Math in Moscow “It is in the nature of Cliff Taubes’s work that his papers are not usually short or easy to read. Rather they are difficult and original, and techni- Scholarships cally demanding by necessity. His faithful readers take comfort in the knowledge that Cliff is at least as hard on himself as he is on the readers, and they appreciate his very personal style peppered with what they affectionately refer to as ‘Cliffisms’.”

Biographical Sketch Clifford Taubes grew up in Rochester, New York. After his undergraduate education at Cornell Uni- versity, he received a Ph.D. in physics from Harvard University in 1980. After a Harvard Junior Fel- lowship, taken in the mathematics department at Harvard, he taught for two years at the University of California, Berkeley. Since 1985 he has been at The AMS invites undergraduate mathematics Harvard, where he is the William Petschek Profes- sor of Mathematics. He received the AMS Veblen and computer science majors in the U.S. to Prize (1991) and the Élie Cartan Prize of the French apply for a special scholarship to attend a Mathematical Society. He is a member of both the Math in Moscow semester at the Independent American Academy of Arts and Sciences and of the University of Moscow. Funding is provided by National Academy of Sciences. the National Science Foundation and is admin- —Allyn Jackson istered by the AMS. The Math in Moscow program offers a unique opportunity for intensive mathematical study and research, as well as a chance for students to experience life in Moscow. Instruction during the semester emphasizes in-depth under- standing of carefully selected material: students explore significant connections with contem- porary research topics under the guidance of internationally recognized research mathema- ticians, all of whom have considerable teaching experience in English. The application deadline for spring semesters is September 30, and for fall semesters is April 15. For more information, see www.ams.org/ employment/mimoscow.html. Contact: Membership and Programs Depart- ment, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294, USA; telephone: 800-321-4267, ext. 4170; email: [email protected].

May 2008 Notices of the AMS 597 2008 Award for an Exemplary Program or Achievement in a Mathematics Department

The Award for an Exemplary Program or Achieve- Latina/o, and Native American U.S. citizens or ment in a Mathematics Department was established permanent residents accounted for 20–25 percent by the AMS Council in 2004 and was given for the of the department’s graduate student population first time in 2006. The purpose is to recognize a over the six-year period ending in 2005. This is department that has distinguished itself by under- an especially impressive percentage, given Iowa’s taking an unusual or particularly effective program demographics, and is currently among the highest of value to the mathematics community, internally at U.S. majority institutions. or in relation to the rest of society. Departments The department’s recruitment effort is sup- of mathematical sciences in North America that ported by a carefully designed program that offer at least a bachelor’s degree in mathematical includes an intensive summer institute, weekly sciences are eligible. The award carries a cash prize help sessions, and intensive faculty and peer men- of US$1,200 and is given annually. toring. The program is open to majority students The award is presented by the AMS Council as well and, as often happens with well-designed acting on the recommendation of a selection com- programs developed for particular groups, has mittee. For the 2008 award, the members of the raised the level of educational achievement for all selection committee were: Steven A. Bleiler, Joel B. students. It has also made an impressive difference Brawley, Karl Knight (chair), Donal B. O’Shea, and on a national level. The three minority students Roger A. Wiegand. that received their Ph.D.’s in the department in The previous recipients of the award are Harvey 2002–2003 represented roughly 10 percent of the Mudd College (2006) and the University of Califor- math doctorates awarded nationally to U.S. minor- nia, Los Angeles (2007). ity students during that year. The recipient of the 2008 Award for an Exem- Members of the University of Iowa’s Math- plary Program or Achievement in a Mathematics ematics Department have willingly shared their Department is the the Mathematics Depart- methods with other departments at invited talks ment at the University of Iowa. What follows and conferences, including a session at a national is the selection committee’s citation. AMS meeting and at a conference at NSF [National Science Foundation]. Furthermore, the depart- Citation ment has established partnerships with other The American Mathematical Society (AMS) presents institutions in the United States and abroad that its third annual Award for an Exemplary Program support the goal of increasing minority participa- or Achievement in a Mathematics Department to tion in mathematics. For example, the University the University of Iowa. The Mathematics Depart- of Iowa Mathematics Department has worked ment at the University of Iowa is a national leader with the Department of Mathematics at Florida in recruiting and developing underrepresented U.S. A&M University to build a partnership called the minority doctoral students in mathematics. The Alliance for the Production of African American department has accomplished this by devising a Ph.D.’s in the Mathematical Sciences, supported model for recruiting and developing U.S. minor- by a US$1.8 million NSF grant, with the goal of ity doctoral students that could be used at other providing a seamless transition for graduates of institutions. Alliance undergraduate institutions who wish to The department’s long-term commitment to study at majority Ph.D. institutions. graduate education in mathematics for students The mathematics community is fortunate to from underrepresented minority groups began in have the University of Iowa present such an out- 1995 and has continued with support from several standing example of an exemplary program in a Department of Education grants. African American, mathematics department.

598 Notices of the AMS Volume 55, Number 5 University of Iowa Wins Exemplary Program Award Allyn Jackson

We are happy to get the awards, but we Muhly. Although clearly on track to a successful are even happier to watch the students research career, she is still sometimes beset by get Ph.D.’s. anxieties that stem from having so few role models. —Philip Kutzko “I have never seen any black people do this,” she told Kutzko. In the mid-1990s, the mathematics department Over the years, the Iowa department has lis- at the University of Iowa decided to apply for a tened carefully to its students and has observed large government grant to support fellowships for closely their successes and failures. The depart- graduate students. The aim was to use the grant ment has used this knowledge to rejuvenate its to recruit students from minority groups that are graduate program, making it a place where stu- underrepresented in mathematics. Eight such stu- dents of all colors can thrive. The department has dents came. Some did well, others less well. One finished a doctorate in the department; others had received several awards for its success in recruiting new doors opened to them: One ended up getting minority students, including the 2004 Presidential an MBA, and another earned a Ph.D. in computer Award for Science and Engineering Mentoring and science. But the department did not stop there. designation as a “Program that Makes a Difference” Rather, faculty members got to know the students by the AMS Committee on the Profession. This and tried to understand the factors behind their year, the Iowa department was chosen for the AMS achievements and setbacks. The experience of Award for Exemplary Program or Achievement by bringing in those eight students put the depart- a Mathematics Department. ment on a new path. “What happened as a result Mentoring is Key to Success of that first year or two is, we began to change as a department,” says Iowa faculty member Philip It’s an attitude of, “It’s our job to make Kutzko. “It’s a bit funny to say it this way, but we sure everybody succeeds,” as opposed started to become a little less white.” to, “It’s our job to find out who the best Nowadays if you ask members of the Iowa de- students are.” partment about their minority students, they can —David Manderscheid hardly stop rattling off the success stories. There is Juan Ariel Ortiz, who came from the University Over the past decade, the University of Iowa of Puerto Rico at Humacao, fell in love with topol- mathematics department produced about 1 per- ogy, and is now a postdoc at the University of cent of the total number of doctorates granted in Rochester. There is Sara del Valle, who was a recent the U.S., and about 4 percent of those granted to immigrant from Mexico with limited English skills students who are members of underrepresented but tremendous intelligence, and who now holds minorities. During that time, twelve minority stu- a Ph.D. and is on the permanent faculty at Los dents received Ph.D.’s at Iowa. Today about a quar- Alamos National Laboratory. Among the current ter of the department’s approximately 115 gradu- students is Paulette Willis, an African-American ate students are minority, and about 40 percent are from New Orleans whom Kutzko says is one of women. Because the department’s retention rate the strongest students in the department. Willis has risen so much in recent years, more success has passed all of her exams and is now working stories are surely on the way. Before the minority on her dissertation under the direction of Paul recruitment initiative, the Iowa graduate student

May 2008 Notices of the AMS 599 population was dominated by international stu- Building Community dents. Today, the majority are American. The commitment that the department made Iowa is largely a white population…so to the minority students who started arriving in for a minority student to be at Iowa, substantial numbers in the mid-1990s inspired a isolated, would be very difficult. We try transformation of the department’s basic philoso- to build a community so that they feel phy. As department chair Yi Li explains it, “The at ease, at home, so they have a sense old business-as-usual would be: Okay, you come of belonging. to our program, that’s it. If you study and you do —Yi Li well, that’s okay; if you don’t do well, you leave.” One of the hallmarks of the Iowa department is At Iowa, this you’re-on-your-own, sink-or-swim at- the strong sense of community that has developed, titude has been replaced by one that puts student and this happened in large part as a result of the success as the top priority. With this student- minority program. “Before we started bringing in centered attitude has also come a new spirit of minority students, the graduate students were inquiry that has allowed the department to analyze not a very cohesive group,” says faculty member critically its graduate program to address trouble Juan Gatica. “They didn’t work together; they spots and make changes. kept pretty much to themselves. When we started One of the most important changes has been the bringing in minority students, we asked them to institution of a mentoring program. Every new stu- get together and have study groups, and the non- dent is assigned, or is allowed to choose, a mentor minority students started participating in this too. from among the department’s faculty. The mentor It was a surprise that this became a big movement is usually a person different from the thesis advi- in the department and transformed it in many sor—someone with whom the student can discuss ways.” There are now study groups for algebra, a wide range of problems, from difficulties fitting analysis, topology, and other topics, as well as in with other students, to lack of background in exam-preparation study groups. a particular mathematical area. “Having seen the Another strategy to build community sounds impact and having seen what a broad change it mundane but made a big difference: Replacing the brought to our program, I am a firm believer of worn-out 1970s vinyl furniture in the department mentoring early and in time,” says Li. He noted lounge. “I think one of the most brilliant things I that it is particularly important that students have did as department chair was getting new furniture a mentor from the very beginning of their gradu- for our lounge,” says David Manderscheid, who ate studies, so that problems are not left to fester. was on the faculty at Iowa for twenty years before Many students come from smaller schools where taking a position as the dean of the College of Arts & Sciences at the University of Nebraska in 2007. the instruction in mathematics was not as rigorous “It sounds sort of silly, and my dean thought it as in a Ph.D. department like the one at Iowa, and was sort of silly when I proposed it to her. But I the change can be a shock even for highly talented really pushed it. It made the lounge a comfortable and motivated students. Proper guidance in the place for the students and faculty to hang out.” early stages can make a big difference. The lounge is now the heart of the department, After each midterm examination in the first- where faculty and students can meet informally year graduate courses, the results are sent to the and where coffee and cookies are served every af- department’s Graduate Committee, which identi- ternoon. The department used to keep the lounge fies students who seem to be struggling. That open only until 5 p.m. but now keeps it open information is then passed along to the mentors, until 11 p.m., as a way of encouraging students who talk to the students about what might have to gather and study together. On the way home in caused poor performance on the exams. “We are the evening, faculty often pass through the lounge trying to help the students as much as we can and and stop to talk to the students or to help with to find out, if they are not performing, what the mathematical questions. problem is,” explains Li. “There may be a cultural Also reinforcing a cohesive community among problem, maybe homesickness, other personal the students are recent changes to the graduate problems, or language problems.” The mentors program. When the department decided to apply also try to determine if some part of the student’s for a VIGRE (Vertically Integrated Research and mathematical background is lacking or needs shor- Education) grant from the National Science Foun- ing up. In addition, the mentoring system helps dation, it gave a lot of thought to the VIGRE re- build support for the minority program across quirement that departments get students involved the whole department: Helping the students they in research early on in their graduate studies. mentor succeed has built faculty members’ loyalty What emerged, along with a successful proposal, to the program. Says Li, “We all see that this is a was a new structure for the graduate program. great thing for the department, for the students, Previously, students took a couple of years’ worth and for the educational purpose.” of graduate courses with the aim of passing the

600 Notices of the AMS Volume 55, Number 5 comprehensive examination as the gateway to The department has several ways of opening starting research. Now, all students now must take paths into graduate study in mathematics. One is a standard set of first-year graduate courses in its NSF-funded Alliance program, a collaborative analysis, topology, and differential equations, and effort of the mathematical sciences departments in either algebra or numerical analysis. If students at the University of Iowa, Iowa State University, are not prepared to jump into these courses right and the University of Northern Iowa, together with away, they can take undergraduate-level courses the mathematics departments at fifteen to twenty to build the necessary background. Once finished minority-serving institutions around the nation. with the first-year courses, students must take a Through the Alliance, students at the minority- qualifying examination on the material covered. serving schools are mentored by local faculty and After that they can start doing reading courses by faculty in Iowa, and they also can attend the with an advisor, take advanced graduate courses, summer Research Experiences for Undergradu- and prepare for the comprehensive examination. ates program run by the three Iowa schools. The This new structure, with its clearer timetable, gets University of Iowa department also has the Heart- students into research more quickly. land Partnership program, which has a structure Having students take all the first-year courses similar to the Alliance and serves twelve small colleges in Iowa and surrounding states. Finally, together has reinforced the community bonds. the department’s VIGRE grant supports under- “They know each other much better because they graduates attending the summertime REU. In addi- are all taking these core courses, they study to- tion to giving undergraduate math majors a taste gether, they help each other, they lecture to each of research, these programs cultivate a diverse other,” says Li. “You will see them standing in front talent pool that is on track to graduate school in of blackboards, teaching each other. They develop mathematics, whether at the University of Iowa or a very active semi-research activity already” in elsewhere. their initial studies. In addition, students rose to When minority students apply to graduate the challenge of the new and tougher degree re- school at Iowa, their applications are carefully quirements. “People were concerned” about this studied by the department’s Minority Recruitment change, says Manderscheid. “Would it have a nega- and Development Committee, currently chaired by tive impact on our minority students?” In fact the Gatica. This committee has over the years gained a opposite happened: Students did better under the lot of experience and skill in identifying students new system, in which expectations and milestones who have the potential to succeed in the graduate are clearly laid out. “Students were getting more program. Picking students “is a hard job, and we feedback more quickly, and they loved it,” notes are getting pretty good at that now,” says Kutzko. Manderscheid. “There are students who we know won’t fit stan- In another innovative twist, the department dard profiles but who we are pretty sure are going started hiring third- and fourth-year graduate to succeed.” Since the department has developed students to be teaching assistants in recitation sec- a reputation as a place with a supportive environ- tions in the first-year graduate courses. Not only ment in which students flourish, it has started does the extra instruction help the students, but to receive applications from students with very the TAs serve as peer mentors to the younger stu- strong backgrounds who would be able to get into dents, further enhancing the sense of community the top schools in the country. While this is a clear in the department. The Iowa faculty are quick to boon for the department, the Minority Committee point out that the changes inspired by the minority does not choose to take the easy path. Says Kutzko, program have boosted the success of all students, “If we start resting on our laurels now and only ac- minority, majority, and international. “These pro- cept black and Latino kids from elite institutions, grams are always designed for the benefit of all of because they want to come to graduate school at a our students,” says Manderscheid. comfortable place, we are not going to accomplish what our ultimate goal is, which is to change the Developing a Path into Mathematics population who do mathematics.” The department wants to remain a place where high-potential stu- I remember one of our faculty members dents with non-standard backgrounds are welcome was slow to become involved in our and can excel. initiative. Then he mentored during With the success of its minority program, the our summer program, and I remember department has found its esteem rising within the him getting up and saying at the clos- university. It has also helped other departments on ing ceremonies, to all of these mostly campus to launch recruitment programs of their African-American kids, “I want to thank own. The national recognition the department has you for reminding me why I came into garnered has opened the door for collaborations this profession.” with other mathematics departments interested in —Philip Kutzko enhancing the achievement of minority students.

May 2008 Notices of the AMS 601 It has also helped the department to attract high- quality faculty members. For example, the depart- ment recently hired Julianna Tymoczko, who earned a Ph.D. from Princeton in 2003. She was a Clay Mathematics Institute Liftoff Fellow as well as an NSF Postdoctoral Fellow. Says Manderscheid, “The fact that Iowa has this very active, vibrant graduate program that is doing things differently Moving? I think made the difference” to Tymoczko in decid- ing where to take a permanent job.

A Harmonious Department

The opportunity that this department has afforded me [to work in the minor- ity program] has been invaluable. It has transformed my life and given me great satisfaction. Please make sure that the —Juan Gatica One perhaps surprising fact about the faculty in AMS Notices and Bulletin the Iowa mathematics department is that it does not have a large minority presence: Less than 10 find their new home. percent, three out of forty, are members of un- derrepresented minorities. Furthermore, the Iowa minority program has not been based on the model of a single charismatic figure who serves as a mag- net for students. Rather, it has been a communal effort of the department—and the whole depart- ment has benefited. “This was a place that had its political troubles before we started doing this,” says Kutzko. “I think now we are a department that has a harmony to it that is very, very rare.” For the faculty who have been directly involved in the minority program, the personal satisfaction has been enormous. “It’s energizing,” says Mander- • scheid. “It made me enthused. It made me want to Email your new address to us: come to work every day! Because I saw what great [email protected] things we were doing, and I saw how we were giv- ing opportunities to students who wouldn’t go to graduate school otherwise.” • or make the change yourself online at: www.ams.org/cml-update

• or send the information to: Member and Customer Services American Mathematical Society 201 Charles Street Providence, RI 02904-2294 USA Phone: (800) 321-4267 (US & Canada) (401) 455-4000 (Worldwide)

602 Notices of the AMS Volume 55, Number 5 Mathematics Programs that Make a Difference

Each year, the AMS Committee on the Profession The main goals of SUMSRI include 1) addressing (CoProf) selects two or more outstanding math- the shortage of minority mathematical scientists ematics department programs to be designated by encouraging minority students and women to as Mathematics Programs that Make a Difference. become mathematical research scientists, 2) to pro- For 2008 the honored programs are the Summer vide the students with a research environment and Undergraduate Mathematical Science Re- improve their research abilities, 3) to improve the search Institute (SUMSRI) at Miami University students’ ability to work in groups and give them a (Ohio), and the Mathematics Summer Program long term support group, and 4) to provide profes- in Research and Learning (Math SPIRAL) at the sional role models. The Institute is especially inter- University of Maryland, College Park. ested in, but not limited to, African Americans and CoProf created the Mathematics Programs that other underrepresented minorities and women. Make a Difference designation in 2005 as a way to SUMSRI describes itself as a “mixed format” REU bring recognition to outstanding programs that for rising juniors and seniors, emphasizing lecture successfully address the issue of underrepresented classes the first three weeks and group research groups in mathematics. Each year CoProf identifies the last four weeks. two exemplary programs that: Of 114 program graduates to date, forty-six have 1. aim to bring more individuals from underrep- either received a master’s degree or passed their resented minority backgrounds into some portion Ph.D. qualifying exams and another thirty-five have of the pipeline beginning at the undergraduate started their graduate programs (70 percent); three level and leading to an advanced degree in math- have received their Ph.D.s. Another twenty-one are ematics, or retain them in the pipeline; still undergraduates. Fifty-six program graduates 2. have achieved documentable success in doing are from underrepresented ethnic groups; of the so; and forty-three of those who have completed college, 3. are replicable models. 88 percent are either in a graduate program or have Previously designated Mathematics Programs received a graduate degree. that Make a Difference are: the graduate program Math SPIRAL is a six-week program (primarily at the University of Iowa and the Summer Institute for rising juniors) that seeks to enrich the math- in Mathematics for Undergraduates/Research ematical education of outstanding students from Experience for Undergraduates at Universidad underrepresented groups, and to inspire them de Puerto Rico, Humacao (2006); and Enhancing to pursue advanced mathematics. The model is Diversity in Graduate Education (EDGE) and the unique in that a large research university (Mary- Mathematical Theoretical Biology Institute (MTBI) land) has partnered with eight “affiliate” institu- (2007). tions, including several historically black colleges The 2008 CoProf Subcommittee on Mathemat- and universities. SPIRAL’s student participants ics Programs that Make a Difference consisted of: are recruited from these affiliates, and SPIRAL Sylvia Bozeman, Rhonda Hughes, Kimberly Pearson directors annually meet with affiliate liaisons and (chair), and Francis Su. communicate regularly through the year. SPIRAL Below is CoProf’s citation, followed by brief operates under the umbrella of STAND (Science & descriptions of the programs prepared by Notices Technology: Addressing the Need for Diversity) at staff. the University of Maryland. Since its inception in 2003, a total of seventy- Citation three students have participated. Sixty-nine are This year, the subcommittee recommends that the African American or foreign students of African AMS recognize the Summer Undergraduate Math- heritage. One has completed a master’s degree in ematical Science Research Institute (SUMSRI) at operations research, eight are enrolled in doctoral Miami University (Ohio) and the Mathematics Sum- programs, and five are enrolled in master’s degree mer Program in Research and Learning (Math programs in various mathematical sciences; all SPIRAL) at the University of Maryland. of these students are African American with the

May 2008 Notices of the AMS 603 exception of one African student and one Cauca- Program Description: Math SPIRAL sian. Math SPIRAL, a multi-year summer program funded Both SUMSRI and SPIRAL have program models by the National Science Foundation (NSF) and the and recruitment strategies that are clearly repli- National Security Agency (NSA), brings gifted ris- cable. SUMSRI is supported by Miami University ing sophomores and juniors to the University of (Ohio), the National Security Agency, and the Maryland, College Park, for a six-week intensive National Science Foundation. SPIRAL is supported program to help prepare them for graduate study by the NSA, the NSF, and the Mark & Catherine in the mathematical sciences. Math SPIRAL was Winkler Foundation. developed in close coordination with a group of nine affiliated minority-serving colleges and uni- Program Description: SUMSRI versities; this network is a central strength of the SUMSRI, conducted under the guidance of Miami program. University’s Department of Mathematics and Math SPIRAL has three core components: aca- Statistics, is aimed at talented undergraduate demics, research, and professional development. students in the mathematical sciences who are in- Students are enrolled in a 3-credit summer course terested in pursuing advanced degrees. Because of consisting of two parallel sub-courses. The first the shortage of minority and women mathematical focuses on combinatorics and a strategic analy- scientists, the program is especially focused on, sis of winning strategies for a variety of games, but not limited to, African Americans and other while the second emphasizes the core methods underrepresented minorities and women. of mathematical reasoning and proof. In addition The main goals of SUMSRI are to encourage to solving problems, students must accurately minority students and women to become math- communicate their solutions both in writing and ematical research scientists, and to help the stu- verbally. Formal public presentations of the aca- dents improve their research abilities. In addition, demic and the research results are a key part of SUMSRI aims to foster the students’ ability to work the SPIRAL program. in groups, to give them a long-term support group, The research program has focused on the and to provide them with professional role models. analysis of games, an area that provides a genuine In the program, students increase their technical research experience without requiring knowledge writing skills and are given an opportunity to write of higher-level mathematics courses. Research a technical research paper and present a talk at a teams of three or four students carry out the inves- mathematics conference. They also receive infor- tigations. Teams meet frequently with a graduate mation about available financial aid, opportunities student mentor and a faculty advisor and make for graduate school, and career opportunities in weekly oral presentations of their progress. The the mathematical sciences. highlight of the program is the final formal pre- SUMSRI runs for seven weeks on Miami Uni- sentations by the students. versity’s campus in Oxford, Ohio. During that Professional development activities comprise time, students participate in problem seminars field trips, colloquia, and panel discussions. Past in mathematics or statistics. The program also field trip destinations have included Booz Allen includes a technical writing seminar, a GRE prepa- Hamilton, GEICO, the National Institute of Stan- ration workshop, two short courses on algebra and dards and Technology, the National Security real analysis, and colloquium talks given by well- Agency, and Northrup Grumman. Colloquia are known mathematical scientists. In addition, there given by established figures from academia, gov- are panel discussions about graduate school and ernment, and industry to offer personal insights. career opportunities. SUMSRI pays for participants’ The panel discussions provide advice on preparing travel, room, board, and supplies and provides for and succeeding in graduate school as well as each student with a stipend. Funds are available for on how to obtain financial support. travel and support to selected national meetings. The founding program director was Dan The ideal candidate for SUMSRI is a sopho- Rudolph, who is now at the University of Colorado. more or junior student who has completed with Brian Hunt (UMCP) took the reins when Rudolph distinction the calculus series and at least one left for Colorado, and Ken Berg (UMCP) became proof-based mathematics or statistics course. All director in the fall of 2007. SUMSRI students return to their home institu- Program Director: Ken Berg tions as undergraduates after participating in the Associate Directors: Marshall Cohen (Morgan program. State University); Bill Gasarch (UMCP); Leon Wood- Program Directors: Dennis Davenport and son (Morgan State University) Vasant Waikar Program Coordinator: Cyntrica Eaton Website: http://www.units.muohio.edu/ Website: http://www.math.umd.edu/ sumsri/. undergraduate/spiral/.

604 Notices of the AMS Volume 55, Number 5 2008 JPBM Communications Award

The 2008 Communications Award of the Joint Biographical Sketch Policy Board for Mathematics (JPBM) was presented Carl Bialik was born and raised in New York City, at the Joint Mathematics Meetings in San Diego in where his sister taught him early math lessons, January 2008. his father crunched baseball numbers The JPBM Communications Award is presented with him, and his mother trained him annually to reward and encourage journalists in statistics. He attended the Bronx and other communicators who, on a sustained High School of Science, where he edited basis, bring accurate mathematical information the Math Bulletin, was a member of the to nonmathematical audiences. JPBM represents school and city math team, and was a the AMS, the American Statistical Association, the finalist in the 56th Science Talent Search Mathematical Association of America, and the So- for his biophysics research at Mount ciety for Industrial and Applied Mathematics. The Sinai Hospital. He majored in math and award carries a cash prize of US$1,000. physics at Yale, where he served as Previous recipients of the JPBM Communications executive editor of the weekly Herald Award are: James Gleick (1988), Hugh Whitemore newspaper. Bialik has written for the Wall Street (1990), Ivars Peterson (1991), Joel Schneider (1993), Journal Online since early 2002. He be- Martin Gardner (1994), Gina Kolata (1996), Philip Carl Bialik came a technology reporter the following J. Davis (1997), Constance Reid (1998), Ian Stewart year. He began writing the weekly online “Numbers (1999), John Lynch and Simon Singh (special award, Guy” column in 2005. In 2006 Bialik won second 1999), Sylvia Nasar (2000), Keith J. Devlin (2001), place in the online category of the National Society Claire and Helaman Ferguson (2002), Robert Os- of Newspaper Columnists contest. In March 2007 serman (2003), Barry Cipra (2005), Roger Penrose the column began running every other week on (2006), and Steven H. Strogatz (2007). the Marketplace page of the print Journal, comple- The 2008 JPBM Communications Award was mented by a blog updated each weekday. Bialik has presented to Carl Bialik. The text that follows also coauthored the online Journal’s “Daily Fix” presents the selection committee’s citation, a brief sports column since 2002. Outside the Journal, biographical sketch, and the recipient’s response he is cofounder of the online Gelf Magazine and upon receiving the award. hosts the magazine’s Varsity Letters sports reading Citation series in New York. The 2008 JPBM Communications Award is awarded Response to Carl Bialik, the Wall Street Journal’s “Numbers I’m immensely honored to receive this award, Guy”, for increasing the public’s understanding of particularly because of my admiration for all the mathematical concepts. prior recipients—and my particular appreciation In his regular columns and blogs, Carl Bialik for several who have helped me frequently with my exposes the misuse of numbers and statistics column. Many other members of the AMS and ASA throughout society and in applications ranging also have provided indispensable help as I try to decipher tricky numbers and explain them to read- over every part of life, from economics and politics ers, a daily challenge that is always enjoyable. to sports and medicine. His writing does more than I encourage your organizations to continue to en- document the misuse, however, because he gently gage with journalists, as you have done so graciously introduces sound mathematical reasoning in ev- with me. Numbers are a popular tool to obfuscate erything he writes. He shows how to use numbers and mislead. Too often the press falls prey to faulty and mathematics in a way that illustrates sound figures. We would like to do a better job of writing principles of scientific inquiry, paying careful at- about numbers and deciding which numbers don’t tention to original sources and using professional deserve press. And we need your help to do so. mathematical scientists to validate his work. My column is, I hope, a step in the right di- Carl Bialik exemplifies the best traditions of rection. Its existence and success are a credit to scientific journalism, bringing mathematics and Bill Grueskin, the editor who conceived of it and mathematical thinking to a large readership. The handed me this fun assignment, and to Jason breadth, volume, and quality of his writing are all Anders, who has ably edited and improved the spectacular. column since its inception.

