ISSISISSSSNN0 00000200202-99-999992020

of the American Mathematical Society

May 2011 Volume 58, Number 5

Discrete Wavelet Transformations and Undergraduate Education page 656

Mathematical Intimidation: Driven by the Data page 667

Remembering Leon Ehrenpreis (1930–2010) page 674

How a Medieval Troubadour Became a Mathematical Figure page 682

Abouut thhe CoC vever:r Wava ellete s inin imamagege comomprprese sionon (sesee ppaagege 71717) “So r r y , t h a t ’s n o t c o r r e c t .” “Th a t ’s c o r r e c t .”

Two Online Homework Systems Went Head to Head. Only One Made the Grade.

What good is an online homework system if it can’t recognize right from wrong? Our sentiments exactly. Which is why we decided to compare WebAssign with the other leading homework system for math. The results were surprising. The other system failed to recognize correct answers to free response questions time and time again. That means students who were actually answering correctly were receiving failing grades. WebAssign, on the other hand, was designed to recognize and accept more iterations of a correct answer. In other words, WebAssign grades a lot more like a living, breathing professor and a lot less like, well, that other system. So, for those of you who thought that other system was the right answer for math, we respectfully say, “Sorry, that’s not correct.”

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Notices of the American Mathematical Society May 2011 Communications

688 WHAT IS... an 674 Infra-nilmanifold Endomorphism? Karel Dekimpe

690 The Story of Gyrangle Reza Sarhangi

693 Report on 2009–2010 Academic Recruitment and Hiring James W. Maxwell and 697 690 Colleen Rose 704 Doceamus: Revitalizing the Features 1960 Mathematics Major Alan Tucker The May issue showcases diverse features of the mathemati- cal life. John Ewing, former executive director of the AMS and 706 JPBM Communications now president of Math for America, tells us of the dangers of Award value-added modeling. Michael Saclolo writes of a mathemati- 708 MAA Prizes Presented in cal analysis of the poetry of medieval troubadours. Catherine New Orleans Bénéteau and Patrick Van Fleet explain how wavelets can be used to augment undergraduate mathematics education. Finally, we AWM Awards Given in New 711 share memories of noted mathematician Leon Ehrenpreis. Orleans —Steven G. Krantz, Editor 713 2011 Mathematics Programs That Make a 656 Discrete Wavelet Transformations and Difference Undergraduate Education 716 2011 Award for an Exemplary Program Catherine Bénéteau and Patrick J. Van Fleet or Achievement in a Mathematics Department 667 Mathematical Intimidation: Driven by the Data 718 Arizona’s Math Center Wins AMS Award John Ewing Allyn Jackson 674 Remembering Leon Ehrenpreis (1930– Commentary 2010) Daniele C. Struppa, Hershel Farkas, Takahiro Kawai, 653 Letters to the Editor Peter Kuchment, Eric Todd Quinto, Shlomo Sternberg, Alan Taylor 697 At Home with André and Simone Weil— A Book Review 682 How a Medieval Troubadour Became a Reviewed by Michèle Audin Mathematical Figure

699 The Value of Nothing: A Michael P. Saclolo Review of The Quants Reviewed by David Steinsaltz Notices Departments of the American Mathematical Society About the Cover ...... 717

EDITOR: Steven G. Krantz Mathematics People ...... 728 ASSOCIATE EDITORS: Butcher Receives Inaugural Jones Medal, Polterovich Awarded Coxeter- Krishnaswami Alladi, David Bailey, Jonathan Borwein, James Prize, Scholze Awarded 2011 Clay Research Fellowship, Susanne C. Brenner, Bill Casselman (Graphics Editor), Robert J. Daverman, Susan Friedlander, Robion Kirby, Mazzucato Awarded Michler Prize, Spohn Awarded Heineman Prize, Rafe Mazzeo, Harold Parks, Lisette de Pillis, Peter National Academy of Engineering Elections. Sarnak, Mark Saul, Edward Spitznagel, John Swallow ...... SENIOR WRITER and DEPUTY EDITOR: Mathematics Opportunities 729 Allyn Jackson NSF Postdoctoral Research Fellowships, International Mathematics MANAGING EDITOR: Sandra Frost Competition for University Students. CONTRIBUTING WRITER: Elaine Kehoe Inside the AMS ...... 730 CONTRIBUTING EDITOR: Randi D. Ruden EDITORIAL ASSISTANT: David M. Collins Epsilon Awards for 2010, AMS Holds Workshop for Department Chairs, PRODUCTION: Kyle Antonevich, Anna Hattoy, From the AMS Public Awareness Office, Deaths of AMS Members, Teresa Levy, Mary Medeiros, Stephen Moye, Erin Correction. Murphy, Lori Nero, Karen Ouellette, Donna Salter, Deborah Smith, Peter Sykes, Patricia Zinni Reference and Book List ...... 732 ADVERTISING SALES: Anne Newcomb SUBSCRIPTION INFORMATION: Subscription prices Mathematics Calendar ...... 739 for Volume 58 (2011) are US$510 list; US$408 insti- tutional member; US$306 individual member; US$459 Classified Advertisements ...... 745 corporate member. (The subscription price for mem- bers is included in the annual dues.) A late charge of New Publications Offered by the AMS ...... 746 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Add for postage: Surface Meetings and Conferences of the AMS ...... 750 delivery outside the United States and India—US$27; in India—US