May 2008 Notices of the AMS 605 MAA Prizes Presented in San Diego

At the Joint Mathematics Meetings in San Diego and had a considerable impact on the U.S. math- in January 2008, the Mathematical Association of ematical community. America (MAA) presented several prizes. Lida Barrett wrote the following response, which appeared in the prize booklet: “I am honored to Gung and Hu Award for Distinguished have received this prize. The Mathematical Associ- Service ation of America has been an important part of my The Yueh-Gin Gung and Dr. Charles Y. Hu Award life. The many activities offered have contributed for Distinguished Service to Mathematics is the significantly to my career: the hour addresses that most prestigious award made by the MAA. It hon- kept me aware of the vast scope of mathematics, ors distinguished contributions to mathematics the panel discussions and other presentations on and mathematical education, in one particular current professional topics, and the opportunities aspect or many, and in a short period or over a to meet and discuss mathematics and educational career. activities with my fellow mathematicians. Working Lida K. Barrett received the 2008 Gung and Hu on committees and projects within MAA and within Award. The prize citation says: “Lida K. Barrett’s the broader mathematical community has enriched solid mathematical background and her ability to my professional life. Friendships with the many get at the heart of problems and to find bold solu- fine folks in MAA have provided a special plus. I tions led her into positions in mathematical policy: am especially grateful to Professor Harlan Miller, as a senior administrator at several universities, who pushed me to work on a Ph.D. at Texas, and as president of the Mathematical Association of to my late husband, John Barrett, who, after he America, as senior staff associate at the National completed his degree, insisted I finish mine and Science Foundation [NSF], and as professor of kept house for us while I did.'' mathematics at the U.S. Military Academy at West Point. To this day, she continues to serve on Haimo Awards for Teaching many committees and boards and to contribute The Deborah and Franklin Tepper Haimo Awards to mathematics, to mathematics education, and to for Distinguished College or University Teaching increasing the participation of members of under- were established in 1991. These awards honor col- represented groups in mathematics.” Her concern lege or university teachers who have been widely for education and students likely has its roots in recognized as extraordinarily successful and whose her background: For example, in graduate school at teaching effectiveness has been shown to have had the University of Texas, she and Mary Ellen Rudin influence beyond their own institutions. were the only female students. Barrett finished The 2008 Haimo Awards were presented to her master’s degree there in 1949 and her Ph.D. in Annalisa Crannell, Kenneth I. Gross, and 1954, at the University of Pennsylvania. Her hus- James Morrow. band was also a mathematician, and she suffered “Annalisa Crannell is well known for her bound- under the anti-nepotism rules that were common less energy and enthusiasm for all things mathe- at that time. Her husband’s death at an early age matical,” the prize citation states. As a new faculty left Barrett to raise three children on her own. member at Franklin & Marshall College, she im- Despite these hardships, she built an outstanding mediately began to incorporate essay-writing into career as a faculty member and an administrator her mathematics classes. Her experience in this

606 Notices of the AMS Volume 55, Number 5 teaching technique led to many invitations to Chauvenet Prize speak on “writing across the curriculum” pro- The Chauvenet Prize recognizes a member of the grams, as well as to the co-authoring of the book MAA who has written an outstanding expository Writing Projects for Mathematics Courses: Crushed article. First awarded in 1925, the prize is named Clowns, Cars and Coffee to Go, published in 2004 for William Chauvenet, who was a professor of by the MAA. Crannell has also actively pursued mathematics at the United States Naval Acad- the connections between mathematics and art, emy. producing a book, together with colleague Marc Andrew Granville received the 2008 Frantz, Viewpoints: Mathematical Perspective and Chauvenet Prize for his article “It is easy to deter- Fractal Geometry in Art, which will be published mine whether a given integer is prime”, Bulletin by Princeton University Press. The prize citation of the AMS (N.S.) 42 (2005), 3–38. “This article is concludes, “[Crannell] continues to search for in- fascinating, readable, and understandable, with lots of proofs,” the prize citation says. It presents novative ways to excite those around her about the statement and proof of the surprising 2002 mathematics.” result by Agrawal, an Indian computer scientist, “Kenneth I. Gross has had a dramatic impact and his two undergraduates, Kayal and Saxena, on mathematics, education, and the lives of his giving a “polynomial-time deterministic” test for students,” the prize citation states. “[His] teach- deciding if integers are primes. “The paper is full ing and mentoring have been inspirational for all of significant information, including discussions of levels of students, from high school students to Carmichael numbers, random polynomial time al- entry-level college students, undergraduate math- gorithms, probabilistic (almost) proofs, and much ematics majors, and graduate students who are more,” says the citation. now accomplished mathematicians and scientists, elementary and middle school teachers, and adult Beckenbach Book Prize learners who desire to further their education.” In The Beckenbach Book Prize, presented since 1982, 1993 Gross and a high school teacher co-founded is awarded to an author of a distinguished, innova- a week-long residential summer enrichment pro- tive book published by the MAA. gram for talented Vermont high school students, William Dunham received the 2008 Becken- aimed especially at girls and rural Vermonters. bach Prize for his book Euler: The Master of Us Then, in 1999, Gross founded the Vermont Mathe- All, MAA, Dolciani Mathematical Expositions, Vol. 22, 1999. Dunham’s exposition “is itself innova- matics Initiative (VMI), a statewide master’s degree- tive and brilliant in its organization and scope, its granting program that trains elementary and clarity and verve, and its accessibility and appeal,” middle school teachers to serve as mathematics says the prize citation. After providing a biographi- leaders in their schools and districts. To date, over cal sketch, Dunham devotes one chapter each to two hundred teachers from nearly 90 percent of important contributions by Euler to eight areas of the school districts in Vermont have participated mathematics. “Dunham is well known for writing in the program. mathematical page-turners, and this book is no James Morrow “has had a fundamental impact exception: the seamless presentation of mathemat- at the University of Washington and throughout ics and its history is so entertaining, accessible, the Pacific Northwest,” the prize citation says. clear, and lively that it is difficult to put the book Since 1988 he has directed a Research Experiences down until one has read it from cover to cover,” the for Undergraduates site focusing on questions re- citation says. “Besides his inimitable writing style, lated to inverse problems in tomography. Eight of the author is to be commended for his inspired yet its participants have received NSF graduate fellow- careful selection and organization of historical and ships, and many have gone on to substantial suc- mathematical material and for his presentation cess in this area and other fields of mathematics. of Euler’s mathematical work in such a clear and For the past six years he has also been preparing accessible yet faithful manner.” students for the Mathematical Contest in Model- Euler Book Prize ing, in which his students “have an enviable record The Euler Book Prize is given to the author(s) of of success.” Since 1994 Morrow has organized a an outstanding book about mathematics. The Mathday at the University of Washington, bringing prize was given for the first time in 2007, to com- 1,200 high schoolers to the campus to showcase memorate the 300th anniversary of the birth of for them the relevance of mathematics to a variety Leonhard Euler. of disciplines. He is also codirector of the Sum- Benjamin H. Yandell was posthumously mer Institute for Mathematics at the University awarded the Euler Prize for his book The Hon- of Washington, which brings twenty-four high ors Class. Hilbert’s Problems and Their Solvers, schoolers from the U.S. and Canada to campus for A K Peters, Natick, MA, 2002. This book provides six weeks in the summer. portraits of the people who solved problems on

May 2008 Notices of the AMS 607 David Hilbert’s famous list of 23 problems, which he presented in 1900. “Even when discussing well- known mathematicians such as Hilbert, Gödel, and Turning Kolmogorov, Yandell manages to say something fresh and to correct some oft-repeated errors,” the 40? citation says. “The book is a monumental labor of love, yet breathtakingly readable and inspiring. It is written at a level that bright mathematics stu- dents can understand, but it will also widen the horizons of professional mathematicians, since almost no one is as familiar with as many fields as Hilbert was. The Honors Class should be in every Turning mathematician’s library.” David P. Robbins Prize 50? In 2005 the family of David P. Robbins gave the MAA funds sufficient to support a prize honoring the author or authors of a paper reporting on novel research in algebra, combinatorics, or discrete mathematics. The Robbins Prize is awarded every third year. The 2008 Robbins Prize was awarded to Neil J. A. Sloane of AT&T Shannon Labs for his paper Turning “The on-line encyclopedia of integer sequences”, Notices of the AMS, 50 (2003), 912–915. “Although 60? not quite a research paper in the usual sense, the paper describes an extraordinary research tool that has had an impact on mathematics far beyond that of almost any paper, especially in the areas that David Robbins cared so much about,” the prize citation says. Sloane’s Online Encyclopedia of Integer Sequences (OEIS) enables mathematicians to identify sequences from just a few terms, “giv- ing them access to a wealth of information that might immediately point their research in useful directions…. The importance and pervasiveness of Celebrate this tool is evident from the number and diversity of papers that cite the OEIS.” The OEIS database your milestone has more than 120,000 entries, an active editorial board with twenty-five members, and a Wikipedia by becoming an entry. Certificates of Meritorious Service AMS Life Member Each year the MAA presents Certificates of Merito- rious Service for service at the national level or for service to a section of the MAA. Those honored in Rates are US $2400, US $1600, or US $800, 2008 are: Illinois Section: Herbert Kasube, Bradley depending on age. Members by reciprocity University; Kentucky Section: Donald E. Bennett, (outside the U. S.) pay US $1200, US $800, or Murray State University; Missouri Section: Vic- US $400. tor Gummersheimer, Southeast Missouri State University; Northern California, Nebraska, and Hawaii Section: Leonard F. Klosinski, Santa Clara Call your Member and Customer Services University; Seaway Section: H. Joseph Straight, representative at 800-321-4267 or email State University of New York, Fredonia; Wisconsin [email protected] Section: Andrew Matchett, University of Wis- consin-LaCrosse.

—From MAA announcements www.ams.org

608 Notices of the AMS Volume 55, Number 5 AWM Awards Given in San Diego

The Association for Women in Mathematics (AWM) commitment to the goal of leading as many presented two awards at the Joint Mathematics students as possible to a genuine and deep ap- Meetings in San Diego in January 2008. preciation for mathematics and mathematical thinking.” Louise Hay Award The Louise Hay Award for Contributions to Math- Schafer Prize ematics Education was established in 1990 to The Alice T. Schafer Prize for Excellence in Math- honor the memory of Louise Hay, who was widely ematics by an Undergraduate Woman was estab- recognized for her contributions to mathematical lished in 1990. The prize is named in honor of Alice logic and for her devotion to students. T. Schafer, one of the founders of AWM and one of The 2008 Louise Hay Award was presented to its past presidents. Harriet S. Pollatsek of Mount Holyoke College The 2008 Schafer Prize was awarded to Galyna “in recognition of her wide range of outstanding Dobrovolska of the Massachusetts Institute of contributions to mathematics education”. The Technology and to Alison Miller of Harvard award citation lauds Pollatsek for maintaining an University. active presence in mathematical research while also making substantial contributions to improv- Dobrovolska is a senior mathematics major at ing mathematics education at the collegiate level. MIT. She has exhausted all of the undergraduate “What has most characterized her entire career is offerings in the mathematics department, earning her love of mathematics and her energy and enthu- the highest grades, and has begun taking graduate siasm for fostering a love of it in others,” the cita- courses. “Dobrovolska has further distinguished tion says. “She believes that everyone can benefit herself through her impressive and original math- from learning mathematics and that the way it is ematical research,” the prize citation says. “Her taught should give students multiple opportunities research is focused in algebra and would be con- to be brought into the mathematical fold.” sidered broad even for a mathematician much Pollatsek came to Mount Holyoke in 1970, and further along in her career.” She co-authored a since then she has worked tirelessly to improve paper that has now been published. In addition to courses for math majors and nonmajors alike. winning a gold medal at the International Math- She was one of the designers of the Five College ematics Olympiad, Dobrovolska won the top prize Calculus in Context sequence; played a key role in in 2006 in the Summer Program of Undergraduate a Dana Foundation effort to increase underrepre- Research at MIT. sented individuals in mathematics courses; and Miller, a senior at Harvard University, is the was one of the developers of a program, funded first woman ever to have won a gold medal in the by the National Endowment for the Humanities, International Mathematical Olympiad. She also was to spread mathematics across the curriculum. For twice the winner of the Elizabeth Lowell Putnam majors and potential majors she co-developed an award for outstanding performance by a woman innovative mathematics laboratory course and on the Putnam competition. Her participation in a then became a coauthor and the lead editor of Research Experiences for Undergraduates program a textbook for it, Laboratories in Mathematical at the University of Wisconsin led to her writing Experimentation. This course has become the two papers in number theory. The first answers a cornerstone of the mathematics major at Mount Holyoke. Pollatsek chaired the Mathematical As- deep and difficult question originating in the work sociation of America’s Committee on the Under- of Richard Borcherds and has been published in graduate Program in Mathematics (CUPM) and led the Proceedings of the AMS. The second paper has the writing team that produced the CUPM Cur- appeared as a preprint. riculum Guide 2004. On top of all this, Pollatsek The AWM also awarded honorable mentions has also worked on mathematics education at the to three outstanding senior mathematics majors: precollege level. Naomi Brownstein, University of Central Florida; The award citation concludes: “By the Lou- Reagin Taylor McNeill, Smith College; and Mary ise Hay Award, AWM is proud to honor Harriet Wootters, Swarthmore College. S. Pollatsek for her steadfast enthusiasm and —From AWM announcements

May 2008 Notices of the AMS 609 D E G R U Y T E R Just published n Homotopy of Extremal Problems Theory and Applications Hans-Otto Georgii By Stanislav V. Emelyanov / n Stochastics Sergey K. Korovin / Nicolai A. Introduction to Probability and Bobylev / Alexander V. Bulatov Statistics September 2007. XI, 303 pages. Hardcover. € [D] 128.00 / sFr 205.00 / *US$ 158.00. Transl. by Marcel Ortgiese / Ellen ISBN 978-3-11-018942-1 Baake / Hans-Otto Georgii Series: de Gruyter Series in Nonlinear Analysis February 2008. Approx. IX, 370 pages. and Applications 11 Paperback. € [D] 39.95 / sFr 64.00 / *US$ 49.00. n Banach Spaces and their ISBN 978-3-11-019145-5 Series: de Gruyter Textbook Applications in Analysis In Honor of Nigel Kalton’s 60th n Combinatorial Number Birthday Theory Ed. by Beata Randrianantoanina / Proceedings of the ‘Integers Narcisse Randrianantoanina Conference 2005’ in Celebration September 2007. IX, 453 pages. 1 frontis- piece. Hardcover. of the 70th Birthday of Ronald € [D] 138.00 / sFr 221.00 / *US$ 158.00. Graham, Carrollton, Georgia, ISBN 978-3-11-019449-4 October 27-30, 2005 Series: de Gruyter Proceedings in Mathematics Ed. by Bruce Landman / P. A. Krylov / A. A. Tuganbaev Melvyn Nathanson / Jaroslav n Nešetril / Richard Nowakowski / Modules over Discrete Carl Pomerance Valuation Domains March 2007. IX, 489 pages. 1 frontispiece. January 2008. Approx. IX, 357 pages. Hardcover. Hardcover. € [D] 128.00 / sFr 205.00 / *US$ 168.00. € [D] 168.00 / sFr 269.00 / *US$ 186.00. ISBN 978-3-11-020053-9 ISBN 978-3-11-019029-8 Series: de Gruyter Expositions in Mathematics 43 Series: de Gruyter Proceedings in Mathematics

New Journal starting in 2008

n Advances in Calculus of n Journal of Mathematical Variations Cryptology Managing Editors: Frank Duzaar, Managing Editors: Erlangen, Germany / Spyros Magliveras, Boca Raton, Nicola Fusco, Naples, Italy USA / Rainer Steinwandt, Boca ISSN (Print) 1864-8258 Raton, USA / Tran van Trung, ISSN (Online) 1864-8266 Essen, Germany Annual Subscription Rates for 2008: Four issues per year (approx. 400 pages). ISSN 1862-2976 (Print) Print only or online only: ISSN 1862-2984 (Online) € 294.00 / US$* 435.00 Subscription Rates for Volume 2 (2008): Print + Online: € 338.00 / US$* 500.00 Four issues per year (approx. 400 pages). Single issue: € 80.00 / US$* 118.00 Print only or online only : www.degruyter.com/journals/acv € 300.00, *US$ 375.00 Print + Online: € 345.00, *US$ 431.00 Single Issue: € 81.00, *US$ 120.00 www.degruyter.com/journals/jmc

* for orders placed in North America. Prices are subject to change. www.degruyter.de Prices do not include postage and handling. Mathematics People

efforts to help underrepresented students earn doctoral Gilbert Receives NAS Award degrees in the sciences. Anna C. Gilbert of the University of Michigan, Ann Arbor, Chavez, who earned his Ph.D. from the University of has received the 2008 National Academy of Sciences (NAS) Wisconsin, has served as dissertation adviser for four Award for Initiatives in Research. According to the prize Hispanic Americans who earned their doctorates in math- citation, Gilbert was honored for “innovative algorithms ematics or the biological sciences. Another eleven Hispanic using wavelets and sampling techniques and their impact Americans whom he mentored in an undergraduate re- on data analysis and sparse approximation.” The award, search program have gone on to earn doctorates in the which carries a cash prize of US$15,000, is presented biological sciences, mathematics, statistics, or bioinfor- annually to recognize innovative young scientists and matics at various institutions. He has also raised funding to encourage research likely to lead to new capabilities for and run a summer research program, the Mathematical for human benefit. For 2008 the award was given in the and Theoretical Biology Institute, aimed at encouraging fields of computational science and applied mathematics. Hispanic American and Native American undergraduate It was established by AT&T Bell Laboratories in honor of students to enter Ph.D. programs with an emphasis on William O. Baker and is supported by Alcatel-Lucent. mathematical or computational biology. As a result of this program, fifty-nine Hispanic Americans and Native —From an NAS announcement Americans have gone on to graduate programs. The AAAS Mentor Award honors members of the AAAS who have mentored and guided significant numbers of un- Feigenbaum Awarded derrepresented students toward Ph.D. degrees in the sci- ences and who have demonstrated scholarship, activism, Heineman Prize and community building on behalf of underrepresented groups, including women of all racial or ethnic groups; Mitchell J. Feigenbaum of Rockefeller University has African American, Native American, and Hispanic men; been awarded the 2008 Dannie Heineman Prize in Math- ematical Physics “for developing the theory of determin- and people with disabilities. This award recognizes indi- istic chaos, especially the universal character of period viduals in the early or mid-career stage who have mentored doubling, and for the profound influence of these dis- students for less than twenty-five years. The recipient coveries on our understanding of nonlinear phenomena receives US$5,000 and a commemorative plaque. in physics.” The prize carries a cash award of US$7,500 and is pre- —From an AAAS announcement sented in recognition of outstanding publications in the field of mathematical physics. The prize was established in 1959 by the Heineman Foundation for Research, Edu- Schedler Receives AIM Five- cational, Charitable, and Scientific Purposes, Inc., and is administered jointly by the American Institute of Physics Year Fellowship (AIP) and the American Physical Society (APS). The prize Travis Schedler of the University of Chicago has been is presented annually. named the recipient of the 2008 American Institute of

Mathematics (AIM) Five-Year Fellowship. —From an APS announcement Schedler will complete his Ph.D. at the University of Chicago under the direction of Victor Ginzburg. He works in the area of noncommutative algebraic geometry. His Chavez Receives AAAS Mentor thesis defines and applies a new formalism of differential operators for associative algebras. Other work involves Award computing Hochschild and cyclic homology of algebras Carlos Castillo Chavez of Arizona State University has associated with quivers. He has written or coauthored received the 2007 Mentor Award from the American As- eleven papers, one of which has appeared in the Journal sociation for the Advancement of Science (AAAS) for his of the American Mathematical Society. He received his A.B.

May 2008 Notices of the AMS 611 Mathematics People from Harvard in 2002 and spent a year of graduate study that there exist non-contact vector fields, even on the at the École Normale Supérieure. 3-sphere, with no closed orbits. These are the counter- examples (due to Schweitzer, Harrison, and Kuperberg) —From an AIM announcement to the Seifert conjecture. Hofer affirmed the Weinstein conjecture in many 3-dimensional cases, for example the three-sphere and contact structures on any 3-dimensional, 2008 Clay Awards Announced reducible manifold. Taubes’s affirmative solution of the Weinstein conjecture for any 3-dimensional contact mani- The Clay Mathematics Institute (CMI) has announced the fold is based on a novel application of the Seiberg-Witten recipients of the 2008 Clay Research Fellowships and equations to the problem. Research Awards. The Kodaira conjecture was formulated in 1960, when Kunihiko Kodaira showed that any compact complex Clay Research Fellowships Kähler surface can be deformed to a projective algebraic Spyros Alexakis of Princeton University received his surface. For the proof, Kodaira used his classification theo- Ph.D. from Princeton in 2005. In his thesis, he proved a rem for complex surfaces. The conjecture asks whether special case of the Desser-Schwimmer conjecture in con- Kähler manifolds of higher dimension can be deformed to formal geometry, and he has recently proved the full case. a projective algebraic manifold. Voisin constructs coun- This conjecture characterizes all pointwise Riemannian terexamples: in each dimension four or greater there is a invariant polynomials in the metric tensor and its deriva- compact Kähler manifold that is not homotopy equivalent tives whose integrals over a compact manifold without to a projective one. For dimension at least six, she gives boundary are invariant under conformal deformations. examples that are also simply connected. A later result Adrian Ioana of the California Institute of Technology gives a substantial strengthening: in any even dimension received his Ph.D. in 2007 from the University of Califor- ten or greater, there exist compact Kähler manifolds, no nia, Los Angeles. In a 2006 paper he showed that any group bimeromorphic model of which is homotopy equivalent to that contains a copy of the free group on two letters has a projective algebraic variety. Distinguishing the homotopy uncountably many orbit inequivalent actions. type of projective and nonprojective Kähler manifolds is Xinyi Yuan will receive his Ph.D. degree in 2008 from achieved through novel Hodge-theoretic arguments that Columbia University. In 2006 he proved an arithmetic place subtle restrictions on the topological intersection analogue of a theorem of Siu and derived a natural suf- ring of a projective manifold. ficient condition for the case in which the orbit under the absolute Galois group is equidistributed. —From a CMI announcement Clay Research Fellows are appointed for terms ranging from two to five years; graduating doctoral students and mathematicians within three years of receiving the doc- toral degree are eligible for the fellowships. Iyama Wins ICRA Award Osamu Iyama of Nagoya University has been selected to Clay Research Awards receive the first ICRA Award from the International Con- The 2008 Clay Research Awards have been presented ferences on Representations of Algebras (ICRA). Iyama was to Clifford Taubes of Harvard University for his proof honored for “original and influential work on developing a of the Weinstein conjecture in dimension three, and to ‘higher’ theory for almost split sequences and Auslander Claire Voisin of the Centre National de la Recherche correspondence and his subsequent work on Calabi-Yau Scientifique, the Institut des Hautes Études Scientifiques, categories, which have strong connections with the cluster and the Institut Mathématique de Jussieu for her disproof algebras of Fomin-Zelevinsky.” of the Kodaira conjecture. The ICRA conference series was established in 1974 to The Weinstein conjecture is a conjecture about the bring together both experts and young researchers in the existence of closed orbits for the Reeb vector field field of representations of finite-dimensional algebras. on a contact manifold. A contact manifold is an odd- The award will be given at each conference session to a dimensional manifold with a one-form A such that A young mathematician who has done outstanding work in wedged with the n​-th exterior power of d​A is everywhere the field. nonzero. In particular, the kernel of A is a maximally non- integrable field of hyperplanes in the tangent bundle. The —From an ICRA announcement Reeb vector field generates the kernel of d​A and pairs to one with A. Alan Weinstein asked some thirty years ago whether this vector field must, in all cases, have a closed orbit. (The unit sphere in complex n​-space with A the National Academy of annihilator of the maximal complex subspace of the real Engineering Elections tangent space is an example of a contact manifold and contact 1-form. In this case, the orbits of the Reeb vector The National Academy of Engineering (NAE) has an- field generate the circle action whose quotient gives the nounced the election of sixty-five new members and nine associated complex projective space.) Note, by contrast, foreign associates, including six whose work involves the

612 Notices of the AMS Volume 55, Number 5 Mathematics People NEW RELEASES mathematical sciences. Their names, institutions, and the research for which they were elected follow. The Symmetries of Things Jon M. Kleinberg, Cornell University, for contributions to the understanding of the structure and behavior of the John H. Conway, Heidi Burgiel, World Wide Web and other complex networks; Prabhakar Chaim Goodman-Strauss Raghavan, Yahoo! Research, Santa Clara, California, for $69.00; Hardcover significant contributions to algorithms and the structure of the World Wide Web; Vladimir Rokhlin, Yale University, Inspired by the for the development of fast multipole algorithms and their geometric intuition application to electromagnetic and acoustic scattering; of Bill Thurston and and James A. Sethian, University of California, Berkeley, empowered by his for the development of efficient methods of tracking mov- analytical skills, ing interfaces. Elected as foreign associates were Arthur John Conway and John Robin Gorell Milner, University of Cambridge, for his coauthors have fundamental contributions to computer science, including developed a com- the development of LCF, ML, CCS, and the pi-calculus; and Ekkehard Ramm, University of Stuttgart, for contribu- prehensive math- tions to the finite element analysis of plates and shells ematical theory of and leadership in computational mechanics. symmetry that al- lows the description —From an NAE announcement and classification of symmetries in numer- ous geometric environments. This richly and compellingly illustrated Alex Rosenberg (1926–2007) book addresses the phenomenological, Alex Rosenberg died on October 27, 2007, in Schwerte, analytical, and mathematical aspects of Germany, his home for the last decade. He was born in symmetry on three levels that build on one Berlin, Germany, on December 5, 1926. His family fled another and will speak to interested lay Germany in August 1939, first to Les-Plans-Sur-Bex, Swit- people, artists, working mathematicians, zerland, where they stayed for almost a year. After a brief and researchers. stay in England, the family resettled in Ontario. Alex studied at the University of Toronto. He earned a B.A. (math/physics) in 1948 and stayed on for an M.A. in The Simple Book of 1949. Moving to the University of Chicago for his further Not-So-Simple Puzzles graduate study, Rosenberg obtained his Ph.D. in 1951 under the supervision of Irving Kaplansky. Serhiy Grabarchuk, Peter Grabarchuk, In 1961 Rosenberg joined the faculty at Cornell Univer- Serhiy Grabarchuk, Jr. sity as professor of mathematics and remained there for a $19.95; Paperback quarter of a century. He was chairman of the mathematics department from 1966 to 1969, when it was at its largest. “The Grabarchuk family— Later, in 1986, he moved to the University of California, father and sons—make Santa Barbara, as chair of the department of mathematics. some of the most original A few years after his retirement in 1994, he moved back and ingenious brain teas- to Germany, where he lived until his death. ers in the world. I could Rosenberg made fundamental contributions to algebra happily spend weeks with by applying newly developed homological techniques to Galois theory and quadratic forms as well as to other this book.” areas. He was also an active member of the mathematical —Will Shortz, community, holding many important posts in the leader- Crossword Editor, ship of both the AMS and the Mathematical Association The New York Times of America, including serving as editor of the Proceedings of the AMS (1960–65). Alex Rosenberg, whose occasionally gruff manner masked his wit, kindness, and generosity, was a major Save 20% at www.akpeters.com discount code AMS figure in the post-World War II U.S. mathematical com- munity whose wise counsel was crucial to mathematics in the U.S. For additional information, see http://www. spelman.edu/~colm/alexrosenbergobit.html. www.akpeters.com —Lance Small, University of California, San Diego

May 2008 Notices of the AMS 613 Mathematics Opportunities

May 12–16, 2008: Imaging in Random Media. George NSF Postdoctoral Research Papanicolaou, lecturer. Rice University. Organizers: Liliana Fellowships Borcea, 713-348-5723, email: [email protected]; Danny C. Sorensen, 713-348-5193, email: sorensen@caam. The National Science Foundation (NSF) awards Mathemati- rice.edu; William W. Symes, 713-348-5997, email: symes@ cal Sciences Postdoctoral Research Fellowships (MSPRF) caam.rice.edu; conference website: http://www.caam. for appropriate research in areas of the mathematical rice.edu/~CBMS2008/. sciences, including applications to other disciplines. May 13–18, 2008: Water Waves: Theory and Experiment. Awardees are permitted to choose research environments Harvey Segur, lecturer. Howard University. Organizer: that will have maximal impact on their future scientific Mohammad F. Mahmood, 202-806-6295, email: mahmood@ development. Awards are made in the form of either howard.edu; conference website: http://www.coas. Research Fellowships or Research Instructorships. The howard.edu/mathematics/CBMS-Mahmood.html. Research Fellowship option provides full-time support for May 27–31, 2008: Inverse Scattering for Radar Imaging. any eighteen academic-year months in a three-year period Margaret Cheney, lecturer. University of Texas, Arling- in intervals not shorter than three consecutive months. ton. Organizer: Tuncay Aktosun, 817-272-1545, email: The Research Instructorship option provides a combina- [email protected]; conference website: http://omega. tion of full-time and half-time support over a period of uta.edu/~aktosun/cbms2008. three academic years, usually one academic year full time June 2–6, 2008: Topology, C*-Algebras, and String Du- and two academic years half time. Under both options, the ality. Jonathan Rosenberg, lecturer. Texas Christian Uni- award includes six summer months; however, no more versity. Organizers: Greg Friedman, 817-257-6343, email: than two summer months of support may be received in [email protected]; Robert Doran, 817-257-7335, any calendar year. Under both options, the stipend support email: [email protected]; conference website: http:// for twenty-four months (eighteen academic-year months www.math.tcu.edu. plus six summer months) will be provided within a forty- June 22–27, 2008: Convex Duality Method in Mathemati- eight-month period. cal Finance. Marco Frittelli, lecturer. University of Califor- The deadline for proposals is October 15, 2008. See nia, Santa Barbara. Organizers: Jean-Pierre Fouque, 805- http://www.nsf.gov/funding/pgm_summ.jsp?pims_ 893-5637, email: [email protected]; Guillaume id=5301&org=DMS. Bonnet, 805-893-4188, email: [email protected]; Raya Feldman, 805-893-2826, email: feldman@pstat. —From an NSF announcement uscb.edu; conference website: http://www.pstat. ucsb.edu/projects/cbms/. June 22–28, 2008: Ergodic Ramsey Theory: A Dynamical NSF-CBMS Regional Approach to Static Theorems. Vitaly Bergelson, lecturer. Eastern Illinois University. Organizer: Patrick R. Coul- Conferences, 2008 ton, 217-581-6276, email: [email protected]; confer- With funding from the National Science Foundation (NSF), ence website: http://www.ux1.eiu.edu/~prcoulton/ the Conference Board of the Mathematical Sciences (CBMS) cbms07/. will hold nine NSF-CBMS Regional Research Conferences July 9–13, 2008: Knots and Topological Quantum Com- during the summer of 2008. puting. Zhenghan Wang, lecturer; Ara Basmajian, Short These conferences are intended to stimulate interest Course on Knots. University of Central Oklahoma. Organiz- and activity in mathematical research. Each five-day con- ers: Charlotte Simmons, 405-974-5294, email: cksimmons@ ference features a distinguished lecturer who delivers ten ucok.edu; Jesse Byrne, 405-974-5575, email: jbyrne@ lectures on a topic of important current research in one ucok.edu; conference website: http://www.math.ucok. sharply focused area of the mathematical sciences. The edu/cbms/cbms.html. lecturer subsequently prepares an expository monograph August 7–12, 2008: Malliavin Calculus and Its Applica- based on these lectures. tions. David Nualart, lecturer. Kent State University. Orga- Support for about thirty participants will be provided nizers: Oana Mocioalca, 330-672-9083, email: oana@math. for each conference. Both established researchers and kent.edu; Kazim M. Khan, 330-672-9110, email: kazim@ interested newcomers, including postdoctoral fellows and math.kent.edu; conference website: http://www.math. graduate students, are invited to attend. kent.edu/math/CBMS2008.cfm. Information about an individual conference may be December 13–17, 2008: Tropical Geometry and Mirror obtained by contacting the conference organizer. The Symmetry. Mark Gross, lecturer. Kansas State University. conferences to be held in 2008 are as follows. Organizers: Ricardo Castano-Bernard, 785-532-0585, email:

614 Notices of the AMS Volume 55, Number 5 Mathematics Opportunities [email protected]; Yan Soibelman, 785-532-0584, The deadline for registration is May 31, 2008. For email: [email protected]; Ilia Zharkov, 617-495-8797, details, see the website http://www.imc-math.org.uk/ email: [email protected]; conference website: or contact John Jayne, University College London, Gower http://www.math.ksu.edu/~rcastano/CBMS.html. Street, London WC1E 6BT, United Kingdom; telephone: +44-20-7679-7322; email: [email protected]. —From a CBMS announcement —John Jayne, University College London Call for Proposals for 2009 NSF-CBMS Regional News from the IMA The 2008–2009 thematic program at the Institute for Conferences Mathematics and its Applications (IMA) at the University To stimulate interest and activity in mathematical re- of Minnesota will be on “Mathematics and Chemistry”. search, the National Science Foundation (NSF) intends to Computational chemistry has reached a stage of develop- support up to seven NSF-CBMS Regional Research Confer- ment where many chemical properties of both simple and ences in 2009. A panel chosen by the Conference Board of complex systems may now be computed more accurately, the Mathematical Sciences will make the selections from more economically, or more speedily than they can be among the submitted proposals. measured. Further advances in accuracy and practicality Each five-day conference features a distinguished lec- will depend on the development of both new theory and turer who delivers ten lectures on a topic of important new algorithms, and mathematical techniques will play current research in one sharply focused area of the math- an important role in both of these areas. The advances in ematical sciences. The lecturer subsequently prepares an chemical theory and computations have built on interfaces expository monograph based on these lectures, which is with a number of areas of mathematics, including differen- normally published as a part of a regional conference se- tial equations, linear and nonlinear algebra, optimization ries. Depending on the conference topic, the monograph theory, probability theory, stochastic analysis, sampling will be published by the American Mathematical Society, theory, complex analysis, geometry, group theory, and by the Society for Industrial and Applied Mathematics, numerical analysis. Further progress in computational or jointly by the American Statistical Association and the chemistry will require that the ties between chemistry Institute of Mathematical Statistics. and mathematics be strengthened. This IMA program Support is provided for about thirty participants at will provide a setting for the chemistry and mathematics each conference, and both established researchers and communities to examine some of these problems together. interested newcomers, including postdoctoral fellows and The year will focus on issues in electronic structure, graduate students, are invited to attend. dynamics, and statistical mechanics, including both the The proposal due date is April 21, 2008. For further mathematical underpinnings of modern molecular model- information on submitting a proposal, consult the CBMS ing and simulation and practical issues in state-of-the-art website, http://www.cbmsweb.org/NSF/2009_call. applications. Applications areas will include organic and htm, or contact: Conference Board of the Mathematical inorganic chemistry, biochemistry, solid-state chemistry, Sciences, 1529 Eighteenth Street, NW, Washington, DC nanochemistry, advanced materials, photochemistry, 20036; telephone: 202-293-1170; fax: 202-293-3412; email: catalysis, and environmental chemistry. Emphasis will be [email protected] or [email protected]. placed on mingling applied mathematicians with theoreti- cal and computational chemists in each workshop. Limited —From a CBMS announcement financial support is available for the workshops. Detailed information about this program can be found at http:// www.ima.umn.edu/2008-2009. International Mathematics The 2009–2010 IMA thematic program will be on “Com- plex Fluids and Complex Flows”. This program is broadly Competition for University concerned with fundamental challenges of modeling, analysis, and computation for (mostly) incompressible Students fluid dynamics. Much attention will be focused on non- The fifteenth International Mathematics Competition (IMC) Newtonian fluids in which complex material constitu- for University Students will be held July 25–31, 2008, at the tions produce nonlinear and/or nonlocal relationships American University in Blagoevgrad, Bulgaria. Participat- between stresses and rates-of-strain (and sometimes ing universities are invited to send several students and strains) leading to unique and often unforeseen flow one teacher; individual students are welcome. Students phenomena. Complex fluids are ubiquitous in engineer- completing their first, second, third, or fourth years of ing applications and the applied sciences from biology to university education are eligible. The competition will con- geology. They serve as the focus of active areas of research sist of two sessions of five hours each. Problems will come within the larger fluid dynamics community. Complex from the fields of algebra, analysis (real and complex), and flows include those of both simple and complex fluids in combinatorics. The working language will be English. simple and complex domains, in the presence of moving

May 2008 Notices of the AMS 615 Mathematics Opportunities boundaries, and turbulent flows. Key questions for such IPAM is seeking a second associate director, to begin flows include transport and mixing properties, and flow- July 2008. Information about the position and how to structure interactions generating motions including swim- apply is available on our website. ming, flying, sliding, and crawling. Recent research has Optimal Transport. March 10–June 13, 2008. Applica- revealed new connections between fluid characteristics, tions for the long program are closed, but individuals may flow complexity, and transport properties that will in part still register for the three remaining workshops: serve as a unifying theme throughout the program. The Workshop III: Transport Systems in Geography, Geosci- mathematical scope of this program will be very broad, ences, and Networks: May 5–9, 2008. ranging from fundamental modeling questions through Workshop IV: Optimal Transport in the Human Body: issues of computation, simulation, approximation and Lungs and Blood: May 19–23, 2008. analysis. Program participants will include researchers Mini-Workshop: Entropies and Optimal Transport in from the engineering and applied sciences—including Quantum Mechanics: June 5–6, 2008. both theorists and experimentalists—numerical analysis, Summer School. Mathematics in Brain Imaging, and scientific computation, and both applied and abstract July 14–25, 2008. Individuals may register online. analysts. A central goal of the program will be to bring Internet Multi-Resolution Analysis. September 8– these interdisciplinary perspectives together and facilitate December 12, 2008. This long program includes the fol- productive engagement. Opportunities for participation lowing workshops that are also open for participation. in the 2009–2010 program include New Directions re- Individuals may apply online for support to be core par- ticipants for the entire program or to attend individual search professorships for established mathematicians workshops. seeking to branch into new interdisciplinary research Tutorials: September 9–12, 2008. directions, regular and industrial postdoctoral fellowships Workshop I: Multiscale Representation, Analysis and (application deadline is January 5, 2009), and general Modeling of Internet Data and Measurements: September memberships (visits of a month or more, no application 22–26, 2008. deadline). Workshop II: Applications of Internet MRA to Cyber- The IMA actively solicits proposals for programs from Security: October 13–17, 2008. members of the mathematical sciences community. Pos- Workshop III: Beyond Internet MRA: Networks of Net- sibilities include annual programs (running September– works: November 3–7, 2008. June), summer programs (typically running two to four Workshop IV: New Mathematical Frontiers in Network weeks and involving between 60 and 120 participants), Multi-Resolution Analysis: November 17–21, 2008. and Hot Topics workshops (typically lasting a few days Winter 2009 Short Programs. Individuals may apply and treating a topic of exceptional contemporary interest online for support to attend each workshop. and potential impact). Submission timelines: Preproposals Quantitative and Computational Aspects of Metric for annual programs, at least four years in advance of the Geometry: January 12–16, 2009. proposed start date; summer program proposals, roughly Numerical Approaches to Quantum Many-Body Systems: two to three years in advance; Hot Topics workshop pro- January 22–30, 2009. posals, a year in advance, cosponsorship by an industrial Laplacian Eigenvalues and Eigenfunctions: Theory, partner or institute is preferred. Additional information is Computation, Application: February 9–13, 2009. available at http://www.ima.umn.edu/solicit. Rare Events in High-Dimensional Systems: February 23– 27, 2009. Quantum and Kinetic Transport Equations: Analysis, —From an IMA announcement Computations, and New Applications. March 9–June 12, 2009. This long program includes the following workshops that are also open for participation. Individuals may apply News from IPAM online for support to be core participants for the entire program or to attend individual workshops. The Institute for Pure and Applied Mathematics (IPAM), Tutorials: March 10–13, 2009. located at the University of California, Los Angeles, holds Workshop I: Computational Kinetic Transport and long- and short-term research programs and workshops Hybrid Methods: March 30–April 3, 2009. throughout the academic year for junior and senior math- Workshop II: The Boltzmann Equation: DiPerna-Lions ematicians and scientists who work in academia, the na- Plus 20 Years: April 15–17, 2009. tional laboratories, and industry. IPAM sponsors two sum- Workshop III: Flows and Networks in Complex Media: mer programs as well. IPAM’s programs for 2008–2009 April 27–May 1, 2009. are listed below. Please go to http://www.ipam.ucla. Workshop IV: Asymptotic Methods for Dissipative Particle edu for detailed information and online application and Systems: May 18–22, 2009. registration forms. IPAM’s Science Advisory Board meets in November, —IPAM announcement when it considers program proposals. Proposals from the community are encouraged; instructions are available at our website.

616 Notices of the AMS Volume 55, Number 5 Inside the AMS

for mathematically talented high school students (includ- Epsilon Awards for 2008 ing those with and without Epsilon grants) is available at The AMS Epsilon Fund for Young Scholars was established http://www.ams.org/outreach/mathcamps.html. in 1999 to provide financial assistance to summer pro- grams for mathematically talented high school students —AMS Development Office in the United States. For many years these programs have provided mathematically talented youngsters with their first serious mathematical experiences. The name for the From the AMS Public fund was chosen in remembrance of the late Paul Erdo˝s, who was fond of calling children “epsilons”. Awareness Office The AMS has chosen eight summer mathematics pro- Podcasts with Mathematical Moments. Now you can listen grams to receive Epsilon grants for activities in the sum- to researchers talk about their work, such as investigating mer of 2008. The grants will support program expenses connections in the U.S. Congress or the mathematics asso- and student scholarships and, in some cases, scholarships ciated with recent results on invisibility. Look for the POD only. The programs were chosen on the basis of math- icon at http://www.ams. ematical excellence and enthusiasm. Award amounts were org/ams/mathmoments. Unearthing Power Lines governed by the varying financial needs of each program html to listen or down- AMS Podcast Votes are cast by the full membership in each house of Congress, but much of the Series important maneuvering occurs in committees. Graph theory and linear algebra are two mathematics subjects that have revealed a level of organization in Congress— and total US$100,000. load, or get the podcasts groups of committees—above the known levels of subcommittees and committees. The result is based on strong connections between certain committees that can be detected by examining their memberships, but which were virtually unknown The programs receiving grants are: All Girls/All Math, at iTunes. until uncovered by mathematical analysis. Mathematics has also been applied to individual congressional voting records. Each legislator’s record is represented in a matrix whose larger dimension is the number of votes cast (which in a House term is approximately 1000). Using eigen- University of Nebraska, Lincoln; Hampshire College Sum- values and eigenvectors, researchers have shown that the entire collection of votes AMS Exhibit at the An- for a particular Congress can be approximated very well by a two-dimensional space. Thus, for example, in almost all cases the success or failure of a bill can be mer Studies in Mathematics, Amherst, Massachusetts; predicted from information derived from two coordinates. Consequently it turns nual AAAS Meeting. The out that some of the values important in Washington are, in fact, eigenvalues. For More Information: Porter, Mason A; Mucha, Peter J.; Newman, M. E. J.; and MathPath, University of Vermont, Burlington; Michigan Warmbrand, Casey M., “A Network Analysis of Committees in the United States House of Representatives,” Proceedings of the National Academy of Sciences, Vol. 102 Public Awareness Office [2005], No. 20, pp. 7057-7062. Math and Science Scholars Summer Program, University hosted an exhibit at the of Michigan, Ann Arbor; PROMYS, Boston University; American Association for PROTaSM (Puerto Rico Opportunities for Talented Students the Advancement of Sci- in Mathematics), University of Puerto Rico, Mayaguez; Ross ence (AAAS) annual meet- courtesy House, Community Structure in the Image: U.S. Porter. A. Mucha and of Mason Peter J. The Mathematical Moments program promotes Mathematics Program, Ohio State University, Columbus; appreciation and understanding of the role mathematics ing held in Boston, MA, plays in science, nature, technology, and human culture. and Texas State University Honors Summer Math Camp, www.ams.org/mathmoments February 15–18, 2008. MM/54 Texas State University, San Marcos. The exhibit provided an- The grants for summer 2008 are paid for by the AMS other way for mathematics to be represented at this meet- Epsilon Fund for Young Scholars (supplemented by the ing, which draws scientists from many disciplines, science AMS Program Development Fund). The AMS is continuing writers and media, students, and families. On display were to build the endowment for the Epsilon Fund, with a goal a sampling of AMS books, the Calendar of Mathematical of raising US$2 million through individual donations and Imagery, and a selection from the 60-plus Mathematical grants. Moments that show the role mathematics plays in science, For further information about the Epsilon Fund for nature, technology, and human culture. Young Scholars, visit the website http://www.ams. AMS Presidents: A Timeline. AMS presidents have org/giving-to-ams/ or contact development@ams. played a key role in leading the Society in its publications, org. Information about how to apply for Epsilon grants is meetings, professional visibility, and support for research, available at http://www.ams.org/outreach/epsilon. and many have interesting biographies. Some presidents html. A fairly comprehensive listing of summer programs came from humble backgrounds, others from families

May 2008 Notices of the AMS 617 Inside the AMS of privilege. Several of the Society’s presidents were David Gale, professor emeritus, University of Califor- born or trained outside the U.S. The early presidents had nia, Berkeley, died on March 7, 2008. Born on December been awarded honorary Ph.D.’s. Some stayed at the same 13, 1921, he was a member of the Society for 61 years. institution for decades, others traveled the world to do Alfred W. Goldie, from Cumbria, England, died on research, give talks, and represent the AMS. Most worked October 8, 2005. Born on December 10, 1920, he was a in academia, and a few worked in applied mathematics; member of the Society for 18 years. some trained in well-known mathematics departments, Raoul Hailpern, from Amherst, NY, died on February others at small colleges. Some were quiet leaders, others 9, 2008. Born on July 19, 1916, he was a member of the outgoing and highly visible. All have in common an inter- Society for 45 years. national recognition for their mathematical achievements James E. Householder, from Las Vegas, NV, died on Janu- and effective leadership. See a brief biography of each AMS ary 23, 2008. Born on December 26, 1916, he was a member president from 1888 through 2008 at http://www.ams. of the Society for 52 years. org/ams/amspresidents.html. Raymond F. Kramer Jr., from Manhattan Beach, CA, died on February 23, 2008. Born on June 6, 1932, he was a

member of the Society for 49 years. —Annette Emerson and Mike Breen Benjamin N. Moyls, from Vancouver, Canada, died on AMS Public Awareness Officers November 10, 2007. Born on May 1, 1919, he was a member [email protected] of the Society for 61 years. Gen-ichiro Sunouchi, from Sendai, Japan, died on March 7, 2008. Born on October 29, 1911, he was a member MathSciNet Links to of the Society for 53 years. Peter Szüsz, professor emeritus, SUNY Stony Brook, died Mathematics Genealogy on February 16, 2008. Born on November 11, 1924, he was Project a member of the Society for 42 years. MathSciNet now offers direct linking to the Mathematics Genealogy Project (MGP, http://www.genealogy.ams. org/) through the MathSciNet “Authors” search tab. The results obtained after doing an author search on this page include a drop-down menu (hover the cursor over the author of interest) that includes a link to the author’s MGP page. On MGP users can find information about that author: name of the university that awarded his or her degree, the year in which the degree was awarded, the com- plete title of the dissertation, the name(s) of the advisor(s), and for some, a list of the mathematician’s students.

—AMS Announcement

Deaths of AMS Members Kevin Short, a mathematician at the University of Richard D. Anderson, former AMS vice president, died on New Hampshire, is co-recipient of a 2008 Grammy March 4, 2008. Born on February 17, 1922, he was a member Award. Short used his “Chaotic Compression Tech- of the Society for 62 years. nology” to restore a bootleg wire recording of a Nikolay V. Azbelev, professor, Perm State Technical Woody Guthrie concert that is the only known re- University, Russia, died on November 3, 2006. Born on cording of the folk singer performing before a live April 15, 1922, he was a member of the Society for 11 audience. The result, The Live Wire: Woody Guthrie years. In Performance 1949, earned him and the team of Charles L. Clark, professor emeritus, California State producers and engineers the 2008 Grammy Award University, Los Angeles, died on February 22, 2008. Born for Best Historical Album. in November 1917, he was a member of the Society for Manil Suri, a mathematician at the University of 68 years. Maryland, Baltimore County, has published his sec- Helen F. Cullen, from Harwich, MA, died on August ond novel. His first novel, The Death of Vishnu, was 25, 2007. Born on January 4, 1919, she was a member of published to high acclaim and has been translated the Society for 58 years. into twenty-two foreign languages. Suri received a Belmont G. Farley, former faculty member at the Uni- Guggenheim Fellowship for fiction in 2004. His lat- versity of Pennyslvania, and professor emeritus of Temple est novel, The Age of Shiva, appeared in February University, died on February 28, 2008. Born on December of this year. 29, 1920, he was a member of the Society for 66 years.

618 Notices of the AMS Volume 55, Number 5 Reference and Book List

The Reference section of the Notices Upcoming Deadlines May 1, 2008: Applications for is intended to provide the reader April 18, 2008: Applications for Proj- AWM Travel Grants. See http:// with frequently sought information in ect NExT: New Experiences in Teach- www.awm-math.org/travelgrants. an easily accessible manner. New ing. See http://archives.math. html; telephone 703-934-0163; email: utk.edu/projnext/. information is printed as it becomes [email protected]; or contact As- available and is referenced after the April 21, 2008: Proposals for 2009 sociation for Women in Mathematics, first printing. As soon as information NSF-CBMS Regional Conferences. See 11240 Waples Mill Road, Suite 200, is updated or otherwise changed, it “Mathematics Opportunities” in this will be noted in this section. issue. Fairfax, VA 22030.

Contacting the Notices Where to Find It The preferred method for contacting A brief index to information that appears in this and previous issues of the Notices. the Notices is electronic mail. The AMS Bylaws—November 2007, p. 1366 editor is the person to whom to send AMS Email Addresses—February 2008, p. 274 articles and letters for consideration. AMS Ethical Guidelines—June/JulyWhere to2006, Find p. It701 Articles include feature articles, me- AMSA brief Officers index to 2006information and 2007 that appears Updates in —thisMay and 2008, previous p. 629 issues of the Notices. morial articles, communications, AMS OfficersBylaws— andNovember Committee 2005, Members—p. 1239 October 2007, p. 1178 opinion pieces, and book reviews. ConferenceAMS Email Addresses Board of— theFebruary Mathematical 2006, p. 251 Sciences—September 2007, The editor is also the person to whom p.AMS 1019 Ethical Guidelines—June/July 2006, p. 701 to send news of unusual interest IMUAMS ExecutiveOfficers 2005 Committee— and 2006December (Council, 2007, Executive p. 1526 Committee, about other people’s mathematics InformationPublications forCommittees, Notices Authors— Board ofJune/July Trustees) 2007,—May p. 2006,765 p. 604 research. MathematicsAMS Officers and Research Committee Institutes Members— ContactOctober Information— 2006, p. 1076August 2007, The managing editor is the person p.Conference 898 Board of the Mathematical Sciences—September 2006, to whom to send items for “Math- Nationalp. 911 Science Board—January 2008, p. 69 ematics People”, “Mathematics Op- NewInformation Journals for for Notices 2005, 2006—Authors—June/JulyJune/July 2007, 2006, p. 767 p. 696 portunities”, “For Your Information”, Mathematics Research Institutes Contact Information—August 2006, “Reference and Book List”, and “Math- NRC Board on Mathematical Sciences and Their Applications—March 2008,p. 798 p. 401 ematics Calendar”. Requests for NRCNational Mathematical Science Board— SciencesJanuary Education 2006, Board—p. 62 April 2008, p. 515 permissions, as well as all other New Journals for 2004—June/July 2006, p. 697 inquiries, go to the managing editor. NSF Mathematical and Physical Sciences Advisory Committee—February 2008,NRC Boardp. 276 on Mathematical Sciences and Their Applications—March The electronic-mail addresses are Program2006, p. 369 Officers for Federal Funding Agencies—October 2007, [email protected] in the case of p.NRC 1173 Mathematical (DoD, DoE); DecemberSciences Education 2007, p. 1359 Board— (NSF),April December 2006, p. 2007, 488 the editor and [email protected] in p.NSF 1526 Mathematical (NSF Mathematics and Physical Education) Sciences Advisory Committee—February the case of the managing editor. The Program2006, p. 255 Officers for NSF Division of Mathematical Sciences—Novem- fax numbers are 405-325-7484 for berProgram 2007, Officersp. 1358 for Federal Funding Agencies—October 2006, the editor and 401-331-3842 for the Stipendsp. 1072 (DoD, for Study DoE); Decemberand Travel— 2006September p. 1365 (NSF)2007, p. 1022 managing editor. Postal addresses Stipends for Study and Travel—September 2006, p. 913 may be found in the masthead.

May 2008 Notices of the AMS 619 Reference and Book List

May 1, 2008: Applications for [email protected]; or contact Asso- and Nicolson, May 2007. ISBN-13: 978- May review for the National Acad- ciation for Women in Mathematics, 0-29764-547-4. emies Postdoctoral and Senior Re- 11240 Waples Mill Road, Suite 200, The Art of Mathematics: Cof- search Associateship Programs. See Fairfax, VA 22030. fee Time in Memphis, by Béla Bol- http://www7.nationalacademies. October 15, 2008: Proposals for lobás. Cambridge University Press, org/rap/index.html or contact NSF Postdoctoral Research Fellow- September 2006. ISBN-13: 978-0-52169- Research Associateship Programs, ships. See “Mathematics Opportuni- 395-0. National Research Council, Keck 568, ties” in this issue. The Artist and the Mathematician: 500 Fifth Street, NW, Washington, DC November 1, 2008: Applications The Story of Nicolas Bourbaki, the 20001; telephone 202-334-2760; fax for November review for the National Genius Mathematician Who Never 202-334-2759; email: [email protected]. Academies Postdoctoral and Senior Existed, by Amir D. Aczel. Thunder’s May 15-June 15, 2008: Proposals Research Associateship Programs. See Mouth Press, August 2006. ISBN for DMS Workforce Program in the http://www7.nationalacademies. 1-560-25931-0. (Reviewed October Mathematical Sciences. See http:// org/rap/index.html or contact 2007.) www.nsf.gov/funding/pgm_summ. Research Associateship Programs, Benjamin Franklin’s Numbers: An jsp?pims_id=503233. National Research Council, Keck 568, Unsung Mathematical Odyssey, by May 31, 2008: Registration for In- 500 Fifth Street, NW, Washington, DC Paul C. Pasles. Princeton University ternational Mathematics Competition 20001; telephone 202-334-2760; fax Press, October 2007. ISBN-13: 978- for University Students. See “Math- 202-334-2759; email: [email protected]. 0-69112-956-3. ematics Opportunities” in this issue. Bourbaki, a Secret Society of Math- Book List June 1, 2008: Applications for ematicians, by Maurice Mashaal. AMS, Christine Mirzayan Science and The Book List highlights books that June 2006. ISBN 0-8218-3967-5. (Re- Technology Policy Graduate Fel- have mathematical themes and are viewed October 2007.) aimed at a broad audience potentially lowship Fall Program. See http:// The Calculus Wars: Newton, Leib- www7.nationalacademies.org/ including mathematicians, students, niz, and the Greatest Mathematical policyfellows or contact The Na- and the general public. When a book Clash of All Time, by Jason Socrates tional Academies Christine Mirza- has been reviewed in the Notices, a Bardi. Thunder’s Mouth Press, April yan Science and Technology Policy reference is given to the review. Gen- 2007. ISBN-13: 978-1-56025-992-3. Graduate Fellowship Program, 500 erally the list will contain only books The Cat in Numberland, by Ivar Fifth Street, NW, Room 508, Wash- published within the last two years, Ekeland. Cricket Books, April 2006. ington, DC 20001; telephone: 202- though exceptions may be made in ISBN-13: 978-0-8126-2744-2. 334-2455; fax: 202-334-1667; email: cases where current events (e.g., the A Certain Ambiguity: A Mathemati- [email protected]. death of a prominent mathematician, cal Novel, by Gaurav Suri and Hartosh June 10, 2008: Proposals for En- coverage of a certain piece of math- Singh Bal. Princeton University Press, hancing the Mathematical Sciences ematics in the news) warrant drawing June 2007. ISBN-13: 978-0-691-12709- Workforce in the Twenty-First Cen- readers’ attention to older books. Sug- tury. See http://www.nsf.gov/ gestions for books to include on the list 5. (Reviewed February 2008.) publications/pub_summ.jsp?ods_ may be sent to notices-booklist@ Chases and Escapes: The Math- key=nsf05595. ams.org. ematics of Pursuit and Evasion, by August 1, 2008: Applications for *Added to “Book List” since the Paul J. Nahin. Princeton University August review for the National Acad- list’s last appearance. Press, May 2007. ISBN-13: 978-0- emies Postdoctoral and Senior Re- 69112-514-5. search Associateship Programs. See Alfred Tarski: Life and Logic, by Descartes: A Biography, by Desmond http://www7.nationalacademies. Anita Burdman Feferman and Solo- Clarke. Cambridge University Press, org/rap/index.html or contact mon Feferman. Cambridge Univer- March 2006. ISBN 0-521-82301-3. (Re- Research Associateship Programs, sity Press, October 2004. ISBN 0- viewed January 2008.) National Research Council, Keck 568, 521-80240-7. (Reviewed September Does Measurement Measure Up?: 500 Fifth Street, NW, Washington, DC 2007.) How Numbers Reveal and Conceal the 20001; telephone 202-334-2760; fax Amongst Mathematicians: Teach- Truth, by John Henshaw. Johns Hopkins 202-334-2759; email: [email protected]. ing and Learning Mathematics at University Press, March 2006. ISBN-13: August 18, 2008: Applications University Level, by Elena Nardi. 978-0-8018-8375-0. for NSF Research Experiences for Springer, November 2007. ISBN-13: Ernst Zermelo: An Approach to Undergraduates (REU) program 978-0-387-37141-2. His Life and Work, by Heinz-Dieter sites. See http://www.nsf.gov/ Ants, Bikes, and Clocks: Problem Ebbinghaus. Springer, April 2007. publications/pub_summ.jsp?ods_ Solving for Undergraduates, by Wil- ISBN-13: 978-3-540-49551-2. key=nsf07569. liam Briggs. Society for Industrial and Flatland—The Movie: A Journey of October 1, 2008: Applications for Applied Mathematics, 2005. ISBN 0- Many Dimensions. Flatworld Produc- AWM Travel Grants. See http:// 89871-574-1. tions, 2007. Special Educator Edition www.awm-math.org/travelgrants. The Archimedes Codex, by Reviel DVD, http://store.flatlandthemovie. html; telephone: 703-934-0163; email: Netz and William Noel. Weidenfeld com. (Reviewed November 2007.)

620 Notices of the AMS Volume 55, Number 5 Reference and Book List

Fly Me to the Moon: An Insider’s Leonhard Euler, a Man to Be Reck- Music: A Mathematical Offering, by Guide to the New Science of Space oned With, by Andreas K. Heyne and David J. Benson. Cambridge Univer- Travel, by Edward Belbruno. Prince­ Alice K. Heyne. Birkhäuser, 2007. ISBN- sity Press, December 2006. ISBN-13: ton University Press, January 2007. 13: 978-3-7643-8332-9. (Reviewed 978-0-521-61999-8. ISBN-13: 978-0-691-12822-1. (Re- March 2008.) New Theories of Everything, by viewed April 2008.) *Making Mathematics Work with John D. Barrow. Oxford University The Great π/e Debate: Which Is the Needlework: Ten Papers and Ten Press, July 2007. ISBN-13: 978-0-192- Better Number?, DVD by Colin Adams Projects, edited by Sarah-Marie Bel- 80721-2. and Thomas Garrity. Mathematical castro and Carolyn Yackel. A K Pe- Nonplussed! Mathematical Proof Association of America, 2007. ISBN ters, September 2007. ISBN-13: 978- of Implausible Ideas, by Julian Havil. 0-88385-900-9. 1-56881-331-8. Princeton University Press, May 2007. *Group Theory in the Bedroom, and The Math behind the Music, by ISBN-13: 978-0-691-12056-0. Other Mathematical Diversions, by Leon Harkleroad. Cambridge Univer- The Numbers behind NUMB3RS: Brian Hayes. Hill and Wang, April 2008. sity Press, August 2006. ISBN-13: 978- Solving Crime with Mathematics, by ISBN-13: 978-0-8090-521-96. 0-521-00935-5. Keith Devlin and Gary Lorden. Plume, A History of Abstract Algebra, by Math Doesn’t Suck: How to Survive August 2007. ISBN-13: 978-0-4522- Israel Kleiner. Birkhäuser, October Middle-School Math without Losing 8857-7. 2007. ISBN-13: 978-0-8176-4684-4. Your Mind or Breaking a Nail, by Out of the Labyrinth: Setting Math- How Mathematicians Think: Using Danica McKellar. Hudson Street Press, ematics Free, by Robert Kaplan and Ambiguity, Contradiction, and Para- August 2007. ISBN-13: 978-1-5946- Ellen Kaplan. Oxford University Press, dox to Create Mathematics, by William 3039-2. January 2007. ISBN-13: 978-0-19514- Byers. Princeton University Press, May Mathematical Mind-Benders, by 744-5. 2007. ISBN-13: 978-0-6911-2738-5. Peter Winkler. A K Peters, August Perfect Figures: The Lore of Num- (Reviewed December 2007.) 2007. ISBN-13: 978-15688-1336-3. bers and How We Learned to Count, by *How Round Is Your Circle, by John The Mathematician’s Brain, by Bunny Crumpacker. Thomas Dunne Bryant and Chris Sangwin. Princeton David Ruelle. Princeton University Books, August 2007. ISBN-13: 978-0- University Press, January 2008. ISBN- Press, July 2007. ISBN-13: 978-0-691- 3123-6005-4. 13: 978-0-6911-311-84. 12982-2. The Poincaré Conjecture: In Search I Am a Strange Loop, by Douglas R. Mathematics at Berkeley: A History, of the Shape of the Universe, by Donal Hofstadter. Basic Books, March 2007. by Calvin C. Moore. A K Peters, February O’Shea. Walker, March 2007. ISBN-13: ISBN-13: 978-0-46503-078-1. (Reviewed 2007. ISBN-13: 978-1-5688-130-28. 978-0-8027-1532-6. (Reviewed Janu- August 2007.) The Millennium Prize Problems, ary 2008.) The Indian Clerk, by David Leavitt. edited by James Carlson, Arthur Jaffe, Poincaré’s Prize: The Hundred-Year Bloomsbury USA, September 2007. and Andrew Wiles. AMS, June 2006. Quest to Solve One of Math’s Great- ISBN-13: 978-1-5969-1040-9. ISBN-13: 978-0-8218-3679-8. est Puzzles, by George Szpiro. Dutton An Introduction to Gödel’s Theo- The Mind of the Mathematician, by Adult, June 2007. ISBN-13: 978-0-525- rems, by Peter Smith. Cambridge Uni- Michael Fitzgerald and Ioan James. 95024-0. (Reviewed January 2008.) versity Press, August 2007. ISBN-13: Johns Hopkins University Press, May *The Presidential Election Game, by 978-0-52167-453-9. 2007. ISBN-13: 978-0-8018-8587-7. Steven J. Brams. A K Peters, December *Irreligion: A Mathematician Ex- More Mathematical Astronomy 2007. ISBN-13: 978-1-5688-134-86. plains Why the Arguments for God Morsels, by Jean Meeus. Willmann- The Probability of God: A Simple Just Don’t Add Up, by John Allen Pau- Bell, 2002. ISBN 0-943396-743. Calculation That Proves the Ultimate los. Hill and Wang, December 2007. More Sex Is Safer Sex: The Uncon- Truth, by Stephen D. Unwin. Three ISBN-13: 978-0-8090-591-95. ventional Wisdom of Economics, by Rivers Press (October 26, 2004). ISBN- John von Neumann: Selected Let- Steven E. Landsburg. Free Press, April 13: 978-1-4000-5478-7. (Reviewed ters, edited by Miklós Rédei. AMS, 2007. ISBN-13: 978-1-416-53221-7. February 2008.) November 2005. ISBN 0-8218-3776-1. The Motion Paradox: The 2,500- Pythagoras: His Life, Teaching and (Reviewed June/July 2007.) Year Old Puzzle behind All the Mys- Influence, by Christoph Riedweg. Karl Pearson: The Scientific Life teries of Time and Space, by Joseph Translated by Steven Rendall. Cornell in a Statistical Age, by Theodore M. Mazur. Dutton Adult, April 2007. University Press, March 2005. ISBN- Porter. Princeton University Press, ISBN-13: 978-0-52594-992-3. 13: 978-0-80144-240-7. (new edition) December 2005. ISBN- Mr. Hopkins’ Men: Cambridge Pythagoras: The Mathemagician, 13: 978-0-69112-635-7. (Reviewed Reform and British Mathematics in by Karim El-koussa. Cloonfad Press, December 2007.) the 19th Century, by A. D. D. Craki. September 2005. ISBN-13: 978-0- The Legacy of Mario Pieri in Geom- Springer, July 2007. ISBN-13: 978-1- 97694-042-5. etry and Arithmetic, by Elena Anne 8462-8790-9. The Pythagorean Theorem: A 4000- Marchisotto and James T. Smith. Music and Probability, by David Year History, by Eli Maor. Princeton Birkhäuser, May 2007. ISBN-13: 978- Temperley. MIT Press, January 2007. University Press, May 2007. ISBN-13: 0-8176-3210-6. ISBN-13: 978-0-262-20166-7. 978-0-69112-526-8.

May 2008 Notices of the AMS 621 Reference and Book List

Solving Mathematical Problems: A 2005. ISBN 0-465-09293-4. (Reviewed Personal Perspective, by Terence Tao. August 2007.) Oxford University Press, September Yearning for the Impossible: The 2006. ISBN-13: 978-0-199-20560-8. Surprising Truths of Mathematics, by The Square Root of 2: A Dialogue John Stillwell. A K Peters, May 2006. Concerning a Number and a Se- ISBN 1-568-81254-X. (Reviewed June/ quence, by David Flannery. Springer, July 2007.) December 2005. ISBN-13: 978-0- You Failed Your Math Test, Com­ 38720-220-4. rade Einstein: Adventures and Mis­ *Super Crunchers: Why Thinking- adventures of Young Mathematicians, by-Numbers Is the New Way to Be or Test Your Skills in Almost Recre- Smart, by Ian Ayres. Bantam, August ational Mathematics, edited by M. 2007. ISBN-13: 978-0-5538-054-06. Shifman. World Scientific, June 2005. Superior Beings: If They Exist, How ISBN-13: 978-9-8125-6279-1. Would We Know? Game-Theoretic Im­ plications of Omnipotence, Omniscience, Immortality, and Incomprehensibility, by Steven Brams. Springer, second edition, November 2007. ISBN-13: 978- 0-387-48065-7. (Reviewed February 2008.) Thinking about Gödel and Turing: Essays on Complexity, 1970–2007, by Gregory J. Chaitin. World Scientific, August 2007. ISBN-13: 978-9-8127- 0895-3. The Triumph of Numbers: How Counting Shaped Modern Life, by I. B. Cohen. W. W. Norton, July 2006. ISBN-13: 978-0-393-32870-7. (Re- viewed December 2007.) The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, by Lee Smolin. Joseph Henry Press, October 2006. ISBN 0-309-10192-1. (Reviewed Sep- tember 2007.) *Unknown Quantity: A Real and Imaginary History of Algebra, by John Derbyshire. Joseph Henry Press, May 2006. ISBN 0-309-09657-X. (Reviewed in this issue.) Useless Arithmetic: Why Environ- mental Scientists Can’t Predict the Future, by Orrin Pilkey and Linda Pilkey-Jarvis. Columbia University Press, February 2007. ISBN 0-231- 13212-3. (Reviewed April 2008.) The Volterra Chronicles: The Life and Times of an Extraordinary Mathe- matician, by Judith R. Goodstein. AMS, February 2007. ISBN-13: 978-0-8218- 3969-0. (Reviewed March 2008.) Why Beauty Is Truth: The Story of Symmetry, by Ian Stewart. Perseus Books Group, April 2007. ISBN-13: 978-0-46508-236-0. A World Without Time: The Forgot- ten Legacy of Gödel and Einstein, by Palle Yourgrau. Basic Books, January

622 Notices of the AMS Volume 55, Number 5 American Mathematical Society—Contributions

Dear Friends and Colleagues,

During 2007 your generous support helped the Society and our profession in many ways. I thank each of you for that support.

The Young Scholars program is in its eighth year, supporting summer workshops for talented high school students—the future of our profession. We are building an endowment, the Epsilon Fund, to sup- port this program far into the future, and we hope to reach our goal of two million dollars over the next few years. Supporting such programs is important for mathematics.

The Centennial Fellowships play a key role for outstanding young mathematicians at the formative stages of their careers, from three to twelve years beyond the degree. These fellowships are funded by contributions from mathematicians throughout the world.

We use contributions to the General Fund to support all of our activities, including survey work, public awareness, and outreach to mathematicians in the developing world.

Your generosity allows the Society to carry out all these programs and shows that mathematicians care deeply about our profession. Thank you for that expression of caring.

John H. Ewing

Thomas S. Fiske Society

The Executive Committee and Board of Trustees have established the Thomas S. Fiske Society to honor those who have made provisions for the AMS in their estate plans. For further information contact the Development Office at 800-321-4AMS, or [email protected].

Pedro B. Barquero Isidore Fleischer Joseph S. Mamelak Theda Salkind Kathleen Baxter Ramesh Gangolli Trevor McMinn Margaret W. Taft Shirley and Gerald Bergum Sidney Glusman Cathleen S. Morawetz B. A. Taylor Shirley Cashwell Rosalind Guaraldo Franklin P. Peterson Steven H. Weintraub Carl Faith Yanguang Charles Li Moshe Rosenfeld Sally Whiteman Ky Fan

Bequests Received

Ralph Mansfield

May 2008 Notices of the AMS 623 Gifts in Memory and Gifts in Honor The American Mathematical Society welcomes gifts made in memory or honor of members of the mathematical com- munity or others. Unless directed toward a special fund or program, such gifts are used to support the general mission of the Society.

Gifts were made in memory of the following individuals: David P. Robbins by Sheila Johnson Robbins Maurice Auslander by Bernice L. Auslander Gian-Carlo Rota by Norton Starr Ralph DeMarr by Moira Robertson Frederick Bodo Strauss by Delmar L. Boyer Casper Goffman by Eugene M. Friedman Rachel Shai-Aridor by Meir Shemesh Deborah Tepper Haimo by Carol-Ann Blackwood Kathryn B. Toll by Eugene Toll William J. LeVeque by Ellen Heiser Al Wilcox by Carol-Ann Blackwood Vincent O. McBrien by Joseph W. Paciorek Robert Payton by Burt J. Morse Gifts were made in honor of the following individuals: N. Tenney Peck by Emily Mann Peck Lenore Cowen by Margaret A. Readdy & Richard Ehrenborg Eugene A. Pflumm by Mollie Pflumm D. Jacob Wildstrom by Susan Schwartz Wildstrom Everett Pitcher by Carol-Ann Blackwood Irving Reiner by Irma M. Reiner

Contributors to the AMS During 2007 * Donors who have given for three years consecutively. ε Donors who have given to the AMS Epsilon Fund, the endowment for the support of young scholars programs. The names of donors who have given $1,000 or more in a single year are affixed to a plaque that is prominently displayed in the Society’s headquarters.

PRESIDENT’S e Karen Vogtmann & John PATRONS e Rohit K. Chatterjee e Christopher L. Frenzen Smillie * Concordia C. Chen F. Brock Fuller (Gifts of $100 and above) ASSOCIATES e* Steven H. Weintraub e* Richard C. Churchill e* William Fulton (Gifts of $5,000 and above) e* Susan Schwartz Wildstrom e* Clarence M. Ablow e* Stuart Citrin e* Joseph M. Gani * William W. Adams e* William Craig Anonymous (4) e e* Robert A. Clark e John B. Garnett Estate of Sidney Glusman e* Irving Adler e William A. Clee e* Anthony A. Gioia * Roy L. Adler e* Harry Lucas Jr. Michael David Cochran e* Milton Alfred Glass * Jacques Neveu SPONSORS e* Alfred Aeppli e* Daniel I. A. Cohen * James G. Glimm e Oehmke Charitable Fund (Gifts of $500 and above) e* J. Ralph Alexander Jr. e* Donald B. Coleman e* Richard P. Goblirsch e* M. Kursheed Ali e* Peter S. Constantin e* Wilfred Martin Greenlee e Thomas R. Savage * Arielle & Jerald Brodkey * Robert & Maria W. Steinberg Bernard C. Anderson e* Louis J. Cote e* Phillip A. Griffith Philanthropic Fund e* George E. Andrews e Lenore J. Cowen & William e Gerhard E. Hahne M. Salah Baouendi & Linda e* Kenneth I. Appel Bogstad e* Ruth M. Hailperin ASSOCIATES Preiss Rothschild e* Richard F. Arenstorf Walter Craig & Deirdre e R. Stanton Hales Jr. (Gifts of $1,000 and above) * Karl E. Byleen * James G. Arthur Haskell e* Mary-Elizabeth Hamstrom * Paul Dana Cole e* Richard D. Anderson e e Walter O. Augenstein e* Stephen H. Crandall * James F. Hannan e Felix E. Browder e Eugenia E. Fitzgerald e Joel D. Avrin e* Albert W. Currier e* Carsten Hansen – Matching e* Nathaniel Chafee e* Timothy & Laurie Francis- e* Donald G. Babbitt e* David Scott Cyphers gift from Microsoft Corp. e Richard A. Cleveland Wright Theodore J. Barth e* Everett C. Dade e David Harbater e John B. Conway e* Richard L. Gantos e* Hyman Bass e Robert J. Daverman e* Joe T. Harris Jr. e* John H. Ewing * Andrew M. Gleason e Frances B. Bauer * Ronald W. DeGray e* Adam O’Neill Hausknecht Stephen P. Gill e* Elizabeth Grossman & Joshua e* R. Michael Beals e* Guy M. De Primo e* William S. Heck e Ronald L. & Fan Chung Boorstein e* Gerald E. & Shirley Bergum e* Robert L. Devaney e Ellen Heiser Graham e* Bill Hassinger Jr. e John J. Bircher e* Charles E. Dickerson * Henry Helson * Joan S. Birman * Gerald P. Dinneen James P. Henniger e* George F. Haddix e* Joseph Kist e e e* Richard L. Bishop Heinz Deitrich Doebner * James B. Herreshoff * Carl E. Harrell e* Maria Margaret Klawe e e e* Peter B. Bjorklund James A. Donaldson e Diane L. Herrmann & Andy e* John M. Hosack e* Robert V. Kohn * Phyllis & Donald Kahn Carol-Ann Blackwood e* Peter L. Duren Carter e Thomas G. Leness Philanthropic Fund Nancy Cole Bluford e* John W. Duskin Jr. e* Gerald A. Heuer e* William James Lewis * James E. Keisler Delmar L. Boyer e Clifford J. Earle e* Gloria C. Hewitt Ralph Mansfield e Greg Kuperberg & Rena J. e* David M. Bressoud e Earl F. Ecklund Jr. Michael Hieb e* James W. Maxwell Zieve e John Bromback Sylvan H. Eisman e William R. Hintzman Sheila Johnson Robbins e Peter D. Lax * Robert L. Bryant e John M. Erdman Jeff L. Hirst Jacob T. Schwartz e* George F. Leger e e* Stephen S. Bullock e Amassa C. Fauntleroy e Melvin Hochster e* M. Susan Montgomery e* Joel H. Spencer e* Robert Bumcrot e* Arnold D. Feldman e Samuel S. Holland Jr. Emily Mann Peck e* Ronald J. & Sharon M. Stern e* Donald L. Burkholder * John C. Fenley e* Tiao-Tiao Hsu e Ivan P. Polonsky e Murray Marvin Stokely III e Daniel M. Burns Jr. e Aurino Ribeiro Filho e* George W. Hukle e* Samuel Murray Rankin III e Karen Uhlenbeck e Arnold B. & Dana K. Calica e Leib Finkelstein e* Craig L. Huneke * Norton Starr e* Buck Ware L. Andrew Campbell e* Gerald B. Folland e* Thomas W. Hungerford e* Jean E. de Valpine Anonymous (5) e James A. Carlson Robert S. Freeman * Franklin T. Iha

624 Notices of the AMS Volume 55 Number 5 AMS Contributions

e Godfrey L. Isaacs e Peter A. Perry Ken-Ichi Yoshihara e* Robert Beig e* James E. Burke e* I. Martin Isaacs e Troels Petersen e* Allen D. Ziebur e Sarah-Marie Belcastro e Mitchell Burman e William H. Jaco e* Walter V. Petryshyn e* Paul F. Zweifel Harold Bell e Stefan A. Burr Hervé M. Jacquet e* Mollie Pflumm Anonymous (55) e* Steven R. Bell e Claude W. Burrill e* John Antone Jaksich e* Ilya Piatetski-Shapiro e* Wolfgang Bell IV e* Ralph Stevens Butcher e* Melvin F. Janowitz * Vera S. Pless e David P. Bellamy e* Thomas R. Butts e* Eugene C. Johnsen e* Aleksey Popelyukhin FRIENDS e* Katalin A. Bencsáth e* Robert Lawrence Byrom e Norman W. Johnson e Philip Quartararo Jr. (Gifts of less than $100) e Julius S. Bendat Luciano Caccianotti * Paul H. Rabinowitz e* James H. Justice e e Johan F. Aarnes e Vaclav E. Benes e Robert Calderbank James V. Ralston e* Henry Price Kagey e William Abikoff e* Carlos Benítez e M. Carme Calderer * Ravi K. Ramakrishna e* Herbert M. Kamowitz e e* Thundiyil Samuel Abraham e* Georgia Benkart e James J. Callahan * M. M. Rao e* Julian R. Karelitz e e* William P. Abrams e Lynn S. Bennethum e James L. Calvert Frank Raymond e* John F. Kellaher e e Norbert A’Campo e Paul M. Bennett e James C. Cantrell * Marc A. Rieffel e* Harry Kesten e e Robert D. M. Accola e* Gary D. Berg e* Corrado Cardarelli Joel W. Robbin e John Killeen e e Colin C. Adams e Steven B. Berger e* Jon F. Carlson Moira Robertson e* Allan M. Kirch e* Iain T. A. C. Adamson e* George M. Bergman Francis W. Carroll Charles D. Robinson e Jane & James Kister e e* Alan C. Adolphson e* Leonard D. Berkovitz e* David W. Carter * Vijay K. Rohatgi e* George H. Knightly e e Ilka Agricola * Salvatore D. Bernardi Paolo Casati * Guillermo Romero Melendez e János Kollár e e* Tadashi Aikou e* Joseph Bernstein e James R. Case Sharon Cutler Ross e* Antoni A. Kosinski e e* Michael I. Aissen e* Manuel P. Berriozábal e Phyllis J. Cassidy Herman Rubin * Irwin Kra e e Michael Aizenman e David S. Berry e Erio A. Castagnoli Dorothy S. Rutledge e* Ralph M. Krause e* Ethan J. Akin e George Berzsenyi e* Afton H. Cayford * David Ryeburn * Masatake Kuranishi e e V. L. Albugues Alain James S. Bethel Thomas E. Cecil * Jeffrey R. Sachs e* Gary J. Kurowski e e Yousef Alavi e Nicholas J. Bezak e* Gulbank D. Chakerian * Habib Salehi e Herbert Kurss e e* Michael O. Albertson e Gautam Bharali e Graham D. Chalmers e* Jeanne LaDuke Murray M. Schacher * Kenneth S. Alexander e* Meempat Bhaskaran Jack-Kang Chan * Paul T. Schaefer e Jean Pierre Lafon e* Roger K. Alexander e Marilyn S. Bickel e Kit Chak Chan Samuel Schechter e* Richard G. Larson e e Stephanie B. Alexander * Klaus D. Bierstedt e Chao-Ping Chang * Michael Schlessinger Richard K. Lashof e* Gerald L. Alexanderson e David Samuel Bindel e* Weita Chang * Richard M. Schoen e* George Laush e e* John S. Alin e* Terrence Paul Bisson e Paul Jackson Channell Seymour Schuster e* Robert N. Leggett Jr. e* Anne H. Allen e Jerome Blackman e* Ruth M. Charney * Jerry D. Schuur Cecil E. Leith e e William C. Allen III e* Denis L. Blackmore e* Ronald J. Chase * George Seifert e* Joan R. Leitzel e e John P. van Alstyne * David E. Blair e Jeff Cheeger e P. J. Lelong * Stuart A. Seligson Vrege Jolfai Amirkhanian e* Paul E. Bland e Dayue Chen * Norman E. Sexauer e* H. W. Lenstra e e* Fredric Davis Ancel e* John D. Blanton e Fen Chen Abdulalim A. Shabazz e D. J. Lewis e e Douglas R. Anderson Don Blasius * Kwan-Wei Chen * Freydoon Shahidi e Robert J. Lipshutz e e* Joel H. Anderson e* David S. Bloom William A. Cherry * Yuzi Shimizuike * Albert T. Lundell e e John D. Anderson e* Gebhard Böeckle * Robert Chew * Goro Shimura e* Russell D. Lyons e e* Michael T. Anderson e* S. Elwood Bohn e* Theodore S. Chihara * William Ivan Shorter John E. Mack e e* Susan Andima * Miklós Bóna e* Jal R. Choksi * Allan J. Silberger e Yoshiaki Maeda e e* Peter P. Andre e* Francis Bonahon e* Charles C. Chouteau * Charles C. Sims e* Joseph S. Mamelak e e Michael M. Anshel e Joseph E. Bonin Paromita Chowla * John R. Smart Joseph F. Manogue e e Michael V. Anshelevich e* William M. Boothby Chris Christensen Keith Paul Smith e Stefano Marchiafava e* Peter H. Anspach e* Rupert D. Boswell Jr. e* William E. Christilles e* Thomas J. Marlowe Jr. e Louis Solomon * Stuart S. Antman e Djamel Bourbia e* Demetrios Christodoulou Michael J. Sormani e Wallace S. Martindale III e e* Myla M. Archer e* Aldridge K. Bousfield * Philip T. Church e* David B. Massey * Steven Robert Spencer Susumu Ariki e* Ward D. Bouwsma e* Kevin F. Clancey * Ivar Stakgold e* Jacob R. Matijevic e e* Thomas E. Armstrong Charles P. Boyer e* Alfred Clark Jr. Arthur P. Mattuck Robert L. Stanley * Robert L. Arnberg e* Mike Boyle e* Chester Dodge Clark Orestes N. Stavroudis Raymond A. Mayer Jr. e Jonathan W. Aronson e* John S. Bradley e Jeffrey W. Clark John R. Stock e Thomas L. McCoy e e Alfredo Arroyo e* Richard C. Bradley e* Jack D. Clayton e* Brockway & Audrey W. * Tina H. Straley Esperanza Blancaflor Arugay e* Louis R. Bragg e* Philip A. Cobb * Richard W. Sullivan McMillan e e Richard A. Askey e* Alberto Branciari e* Alan Cobham * William J. Sweeney e* Bruce E. Meserve e e Bernice L. Auslander e Fred Brauer e* John C. Cock * Margaret W. Taft – Matching e Richard C. Metzler e* Edward A. Azoff * George U. Brauer e John Coffey gift from Oracle Corp. * Ernest A. Michael e Sebastian Baader e Henry G. Bray e* James Wesley Cogdell * B. A. & M. Lynn Taylor David Middleton e Kiyoshi Baba John C. Breckenridge e* Amy Cohen * Jean E. Taylor e Stephen S. Miller e e Allen H. Back e Michael A. Breen e Donald L. Cohn Laurence R. Taylor e Stephen Ames Mitchell e e William G. Bade e Ralph J. Bremigan e Charles A. Cole * James G. Timourian e* Cathleen S. Morawetz e e* Richard J. Bagby e* Richard P. Brent e* George Cole Eugene Toll e* Larry J. Morley e Edward D. Baker e* James G. Bridgeman e* Vincent E. Coll Jr. Mary Powderly Tong e Joseph R. Morris e Joni E. Baker Robert C. Brigham * Frank F. Connor * Wolmer V. Vasconcelos e Robert A. Morris e e Kirby A. Baker * Judith E. Broadwin e Bruce N. Cooperstein Alfred G. Vassalotti e Burt J. Morse e* John T. Baldwin e Edgar H. Brown Jr. * Thomas A. Cootz * Ronald G. Mosier e John H. Walter * Joseph A. Ball * Kenneth S. Brown e* Arthur H. Copeland Jr. e Thomas W. Mullikin e* Evelyn K. Wantland Keith Ball e* Robert F. Brown e* Heinz O. Cordes * Frank W. Warner III e* Albert A. Mullin e William R. Ballard e Sharan Inez Brown e Steve A. Corning * William E. Warren John D. Nelligan e e* Carlo Bardaro e Andrew M. Bruckner * Thomas Carney Corrigan * Charles W. Neville e Alexander H. Weintraub Claude W. Bardos e Paulo Brumatti Chris Cosner e* Peter E. Ney e* Lloyd R. Welch * Julio Edgardo Barety e Jonathan W. Brundan e James P. Cossey e* Eugene D. Nichols Ellen Westheimer * Bruce H. Barnes e* Robert R. Bruner Ovidiu Costin e Jean-Louis Nicolas e* Kathleen B. Whitehead * Jose Barros-Neto e* Billy F. Bryant e* Malcolm A. Coulter * Roger A. & Sylvia M. Wiegand * Paul J. Nikolai e e Karl F. Barth e* Rebecca A. Buchanan e Marion Lonnie Cox * Ruth J. Williams & J. William e* Nobuo Nobusawa e* Philip R. Bartick e* Nicholas P. Buchdahl e* Petru Teodor Craciunas Helton * John W. Norris e* Alexander Barvinok e* Joseph T. Buckley e Jessica Marguerite Craig e Robert F. Olin e Heinz-Wolfgang Wissner Jürgen O. Batt e Richard S. Bucy e Bruce C. Crauder Donald S. & Shari Ornstein e* Christopher J. Wolfe J. Thomas Beale e Royce E. Buehler e* Thomas M. Creese * Scott A. Wolpert e Robert Osserman e e Homer F. Bechtell e* Ioan Sebastian Buhai e Ernest S. Croot III * Jay A. Wood e* Scott C. Otermat e* William A. Beck * J. P. Buhler e Dylan de la Cruz * Arthur Wouk e* Joseph W. Paciorek e David S. Becker e Pierre Victor Bulens * Donald L. Curlovic Hiram Paley e* Tsu C. Wu * William H. Beckmann * Daniel Willis Bump e* Philip C. Curtis Jr. e Nicholas Passell e* Tatsuhiko Yagasaki Eric D. Bedford e* Almut Burchard e Robert Turner Curtis * Masayuki Yamasaki e* Charles M. Patton e e* John A. Beekman * Krzysztof Burdzy e Raúl E. Curto

May 2008 Notices of the AMS 625 AMS Contributions

e Matthew W. Cushman e Edward R. Fadell e Rainer Göttfert e* Birge K. Huisgen- Tatsuo Kimura e Paolo Custodi e* Carl Faith e* Kevin A. Grasse Zimmermann Wilfred M. Kincaid Marius Dadarlat * George F. Feeman e* Larry K. Graves Paul D. Humke e Brendan King e John W. Dalida e Solomon Feferman e* Curtis Greene e* James E. Humphreys e* Donald R. King e David B. Damiano e Howard D. Fegan e* Frederick P. Greenleaf e* Karen C. Hunt e Walter W. Kirchherr e* James N. Damon e* Mark E. Feighn * Stanley J. Greif e* Paul M. Hunt e Alexander A. Kirillov Sr. e* Martin P. Dana e Paul Feit Joshua David Griffin Walker E. Hunt e* Ellen E. Kirkman e George Dassios e Edgar A. Feldman e Rostislav Ivanovich * Beryl E. Hunte e* Jan Kisyn´ski e* Boris A. Datskovsky e* Norman Feldman Grigorchuk e* Marcel Hupperich e Teruaki Kitano * Donald M. Davis Dominique Fellah * Helmut Groemer e James F. Hurley e* Peter H. Kleban e* Martin D. Davis e Helaman Ferguson e Kenneth I. Gross e* Michael G. Hurley e Peter Klein e* Paul L. Davis e* Ian M. Ferris e* Leonard Gross e Taqdir Husain e* Bruce A. Kleiner e* Anthony T. Dean e Victor G. Feser e* Robert Andrew Grossman e* Jang C. Hwang e Israel Kleiner e Stephen M. DeBacker e Gary A. Feuerbacher Gerd Grubb e* John Jew-Chen Hwang e Stanislav V. Klimenko e Henry F. Defrancesco Maurice C. Figueres e* Rosalind J. Guaraldo e* Tom Ilmanen e* Julia Knight e* Percy Alec Deift e* David V. Finch e* Victor W. Guillemin e Ettore Infante e Alan P. Knoerr e Frederik Michel Dekking e Benjamin Fine e Robert D. Gulliver II e* Hiroshi Inoue e* Marvin I. Knopp e* Aristide Deleanu e David L. Finn e Susan C. Gurney e* Arnold J. Insel e Finn Faye Knudsen e Filippo De Mari e William T. Fishback e Richard K. Guy * Ron Irving e Donald E. Knuth e* Ralph E. DeMarr e* Benji N. Fisher e Kwang Chul Ha e* Richard E. Isaac e Donald I. Knutson e Peter Der e* Uri Fixman e Seymour Haber * Noburo Ishii e Younhee Ko e* John E. Derwent e Mary Elizabeth Flahive e Melvin N. Hack Sahidul Islam * Richard M. Koch * Charles A. Desoer Peter H. Fleischmann e e e Petros Hadjicostas e Masanori Itai e* Yoshiharu Kohayakawa * Dennis DeTurck * Bernard A. Fleishman e Lee O. Hagglund e* Masami Ito Semen Koksal Emeric Deutsch Wendell H. Fleming e e e* Peter Hagis Jr. e* Noboru Ito e Alice K. Kolakowska Christopher Joseph * Julie A. Fondurulia e e John A. Haight * N. M. Ivochkina e R. J. Kolesar De Vaney * Paul Fong e e Mark Haiman e* Eric Robert Jablow e Ioannis Konstantinidis Raoul A. De Villiers e* Robert A. Fontenot e* Richard M. Hain * William Burkley Jacob e* Ralph D. Kopperman e Paul F. J. Dhooghe e Joseph David France e Andras Hajnal e* Robert E. Jaffa * Eric J. Kostelich e Anthony Diaco Theodore T. Frankel e Heini Halberstam e* David M. James e* Adnah G. Kostenbauder e Persi W. Diaconis e* Simon John Fraser e Alfred W. Hales e* Herbert Jarszick e P. Robert Kotiuga e Odo Diekmann e James H. Freeman e* Robert Joseph Halk e* Trevor M. Jarvis e Alexander N. Kozhevnikov Donna Dietz e* Peter J. Freyd e* Brian C. Hall e* Charles H. Jepsen e* Jurg Kramer e* Charles R. Diminnie e* Eugene M. Friedman e Wallace L. Hamilton e* David Jerison e* Raymond F. Kramer Jr. e Theresa K. Dodds e* Merwyn M. Friedman e* David Handel * Trygve Johnsen e Herbert C. Kranzer e Boro Doering e Béla András Frigyik e* Beverly Bailey Hargraves e Bradford W. Johnson e* Bernd Krauskopf e* Pierre E. Dolbeault e Daniel E. Frohardt e Andrew William Harrell e Charles N. Johnson e Rick Kreminski * Igor Dolgachev e* Bent Fuglede Bruno Harris Dale Martin Johnson e Alan M. Kriegsman Joanne M. Dombrowski e* Hisanori Fujita e Steven Guy Harris * David Lee Johnson e* Gary R. Krumpholz e* James P. Donaly e Masatoshi Fukushima e Edmund O. Harriss e* Donald G. Johnson e Arthur H. Kruse Robert S. Doran e William R. Fuller e Boris Hasselblatt e* Harold H. Johnson e Wei-Eihn Kuan e* Jay Robert Dorfman e John D. Fulton e* David R. Hayes e* Jon L. Johnson e Franz Viktor Kuhlmann e* Ronald G. Douglas e* Jeffry B. Fuqua e Bruno Heintz e* Kenneth David Johnson e* Robert P. Kurshan e Karl Heinz Dovermann e* Lisl Novak Gaal e* Leo Hellerman e* Theodore D. Johnson e John F. Kurtzke Jr. e Martin J. Dowd e* Steven Allen Gabriel e Simon Hellerstein e Eleanor Green Jones e* Ruishi Kuwabara e* Alex J. Dragt * Andrei Gabrielov e J. Leo van Hemmen e* William B. Jones e* Nosup Kwak e* Ronald Lewis Drake e* Marvin C. Gaer e* Francis McVey Henderson e Jacob C. Joosten Leong-Chuan Kwek Alexander N. Dranishnikov e Joseph A. Gallian e Carsten Hennig e* Virginia V. Jory Arnaud I. Lafonte e* Arthur A. Drisko e Jean H. Gallier e Douglas A. Hensley e Joseph Etienne Juarez * Jeffrey C. Lagarias e* Bruce K. Driver e Subramanian Ganesan * Christopher M. Herald * Thomas L. Drucker * Howard Garland e* Joaquim J. A. Judice e* Daniel Y. Lam e* Patricia Hersh Winfried Just * John Patrick Lambert Zbigniew C. Dudek e Adriano M. Garsia e e Stephen R. Hilbert Manjunath Prasad K * William A. Lampe e* Krishan Lal Duggal e Hillel Gauchman e e Shirley A. Hill * Jeffry N. Kahn Clifton A. Lando e* Steve N. Dulaney * Lloyd A. Gavin e e e * Peter J. Hilton Thomas Kailath * Peter S. Landweber e* William Dart Dunbar Jr. e Jean Raymond Genet e e e * Nancy Hingston Joji Kajiwara William E. Lang e* Loyal Durand e Ross Geoghegan e e e Thomas E. Hinrichs e* Kanat Durgun e* John C. Georgiou e e* Yûichirô Kakihara Leo J. Lange e* Patrick Barry Eberlein Hillel H. Gershenson e* F. E. P. Hirzebruch e Agnes M. Kalemaris e Carl E. Langenhop e* Allan L. Edmonds e* Murray Gerstenhaber e* Peter David Hislop e* Diana Kalish e Heinz Langer e* C. Henry Edwards e Abraham Gill * Chungwu Ho e N. J. Kalton e* David C. Lantz Robert D. Edwards e Richard M. Gillette * Harry Hochstadt e* Richard A. Kanner * Arnold Lapidus e* William I. Eggers e Jane P. Gilman e* Scott H. Hochwald e* Stanley Kaplan e* Michel L. Lapidus e Gertrude Ehrlich e* Maurice Eugene Gilmore e* Jonathan P. E. Hodgson e* Ioannis Karatzas e* Peter A. Lappan Jr. e* Stanley Mamour Einstein- e Anthony J. Giovannitti e* Helmut H. W. Hofer e* Martin Lewis Karel e Lawrence J. Lardy Matthews Vladimir Gisin e* Michael E. Hoffman e Johan Karlsson e Raphael Alexander Laufer e* Elmer Eisner e* Samuel Gitler e* Tom Høholdt Guido Karrer e* Lorraine D. Lavallee e Alexander S. Elder e* Earl C. Gladue * Harald R. A. Holmann e Victor J. Katz e* John W. Lawrence e* David Eliezer e Allen S. Gliniewicz * Charles S. Holmes e* Arthur Kaufman e Ruth Lawrence Jordan S. Ellenberg e* Raoul F. Gloden e* Philip John Holmes e Eric Roger Kaufmann e* H. Blaine Lawson Jr. e* Joanne Elliott e* Kazimierz A. Goebel e Raymond T. Hoobler e* Anthony J. Keeping e* Walter R. Lawson e Wade Ellis Jr. e Edray Herber Goins e* Jean MacGregor Horn e* Edward L. Keller e* Robert F. Lax * Richard S. Elman e David Goldberg e Jim E. Hoste e* Wayne G. Kellner * Robert K. Lazarsfeld e Rod Elsdon e* Samuel Goldberg e* James E. Householder John B. Kelly e* William G. Leavitt e Gérard G. Emch e* Seth I. Goldberg e Everett W. Howe e* John F. Kennison e George Ledin Jr. e* Thomas J. Emerson Dorian Goldfeld e Gary W. Howell e Alec Norton Kercheval e* John M. Lee e Jacob Engelhardt e* William Mark Goldman * J. S. Hsia Robert P. Kertz e* Kotik K. Lee e* Jessie Ann Engle e* Daniel A. Goldston e Pao-sheng Hsu e* Efim Khalimsky e Shawn P. Legrand e* Hans P. Engler e Martin Golubitsky e* Archibald Perrin Hudgins e* Dima Khavinson e* Gerald M. Leibowitz * Philip G. Engstrom e* José Luis Gómez Pardo e* Denise Huet * Michael K- H. Kiessling e Suzanne Marie Lenhart e Mats Engwall e* Kenneth R. Goodearl e Louie C. Huffman e* Jun Kigami e* James I. Lepowsky e Ahmet Eris e* Roe W. Goodman e Anne Hughes e Kazunori Kikuchi e* Steven C. Leth e* Kumar Eswaran e Carolyn S. Gordon e* Mark E. Huibregtse Chul Kim e* William J. LeVeque e* Leonard Evens * Yasuhiro Goto e Gustavus E. Huige e H-J Kimn e Edward L. Lever

626 Notices of the AMS Volume 55, Number 5 AMS Contributions

e Michael David Levy e David M. Merriell e* Mason S. Osborne e John H. Reinoehl e Ridgway Scott e* Andrew M. Lewis e* Marvin V. Mielke e Donal B. O’Shea e* Robert B. Reisel e* Warner Henry Harvey e* George M. Lewis Kentaro Mikami e* Steve G. Oslon e Michael Bela Revesz Scott III e* H. L. Lewis e* Ellen Rammelkamp Miller e* James M. Osterburg Francisco G. Reyes e Anthony Karel Seda e* Roger T. Lewis e Haynes R. Miller e James C. Owings Jr. e* Robert J. Reynolds e Annie Selden e* Frederick W. Leysieffer e Jack M. Miller e* Istvan Ozsvath e Bruce Reznick e John Selden Jaung Liang * Kenneth S. Miller e Judith A. Packer e* Martin G. Ribe e* George B. Seligman Richard Allan Libby e* Michael J. Miller e* Jingyal Pak e* Richard S. Rich e* Richard J. Shaker e Zvie Liberman e* Russell G. Miller e Fotios C. Paliogiannis Norman J. Richert e* Patrick Shanahan * Stephen Lichtenbaum e* Thomas Len Miller e* Diethard Ernst Pallaschke e* Eleanor G. Rieffel e* Priti Shankar e* Elliott H. Lieb e* William David Miller e John H. Palmieri e* Ronald Edgar Rietz Michael Shapiro II e Gary M. Lieberman e* Kenneth C. Millett e Taxiarchis Papakostas e Robert D. Rigdon * Henry Sharp Jr. e* Shen Lin * Milton A. Mintz e Otway O. M. Pardee e Timothy Rupert Riley e Ken Shaw e* Peter A. Linnell e* Norman D. Mirsky e* Kyoo-Hong Park e* Jose Rio Meir Shemesh e* Miriam A. Lipschutz-Yevick e* Michał Misiurewicz e* George D. Parker e* Joseph B. Roberts Zhongwei Shen e* Sally Irene Lipsey e* Guido Mislin e Thomas H. Parker e* Lois J. Roberts John C. Shepherdson e* Robert D. Little e* Theodore Mitchell e* Alberto Parmeggiani e Derek J. S. Robinson e Michael Sherbon e* Ming Chit Liu e William J. Mitchell e* Walter R. Parry e Tom Roby e* Kenichi Shiraiwa e Tsai-Sheng Liu e Lothrop Mittenthal e Bozenna Pasik-Duncan e Waldyr Alves Rodrigues Jr. e Vladimir Shpilrain e* George W. Lofquist e Hisao Mizumoto e* Henry J. Passerini e David W. Roeder e* Steven E. Shreve e* Terry M. Lohrenz e* Ismail J. Mohamed e* John J. Pastor e* David E. Rohrlich e Stanley R. Shubsda Jr. e* Walter L. Lok e Hugh L. Montgomery e* Leonid Pastur e* Judith Roitman e* David S. Shucker e* Charles J. Lombardo e Richard W. Montgomery e Donald A. Patterson e Dale P. O. Rolfsen e* Stuart J. Sidney * John M. Long e* Barbara B. Moore e Nicholas J. Patterson e* Josephine Jardin Romero e Martha J. Siegel e* William C. Lordan e* Hal G. Moore e* Walter M. Patterson III e Nicholas J. Rose e* Daniel S. Silver e Warren S. Loud e* Richard A. Moore e Lawrence E. Payne * Robert A. Rosenbaum Eugene Silvester e* Tsu-Ming Lu e Robert Laurens Moore Oscar Alfredo Paz la Torre e David Rosenberg e Patrick J. Sime e* Jonathan D. Lubin e* Alberto Cezar Moreira James M. Peek e* Jonathan M. Rosenberg Anne-Marie Simon e Thomas G. Lucas e Marc Moreno Maza e* Lambertus A. Peletier e* Gerald Rosenfeld e* Lloyd D. Simons Milan N. Lukic e* Frank Morgan e* Richard P. Pembroke e John Rosenknop e* Yakov G. Sinai e Norman Y. Luther * L. E. Morris e* John W. Pennisten e Haskell P. Rosenthal e Ajit Iqbal Singh e Thomas H. MacGregor e David R. Morrison * Alexander Perlin e Hugo Rossi e* Hardiv H. Situmeang e Moray S. Macphail * John A. Morrison e* Robert V. Perlis e Richard L. Roth e Man-Keung Siu e* Adolf Mader e John Morse e Sanford Perlman e* Christel Rotthaus e* Walter S. Sizer * Hironobu Maeda e* Joseph G. Moser * William L. Perry Cecil C. Rousseau e Bryan A. Smith * Mehran Mahdavi e Andrew P. Mullhaupt e* Justin R. Peters James Rovnyak e* Richard A. Smith e Kausik Kumar Majumdar e* Marvin G. Mundt Christopher S. Peterson e* Virginia G. Rovnyak e Wayne Stewart Smith e Yury Makarychev e James R. Munkres e Elmor L. Peterson e Emilio O. Roxin e* Wilbur L. Smith e Athena Makroglou e Jaime Muñoz Masqué e John W. Petro e James Samuel Royer * Joel A. Smoller e Joel Malard e R. Bradford Murphy e Carol K. Phillips-Bey * Wimberly C. Royster e William F. Smyth e* Peter Malcolmson * Takasi Nagahara e Mark A. Pierson e Daniel Ruberman * Siavash H. Sohrab e* Joseph Malkevitch e* Alexander Nagel e Jonathan Pila * Robert J. Rubin Alexander M. Soiguine e Salvador Malo e Hirotada Naito * Anand Pillay * Joachim H. Rubinstein * Emilio del Solar-Petit e* David M. Malon e* Kuniaki Nakamitsu e* Steven Pincus e Alexei N. Rudakov * David Robert Solomon J. J. Malone e* Kazumi Nakano e* Mark A. Pinsky Wolfgang M. Ruess e Boris Solomyak e Pauline Mann-Nachbar e Makoto Namba e Gilles Pisier e* Bernard Russo e Abdissa Tiruneh Sonka * Edward Manougian e Isaac Namioka Loren D. Pitt e* Alexander A. Rylov e* Linda R. Sons e* Margaret O. Marchand e John F. Nash Jr. e Thane Earl Plambeck e* Cihan K. Saclioglu John J. Sopka e* Eugene A. Margerum e* Joseph Neggers e Sergio Plaza e* Anthony Sacremento e* Birgit Speh * David E. Marker e* Csaba Nemethi * John C. Polking e* Takashi Sakai e* Dennis Spellman e* Charles Michel Marle e* Walter D. Neumann e* Harriet S. Pollatsek e Toshio Sakata e* Stephen E. Spielberg e* Murray Angus Marshall e* Lee P. Neuwirth John A. Poluikis e* Héctor N. Salas e Emily H. Sprague e Ricardo Carlos Martini Ronald C. Newbill * Narahari Umanath Prabhu Salim W. Salem e* Richard H. Squire Robert M. Mason e* Liviu I. Nicolaescu Nirmala Prakash e Luis C. Salinas e Anand Sridharan e* Ronald M. Mathsen e Lance W. Nielsen Stanley Preiser Thomas S. Salisbury Aravamuthan Srinivasan e Yasuo Matsushita e* Louis Nirenberg e Martin E. Price e Paul J. Sally Jr. e* Ram P. Srivastav e* Stephen B. Maurer e Togo Nishiura e* David S. Protas * Laurent Saloff-Coste e Olaf P. Stackelberg Charles N. Maxwell e Zbigniew H. Nitecki e* Józef H. Przytycki e Daniel Saltz e Ross E. Staffeldt e John P. Mayberry e* Virginia A. Noonburg e Loki Der Quaeler e Jose Luis Sanchez Palacio e* Friedemann W. Stallmann e Byron Leon McAllister Rutger Noot e Francis Quayson e Oscar Adolfo Sanchez- e William L. Stamey * Michael J. McAsey e Eric A. Nordgren e Michael F. Quinn Valenzuela e* Paul H. Stanford e Patricia Tulley McAuley e Phil Novinger e* Adbeel N. Quiñones e* Robert W. Sanders e* Lee James Stanley e John P. McCabe e James D. Nulton e* Cary Baker Rader * Angel San Miguel e* Richard P. Stanley e Jon McCammond e Kingsley Ifeanyi Nworah e* Louis B. Rall e* Donald E. Sarason e Michael Starbird Karen McConaghy e* Serge Ochanine e* Melapalayam S. Ramanujan e* Hiroki Sato e* Christopher W. Stark e Mark W. McConnell e* Mitsuyuki Ochiai e Arlan B. Ramsay e* Takakazu Satoh e* Jim Stasheff e Robert A. McCoy * Andrew M. Odlyzko * R. Michael Range e William G. Saunders e Arthur Steger e* Marjorie Frost McCracken e Hajimu Ogawa e* Salvatore Rao * Stanley A. Sawyer e Sherman K. Stein e O. Carruth McGehee e* Andrew P. Ogg e Louise Arakelian Raphael e Juan Jorge Schäffer e David L. Stenson e* William D. McIntosh * Yong-Geun Oh e Wayne Mark Raskind e* Doris W. Schattschneider * Ellen M. Stenson e* Thomas G. McKay e Jack E. Ohm e S. W. Rayment * Gideon Schechtman Kenneth Stephenson e Robert W. McKelvey e Haruto Ohta e Margaret A. Readdy & Richard e Ernest C. Schlesinger e Peter J. Sternberg e* Lionel W. McKenzie e Rika Okamoto Ehrenborg e Markus Schmidmeier e* Glenn H. Stevens e James P. McKeon Loren D. Olson e* Maxwell O. Reade e Thomas A. Schmidt e T. Christine Stevens e* T. G. McLaughlin e* Paul D. Olson * Douglas C. Reber Wolfgang M. Schmidt e* Paul K. Stockmeyer e* Robert F. McNaughton Jr. e Frank W. J. Olver e* Don Redmond e Bertram M. Schreiber e William G. Stokes e George Joseph McNinch e Peter J. Olver * Christopher L. Reedy * John Schue e* Lawrence D. Stone e* Robert C. McOwen e* Philip J. O’Neil e* David E. Reese * George W. Schueller e Philip D. Straffin e* John C. Meakin Barrett O’Neill e* Ernestine Reeves-Hicks e* Charles Freund Schwartz * Emil J. Straube e Alberto Medina * Yoshitsugu Oono e* Eugenio Regazzini * Gerald W. Schwarz e* Walter A. Strauss e* David Meier e Edward T. Ordman e Michael Reid e* Willi Schwarz e* Gerhard O. Strohmer e* José M. R. Méndez-Pérez e* Peter P. Orlik e William H. Reid e Berthold Schweizer e Daniel W. Stubbs e Bruce Mericle * Kent Orr e* Irma M. Reiner e* Peter Scott e* Garrett James Stuck

May 2008 Notices of the AMS 627 AMS Contributions The AMS * Matthew Erik Suhr * Edward C. Waymire * Cary H. Webb e* Kelly John Suman e David L. Webb e Kondagunta Sundaresan Patrick Suppes Glenn F. Webb Hans F. Weinberger Epsilon Fund e Andrew V. Sutherland e * Michael I. Weinstein e* Roman Sznajder e * David M. Wells e Earl J. Taft e Wolfgang L. Wendland for Young Scholars e* Kazuaki Taira e Greg Wene e* Lajos F. Takács e * John C. Wenger e Olukayode Talabi e * Henry C. Wente e* Hisao Tanaka e * Yoshihiro Tanaka e Elisabeth M. Werner * John E. Wetzel e* Daniel Louis Tancreto e Brian Cabell White e Elliot A. Tanis e Neil L. White e S. James Taylor e Andrew P. Whitman e Yoshihiko Tazawa e Kenneth G. Whyburn e Zachariah C. Teitler e Volker Wihstutz e* Paul M. Terwilliger * John F. Wilkinson e* Francisco Javier Thayer e Susan Gayle Williams e Edward C. Thoele e * Charles K. Williamson e* Lawrence E. Thomas e Richard E. Williamson e Peter J. Thomas * Robert Lee Wilson e Robert J. Thompson * Eric J. Wingler e John A. Thorpe Richard A. Winton e* Edward G. Thurber * F. Wintrobe e Christophe Tollu e * Daniel B. J. Tomiuk e Izaak Wirszup Bettina Wiskott e Andre Toom e * Craig A. Tracy e Edward Witten Louis Witten e* Charles R. Traina e Andrejs E. Treibergs * James J. Woeppel Katherine L. Willingham e* Selden Y. Trimble V e Woerner e Valerii Vladimirovich Trofimov * Stephen D. Wolthusen Sung-Sik Woo e Gerard Tronel Japheth L. M. Wood e Kazô Tsuji e HelpHelp bringbring THETHE WORLDWORLD * George V. Woodrow III e Yasuyuki Tsukui e Bostwick F. Wyman e* Johan Tysk e * Zhen Xiang Xiong ofof mathematicsmathematics e Douglas L. Ulmer e Yasuko Yamazaki e* Tomio Umeda e * Michael Ungs e* Michael Yanowitch intointo thethe liveslives ofof youngyoung people.people. * Fawzi M. Yaqub e Harald Upmeier e * Suresh Yegnashankaran e* John A. W. Upton e * J. Michael Yohe e Shukhrat M. Usmanov e Hisashi Yokota e Colleen A. Vachuska e Génjí Yóshínó e Stephen Vági e * Donald F. Young e* Juan Luis Valle e Whether they become scientists, engineers, or Johannes A. Van Casteren e Roy Young Vadim Yurinsky e Charles L. Vanden Eynden e entrepreneurs, young people with mathematical Anatoly M. Vershik e* Radu Zaharopol * Jean-Claude Zambrini talent need to be nurtured. Income from this e James A. G. Vickers e Charles I. Vinsonhaler e* François Zara * Thomas Zaslavsky fund supports the Young Scholars Program, which e* Michael Voichick e Jose Zero e* Dan-Virgil Voiculescu e provides grants to summer programs for talented high Paul S. Voigt e* David E. Zitarelli Paul Zorn e* Paul A. Vojta school students. * Steven M. Zucker e* Hans W. Volkmer e * John A. Zweibel e* Philip D. Wagreich e Paul J. Zwier e* Jonathan M. Wahl e Anonymous (295) . e Sebastian Walcher Please give generously e* David B. Wales e Homer F. Walker Learn about giving opportunities and estate planning e* Justin Clement Walker www.ams.org/giving-to-ams e* William Wallace e* John Thomas Walsh e Hans Ulrich Walther Contact the AMS Development e Jay R. Walton Office 1.800.321.4267 * Seth L. Warner (U.S. and Canada) or e* Bette L. Warren Arthur G. Wasserman 1.401.455.4000 e* Robert H. Wasserman (worldwide) e* Shôji Watanabe email: [email protected] * William C. Waterhouse 09/04 e* Mark E. Watkins

628 Notices of the AMS Volume 55 Number 5 From the AMS Secretary

Officers of the Society 2007 and 2008 Updates

Except for the members at large of Members at Large Publications Committees the Council, the month and year of All terms are for three years and Bulletin Editorial Committee the first term and the end of the pres- expire on January 31 following the Susan J. Friedlander 7/05–1/12 ent term are given. For members at year given. Colloquium Editorial Committee large of the Council, the last year of 2007 Paul J. Sally Jr. 2/05–1/12 the present term is listed. Sara Billey Journal of the AMS Editorial Carolyn S. Gordon Committee Council Sheldon H. Katz Robert K. Lazarsfeld 2/07–1/10 President Michael F. Singer James G. Glimm 2/07–1/09 Catherine H. Yan Mathematical Reviews Editorial Committee President elect 2008 Jonathan I. Hall 2/06–1/09 George E. Andrews 2/08–1/09 William M. Goldman Mathematical Surveys and Immediate Past President Craig L. Huneke Monographs Editorial Committee James G. Arthur 2/07–1/08 Judy Anita Kennedy J. Tobias Stafford 2/05–1/09 Vice Presidents Ken Ono Judy L. Walker Mathematics of Computation Haïm Brezis 2/05–1/08 Editorial Committee 2009 Robert L. Bryant 2/07–1/10 Chi-Wang Shu 2/02–1/12 Ruth M. Charney 2/06–1/09 Robert L. Devaney Proceedings Editorial Committee Bernd Sturmfels 2/08–1/11 Frank S. Quinn Ronald Fintushel 2/06–1/10 Secretary Katherine St. John Transactions and Memoirs Editorial Robert J. Daverman 2/99–1/09 Marjorie Senechal Francis Edward Su Committee Associate Secretaries Robert Guralnick 2/05–1/09 Susan J. Friedlander 2/96–1/10 2010 Michel L. Lapidus 2/02–1/10 Rebecca F. Goldin Board of Trustees Bryna Kra Matthew Miller 2/05–1/09 John B. Conway 2/01–1/11 Lesley M. Sibner 2/93–1/09 Irena Peeva Joseph H. Silverman John M. Franks (ex officio) 2/99–1/09 Treasurer Sarah J. Witherspoon Eric M. Friedlander 2/00–1/10 John M. Franks 2/99–1/09 James G. Glimm (ex officio) 2/07–1/09 Associate Treasurer Members of Executive Linda Keen 2/99–1/09 Donald E. McClure 2/03–1/09 Committee Donald E. McClure (ex officio) 2/03– 1/09 Members of the Council, as provided Jean E. Taylor 2/03–1/08 for in Article 7, Section 4 (last sen- Karen Vogtmann 2/08–1/13 tence), of the Bylaws of the Society. Carol S. Wood 2/02–1/12 Sylvain Cappell 2/06–1/10 Ruth M. Charney 2/07–1/11 Robert Guralnick 2/05–1/09 Craig L. Huneke 2/08–1/12 Paul J. Sally Jr. 2/04–1/08

May 2008 Notices of the AMS 629 Mathematics Calendar

Please submit conference information for the Mathematics Calendar through the Mathematics Calendar submission form at http://www.ams.org/cgi-bin/mathcal-submit.pl. The most comprehensive and up-to-date Mathematics Calendar information is available on the AMS website at http://www.ams.org/mathcal/.

May 2008 * 8–10 International Conference on Inverse Scattering Problems Honoring David Colton and Rainer Kress, Sestri Levante, Genova, * 2–5 The 46th Cornell Topology Festival,CornellUniversity,Ithaca, Italy. New York. Description Description: This year’s festival includes a concentration of talks in : The organization of this conference is in recognition symplectic topology and geometry. There will be two introductory of the international leadership and outstanding scientific achieve- workshops and a panel discussion. ments of David Colton and Rainer Kress in the area of inverse Information: Financial support is available. Young researchers scattering problems. This event is open to participants interested are especially encouraged to apply. For registration and further in inverse scattering problems and applications. Information details see the festival web page: http://www.math.cornell.edu/ :email:[email protected]; http://www-rocq. ~festival/;email:[email protected]; inria.fr/~haddar/ckconf/.

* 5–14 The Sixth Annual Spring Institute on Noncommutative * 19–23 6th Seminar on Stochastic Analysis, Random Fields and GeometryandOperatorAlgebras,VanderbiltUniversity,Nashville, Applications, Centro Stefano Franscini, Ascona, Switzerland. Tennessee. Topics: Stochastics and climatology; stochastic partial differential Description: The Sixth Annual Spring Institute on Noncommutative equations; random fields; stochastic analysis and finance; energy, GeometryandOperatorAlgebrasisaspringschoolandinternational climate and finance. conference. Several mini-courses on a variety of topics from Among the speakers: R. Carmona (Princeton), J. Duan (Illinois), D. noncommutative geometry, operator algebras and related areas Filipovic (Munich),H.Geman(ESSECand London),P.Imkeller (Berlin), will be given by leading experts. A. Kyprianou (Bath), A. J. Majda (New York), B. Maslowski (Prague), Topic: The topic of this year’s conference/school is KK-Theory J. C. Mattingly (Duke), S. Sircar (Princeton), A. N. Shiryaev (Moscow), of Operator Algebras and Noncommutative Geometry. Students A. Stuart (Warwick), J. Worner¨ (Gottingen),¨ Y. Xiao (Michigan). and postdocs are especially encouraged to attend. Mini-courses by: Information:email:[email protected]; http://www.math. Alain Connes, Nigel Higson, Ralf Meyer, Mikael Rordam, Georges univ-paris13.fr/~russo/ASCONA08/Ascona08.html. Skandalis and other. Organizers; Dietmar Bisch, Alain Connes (Director of the Sixth Annual Spring Institute), Bruce Hughes, * 21–24 Sixth Annual Workshop on Combinatorial and Additive Gennadi Kasparov and Guoliang Yu (all at Vanderbilt University). Number Theory (CANT 2008), CUNY Graduate Center, 365 Fifth Information:[email protected];http://www.math. Avenue, New York, New York vanderbilt.edu/~ncgoa08/. Description: This is the sixth in a series of annual workshops

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 [email protected] to specialized topics, as well as announcements of regularly scheduled or [email protected]. 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 Notices prior to An announcement will be published in the Notices if it contains a call the meeting in question. To achieve this, listings should be received in for papers and specifies the place, date, subject (when applicable), and Providence eight months prior to the scheduled date of the meeting. the speakers; a second announcement will be published only if there The complete listing of the Mathematics Calendar will be published are changes 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://www. information. In any case, if there is any application deadline with ams.org/.

630 NOTICES OF THE AMS VOLUME 55, NUMBER 5 Mathematics Calendar

sponsored by the New York Number Theory Seminar on problems students, Ph.D.-students, postdocs and other people interested in in combinatorial and additive number theory and related parts of this field. mathematics. Program information will be posted on the conference Participation and Funding: Participation is free. We are trying website: http://www.NewYorkNumberTheory.com. Mathematicians to obtain funds for limited travel support for participants from who wish to speak at the meeting should submit a title and abstract outside the Netherlands. by email to: [email protected] Information:email:[email protected]; http://www. that there will be some financial support, especially for graduate math.leidenuniv.nl/~mdejeu/NoncomIntWeek_2008. students and young faculty. For more information please contact [email protected]. * 9–20 Symmetry and Integrability of Difference Equations,Uni- Information: http://www.NewYorkNumberTheory.com. versit´edeMontr´eal, Qu´ebec, Canada. Description: The field of symmetries and integrability of difference * 26–31 Stochastic Phenomena, Babes-Bolyai University, Cluj- equations is a very dynamical one in which great progress has Napoca, Romania. been made over the last 15 years or so. The key methods that have Description: The Second Transylvanian Summer School and Work- been developed in this area are based either on the inverse spectral shop proposes to offer a discussion and meeting platform for approach or on the application of geometric and group theoretical researchers from various fields of sciences interested in the techniques. complex interdisciplinary field of stochastic phenomena. We are Topics: Specifically the topics to be covered are the following: expecting scientists and students from the fields of mathematics, (1) Discrete integrable and isomonodromic systems; (2) Discrete physics, informatics, biology, chemistry, electric engineering, soci- Painlev´e equations; (3) Singularity confinement, algebraicentropy ology, geography and economics, working in problems that would and Nevanlinna theory ; (4) Discrete differential geometry; (5) Special fit the general theme of the conference. functions as solutions of difference or q-difference equations; (6) Information:email:[email protected]; Integrability, symmetry and numerical methods; (7) Lie symmetries http://summerschools.ro. of difference systems; (8) Integrable chains. The most relevant applications of this field of scientific activity are to coding theory, June 2008 image reconstruction and processing and visual tracking, starting from discrete and usually sparse data. * 8–14 Reconnect Conference 2008, DyDAn Center, Rutgers Uni- Information:email:[email protected]; http://www. versity, Piscataway, New Jersey. dms.umontreal.ca/~sms/. Description: About the Reconnect Conference: The DyDAn Summer ReconnectConferenceswillexposefacultyteachingundergraduates * 14–28 International Summer School on Modelling and Optimiza- to the role of the mathematical sciences in homeland security by tion in Micro- and Nano-Electronics - MOMINE’08,Conference introducing them to a current research topic that will be relevant Centre Baia Samuele, Ragusa, Sicily, Italy. for classroom presentation. The conferences also offer researchers Descripion: Modelling week: Advanced Modelling Methods for the in government or industry the opportunity to learn about recent Design of Electronic Circuits and Devices, June 14–21, 2008. Opti- techniques in emerging application areas relevant to homeland mization Week: Advanced Optimization Methods and Algorithms security. Topics will be presented in a week-long series of lectures for the Design of Electronic Circuits and Devices June 21-28, 2008. and activities led by an expert in the field. Participants will be There will be several seminars complementing the topics treated involved in both research activities and in writing materials useful in in the course. the classroom or to share with their colleagues, with the possibility Deadline for Early Registration: March 31, 2008. of ultimately preparing these materials for publication in either Information: For any questions please send email to momine08@ our Technical Report or our Educational Modules Series. dmi.unict.it; http://www.dmi.unict.it/~momine08/. Speaker: Nina Fefferman, Rutgers University, feferman@Math. * 15–22 ESF-MSHE-PAN Conference on Operator Theory, Analysis Princeton.EDU. and Mathematical Physics, Mathematical Research and Conference Organizer:FredS.Roberts,RutgersUniversity(froberts@dimacs. Center, Bˆedlewo, Poland. rutgers.edu). Description: First Call for Applications: ESF Conference, in part- Registration Fees: Academic participants: Lodging and meals will nership with MSHE and the Institute of Mathematics on operator be provided through DHS funding. Limited funds are expected theory, analysis and mathematical physics. to be available for travel awards. There are no registration fees. Scope: Random and quasi-periodic differential operators, orthogo- Applicants from government and for-profit corporations are asked nal polynomials, Jacobi and CMV matrices, and quantum graphs. In to provide their own travel and lodging, plus registration fees∗ particular spectral properties of operators from various domains (that cover all meals from Sunday dinner to Saturday lunch) as of mathematical physics. follows: Chairs: Jan Janas, Polish Academy of Sciences; Pavel Kurasov, Lund ◦ ◦ GovernmentLabparticipants:$350. Corporateparticipants: Institute of Technology; Ari Laptev, Royal Institute of Technology; $500. ∗ Serguei Naboko, St. Petersburg State University. Funds may be available to waive part or all of the registration Deadline: Closing date for applications and abstract submission: fee and/or partially support travel and lodging. Who May Apply? March 30, 2008. Anyone may apply. Information: Application: Scientific programme and application Application Deadline: Extended to March 3, 2008. form are accessible on-line through http://www.esf.org/ Information:http://dydan.rutgers.edu/Education/reconnect/ conferences/08279.Forfurtherinformationcontact:AnneBlondeel- 2008/. Or, contact the Reconnect Program Coordinator, at Oman [email protected]; tel: (732) 445-4304. ( [email protected]).

* 9–13 Educational Week on Noncommutative Integration,Leiden * 16–20 15th Conference of the International Linear Algebra University, Leiden, Netherlands. Society, Westin Resort and Spa, Cancun, Mexico. Description: During this educational week the main lecturers Description: The conference deals with all themes related to Linear Fyodor Sukochev (Flinders University, Adelaide) and Ben de Pagter Algebra; theory, applications, numerical aspects, and education. (TU Delft) will cover several aspects of noncommutative integration The program includes 14 plenary talks, 8 mini-symposia, and associated with von Neumann algebras, as well as some applications contributed talks. The conference proceedings will appear as a of this theory. The intended audience consists of advanced master special issue of Linear Algebra and its Applications.

MAY 2008 NOTICES OF THE AMS 631 Mathematics Calendar

Information:email:[email protected]; http://star.izt. Description: We invite draft paper submissions. uam.mx/ILAS08. Deadline: The deadline for submissions: February 19, 2008. Information: The conference will be held at the same time and * 23–27 Differential Equations and Applications to Mathematical place where several other major events are taking place. The web- Biology, Le Havre, France. site contains more details: http://www.promoteresearch.org/; Goal: The goal of this meeting is to bring together international ex- email: [email protected]. perts working either on theoretical aspects of differential equations or on applications to mathematical biology. * 7–10 International Conference on Bioinformatics, Computa- Scientific Committee: Henri Berestycki (EHESS, France), Shui-Nee tional Biology, Genomics and Chemoinformatics (BCBGC-08), Chow (Georgia Tech, USA), Norman Dancer (University of Sydney, Orlando, Florida. Australia), Karl Hadeler (University of Tuebingen, Germany), Vitaly Description: We invite draft paper submissions. Volpert (University of Lyon 1, France), Hans-Otto Walther (University Deadline: The deadline for submissions: February 19, 2008. of Giessen, Germany). Information: The conference will be held at the same time and Plenary Speakers: Danielle Hilhorst, University of Orsay, France; place where several other major events are taking place. The web- Kening Lu, Brigham Young University, USA; Peter Polacik, Uni- site contains more details: http://www.promoteresearch.org/; versity of Minnesota, USA; Genevieve Raugel, University of Orsay, email: [email protected]. France; Yasuhiro Takeuchi, Shizuoka University, Japan; Glenn Webb, Vanderbilt University, USA; Gail Wolkowicz, McMaster University, * 7–10 International Conference on Enterprise Information Sys- Canada; Jianhong Wu, York University, Canada; Dongmei Xiao, tems and Web Technologies (EISWT-08), Orlando, Florida. Shanghai Jiaotong University, China;YingfeiYi,GeorgiaTech,USA. Description: We invite draft paper submissions. Organizing Committee: Pierre Magal, pierre.magal@univ- Deadline: The deadline for submissions: February 19, 2008. ehavre.fr; Shigui Ruan, [email protected]; Huaiping Zhu, Information: The conference will be held at the same time and place [email protected]. where several other major events are taking place. The website Information: Further information about the conference can be contains more details: http://www.promoteresearch.org/;email: found at http://litis.univ-lehavre.fr/MathBioConf/. [email protected].

* 24–26 Current Geometry, the IX Edition of the International * 7–10 International Conference on High Performance Computing, Conference on problems and trends of contemporary geometry, Networking and Communication Systems (HPCNCS-08), Orlando, Hotel Oriente, Via Luigi Serio 10, 80069 Vico Equense, Naples, Italy. Florida. Description: The power of synthesis of Geometry, which led in Description: We invite draft paper submissions. the past to the formulation of “grand unification theories”, has Deadline: The deadline for submissions: February 19, 2008. got an essential role nowadays, especially because of the growing Information: The conference will be held at the same time and place fragmentation of knowledge due to scientific progress. In order to where several other major events are taking place. The website avoid too a big dispersion, geometers need a constant dialogue. contains more details: http://www.promoteresearch.org/;email: Therefore, a stable experience of personal meetings, apart from [email protected]. telematic interchanges, cannot be renounced. Current Geometry International Conference on Software Engineering Theory was born to allow a periodic update about actual progresses in * 7–10 and Practice (SETP-08) Geometry (and its applications) on the international scene. , Orlando, Florida. Description Information:email:[email protected];http://school.diffiety. : We invite draft paper submissions. Deadline org/page82/page82.html. : The deadline for submissions: February 19, 2008. Information: The conference will be held at the same time and place * 30–July 5 International Conference in Algebraic Geometry,IMAR where several other major events are taking place. The website Bucharest, Romania. contains more details: http://www.promoteresearch.org/;email: Invited Speakers: I. Bauer (Bayreuth), L. Badescu (Genova), A. [email protected]. Caldararu (Madison-Wisconsin), F. Catanese (Bayreuth), C. Ciliberto International Conference on Theoretical and Mathematical (Rome), A. Dimca (Nice), J.-M. Drezet (Paris), G. Farkas (Berlin), * 7–10 Foundations of Computer Science (TMFCS-08) H. Flenner (Bochum), K. Hulek (Hannover), H. Lange (Erlangen), , Orlando, Florida. Description A. Lanteri (Milan), M. Lehn (Mainz), L. Maxim (New York), M. : We invite draft paper submissions. Deadline Mella (Ferarra), M. Mustata (Ann Arbor), G. Ottaviani (Florence), : The deadline for submissions: February 19, 2008. Information S. Papadima (Bucharest), G. Pareschi (Rome), M. Popa (Chicago), : The conference will be held at the same time and place K. Ranestad (Oslo), F. Russo (Recife-Pernambuco), F.-O. Schreyer where several other major events are taking place. The website (Saarbruecken), G. Trautmann (Kaiserslautern), C. Voisin (Paris). contains more details: http://www.promoteresearch.org/;email: Organizing Committee: C. Anghel (IMAR), M. Aprodu (IMAR), V. [email protected]. Brinzanescu (IMAR), N. Manolache (IMAR). * 7–10 The Tenth International Conference on Integral Methods Information:email:[email protected]; http://www.imar. in Science and Engineering, University of Cantabria, Santander, ro/%7Eaprodu/ag2008/ag2008.html. Spain. Description July 2008 : The IMSE conferences offer opportunities to scien- tists from around the world to present their most recent work and * 7–10 International Conference on Artificial Intelligence and exchange ideas on a powerful class of methodologies extensively Pattern Recognition (AIPR-08), Orlando, Florida. used for solving mathematical models of physical phenomena and Description: We invite draft paper submissions. processes. Participation is open to all scientists and engineers Deadline: The deadline for submissions: February 19, 2008. whose work makes use of analytic and numerical methods, integral Information: The conference will be held at the same time and equations, ordinary and partial differential equations, asymptotic place where several other major events are taking place. The web- and perturbation methods, boundary integral techniques, conser- site contains more details: http://www.promoteresearch.org/; vation laws, hybrid approaches, vortex methods, signal processing email: [email protected]. and image analysis. Aim: To promote new research tools and procedures that help * 7–10 International Conference on Automation, Robotics and link mathematics, applied sciences and technology. As the tenth Control Systems (ARCS-08), Orlando, Florida. in a successful series of conferences, IMSE2008 will provide an

632 NOTICES OF THE AMS VOLUME 55, NUMBER 5 Mathematics Calendar

international forum for communicating recent advances and an * 18–20 International Conference on Power Control and Opti- opportunity for direct information exchange between delegates mization, Chiang Mai Plaza Hotel, 92 Sridonchai Road, Chiang Mai from both academia and industry. 50100, Thailand. Information:email:[email protected]; http://www.imse08. Description: It is our great pleasure to announce the first event of unican.es. the International Conference on Power Control and Optimization (PCO-08) organized by Department of Electrical Engineering, Chiang * 7–11 International Conference on Vertex Operator Algebras Mai University, Thailand and Curtin University of Technology, and Related Areas on the occasion of Geoffrey Mason 60th’s Malaysia. The vision of PCO-08 is to bring today’s highly inspiring Birthday, Department of Mathematics, Illinois State University, and precision innovative research and resource development for Normal, Illinois. tomorrow’s industry in power and control. It has the mission to Aim: To present some of the new developments in vertex operator highlight innovative research and development of academics and algebras and related areas. The main aspects of this conference industrial experts in the area of power control and its optimization are connections and interactions of vertex operator algebras with techniques, and to provide a forum to disseminate the results to all physics, Hopf algebras, Infinite dimensional Lie algebras, group industrial sectors in power quality, automation, business, finance, theory and number theory. A major part of the conference will focus economics and management. The main objective of PCO-08 is to onbringingleaders inthefields together withstudents,postdoctoral provide a platform for researchers, engineers, practitioners and fellows and young academics in a stimulating, engaging and academicians as well as industrial professionals to present their mentoring environment. This conference will provide opportunities research results and development activities. for mathematicians and physicists in the areas to discuss the Information: Contacts: Nader Barsoum and Pandian M. Vas- recent developments in the fields and the direction of future ant; email: [email protected] and [email protected]; tel: 601 research. Graduate students and young researchers will gain better 6354154 & 6085443821. For further information, please visit: http: perspectives of what is going on and what the important problems //www.engedu2.net.; are in these areas. email: [email protected];. Organizers: Gaywalee Yamskulna(ISU), Maarten Bergvelt (UIUC), Wenhua Zhao (ISU). * 21–23 19th Postgraduate Combinatorial Conference,Centrefor Deadline: June 1, 2008. Discrete Mathematics and its Applications (DIMAP), University of Information: http://www.math.ilstu.edu/voa. Warwick, Coventry, CV4 7AL, United Kingdom. Description: The Postgraduate Combinatorial Conference is aimed * 10–11 Symposium in honor of Kiyosi Ito:ˆ Stochastic Analysis and at research students in all areas of combinatorics and discrete Its impact in Mathematics and Science, Institute for Mathematical mathematics who are currently working on their Ph.D. Sciences, National University of Singapore, Singapore. Organizer: The conference is organized under the auspices of Description: The objective of the symposium is to gather together the British Combinatorial Committee and the Centre for Discrete leading mathematicians and scientists to deliver expository lectures Mathematics and its Applications (DIMAP). on Itoˆ’s work and the historical development of stochastic analysis, Sponsors: Include the London Mathematical Society and the Open and their influence and impact in various branches of mathematics University. and science. It will be aimed at specialists as well as mathematicians Information: http://go.warwick.ac.uk/pcc2008; and scientists in general. email: [email protected]. Organizers: Jointly organized with Research Institute for Mathe- Summer Course on Multiscale Modeling and Anal- matical Sciences, Kyoto. * 21–August 8 ysis, University of Texas at Austin, Austin, Texas. Organizing Committee:Co-ChairsHansFollmer¨ (Humboldt- Description: This is a three-week program on multiscale modeling University of Berlin), Masatoshi Fukushima (Osaka University); and analysis for advanced undergraduate and 1st year graduate Members Edwin Perkins (University of British Columbia), Yoichiro students. This program will contain 5-6 short courses, each consist- Takahashi (Research Institute for Mathematical Sciences, Kyoto). ing of 4-6 one-hour lectures. The lectures will be complemented by Partial List of Invited Speakers: Alain Bensoussan, University of problem sessions in the afternoons conducted by senior graduate Texas at Dallas; Donald Dawson, Carleton University; Masatoshi students. The prerequisites of the course are advanced calculus Fukushima, Osaka University; Shigeo Kusuoka, University of Tokyo; and linear algebra. Some familiarity with numerical analysis and Pierre-Louis Lions, Coll`ege de France; Terry Lyons, University of computer programming will be helpful. Oxford; Shinzo Watanabe, Kyoto University; Marc Yor, Universit´e Information:email:[email protected]; http://www.math. Paris VI. utexas.edu/rtg/course.html. Information:email:[email protected]; http://www.ims.nus. edu.sg/Programs/kiyosi08/index.htm. * 28–September 21 Mathematical Horizons for Quantum Physics, Institute for Mathematical Sciences, National University of Singa- * 17–August 1 XI Edition of the Italian Diffiety School,Santo pore, SIngapore. Stefano del Sole (Avellino), Italy. Description: The Programme will consist of four overlapping Description : The aim of this permanent school is to introduce three-week sessions, each devoted to a selected topic. undergraduate and Ph.D. students in Mathematics and Physics, OrganizingCommittee:Co-chairs:BertholdGeorgEnglert(National as well as post-doctoral researchers, in a recently emerged area UniversityofSingapore),KwekLeongChuan(NanyangTechnological of Mathematics and Theoretical Physics: Secondary Calculus. A University). Secretary: Junuzuki (National University of Singapore). Diffiety is a new geometrical object that properly formalizes the Overall Programme Coordinator: Huzihiro Araki (University of concept of the solution space of a given system of nonlinear PDEs, Kyoto). much as an algebraic variety does with respect to solutions of a Information:email:[email protected]; http://www.ims.nus. given system of algebraic equations. Secondary Calculus is a natural edu.sg/Programs/mhqp08/index.htm. diffiety analogue of the standard calculus on smooth manifolds, and as such leads to a very rich general theory of nonlinear PDEs. August 2008 Moreover, it appears to be the unique natural language for quantum physics, just as the standard calculus is the natural language for * 1–3 Jairo Charris Seminar in Algebra and Analysis 2008: SJCH classical physics. 2008, Universidad Sergio Arboleda, Bogot´a, Colombia. Information: http://school.diffiety.org/page3/page0/ Description: This seminar is dedicated to Jairo Antonio Charris page64/page64.html;email: [email protected]. Castaneda˜ (in memoriam) and in this occasion is devoted to

MAY 2008 NOTICES OF THE AMS 633 Mathematics Calendar

orthogonal polynomials, complex variables and their applications, * 2–4 2008 MBI Workshop for Young Researchers in Mathematical emphasizing his scientific legacy. Biology (WYRMB), Mathematical Biosciences Institute, The Ohio Information:email:[email protected]; http://www- State University, Columbus, Ohio. ma2.upc.edu/primi/sjch2008.htm. Description: The workshop is intended to broaden the scientific perspective of young researchers in mathematical biology and to * 14–19 International Conference on Complex Analysis and Re- encourage interactions with other scientists. Workshop activities lated Topics (The XIth Romanian-Finnish Seminar),Universityof include plenary talks and poster sessions, as well as group Alba Iulia, Romania. discussions on issues relevant to mathematical biologists. We Topics: The following sections will be included: 1. Analytic functions cordially invite young mathematical biologists to participate. of one complex variable; 1A. Univalence, 1B. Other subjects; 2. Application deadline: April 17, 2008. Quasiconformal mappings and Teichmuller spaces; 3. Several Information: http://www.mbi.ohio-state.edu/ complex variables; 4. Potential theory; 5. Functional analytical postdocworkshop/wyrmb2008.html;email: [email protected]. methods in complex analysis. Calculus of Variations and Its Applications From Engi- Description: The organizers are the Institute of Mathematics * 8–10 neering to Economy “Simion Stoilow” of the Romanian Academy; University of Alba , Departamento de Matem´atica Faculdade Iulia; University of Pitesti; University of Bucharest; and the Faculty de Ciˆencias e Tecnologia, Universidade Nova de Lisboa Caparica, of Mathematics and Informatics of the “Babes-Bolyai” University Portugal. Description of Cluj-Napoca, in cooperation with the Universities of Helsinki, : The aim of this event is to promote the scientific Joensuu, and Jyvaskyla from Finland. exchange of ideas and methods in such a broad and useful area as Information:http://www.imar.ro/~purice/conferences/index. the calculus of variations. With the goal of applications to differ- html;email:[email protected]. ent areas such as mathematics, mechanics, engineering, economy, finances, chemistry, biology, just to name a few, models and meth- * 24–27 39th Annual Iranian Mathematics Conference (AIMC39), ods have been developed, with apparent different languages that Department of Mathematics, Shahid Bahonr University of Kerman, are susceptible of an unified analytical and numerical treatment. Kerman, Iran. Taking into account the most recent developments in this area of Description: The 39th AIMC will be held at Shahid Bahonar Univer- mathematics, we wish to address problems associated with partial sity of Kerman Under the auspices of Iranian Mathematical Society differential equations, optimal control, finite or infinite dimen- in Kerman (a beautiful and historical city), during 24-27 August, sion optimization, shape optimization in structural engineering, 2008. This conference includes invited speakers and presentations together with the associated computational aspects. Information of submitted research papers. All areas listed on the cover of :email:[email protected]; http://ferrari.dmat.fct. Mathematical Reviews, are partitioned in 12 branches by the sci- unl.pt/cva2008/. entific committee for grouping presentations as follows: Algebra, * 13 63rd Algebra Day, Carleton University, Ottawa, Canada. Analysis, Combinatorics and Graph Theory, Computer Sciences Speakers: Osamu Iyama (Nagoya), Bernhard Keller (Paris), Claus and Logic, Control theory and Optimization, Differential Equation Michael Ringel (Bielefeld), Paul Smith (Washington). and Dynamical Systems, Fuzzy Mathematics, Geometry and Topol- Information: [email protected], bsteinbg@math. ogy, Mathematical Education, Numerical Analysis, Probability and carleton.caor [email protected]. Statistics, and other areas of mathematics not listed above. Information :email:[email protected]; http://www. * 15–21 Ninth Crimean Workshop on the Method of Lyapunov aimc39.ir/. Functions and Its Applications,Alushta,Crimea,Ukraine. Description: The conference is dedicated to 70th anniversary of * 31–September 6 Summer School on General Algebra and Ordered Academician A. M. Samoilenko. Sets,Trest,CzechRepublic. Focus: The workshop will bring together researchers in the theory Description : The summer school focuses on recent trends in uni- of stability and related fields of pure and applied mathematics, in versal algebra, especially in connection with theoretical computer particular, qualitative theory of differential equations, mechanics, science and logic. The program will consist of three tutorials, mathematical modelling and control. two plenary invited lectures, and short contributed talks of the Program Committee: A. M. Samoilenko (chairman), I. V. Gaishun, participants. M. M. Khapaev, D. Ya. Khusainov, V. I. Korobov, A. M. Kovalev, A. I. Information :email:[email protected]; http://www. Malikov, A. A. Martynyuk, N. A. Perestyuk, S. N. Vassilyev. karlin.mff.cuni.cz/~ssaos. Organizing Committee:O.V.Anashkin(chairman),E.P.Belan,V. I. Shostka, V. V. Zhuravlev. September 2008 Information: Oleg V. Anashkin; email: [email protected]. School on Algebraic Topics of Automata * 1–12 ,ComplexoIn- * 21–24 Applied Statistics 2008, Hotel Ribno, Ribno, Slovenia. terdisciplinar da Universidade de Lisboa Av. Prof. Gama Pinto, 2 Description: The conference, organized in Ribno in the vicinity of 1649-003, Lisboa, Portugal. the beautiful Lake Bled, will provide an opportunity for researchers Description : This school aims to present to the scientific com- in statistics, data analysts, and other professionals from various munities, in particular to post-graduate students, various topics statisticalandrelatedfieldstocometogether,presenttheirresearch, on algebraic theory of automata, delivered as courses, advanced and learn from each other. Cross-discipline and applied paper seminars and student’s seminars. submissions are especially welcome. A three day program consists Topics: The programme includes eight courses on various aspects of invited paper presentations, contributed paper sections from of algebraic theory of automata, plus an advanced seminar on diverse topics, and finishes with a workshop. Selected papers mainstream topics and a student’s seminar on their research work. will be published in Advances in Methodology and Statistics,a Sponsor:Bytheprojectautomata:frommathematicstoapplications peer-reviewed journal of the statistical society of Slovenia. (AutoMathA) of the European Science Foundation (ESF). Keynote Speakers: Jaak Billiet, Katholieke Universiteit Leuven, Organizer: Within the activities of Centro de Algebra da Universi- Belgium; Ornulf Borgan, University of Oslo, Norway; William S. dade de Lisboa (CAUL) and Centro de Matematica da Universidade Cleveland, Purdue University, USA. do Porto (CMUP). Important Dates: Abstract Submission: June 1, 2008. Registration: Information: http://caul.cii.fc.ul.pt/SATA2008/;email: July 1, 2008. [email protected]. Contact: Andrej Blejec, [email protected].

634 NOTICES OF THE AMS VOLUME 55, NUMBER 5 Mathematics Calendar

Information:http://conferences.nib.si/AS2008;email:andrej. Topics: Flow and transport in heterogeneous porous media, mul- [email protected]. tiphase flows, multiscale phenomena, scaling and heterogeneity, scaling in porous media, in particular scaling of processes from the * 22–26 Multiscale Representation, Analysis and Modeling of microscale to the mesoscale, the use of coarse grid descriptions in Internet Data and Measurements, Institute for Pure and Applied modeling multiphase flow phenomena, numerical homogenization, Mathematics (IPAM), UCLA, Los Angeles, California. numerical simulation of multiphase flow in heterogeneous porous Overview: We will discuss the structure of the Internet and of media, mathematical modeling of multiphase flow in porous media. network traffic on the Internet. Topics will include current tools Information:email:[email protected]; http://web. to measure and infer the connectivity structure of the Internet, math.hr/~jurak/Dubrovnik08/. and the modeling of both the emergence of network structures and traffic patterns. Challenges and opportunities in constructing * 18–20 The Second International Workshop on Post-Quantum multiscale models for such complex networks and traffic patterns Crytpography (PQCrypto 2008), University of Cincinnati, Cincin- will be studied from various perspectives. nati, Ohio. Organizing Committee: Mauro Maggioni, Paul Barford, Anna Description: Can we build large quantum computers? What will Gilbert, Morley Mao, Rob Nowak. they do to the cryptographic world, in particular, public key Application/Registration: An application/registration form is cryptographic world? PQCrypto 2008 is the second of the new available at http://www.ipam.ucla.edu/programs/mraws1/.If series of workshops on Post-Quantum cryptography, which is you don’t intend to request financial support, you may simply devoted to the cryptographic research in preparing us for the world register. We urge you to apply as early as possible. Applications of the possible future quantum computers. received by August 11, 2008 will receive fullest consideration. Organizers:Thisseriesofworkshopisorganizedduetothegrowing Encouraging the careers of women and minority mathematicians interest from academic researchers, industries and governments and scientists is an important component of IPAM’s mission and in this area. PQCrypto 2008 will serve as a forum for researchers to we welcome their applications. present results and exchange ideas in post-quantum cryptography. Information:email:[email protected]; http://www.ipam. Information:email:[email protected]; http://math.uc.edu/ ucla.edu/programs/mraws1/. ~aac/pqcrypto2008/.

October 2008 * 20–22International Conferenceon Analysis andIts Applications, Aligarh Muslim University, Aligarh, India. IIIberianMathematicalMeeting * 3–5 ,DepartamentodeMatem´aticas, Information: http://www.amudirectory.com/ICAA08. For update Universidad de Extremadura, 06071 Badajoz, Spain. informations: http://ICAA-08.tripod.com Description: The II Iberian Mathematical Meeting, jointly organized by the Spanish Royal Mathematical Society (http://www.rsme.es/), November 2008 the Portuguese Mathematical Society (http://www.spm.pt/), and the Department of Mathematics of the University of Extremadura * 10–12 International Conference on Recent Trends in Mathemat- ( http://matematicas.unex.es/), will be held on October 3– ical Sciences, Manama, Kingdom of Bahrain. 5, 2008 in Badajoz (Spain). In this second meeting , the main Description: The aim of the conference is to bring together the scientific areas will be: Algebra and Algebraic Methods; Functional teachers, researchers and scientists working in the field of pure Analysis–Statistics and Biometry. mathematics, applied mathematics, statistics and operation areas Information: http://imm2.unex.es;email:[email protected];tel: including operation research. +34924289568; fax: +34924272911; email: [email protected]. Organizer: The International Department of Mathematics, College of Science, University of Bahrain. * 5–12 International Conference on Differential Equations, Func- Information:email:[email protected]; http://www.icrms. tion Spaces, and Approximation Theory: Dedicated to the 100th uob.edu.bh/page-1.htm. anniversary of the birthday of S. L. Sobolev, Sobolev Institute of Mathematics, Novosibirsk, Russia. December 2008 Description: October 6, 2008, will be the 100th anniversary of the birthday of Sergei L’vovich Sobolev (1908-1989), an outstanding * 1–4 SGT-in-Rio: Workshop on Spectral Graph theory with appli- mathematician of the 20th century. The Sobolev Institute of cations on Computer Science, Combinatorial Optimization and Mathematics of the Siberian Branch of the Russian Academy of Chemistry, Military Institute of Engineering, Rio de Janeiro, Brazil. Sciences jointly with Novosibirsk State University are organizing Description: The theory of graph spectra is now a well established the International Conference on Differential Equations, Function field of research in Mathematics and in several applied sciences Spaces, and Approximation Theory dedicated to this significant (e.g. chemistry, computer science and operational research), and event. many results have been published over the last few decades. Topics: Ordinary differential equations; partial differential equa- Goals: The main goals of the workshop are to bring together tions; equations of mathematical physics; operator theory; spectral the leading researchers on graph spectra and related topics, to theory; function spaces; embedding theorems; numerical methods; establish the state of the art, and to discuss recent achievements approximation theory; cubature formulas; mathematical modeling. and challenges. Information:email:[email protected]; http://www.math. Topics:Thetopicsincludeapplicationsofgraphspectratocomputer nsc.ru/conference/sobolev100/english. science, combinatorial optimization, chemistry and other branches of science. * 13–16 Scaling up for modeling transport and flow in porous Organizer: In recognition of the strong developments in the media, Centre for Advanced Academic Studies, Dubrovnik, Croatia. subject, this workshop has been organized as a forum for the many Description: The aim of the conference is to bring together re- researchers around the world. searchers, scientists, engineers, and students to exchange and share Information:email:[email protected]; http://www.sgt.pep. their experiences, new ideas, and research results about upscaling ufrj.br/~tegrio. for modeling, analysis and simulation of flow and transport in porous media and application to problems including subsurface hy- * 8–12 Small Ball Inequalities in Analysis, Probability and Irreg- drology, petroleum exploration, contaminant remediation, carbon ularities of Distribution, American Institute of Mathematics, Palo sequestration and nuclear waste storage. Alto, California.

MAY 2008 NOTICES OF THE AMS 635 Mathematics Calendar

Description: This workshop, sponsored by AIM and the NSF, will May 2009 be devoted to a theme common to irregularity of distributions, * 10–15 ICMI Study 19: Proof and Proving in Mathematics Educa- approximation theory, probability theory and harmonic analysis. In tion, Taipei, Taiwan. each of these subjects, there are outstanding conjectures in dimen- Call for contributions: Participation in the conference is by invita- sions three and higher that stipulate that functions which satisfy tion to the authors of accepted contributions following a refereeing certain conditions on its mixed derivative are necessarily large in process. The International Program Committee (IPC) invites indi- sup norm. This workshop will survey these conjectures, seeking viduals or groups to submit original contributions. A submission both commonalities and differences, describe recent advances, and should represent a significant contribution to knowledge about discuss proof techniques and strategies. learning and teaching proof. It may address questions from one Information: http://aimath.org/ARCC/workshops/ or more of the study themes, or further issues relating to these, smallballineq.html. but it should identify its primary focus. The Study themes are set * 13–17 The 48th American Society for Cell Biology Annual out in the Discussion Document which is available on the ICMI Meeting, The Moscone Center, San Francisco, California. Study 19 website (still under construction but functional) http:// Deadlines: Abstract Deadline (to be considered for minisymposia jps.library.utoronto.ca/ocs/index.php?cf=8 (or via Google: presentations): August 7, 2008. Abstract Deadline (to be considered ICMI 19). Submissions will be a maximum of 6 pages, including for poster presentations only): September 3, 2008. Late Abstract references and figures, written in english, the language of the con- Deadline (to be considered for poster presentations only): October ference. Further technical details about the format of submissions 16, 2008. will be available on the study website. Important dates Information: For more information, visit: http://ascb.org/ : By 30 June 2008: Potential authors upload their meetings/. papers to the conference website. By 15 November 2008: Potential authors receive the result of the refereeing process. Invitations to January 2009 participate in the conference are sent to authors whose papers are accepted. * 5–8 Joint Mathematics Meetings, Washington, D.C. ICMI Executive Advisors: Hyman Bass (USA); Mariolina Bartolini- Information: http://www.ams.org/amsmtgs/national.html. Bussi (Italy).

* 5–16 Group Theory, Combinatorics and Computation,TheUni- * 27–June 1 The International Conference “Infinite Dimensional versity of Western Australia, Perth, Australia. Analysis and Topology”, Yaremche, Ivano-Frankivsk, Ukraine. Description: Special Theme Program on group theory, combina- Topics: The main scientific topics to be presented at the con- torics and computation at the University of Western Australia. ference are: Infinite dimensional holomorphy, topological tensor Invited Speakers: Rosemary Bailey, Peter Cameron, Marston Con- products, Banach space theory, operator theory, general topol- der, Marcel Herzog, Kathy Horadam, Sasha Ivanov, William Kantor, ogy, set-theoretic topology, geometric and infinite dimensional Cai Heng Li, Charles Leedham-Green, Martin Liebeck, Brendan topology. McKay, Peter Neumann, Eamonn O’Brien, Tim Penttila, Jan Saxl, Language: Official language of the Conference is English. Akos Seress. Deadline: For registration is May 1, 2009. Topics: Week 1: An international conference in honour of Professor Organizers: The organizers of the conference are: Precarpathian Praeger’s 60th birthday. It will contain invited 1 hour talks and National University, Ivano-Frankivsk, Ukraine; Lviv Ivan Franko short contributed talks by participants. Week 2: An informal week National University, Lviv, Ukraine; Institute for Applied Problems of of short courses, workshops and problem sessions, especially Mechanics and Mathematics, Lviv, Ukraine; Institute of Mathematics benefical to early career researchers and postgraduate students. of National Academy of Sciences, Kyiv, Ukraine. Information: http://sponsored.uwa.edu.au/gcc09/welcome; Information:email:[email protected]; http://www.idat. email: [email protected]. frankivsk.org.

April 2009 July 2009

* 6–10 The 3D Euler and 2D surface quasi-geostrophic equations, * 27–31 33rd Conference on Stochastic Processes and their American Institute of Mathematics, Palo Alto, California. Applications,Berlin,Germany. Description: This workshop, sponsored by AIM and the NSF, will be Main Venue: Will be the Mathematics Institute of Technische devoted to the 3D Euler equations of incompressible fluids and the Universitaet, located in the center of Berlin. 2D surface quasi-geostrophic (QG) equation of geophysical flows. Description: The conference is the major annual meeting for Information:email:[email protected]; http://aimath.org/ researchers working in the field of Stochastic Processes. The con- ARCC/workshops/3deuler.html. ferencecoversawiderangeofactiveresearchareas,inparticular featuring 20 invited plenary lectures presented by leading special- * 19–26 NoDIA-2009: Nonlinear Differential Equations, Integra- ists. In addition, there will be a large variety of special sessions, bility and Applications, Cape Town, South Africa. consisting of three talks each. Description: The conference aims to bring together both experts Confirmed Plenary Speakers: J. Baik, S. Chatterjee, F. Delbaen, and young researchers in the subject of nonlinear differential A. Dembo, S. Hamad`ene, C. Kluppelberg,¨ J. Martin, S. Martinez, P. equations, with emphasis on the following subjects: integrability of Mathieu, J. Mattingly, P. Morters,E.Perkins,G.Reinert,L.Saloff-¨ differential equations and systems, hierarchies and sequences of Coste, S. Smirnov, A. Schied, G. Slade, M. Takeda, F. Y. Wang, A. equations, singularity analysis, symmetry analysis and applications. Wakolbinger. The meeting is financed partially by SIDA (Sweden) and NRF (South Information:email:[email protected]; http://www. Africa). math.tu-berlin.de/SPA2009. Information: http://www.sm.luth.se/~norbert/nodia09.html; email: [email protected].

The following new announcements will not be repeated until the criteria in the next to the last paragraph at the bottom of thefirstpageofthissectionaremet.

636 NOTICES OF THE AMS VOLUME 55, NUMBER 5 New Publications Offered by the AMS To subscribe to email notification of new AMS publications, please go to http://www.ams.org/bookstore-email.

Algebra and Algebraic and categories of modules; Hopf algebras; Exercises–Part VI; Bibliography; Index. Geometry Graduate Studies in Mathematics, Volume 91 June 2008, approximately 613 pages, Hardcover, ISBN: 978-0-8218- 4153-2, 2000 Mathematics Subject Classification: 16-01, 17-01; Graduate Algebra: 17Bxx, 20Cxx, 20Fxx, AMS members US$68, List US$85, Order code GSM/91 Graduate Algebra: Noncommutative Noncommutative View View Louis Halle Rowen, Bar-Ilan Analysis Louis Halle Rowen University, Ramat Gan, Israel

Graduate Studies in Mathematics This book is a companion volume to Volume 91 American Mathematical Society Selected Papers on Graduate Algebra: Commutative View TRANSLATIONS Series 2 • Volume 223 American Mathematical Society (published as volume 73 in this series). The Analysis and Related main and most important feature of the book is that it presents a unified approach Topics Selected Papers on to many important topics, such as group theory, ring theory, Lie Analysis and Related This volume contains translations of algebras, and gives conceptual proofs of many basic results of Topics papers that originally appeared in the noncommutative algebra. There are also a number of major results Japanese journal Sugaku. The papers in noncommutative algebra that are usually found only in technical range over a variety of topics, including works, such as Zelmanov’s proof of the restricted Burnside problem operator algebras, analysis, and statistics. in group theory, word problems in groups, Tits’s alternative in American Mathematical Society algebraic groups, PI algebras, and many of the roles that Coxeter This volume is suitable for graduate diagrams play in algebra. students and research mathematicians interested in analysis and its applications. The first half of the book can serve as a one-semester course on noncommutative algebra, whereas the remaining part of the book Contents: M. Takesaki, Entrance to operator algebras; M. Izumi, describes some of the major directions of research in the past Classification of C∗-algebras; A. Miyachi, Weighted Hardy spaces 100 years. The main text is extended through several appendices, and Jacobi series; S. Igari, Legacy of J. Marcinkiewicz to real analysis which permits the inclusion of more advanced material, and in the 20th century; H. Tanaka, The Kakeya conjecture; T. Kumagai, numerous exercises. The only prerequisite for using the book is an Recent developments of analysis on fractals; S. Akiyama, Symbolic undergraduate course in algebra; whenever necessary, results are dynamical system and number theoretical tilings; N. Obata, Notions quoted from Graduate Algebra: Commutative View. of independence in quantum probability and spectral analysis of graphs; K. Tanaka, On various applications of the wavelet analysis Contents: The structure of rings: Fundamental concepts in ring to statistics; H. Tanaka, Bhattacharyya type inequalities. theory; Semisimple modules and rings and the Wedderburn-Artin theorem; The Jacobson program applied to left Artinian rings; American Mathematical Society Translations—Series 2, Volume Noetherian rings and the role of prime rings; Algebras in terms 223 of generators and relations; Tensor products; Exercises–Part IV; July 2008, approximately 194 pages, Hardcover, ISBN: 978-0- Representations of groups and Lie algebras: Group representations 8218-3928-7, 2000 Mathematics Subject Classification: 46-06, AMS and group algebras; Characters of finite groups; Lie algebras and other nonassociative algebras; Dynkin diagrams (Coxeter-Dynkin members US$79, List US$99, Order code TRANS2/223 graphs and Coxeter groups); Exercises–Part V; Representable algebras: Polynomial identities and representable algebras; Central simple algebras and the Brauer group; Homological algebra

May 2008 Notices of the AMS 637 New Publications Offered by the AMS

Translations of Value Distribution large databases. The enormous increase in the size of available MATHEMATICAL scientific and commercial databases (data avalanche) as well as the MONOGRAPHS of Meromorphic continuing and exponential growth in performance of present day Volume 236 Functions computers make data mining a very active field. In many cases, Value Distribution the burgeoning volume of data sets has grown so large that it of Meromorphic Anatoly A. Goldberg, Bar-Ilan threatens to overwhelm rather than enlighten scientists. Therefore, Functions University, Ramat Gan, Israel, traditional methods are revised and streamlined, complemented Anatoly A. Goldberg by many new methods to address challenging new problems. Iossif V. Ostrovskii and Iossif V. Ostrovskii, Bilkent University, Ankara, Turkey Mathematical Programming plays a key role in this endeavor. It helps us to formulate precise objectives (e.g., a clustering criterion

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F O 8 UN 188 or a measure of discrimination) as well as the constraints imposed DED This book contains a comprehensive exposition of the Nevanlinna theory of on the solution (e.g., find a partition, a covering or a hierarchy in meromorphic functions of one complex variable, with detailed clustering). It also provides powerful mathematical tools to build study of deficiencies, value distribution, and asymptotic properties highly performing exact or approximate algorithms. of meromorphic functions. This book is based on lectures presented at the workshop on “Data A self-contained exposition of the inverse problem for meromorphic Mining and Mathematical Programming” (October 10–13, 2006, functions of finite order with finitely many deficiencies is given in Montreal) and will be a valuable scientific source of information to full detail. Many results included in the book belong to the authors faculty, students, and researchers in optimization, data analysis and were previously available only in journal articles. and data mining, as well as people working in computer science, engineering and applied mathematics. The main body of the book is a translation of the Russian original published in 1970, which has been one of the most popular sources Titles in this series are co-published with the Centre de Recherches in this field since then. New references and footnotes related to Mathématiques. recent achievements in the topics considered in the original edition Contents: E. Carrizosa, Support vector machines and distance have been added and a few corrections made. A new Appendix minimization; H. Chen and J. Peng, 0-1 semidefinite programming with a survey of the results obtained after 1970 and extensive for graph-cut clustering: Modelling and approximation; bibliography has been written by Alexandre Eremenko and James K. Z. Csizmadia, P. L. Hammer, and B. Vizvári, Artificial attributes in Langley for this English edition. analyzing biomedical databases; Y.-J. Fan, C. Iyigun, and W. A. The only prerequisite for understanding material of this book is an Chaovalitwongse, Recent advances in mathematical programming undergraduate course in the theory of functions of one complex for classification and cluster analysis; P. G. Georgiev, Nonlinear variable. skeletons of data sets and applications—Methods based on subspace clustering; M. R. Guarracino, S. Cuciniello, D. Feminiano, Contents: Characteristics of the behavior of a meromorphic G. Toraldo, and P. M. Pardalos, Current classification algorithms function and the first fundamental theorem; Meromorphic for biomedical applications; G. Kunapuli, K. P. Bennett, J. Hu, and functions of finite order; The second fundamental theorem; J.-S. Pang, Bilevel model selection for support vector machines; Deficient values; Asymptotic properties of meromorphic functions V. Makarenkov, A. Boc, A. Boubacar Diallo, and A. Baniré Diallo, and deficiencies; Value distribution with respect to the arguments; Algorithms for detecting complete and partial horizontal gene Applications of Riemann surfaces to value distribution; On the transfers: Theory and practice; O. L. Mangasarian and E. W. Wild, magnitude of an entire function; Notes; A survey of some results Nonlinear knowledge in kernel machines; F. Murtagh, Ultrametric after 1970; Bibliography; Author index; Subject index; Notation embedding: Application to data fingerprinting and to fast data index. clustering; O. Seref, O. E. Kundakcioglu, and P. M. Pardalos, Translations of Mathematical Monographs, Volume 236 Selective linear and nonlinear classification. June 2008, approximately 505 pages, Hardcover, ISBN: 978-0-8218- CRM Proceedings & Lecture Notes, Volume 45 4265-2, 2000 Mathematics Subject Classification: 30D30, 30D35; May 2008, 234 pages, Softcover, ISBN: 978-0-8218-4352-9, LC 30D20, 30D15, AMS members US$103, List US$129, Order code 2008002772, 2000 Mathematics Subject Classification: 68R01, MMONO/236 68P01, 68P10, 90-08, 90C09, 90C27, AMS members US$68, List US$85, Order code CRMP/45 Applications

Volume 45 Data Mining and C CRM R PROCEEDINGS & Mathematical M LECTURE NOTES

Centre de Recherches Mathématiques Montréal Programming Data Mining Panos M. Pardalos, University and Mathematical Programming of Florida, Gainesville, FL, and

Panos M. Pardalos Pierre Hansen Pierre Hansen, HEC Montréal, Editors QC, Canada, Editors

American Mathematical Society Data mining aims at finding interesting, useful or profitable information in very

638 Notices of the AMS Volume 55, Number 5 New Publications Offered by the AMS Differential Equations Geometry and Topology

Volume 44 Singularities in PDE Comparison C CRM Comparison R PROCEEDINGS & M and the Calculus of Theorems Theorems in LECTURE NOTES in Riemannian Centre de Recherches Mathématiques Montréal Variations Geometry Riemannian Geometry Singularities in Stanley Alama and Lia Bronsard, Jeff Cheeger, New York PDE and the Calculus Jeff Cheeger of Variations McMaster University, Hamilton, David G. Ebin University-Courant Institute,

Stanley Alama Lia Bronsard ON, Canada, and Peter J. NY, and David G. Ebin, State Peter J. Sternberg Editors Sternberg, Indiana University, AMS CHELSEA PUBLISHING University of New York at Stony American Mathematical Society • Providence, Rhode Island Bloomington, IN, Editors Brook, NY American Mathematical Society This book contains papers presented ... this is a wonderful book, full of at the “Workshop on Singularities in PDE and the Calculus of fundamental techniques and ideas. Variations” at the CRM in July 2006. The main theme of the meeting – Robert L. Bryant, was the formation of geometrical singularities in PDE problems with Director of the Mathematical Sciences Research Institute a variational formulation. These equations typically arise in some applications (to physics, engineering, or biology, for example) and Cheeger and Ebin’s book is a truly important classic monograph in their resolution often requires a combination of methods coming Riemannian geometry, with great continuing relevance. from areas such as functional and harmonic analysis, differential – Rafe Mazzeo, Stanford University geometry and geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard model of phase transitions The central theme of this book is the interaction between the and domain walls; vortices in Ginzburg-Landau type models for curvature of a complete Riemannian manifold and its topology and superconductivity and superfluidity; the Ohna-Kawasaki model global geometry. for di-block copolymers; models of image enhancement; and The first five chapters are preparatory in nature. They begin with a Monge-Ampère functions. The articles give a sampling of problems very concise introduction to Riemannian geometry, followed by and methods in this diverse area of mathematics, which touches a an exposition of Toponogov’s theorem—the first such treatment large part of modern mathematics and its applications. in a book in English. Next comes a detailed presentation of This item will also be of interest to those working in analysis. homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one Titles in this series are co-published with the Centre de Recherches on the injectivity radius. Mathématiques. Chapters 6–9 deal with the most relevant contributions to the Contents: E. R. Alvarez-Buylla, M. Benítez, A. Chaos, Y. Cortés, subject in the years 1959 to 1974. These include the pinching (or G. Escalera-Santos, C. Espinosa, and P. Padilla, Variational sphere) theorem, Berger’s theorem for symmetric spaces, the problems arising in biology; F. Béthuel, G. Orlandi, and D. Smets, differentiable sphere theorem, the structure of complete manifolds On the Cauchy problem for phase and vortices in the parabolic of non-negative curvature, and finally, results about the structure of Ginzburg-Landau equation; R. Choksi, Nonlocal Cahn-Hilliard complete manifolds of non-positive curvature. Emphasis is given to and isoperimetric problems: Periodic phase separation induced the phenomenon of rigidity, namely, the fact that new topological by competing long- and short-range interactions; T. Giorgi types can appear when assumptions on the curvature are relaxed and H. Jadallah, On a generalized Ginzburg-Landau energy from strict to weak inequalities, but only in a restricted way, which for superconducting/normal composite materials; M. Guan, usually involves an isometry. S. Gustafson, K. Kang, and T.-P. Tsai, Global questions for map evolution equations; R. Ignat, Pohožaev-type identities for an Much of the material, particularly the last four chapters, was elliptic equation; R. L. Jerrard, Some remarks on Monge-Ampère essentially state-of-the-art when the book first appeared in 1975. functions; B. Kawohl, Variational versus pde-based approaches Since then, the subject has exploded, but the material covered in the in mathematical image processing; M. Kurzke and D. Spirn, On book still represents an essential prerequisite for anyone who the energy of a Chern-Simons-Higgs vortex lattice; A. Malchiodi, wants to work in the field. Some recent results about a class of singularly perturbed elliptic Contents: Basic concepts and results; Toponogov’s theorem; equations; V. Millot, The dipole problem for H1/2(S2; S1)-maps and Homogeneous spaces; Morse theory; Closed geodesics and application; A. Montero, Hodge decompositions, Γ -convergence the cut locus; The sphere theorem and its generalizations; and the Gross-Pitaevskii energy; Y. Morita, Bifurcation of vortex The differentiable sphere theorem; Complete manifolds of solutions to a Ginzburg-Landau equation in an annulus; X. Ren, nonnegative curvature; Compact manifolds of nonpositive An Allen-Cahn type problem with curvature modification; M. G. curvature; Bibliography; Additional bibliography; Index. Westdickenberg, Rare events, action minimization, and sharp AMS Chelsea Publishing interface limits; W. P. Ziemer, The Gauss-Green theorem for weakly differentiable vector fields. May 2008, 161 pages, Hardcover, ISBN: 978-0-8218-4417-5, LC CRM Proceedings & Lecture Notes, Volume 44 2007052113, 2000 Mathematics Subject Classification: 53C20; 58E10, AMS members US$32, List US$35, Order code CHEL/365.H May 2008, 267 pages, Softcover, ISBN: 978-0-8218-4350-5, LC 2008060012, 2000 Mathematics Subject Classification: 35J50, 47J30, AMS members US$79, List US$99, Order code CRMP/44

May 2008 Notices of the AMS 639 New AMS-Distributed Publications Logic and Foundations New AMS-Distributed

University Borel Equivalence Publications LECTURE Series Relations Volume 44 Structure and Classification Borel Equivalence Relations Vladimir Kanovei, Institute Structure and Classification Algebra and Algebraic for Information Transmission Vladimir Kanovei Problems, Moscow, Russia Geometry

Over the last 20 years, the theory of Borel American Mathematical Society equivalence relations and related topics have been very active areas of research in Introduction to Group set theory and have important interactions with other fields of Theory mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The Oleg Bogopolski, Technische book presents, for the first time in mathematical literature, all Universität Dortmundt, Germany major aspects of this theory and its applications. This book should be of interest to a wide spectrum of mathematicians working in set theory as well as the other areas mentioned. It provides a systematic exposition of results that so far have been only available in journals or are even unpublished. The book presents unified and in some cases significantly streamlined proofs of several difficult results, especially dichotomy theorems. It has rather minimal overlap with other books published in this This book quickly introduces beginners to general group theory and subject. then focuses on three main themes: Contents: Introduction; Descriptive set theoretic background; • finite group theory, including sporadic groups Some theorems of descriptive set theory; Borel ideals; Introduction • combinatorial and geometric group theory, including the to equivalence relations; Borel reducibility of equivalence relations; Bass–Serre theory of groups acting on trees “Elementary” results; Introduction to countable equivalence • the theory of train tracks by Bestvina and Handel for relations; Hyperfinite equivalence relations; More on countable automorphisms of free groups equivalence relations; The 1st and 2nd dichotomy theorems; Ideal I1 and the equivalence relation E1; Actions of the infinite symmetric With its many examples, exercises, and full solutions to selected group; Turbulent group actions; The ideal I3 and the equivalence exercises, this text provides a gentle introduction that is ideal relation E3; Summable equivalence relations; c0-equalities; Pinned for self-study and an excellent preparation for applications. A equivalence relations; Reduction of Borel equivalence relations distinguished feature of the presentation is that algebraic and to Borel ideals; On Cohen and Gandy–Harrington forcing over geometric techniques are balanced. The beautiful theory of train countable models; Bibliography; Index. tracks is illustrated by two nontrivial examples. University Lecture Series, Volume 44 Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced July 2008, approximately 236 pages, Softcover, ISBN: 978-0-8218- undergraduate and graduate students to specialists. 4453-3, LC 2007060598, 2000 Mathematics Subject Classification: A publication of the European Mathematical Society (EMS). 03E15, AMS members US$36, List US$45, Order code ULECT/44 Distributed within the Americas by the American Mathematical Society. Contents: Introduction to finite group theory; Introduction to combinatorial group theory; Automorphisms of free groups and train tracks; Appendix. The Perron–Frobenius Theorem; Solutions to selected exercises; Bibliography; Index. EMS Textbooks in Mathematics March 2008, 187 pages, Hardcover, ISBN: 978-3-03719-041-8, 2000 Mathematics Subject Classification: 20-01, 20D08, 20E05, 20E06, 20E08, 20F28, AMS members US$38, List US$48, Order code EMSTEXT/6

640 Notices of the AMS Volume 55, Number 5 New AMS-Distributed Publications An Invitation to Analysis Quantum Groups and Duality From Hopf Algebras to Rectifiable Sets, Multiplicative Unitaries Densities and Tangent and Beyond Measures Thomas Timmermann, Camillo De Lellis, University of University of Münster, Zürich, Zurich, Switzerland Matematisches Institut, Germany The characterization of rectifiable sets through the existence of densities is a This book provides an introduction to the theory of quantum pearl of geometric measure theory. The groups with emphasis on their duality and on the setting of operator difficult proof, due to Preiss, relies on algebras. many beautiful and deep ideas and novel techniques. Some of Part I of the text presents the basic theory of Hopf algebras, them have already proven useful in other contexts, whereas others Van Daele’s duality theory of algebraic quantum groups, and have not yet been exploited. These notes give a simple and short Woronowicz’s compact quantum groups, staying in a purely presentation of the former and provide some perspective of the algebraic setting. Part II focuses on quantum groups in the setting latter. of operator algebras. Woronowicz’s compact quantum groups This text emerged from a course on rectifiability given at the are treated in the setting of C∗-algebras, and the fundamental University of Zürich. It is addressed both to researchers and multiplicative unitaries of Baaj and Skandalis are studied in detail. students; the only prerequisite is a solid knowledge in standard An outline of Kustermans’ and Vaes’ comprehensive theory of measure theory. The first four chapters give an introduction to locally compact quantum groups completes this part. Part III leads rectifiable sets and measures in Euclidean spaces, covering classical to selected topics, such as coactions, Baaj-Skandalis-duality, and topics such as the area formula, the theorem of Marstrand and approaches to quantum groupoids in the setting of operator the most elementary rectifiability criterions. The fifth chapter is algebras. dedicated to a subtle rectifiability criterion due to Marstrand and The book is addressed to graduate students and non-experts generalized by Mattila, and the last three focus on Preiss’ result. The from other fields. Only basic knowledge of (multi-) linear algebra aim is to provide a self-contained reference for anyone interested in is required for the first part, while the second and third part an overview of this fascinating topic. assume some familiarity with Hilbert spaces, C∗-algebras, and von A publication of the European Mathematical Society (EMS). Neumann algebras. Distributed within the Americas by the American Mathematical This item will also be of interest to those working in analysis. Society. A publication of the European Mathematical Society (EMS). Contents: Introduction; Notation and preliminaries; Marstsand’s Distributed within the Americas by the American Mathematical Theorem and tangent measures; Rectifiability; The Marstrand– Society. Mattila rectifiability criterion; An overview of Preiss’ proof; Contents: Part I. From groups to quantum groups: Hopf algebras; Moments and uniqueness of the tangent measure at infinity; Flat Multiplier Hopf algebras and their duality; Algebraic compact versus curved at infinity; Flatness at infinity implies flatness; quantum groups; Part II. Quantum groups and C∗-/von Neumann Open problems; Appendix A. Proof of Theorem 3.11; Appendix B. bialgebras: First definitions and examples; C∗-algebraic compact Gaussian integrals; Bibliography; Index. quantum groups; Examples of compact quantum groups; Zurich Lectures in Advanced Mathematics Multiplicative unitaries; Locally compact quantum groups; Part III. Selected topics: Coactions on C∗-algebras, reduced crossed March 2008, 134 pages, Softcover, ISBN: 978-3-03719-044-9, 2000 products, and duality; Pseudo-multiplicative unitaries on Hilbert Mathematics Subject Classification: 28A75, 26B15, 49Q15, 49Q20, spaces; Pseudo-multiplicative unitaries on C∗-modules; Appendix; AMS members US$27, List US$34, Order code EMSZLEC/7 Bibliography; Symbol Index; Index. EMS Textbooks in Mathematics February 2008, 427 pages, Hardcover, ISBN: 978-3-03719-043-2, First Steps in Several 2000 Mathematics Subject Classification: 16W30, 46-01, 46L55, Complex Variables: 22A22, 22D25, 22D35, 46L10, AMS members US$62, List US$78, Order code EMSTEXT/5 Reinhardt Domains Marek Jarnicki, Jagiellonian University, Kraków, Poland, and Peter Pflug, University of Oldenburg, Germany

This book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader

May 2008 Notices of the AMS 641 New AMS-Distributed Publications may learn much about this area without encountering too many Orders from other countries should be sent to the SMF. Members of technical difficulties. the SMF receive a 30% discount from list. Chapter 1 describes the fundamental notions and the phenomenon Contents: Introduction; Correspondance; Textes; Notes. of simultaneous holomorphic extension. Chapter 2 presents a fairly Documents Mathématiques, Number 5 complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter November 2007, 188 pages, Hardcover, ISBN: 978-2-85629-241-9, gives a classification of Reinhardt domains of existence for the 2000 Mathematics Subject Classification: 34Mxx, 12H05, 32G20, most important classes of holomorphic functions. The last chapter Individual member US$61, List US$68, Order code SMFDM/5 deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may Number Theory be useful as seminar topics. The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the Probability only prerequisite is a basic knowledge of analysis. and Number A publication of the European Mathematical Society (EMS). Theory—Kanazawa Distributed within the Americas by the American Mathematical Society. 2005 Contents: Reinhardt domains; Biholomorphisms of Reinhardt Shigeki Akiyama, Niigata domains; Reinhardt domains of existence of special classes of University, Japan, Kohji holomorphic functions; Holomorphically contractible families on Reinhardt domains; Bibliography; Symbols; List of symbols; Subject Matsumoto, Nagoya University, index. Japan, Leo Murata, Meijigakuin EMS Textbooks in Mathematics University, Japan, and Hiroshi Sugita, Osaka University, Japan, Editors March 2008, 367 pages, Hardcover, ISBN: 978-3-03719-049-4, 2000 Mathematics Subject Classification: 32-01, 32A05, 32A07, 32A10, This volume is the proceedings of the International Conference on 32D05, 32E05, 32F45, AMS members US$62, List US$78, Order Probability and Number Theory held at Kanazawa, Japan, in June code EMSTEXT/7 2005 and includes several survey articles on probabilistic number theory and research papers on various recent topics around the border area between probability theory and number theory. This volume is useful for all researchers and graduate students who are interested in probability theory and number theory. Differential Equations This item will also be of interest to those working in probability. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Singularités Contents: B. Adamczewski and Y. Bugeaud, On the Littlewood conjecture in fields of power series; K. Alladi and Irrégulières A. Berkovich, Series and polynomial representations for weighted Rogers-Ramanujan partitions and products modulo; G. J. Babu, Correspondance et E. Manstavicius, and V. Zacharovas, Limiting processes with Documents dependent increments for measures on symmetric group of permutations; P. Elliott, The ramifications of a shift by 2; Pierre Deligne, Institute for K. Fukuyama, On lacunary trigonometric product; R. Garunkštis, Advanced Study, Princeton, NJ, On the Backlund equivalent for the Lindelöf hypothesis; Bernard Malgrange, Université P. Hellekalek and P. Liardet, The dynamics associated with certain Grenoble I, St. Martin d’Heres, digital sequences; K.-H. Indlekofer, New approach to probabilistic number theory—compactifications and integration; S. Ito and S.-I. France, and Jean-Pierre Ramis, Yasutomi, On simultaneous Diophantine approximation to periodic Université Toulouse, France points related to modified Jacobi-Perron algorithm; A. Laurinˇcikas, 2 Limit theorems for the Mellin transform of ζ(1/2 + it) . II; The letters collected in this volume concern the irregular K. Matsumoto, On the speed of convergence to limit distributions singularities of linear differential equations: irregularity, for Dedekind zeta-functions of non-Galois number fields; J.-L. asymptotic expansions, Stokes sheaves, Gevrey analogues, moduli Mauclaire, On Q-multiplicative functions having a positive problems, multisummability, Galois and wild fundamental upper-meanvalue; M. Mori, Low discrepancy sequences generated groups, vanishing cycles, Fourier transforms. Most of these by dynamical systems; T. Morita, Renormalized Rauzy inductions; letters were written by the authors during the period 1976–1991. H. Nagoshi, The universality of L-functions attached to Maass Four previously unpublished texts have been added to this forms; Y. Ohkubo, The diaphony of a class of infinite sequences; correspondence. J. Pintz, Approximations to the Goldbach and twin prime A publication of the Société Mathématique de France, Marseilles problem and gaps between consecutive primes; W. Schwarz, (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Some highlights from the history of probabilistic number theory;

642 Notices of the AMS Volume 55, Number 5 New AMS-Distributed Publications

R. Šleževiˇciené-Steuding and J. Steuding, Gaps between consecutive zeros of the zeta-function on the critical line and conjectures from random matrix theory; B. Solomyak, Eigenfunctions for substitution tiling systems; H. Sugita and S. Takanobu, The probability of two Fq-polynomials to be coprime; M. Suzuki, An analogue of the Chowla–Selberg formula for several automorphic L-functions; N. Ushiroya, On a mean value of a multiplicative function of two variables; R. Winkler, Hartman sets, functions and sequences—a survey; Y. Yamasaki, Integral representations of q-analogues of the Barnes multiple zeta functions. Advanced Studies in Pure Mathematics, Volume 49 December 2007, 558 pages, Hardcover, ISBN: 978-4-931469-43-3, 2000 Mathematics Subject Classification: 11Kxx; 60Fxx, 11Mxx, AMS members US$72, List US$90, Order code ASPM/49

May 2008 Notices of the AMS 643 Classified Advertisements Positions available, items for sale, services available, and more

Massachusetts Resources, Massachusetts College of Lib- exciting developments. Applications eral Ats, 375 Church Street, North Adams, should include a curriculum vitae, the MASSACHUSETTS COLLEGE OF LIBERAL MA 01247-4100. Review of applications names of three referees, and a brief state- will begin immediately and continue until ment indicating his/her views on the ARTS position is filled. MCLA is an Equal Oppor- future of research and teaching in math- FACULTY POSITION AVAILABLE tunity, Affirmative Action Employer, with ematics. Review of applications will begin FULL-TIME, BENEFITED POSITION, NON- a longstanding commitment to increasing June 1, 2008, and continue until the posi- TENURE-TRACK the diversity of the employee community. tion is filled. Additional information about Visit http://www.mcla.edu. the department, and the position profile, With a strong focus on undergraduate 000028 can be found at http://www.umanitoba. education and a commitment to infusing ca/science/mathematics. the undergraduate experience with the Applications or nominations should be skills, aptitudes, and values of the liberal forwarded to Dr. Mark Whitmore, Dean, arts, Massachusetts College of Liberal Arts Canada Faculty of Science, University of Mani- has set an ambitious course to become a toba, 250 Machray Hall, Winnipeg, Mani- public liberal arts college of distinction. UNIVERSITY OF MANITOBA toba, Canada, R3T 2N2, mark_whitmore@ Located in the beautiful Berkshire Hills Department of Mathematics umanitoba.ca. of western Massachusetts, one of the Faculty of Science The University of Manitoba encourages nation’s premier cultural resort areas, Department Head MCLA enrolls approximately 1,500 stu- applications from qualified women and men, including members of visible minori- dents. MCLA is a member of the Council The Faculty of Science at the University ties, Aboriginal peoples, and persons with of Public Liberal Arts Colleges. of Manitoba invites applications or nomi- disabilities. All qualified candidates are Endowed Chair, Education Department: nations for the position of Head of the encouraged to apply; however, Canadians Applications and nominations are being Department of Mathematics. The appoint- and permanent residents will be given accepted for this position, commencing ment will begin on a mutually agreed date, priority. Application materials, including fall 2008, with possible renewal. MCLA and will be at the rank of professor or letters of reference, will be handled in ac- is seeking an outstanding individual with associate professor, commensurate with cordance with the Freedom of Information a background in mathematics (either a qualifications and experience. Position and Protection of Privacy Act (Manitoba). Ph.D. or Ed.D.) and experience in math Number: 07196. The successful candidate education and project implementation must have a Ph.D. in mathematics, and an Winnipeg has a great deal to offer, with a record of research and publication, outstanding record of accomplishment in both culturally and recreationally, with proven excellence in undergraduate and both research and teaching. Strong aca- a number of arts groups including the graduate math education. The successful demic leadership experience in research, Royal Winnipeg Ballet, professional candidate will encompass a partnership undergraduate and graduate programs, sports teams, outstanding restaurants, with the Berkshire County school systems, and evidence of excellent communication, and opportunities for all types of outdoor teach at MCLA, and help advance the interpersonal and organizational skills, activities in all seasons. The Winnipeg College’s accredited programs in math- are preferred. housing market is one of the most fa- vourable in Canada. Further information ematics education. The Department of Mathematics is can be found at http://www.tourism. To apply, submit a curriculum vita, in the midst of an extensive renewal winnipeg.mb.ca/. research and teaching plans, and a list program, and the department is seeking 000029 of at least three references to Human new leadership to guide it through these

Suggested uses for classified advertising are positions available, books or June 30, 2008; October 2008 issue–July 29, 2008; November 2008 issue–August lecture notes for sale, books being sought, exchange or rental of houses, 28, 2008; December 2008 issue–October 1, 2008. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, age, The 2007 rate is $110 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 multiple accompanied by a statement that the institution does not discriminate on 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 specific announcements can be placed anonymously. Correspondence will be 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 [email protected]. 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: June/July 2008 billed upon publication. issue–April 28, 2008; August 2008 issue–May 28, 2008; September 2008 issue–

May 2008 Notices of the AMS 644 Meetings & Conferences of the AMS

IMPORTANT information regarding meetings programs: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting.

Special Sessions Claremont, Algebraic Combinatorics, Anne Schilling, University of California Davis, and Michael Zabrocki, York University. California Applications of Delay-Differential Equations to Models of Disease, Ami Radunskaya, Pomona College. Claremont McKenna College C*-algebras, subfactors and free probability, Huaxin May 3–4, 2008 Lin, University of Oregon, and Feng Xu, University of California Riverside. Saturday – Sunday Combinatorics of Partially Ordered Sets, Timothy M. Meeting #1039 Hsu, San Jose State University, Mark J. Logan, University Western Section of Minnesota-Morris, and Shahriar Shahriari, Pomona Associate secretary: Michel L. Lapidus College. Announcement issue of Notices: March 2008 Diophantine Problems and Discrete Geometry, Matthias Program first available on AMS website: March 20, 2008 Beck, San Francisco State University, and Lenny Fukshan- Program issue of electronic Notices: May 2008 sky, Texas A&M University. Issue of Abstracts: Volume 29, Issue 3 Dynamical Systems and Differential Equations, Adolfo Rumbos, Pomona College, Mario Martelli, Claremont McK- Deadlines enna College, and Alfonso Castro, Harvey Mudd College. For organizers: Expired Hopf Algebras and Quantum Groups, Gizem Karaali, For consideration of contributed papers in Special Ses- Pomona College, M. Susan Montgomery, University of sions: Expired Southern California, and Serban Raianu, California State For abstracts: Expired University Dominguez Hills. Knot Theory and the Topology of 3-manifolds, Sam The scientific information listed below may be dated. Nelson, Pomona College, David Bachman, Pitzer College, For the latest information, see www.ams.org/amsmtgs/ Erica Flapan, Pomona College, Jim Hoste, Pitzer College, sectional.html. and Patrick Shanahan, Loyola Marymount University. Invited Addresses Operators, Functions and Linear Spaces, Asuman G. Michael A. Bennett, University of British Columbia, Aksoy, Claremont McKenna College, Stephan R. Garcia, Diophantine equations: From Erdos to Wiles and back. Pomona College, Michael Davlin O’Neill, Claremont Chandrashekhar Khare, University of Utah, Automor- McKenna College, and Winston C. Ou, Scripps College. phic forms and Galois representations. Recent Developments in Riemannian and Kaehlerian Huaxin Lin, University of Oregon, Classification of Geometry, Hao Fang, University of Iowa, Zhiqin Lu, Uni- simple amenable C​∗​-algebras of stable rank one. versity of California, Irvine, Dragos-Bogdan Suceava, Cali- Anne Schilling, University of California Davis, Affine fornia State University Fullerton, and Mihaela B. Vajiac, Schubert news. Chapman University.

May 2008 Notices of the AMS 645 Meetings & Conferences

Group Theory, Rostislav I. Grigorchuk, Volodymyr Rio de Janeiro, Brazil Nekrashevych, and Zoran Sunic, Texas A&M University, and Said N. Sidki and Pavel Zalesskii, University of Instituto Nacional de Matemática Pura e Brasilia. Aplicada (IMPA) History and Philosophy of Mathematics, Sergio Nobre, Universidade Estadual Paulista-Rio Claro, and James J. June 4–7, 2008 Tattersall, Providence College. Wednesday – Saturday Lie Algebras and Their Applications, Ivan K. Dimitrov, Queen’s University, Vyacheslav Futorny, University of Meeting #1040 Sao Paulo, and Vera Serganova, University of California First Joint International Meeting between the AMS and the Berkeley. Sociedade Brasileira de Matemática (SBM). Low Dimensional Dynamics, Andre de Carvalho, Associate secretary: Lesley M. Sibner University of Sao Paulo, and Misha Lyubich and Marco Announcement issue of Notices: February 2008 Martens, SUNY at Stony Brook. Program first available on AMS website: N/A Low Dimensional Topology, Louis H. Kauffman, Univer- Program issue of electronic Notices: N/A sity of Illinois at Chicago, and Pedro M. Lopes, Instituto Issue of Abstracts: N/A Superior Tecnico, Technical University of Lisbon. Mathematical Fluid Dynamics, Susan J. Friedlander, Deadlines University of Southern California, Milton Lopes Filho For organizers: Expired and Helena Nussenzveig Lopes, University of Campinus, For consideration of contributed papers in Special Ses- and Maria Elena Schonbek, University of California Santa sions: Expired Cruz. For abstracts: Expired Mathematical Methods in Biology, Julie C. Mitchell, University of Wisconsin-Madison, and Max O. Souza, Uni- The scientific information listed below may be dated. versidade Federal Fluminense. For the latest information, see www.ams.org/amsmtgs/ Mathematical Methods in Image Processing, Stacey internmtgs.html. Levine, Duquesne University, and Celia A. Zorzo Barcelos, Federal University of Uberlândia. AMS Invited Addresses Partial Differential Equations, Harmonic Analysis, and Ruy Exel, Universidade Federal de Santa Catarina, Non- Related Questions, Haroldo R. Clark, Universidade Federal commutative dynamics. Fluminense, Michael Stessin, University at Albany, and Velimir Jurdjevic, University of Toronto, Integrable Geraldo Soares de Souza, Auburn University. Hamiltonian systems on symmetric spaces. Several Complex Variables and Partial Differential Equa- Andre Nachbin, IMPA, Wave dynamics: Asymptotics tions, Shiferaw Berhanu, Temple University, and Jorge with differential operators and solutions. Hounie, Federal University of San Carlos. Richard M. Schoen, Stanford University, Riemannian manifolds of positive curvature. Ivan P. Shestakov, University of Sao Paulo, Automor- Vancouver, Canada phisms of free algebras. Amie Wilkinson, Northwestern University, Partially University of British Columbia and the hyperbolic dynamics. Pacific Institute of Mathematical Sciences (PIMS) AMS Special Sessions Commutative Algebra and Algebraic Geometry, Izzet October 4–5, 2008 Coskun, University of Illinois at Chicago, and Israel Vain- Saturday – Sunday sencher, UFMG. Complexity, Gregorio Malajovich, Universidade Fed- Meeting #1041 eral do Rio de Janeiro, and J. Maurice Rojas, Texas A&M Western Section University. Associate secretary: Michel L. Lapidus Control and Related Topics, Jair Koiller, FGV, Veli- Announcement issue of Notices: August 2008 mir Jurdgevic, University of Toronto, and Fernando Program first available on AMS website: August 21, 2008 Lizarralde, COPPE/UFRJ. Program issue of electronic Notices: October 2008 Extremal and Probabilistic Combinatorics, Bela Bollobas, Issue of Abstracts: Volume 29, Issue 4 The University of Memphis, and Yoshiharu Kohayakawa, University of Sao Paulo. Deadlines Geometry, Representation Theory, and Mathemati- For organizers: Expired cal Physics, Henrique Bursztyn, IMPA, Anthony Licata, For consideration of contributed papers in Special Ses- Stanford University, and Alistair Savage, University of sions: June 17, 2008 Ottawa. For abstracts: August 12, 2008

646 Notices of the AMS Volume 55, Number 5 Meetings & Conferences

Wavelets, Fractals, Tilings and Spectral Measures (Code: The scientific information listed below may be dated. SS 5A), Dorin Ervin Dutkay, University of Central Florida, For the latest information, see www.ams.org/amsmtgs/ Palle E. T. Jorgensen, University of Iowa, and Ozgur sectional.html. Yilmaz, University of British Columbia. West End Number Theory (Code: SS 9A), Nils Bruin, Invited Addresses Simon Fraser University, Matilde N. Lalin, University of Al- Freeman Dyson, Institute for Advanced Study, Birds berta, and Greg Martin, University of British Columbia. and Frogs (Einstein Public Lecture in Mathematics). Richard Kenyon, Brown University, Title to be an- nounced. Alexander S. Kleshchev, University of Oregon, Title to Middletown, be announced. Mark Lewis, University of Alberta, Title to be an- Connecticut nounced. Audrey A. Terras, University of California San Diego, Wesleyan University Title to be announced. October 11–12, 2008 Special Sessions Saturday – Sunday Algebraic Topology and Related Topics (Code: SS 3A), Meeting #1042 Alejandro Adem, University of British Columbia, and Ste- phen Ames Mitchell, University of Washington. Eastern Section Applications of Algebraic Geometry (Code: SS 14A), Associate secretary: Lesley M. Sibner Elizabeth S. Allman, University of Alaska Fairbanks, and Announcement issue of Notices: August 2008 Rekha R. Thomas, University of Washington. Program first available on AMS website: August 28, 2008 Combinatorial Representation Theory (Code: SS 1A), Program issue of electronic Notices: October 2008 Sara C. Billey, University of Washington, Alexander S. Issue of Abstracts: Volume 29, Issue 4 Kleshchev, University of Oregon, and Stephanie Jane Van Willigenburg, University of British Columbia. Deadlines Harmonic Analysis and Related Topics (Code: SS 12A), For organizers: Expired Malabika Pramanik, University of British Columbia, and For consideration of contributed papers in Special Ses- Burak Erdogan, University of Illinois at Urbana-Cham- sions: June 24, 2008 paign. For abstracts: August 19, 2008 Hilbert Functions and Free Resolutions (Code: SS 4A), Susan Cooper, California Polytechnic State University, The scientific information listed below may be dated. Christopher A. Francisco, Oklahoma State University, For the latest information, see www.ams.org/amsmtgs/ and Benjamin P. Richert, California Polytechnic State sectional.html. University. History and Philosophy of Mathematics (Code: SS 11A), Invited Addresses Shawnee L. McMurran, California State University San Pekka Koskela, University of Jyväskylän, Title to be Bernardino, and James J. Tattersall, Providence College. announced. Moduli Spaces and Singularity Theory (Code: SS 8A), Monika Ludwig, Polytechnic University New York, Title James B. Carrell, Patrick Brosnan, and Kalle Karu, Uni- to be announced. versity of British Columbia. Duong Hong Phong, Columbia University, Title to be Noncommutative Algebra and Geometry (Code: SS 6A), announced. Jason Bell, Simon Fraser University, and James Zhang, Thomas W. Scanlon, University of California, Berkeley, University of Washington. Title to be announced. Noncommutative Geometry (Code: SS 13A), Raphael Ponge, University of Toronto, Bahram Rangipour, Uni- Special Sessions versity of New Brunswick, and Heath Emerson, University of Victoria. Algebraic Geometry (Code: SS 1A), Eyal Markman and Nonlinear Functional Analysis, Approximations and Jenia Tevelev, University of Massachusetts, Amherst. Applications (Code: SS 10A), S. P. Singh and Mahi Singh, Complex Geometry and Partial Differential Equations University of Western Ontario, and Pranesh Kumar, Uni- (Code: SS 3A), Jacob Sturm and Jian Song, Rutgers Uni- versity of Northern British Columbia. versity. Probability and Statistical Mechanics (Code: SS 7A), Dynamical Systems and Applications (Code: SS 8A), David Brydges, University of British Columbia, and Rich- Michael A. Radin, Rochester Institute of Technology. ard Kenyon, Brown University. Geometric Function Theory and Geometry (Code: SS 5A), Special Functions and Orthogonal Polynomials (Code: Petra Bonfert-Taylor, Wesleyan University, Katsuhiko SS 2A), Mizanur Rahman, Carleton University, and Diego Matsuzaki, Okayama University, and Edward C. Taylor, Dominici, State University of New York New Paltz. Wesleyan University.

May 2008 Notices of the AMS 647 Meetings & Conferences

Geometric Group Theory and Topology (Code: SS 6A), Graph Labeling, Graph Coloring, and Topological Graph Matthew Horak, University of Wisconsin-Stout, Melanie Theory (Code: SS 5A), Arthur T. White, Western Michigan Stein, Trinity College, and Jennifer Taback, Bowdoin University, and David L. Craft, Muskingum College. College. Homotopy Theory (Code: SS 8A), Michele Intermont, Number Theory (Code: SS 4A), Wai Kiu Chan and David Kalamazoo College, and John R. Martino and Jeffrey A. Pollack, Wesleyan University. Strom, Western Michigan University. Real and Complex Dynamics of Rational Difference Linear Codes Over Rings and Modules (Code: SS 11A), Equations with Applications (Code: SS 7A), Mustafa Kule- Steven T. Dougherty, University of Scranton, and Jay A. novic, University of Rhode Island. Wood, Western Michigan University. Riemannian and Lorentzian Geometries (Code: SS 2A), Mathematical Finance (Code: SS 3A), Qiji J. Zhu, West- Ramesh Sharma, University of New Haven, and Philippe ern Michigan University, and George Yin, Wayne State Rukimbira, Florida International University. University. Mathematical Knowledge for Teaching (Code: SS 7A), Kate Kline and Christine Browning, Western Michigan Kalamazoo, Michigan University. Nonlinear Analysis and Applications (Code: SS 1A), Western Michigan University S. P. Singh, University of Western Ontario, and Bruce B. Watson, Memorial University. October 17–19, 2008 Optimization/Midwest Optimization Seminar (Code: SS Friday – Sunday 6A), Jay S. Treiman and Yuri Ledyaev, Western Michigan University, and Ilya Shvartsman, Penn State Harrisburg. Meeting #1043 Representations of Real and P-adic Lie Groups (Code: SS Central Section 10A), Alessandra Pantano, University of California Irvine, Associate secretary: Susan J. Friedlander Annegret Paul, Western Michigan University, and Susana Announcement issue of Notices: August 2008 Alicia Salamanca-Riba, New Mexico State University. Program first available on AMS website: September 4, Variational Analysis and its Applications (Code: SS 4A), 2008 Yuri Ledyaev and Jay S. Treiman, Western Michigan Uni- Program issue of electronic Notices: October 2008 versity, Ilya Shvartsman, Penn State Harrisburg, and Qiji Issue of Abstracts: Volume 29, Issue 4 J. Zhu, Western Michigan University.

Deadlines For organizers: Expired Huntsville, Alabama For consideration of contributed papers in Special Ses- sions: July 1, 2008 University of Alabama, Huntsville For abstracts: August 26, 2008 October 24–26, 2008 The scientific information listed below may be dated. Friday – Sunday For the latest information, see www.ams.org/amsmtgs/ sectional.html. Meeting #1044 Southeastern Section Invited Addresses Associate secretary: Matthew Miller M. Carme Calderer, University of Minnesota, Title to Announcement issue of Notices: August 2008 be announced. Program first available on AMS website: September 11, Alexandru Ionescu, University of Wisconsin, Title to 2008 be announced. Program issue of electronic Notices: October 2008 Boris S. Mordukhovich, Wayne State University, Title Issue of Abstracts: Volume 29, Issue 4 to be announced. David Nadler, Northwestern University, Title to be an- Deadlines nounced. For organizers: Expired For consideration of contributed papers in Special Ses- Special Sessions sions: July 8, 2008 Affine Algebraic Geometry (Code: SS 9A), Shreeram For abstracts: September 2, 2008 Abhyankar, Purdue University, Anthony J. Crachiola, Saginaw Valley State University, and Leonid G. Makar- The scientific information listed below may be dated. Limanov, Wayne State University. For the latest information, see www.ams.org/amsmtgs/ Computation in Modular Representation Theory and Co- sectional.html. homology (Code: SS 2A), Christopher P. Bendel, University of Wisconsin-Stout, Terrell L. Hodge, Western Michigan Invited Addresses University, Brian J. Parshall, University of Virginia, and Mark Behrens, Massachusetts Institute of Technology, Cornelius Pillen, University of South Alabama. Title to be announced.

648 Notices of the AMS Volume 55, Number 5 Meetings & Conferences

Anthony Michael Bloch, University of Michigan, Ann Xiaoping Yuan, Fudan University, Title to be an- Arbor, Variational principles and nonholonomic dynam- nounced. ics. Weiping Zhang, Chern Institute, Title to be an- Roberto Camassa, University of North Carolina, Chapel nounced. Hill, Title to be announced. Mark V. Sapir, Vanderbilt University, Title to be an- Special Sessions nounced. Biomathematics: Newly Developed Applied Mathematics and New Mathematics Arising from Biosciences, Banghe Li, Special Sessions Chinese Academy of Sciences, Reinhard C. Laubenbacher, Dynamics and Applications of Differential Equations Virginia Bioinformatics Institute, and Jianju Tian, College (Code: SS 3A), Wenzhang Huang and Shangbing Ai, Uni- of William and Mary. versity of Alabama in Huntsville, and Weishi Liu, Univer- Combinatorics and Discrete Dynamical Systems, Rein- sity of Kansas. hard C. Laubenbacher, Virginia Bioinformatics Institute, Graph Decompositions (Code: SS 2A), Robert A. Beeler Klaus Sutner, Carnegie Mellon University, and Yaokun and Robert B. Gardner, East Tennessee State University. Wu, Shanghai Jiao Tong University. Mathematical Biology: Modeling, Analysis, and Simula- Differential Geometry and Its Applications, Jianguo tions (Code: SS 1A), Jia Li, University of Alabama in Hunts- Cao, University of Notre Dame, and Yu Xin Dong, Fudan ville, Azmy S. Ackleh, University of Louisiana at Lafayette, University. and Maia Martcheva, University of Florida. Dynamical Systems Arising in Ecology and Biology, Qishao Lu, Beijing University of Aeronautics & Astro- nautics, and Zhaosheng Feng, University of Texas-Pan American. Shanghai, People’s Harmonic Analysis and Partial Differential Equations with Applications, Yong Ding, Beijing Normal University, Republic of China and Guo-Zhen Lu, Wayne State University. Integrable System and Its Applications, En-Gui Fan, Fudan University Fudan University, Sen-Yue Lou, Shanghai Jiao Tong Univer- December 17–21, 2008 sity and Ningbo University, and Zhi-Jun Qiao, University of Texas-Pan American. Wednesday – Sunday Integral and Convex Geometric Analysis, Deane Yang, Meeting #1045 Polytechnic University, and Jiazu Zhou, Southwest Uni- versity. First Joint International Meeting Between the AMS and the Lie Algebras, Vertex Operator Algebras and Related Shanghai Mathematical Society Topics, Hu Nai Hong, East China Normal University, and Associate secretary: Susan J. Friedlander Yi-Zhi Huang, Rutgers University. Announcement issue of Notices: June 2008 Nonlinear Systems of Conservation Laws and Related Program first available on AMS website: Not applicable Topics, Gui-Qiang Chen, Northwestern University, and Program issue of electronic Notices: Not applicable Shuxing Chen and Yi Zhou, Fudan University. Issue of Abstracts: Not applicable Quantum Algebras and Related Topics, Naihuan N. Jing, North Carolina State University, Quanshui Wu, Fudan Uni- Deadlines versity, and James J. Zhang, University of Washington. For organizers: Expired Recent Developments in Nonlinear Dispersive Wave For consideration of contributed papers in Special Ses- Theory, Jerry Bona, University of Illinois at Chicago, Bo sions: To be announced Ling Guo, Institute of Applied Physics and Computational For abstracts: October 31, 2008 Mathematics, Shu Ming Sun, Virginia Polytech Institute and State University, and Bingyu Zhang, University of The scientific information listed below may be dated. Cincinnati. For the latest information, see www.ams.org/amsmtgs/ Representation of Algebras and Groups, Birge K. Huis- internmtgs.html. gen-Zimmermann, University of California Santa Barbara, Jie Xiao, Tsinghua University, Jiping Zhang, Beijing Uni- Invited Addresses versity, and Pu Zhang, Shanghai Jiao Tong University. L. Craig Evans, University of California Berkeley, Title Several Topics in Banach Space Theory, Gerard J. to be announced. Buskes and Qingying Bu, University of Mississippi, and Zhi-Ming Ma, Chinese Academy of Sciences, Title to be Lixin Cheng, Xiamen University. announced. Stochastic Analysis and Its Application, Jiangang Ying, Richard Schoen, Stanford University, Title to be an- Fudan University, and Zhenqing Chen, University of nounced. Washington. Richard Taylor, Harvard University, Title to be an- Topics in Partial Differential Equations and Mathemati- nounced. cal Control Theory, Xiaojun Huang, Rutgers University,

May 2008 Notices of the AMS 649 Meetings & Conferences

Gengsheng Wang, Wuhan University of China, and Ste- Issue of Abstracts: To be announced phen S.-T. Yau, University of Illinois at Chicago. Deadlines For organizers: August 29, 2008 Washington, District For consideration of contributed papers in Special Ses- sions: To be announced of Columbia For abstracts: To be announced Marriott Wardman Park Hotel and Omni The scientific information listed below may be dated. Shoreham Hotel For the latest information, see www.ams.org/amsmtgs/ sectional.html. January 5–8, 2009 Special Sessions Monday – Thursday Algebraic Methods in Statistics and Probability (Code: SS Meeting #1046 3A), Marlos A. G. Viana, University of Illinois at Chicago. Joint Mathematics Meetings, including the 115th Annual Geometric Function Theory and Analysis on Metric Meeting of the AMS, 92nd Annual Meeting of the Math- Spaces (Code: SS 6A), Sergiy Merenkov, Jeremy Taylor ematical Association of America (MAA), annual meetings Tyson, and Jang-Mei Wu, University of Illinois at Urbana- of the Association for Women in Mathematics (AWM) and Champaign. the National Association of Mathematicians (NAM), and the Geometric Group Theory (Code: SS 2A), Sergei V. Iva- winter meeting of the Association for Symbolic Logic (ASL), nov, Ilya Kapovich, Igor Mineyev, and Paul E. Schupp, with sessions contributed by the Society for Industrial and University of Illinois at Urbana-Champaign. Applied Mathematics (SIAM). Graph Theory (Code: SS 4A), Alexander V. Kostochka Associate secretary: Bernard Russo and Douglas B. West, University of Illinois at Urbana- Announcement issue of Notices: October 2008 Champaign. Program first available on AMS website: November 1, Mathematical Vizualization (Code: SS 7A), George K. 2008 Francis, University of Illinois at Urbana-Champaign, Louis Program issue of electronic Notices: January 2009 H. Kauffman, University of Illinois at Chicago, Dennis Mar- Issue of Abstracts: Volume 30, Issue 1 tin Roseman, University of Iowa, and Andrew J. Hanson, Indiana University. Deadlines Probabilistic and Extremal Combinatorics (Code: SS 5A), For organizers: Expired Jozsef Balogh and Jozsef Balogh, University of Illinois at For consideration of contributed papers in Special Ses- Urbana-Champaign. sions: To be announced q-Series and Partitions (Code: SS 1A), Bruce Berndt, For abstracts: To be announced University of Illinois at Urbana-Champaign, and Ae Ja Yee, Pennsylvania State University. The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ national.html. Raleigh, North AMS Invited Addresses Oded Schramm, Microsoft, Title to be announced (AMS Carolina Josiah Willard Gibbs Lecture). North Carolina State University April 4–5, 2009 Urbana, Illinois Saturday – Sunday University of Illinois at Urbana-Champaign Meeting #1048 March 27–29, 2009 Southeastern Section Friday – Sunday Associate secretary: Matthew Miller Announcement issue of Notices: To be announced Meeting #1047 Program first available on AMS website: To be an- Central Section nounced Associate secretary: Susan J. 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 an- nounced Deadlines Program issue of electronic Notices: To be announced For organizers: September 4, 2008

650 Notices of the AMS Volume 55, Number 5 Meetings & Conferences

For consideration of contributed papers in Special Ses- sions: To be announced Worcester, For abstracts: To be announced Massachusetts The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ Worcester Polytechnic Institute sectional.html. April 25–26, 2009 Special Sessions Saturday – Sunday Kac-Moody Algebras, Vertex Algebras, Quantum Groups, Meeting #1050 and Applications (Code: SS 1A), Bojko N. Bakalov, Kai- Eastern Section lash C. Misra, and Naihuan N. Jing, North Carolina State Associate secretary: Steven H. Weintraub University. Announcement issue of Notices: To be announced Program first available on AMS website: To be an- nounced San Francisco, Program issue of electronic Notices: To be announced California Issue of Abstracts: To be announced Deadlines San Francisco State University For organizers: September 25, 2008 For consideration of contributed papers in Special Ses- April 25–26, 2009 sions: To be announced Saturday – Sunday For abstracts: To be announced

Meeting #1049 Western Section Waco, Texas Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced Baylor University Program first available on AMS website: To be an- October 16–18, 2009 nounced Friday – Sunday Program issue of electronic Notices: To be announced Central Section Issue of Abstracts: To be announced Associate secretary: Susan J. Friedlander Announcement issue of Notices: To be announced Deadlines Program first available on AMS website: To be an- For organizers: September 25, 2008 nounced For consideration of contributed papers in Special Ses- Program issue of electronic Notices: To be announced sions: To be announced Issue of Abstracts: To be announced For abstracts: To be announced Deadlines The scientific information listed below may be dated. For organizers: March 17, 2009 For the latest information, see www.ams.org/amsmtgs/ For consideration of contributed papers in Special Ses- sectional.html. sions: To be announced For abstracts: To be announced Special Sessions Banach Algebras, Topological Algebras and Abstract The scientific information listed below may be dated. Harmonic Analysis (Code: SS 1A), Thomas V. Tonev, Uni- For the latest information, see www.ams.org/amsmtgs/ sectional.html. versity of Montana-Missoula, and Fereidoun Ghahramani, University of Manitoba. Special Sessions Dynamic Equations on Time Scales: Analysis and Ap- plications (Code: SS 1A), John M. Davis, Ian A. Gravagne, and Robert J. Marks, Baylor University.

May 2008 Notices of the AMS 651 Meetings & Conferences

with sessions contributed by the Society of Industrial and Boca Raton, Florida Applied Mathematics (SIAM). Associate secretary: Matthew Miller Florida Atlantic University Announcement issue of Notices: October 2009 October 30 – November 1, 2009 Program first available on AMS website: November 1, 2009 Friday – Sunday Program issue of electronic Notices: January 2010 Southeastern Section Issue of Abstracts: Volume 31, Issue 1 Associate secretary: Matthew Miller Announcement issue of Notices: To be announced Deadlines Program first available on AMS website: To be an- nounced For organizers: April 1, 2009 Program issue of electronic Notices: To be announced For consideration of contributed papers in Special Ses- Issue of Abstracts: To be announced sions: To be announced For abstracts: To be announced Deadlines For organizers: March 30, 2009 For consideration of contributed papers in Special Ses- Lexington, Kentucky sions: To be announced For abstracts: To be announced University of Kentucky March 27–28, 2010 Riverside, California Saturday – Sunday Southeastern Section University of California Associate secretary: Matthew Miller Announcement issue of Notices: To be announced November 7–8, 2009 Program first available on AMS website: To be an- Saturday – Sunday nounced Western Section Program issue of electronic Notices: To be announced Associate secretary: Michel L. Lapidus Issue of Abstracts: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: To be an- Deadlines nounced For organizers: August 28, 2009 Program issue of electronic Notices: To be announced For consideration of contributed papers in Special Ses- Issue of Abstracts: To be announced sions: To be announced Deadlines For abstracts: To be announced For organizers: April 6, 2009 For consideration of contributed papers in Special Ses- sions: To be announced St. Paul, Minnesota For abstracts: To be announced Macalester College

April 10–11, 2010 San Francisco, Saturday – Sunday Central Section California Associate secretary: Susan J. Friedlander Moscone Center West and the San Fran- Announcement issue of Notices: To be announced cisco Marriott Program first available on AMS website: To be an- nounced January 6–9, 2010 Program issue of electronic Notices: To be announced Wednesday – Saturday Issue of Abstracts: To be announced Joint Mathematics Meetings, including the 116th Annual Meeting of the AMS, 93rd Annual Meeting of the Math- Deadlines ematical Association of America (MAA), annual meetings For organizers: September 10, 2009 of the Association for Women in Mathematics (AWM) and For consideration of contributed papers in Special Ses- the National Association of Mathematicians (NAM), and the sions: To be announced winter meeting of the Association for Symbolic Logic (ASL), For abstracts: To be announced

652 Notices of the AMS Volume 55, Number 5 Meetings & Conferences Notre Dame, Indiana Boston, Notre Dame University Massachusetts September 18–19, 2010 John B. Hynes Veterans Memorial Conven- Saturday – Sunday tion Center, Boston Marriott Hotel, and Central Section Boston Sheraton Hotel Associate secretary: Susan J. Friedlander January 4–7, 2012 Announcement issue of Notices: To be announced Wednesday – Saturday Program first available on AMS website: To be an- Joint Mathematics Meetings, including the 118th Annual nounced Meeting of the AMS, 95th Annual Meeting of the Math- Program issue of electronic Notices: To be announced ematical Association of America, annual meetings of the Issue of Abstracts: To be announced Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the Deadlines winter meeting of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and For organizers: February 19, 2010 Applied Mathematics (SIAM). For consideration of contributed papers in Special Ses- Associate secretary: Michel L. Lapidus sions: To be announced Announcement issue of Notices: October 2011 For abstracts: To be announced Program first available on AMS website: November 1, 2011 Program issue of electronic Notices: January 2012 New Orleans, Issue of Abstracts: Volume 33, Issue 1 Deadlines Louisiana For organizers: April 1, 2011 For consideration of contributed papers in Special Ses- New Orleans Marriott and Sheraton New sions: To be announced For abstracts: To be announced Orleans Hotel January 5–8, 2011 San Diego, California Wednesday – Saturday Joint Mathematics Meetings, including the 117th Annual San Diego Convention Center and San Meeting of the AMS, 94th Annual Meeting of the Math- Diego Marriott Hotel and Marina ematical Association of America, annual meetings of the January 9–12, 2013 Association for Women in Mathematics (AWM) and the Wednesday – Saturday National Association of Mathematicians (NAM), and the Joint Mathematics Meetings, including the 119th Annual winter meeting of the Association for Symbolic Logic (ASL), Meeting of the AMS, 96th Annual Meeting of the Math- ematical Association of America, annual meetings of the with sessions contributed by the Society for Industrial and Association for Women in Mathematics (AWM) and the Applied Mathematics (SIAM). National Association of Mathematicians (NAM), and the Associate secretary: Susan J. Friedlander winter meeting of the Association for Symbolic Logic (ASL), Announcement issue of Notices: October 2010 with sessions contributed by the Society for Industrial and Program first available on AMS website: November 1, Applied Mathematics (SIAM). Associate secretary: Steven H. Weintraub 2010 Announcement issue of Notices: To be announced Program issue of electronic Notices: January 2011 Program first available on AMS website: To be an- Issue of Abstracts: Volume 32, Issue 1 nounced Program issue of electronic Notices: To be announced Deadlines Issue of Abstracts: To be announced

For organizers: April 1, 2010 Deadlines For consideration of contributed papers in Special Ses- For organizers: April 1, 2012 sions: To be announced For consideration of contributed papers in Special Ses- For abstracts: To be announced sions: To be announced

May 2008 Notices of the AMS 653 Meetings & Conferences

For abstracts: To be announced Baltimore, Maryland Baltimore Convention Center January 15–18, 2014 Wednesday – Saturday Joint Mathematics Meetings, including the 120th Annual Meeting of the AMS, 97th Annual Meeting of the Math- ematical Association of America, annual meetings of the Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic, with sessions contributed by the Society for Industrial and Ap- plied Mathematics (SIAM). Associate secretary: Matthew Miller Announcement issue of Notices: To be announced Program first available on AMS website: To be an- nounced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced

Deadlines For organizers: April 1, 2013 For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announced ced San Antonio, Texas Henry B. Gonzalez Convention Center and Grand Hyatt San Antonio January 10–13, 2015 Saturday – Tuesday Joint Mathematics Meetings, including the 121st Annual Meeting of the AMS, 96th Annual Meeting of the Math- ematical Association of America, annual meetings of the Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Associate secretary: Susan J. Friedlander Announcement issue of Notices: October 2014 Program first available on AMS website: To be an- nounced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced

Deadlines For organizers: April 1, 2014 For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announcednn

654 Notices of the AMS Volume 55, Number 5 Meetings and Conferences of the AMS

Associate Secretaries of the AMS Eastern Section: Lesley M. Sibner (until January 31, 2009), Western Section: Michel L. Lapidus, Department of Math- Department of Mathematics, Polytechnic University, Brooklyn, ematics, University of California, Surge Bldg., Riverside, CA NY 11201-2990; e-mail: [email protected]; telephone: 92521-0135; e-mail: [email protected]; telephone: 718-260-3505. Steven Weintraub (after January 31, 2009), 951-827-5910. Department of Mathematics, Lehigh University, Bethlehem, PA 18105-3174; e-mail: [email protected]; tele- Central Section: Susan J. Friedlander, Department of Math- phone: 610-758-3717. ematics, University of Illinois at Chicago, 851 S. Morgan (M/C 249), Chicago, IL 60607-7045; e-mail: [email protected]; Southeastern Section: Matthew Miller, Department of Math- telephone: 312-996-3041. ematics, University of South Carolina, Columbia, SC 29208-0001, e-mail: [email protected]; telephone: 803-777-3690.

The Meetings and Conferences section of the Notices March 27–28 Lexington, Kentucky p. 652 gives information on all AMS meetings and conferences April 10–11 St. Paul, Minnesota p. 652 approved by press time for this issue. Please refer to the page September 18–19 Notre Dame, Indiana p. 653 numbers cited in the table of contents on this page for more detailed information on each event. Invited Speakers and 2011 Special Sessions are listed as soon as they are approved by the January 5–8 New Orleans, Louisiana p. 653 cognizant program committee; the codes listed are needed Annual Meeting for electronic abstract submission. For some meetings the 2012 list may be incomplete. Information in this issue may be January 4–7 Boston, Massachusetts p. 653 dated. Up-to-date meeting and conference information can Annual Meeting be found at www.ams.org/meetings/. 2013 January 9–12 San Diego, California p. 653 Meetings: Annual Meeting 2008 2014 May 3–4 Claremont, California p. 645 January 15–18 Baltimore, Maryland p. 654 June 4–7 Rio de Janeiro, Brazil p. 646 Annual Meeting October 4–5 Vancouver, Canada p. 646 2015 October 11–12 Middletown, Connecticut p. 647 January 10–13 San Antonio, Texas p. 654 October 17–19 Kalamazoo, Michigan p. 648 Annual Meeting October 24–26 Huntsville, Alabama p. 648 December 17–21 Shanghai, People’s Important Information Regarding AMS Meetings Republic of China p. 649 Potential organizers, speakers, and hosts should refer to page 95 in the January 2008 issue of the Notices for general 2009 information regarding participation in AMS meetings and January 5–8 Washington, DC p. 650 conferences. Annual Meeting March 27–29 Urbana, Illinois p. 650 Abstracts April 4–5 Raleigh, North Carolina p. 650 Speakers should submit abstracts on the easy-to-use interac- April 25–26 San Francisco, California p. 651 tive Web form. No knowledge of is necessary to submit April 25–26 Worcester, Massachusetts p. 651 an electronic form, although those who use may submit abstracts with such coding, and all math displays and simi- Oct. 16–18 Waco, Texas p. 651 larily coded material (such as accent marks in text) must Oct. 30–Nov. 1 Boca Raton, Florida p. 652 be typeset in . Visit http://www.ams.org/cgi-bin/ Nov. 7–8 Riverside, California p. 652 abstracts/abstract.pl. Questions about abstracts may be sent to [email protected]. Close attention should be paid to 2010 specified deadlines in this issue. Unfortunately, late abstracts January 6–9 San Francisco, California p. 652 cannot be accommodated. Annual Meeting

Conferences: (see http://www.ams.org/meetings/ for the most up-to-date information on these conferences.) Co-sponsored conferences: June 30–July 3, 2008: Tenth Conference on p-adic and Non-Archimedean Analysis, Michigan State University. See http://bt.pa.msu.edu/NA08/ for more information.

May 2008 Notices of the AMS 655 Take Notice of Cambridge’s New and Forthcoming Titles!

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Patterns in factorization (see page 595)

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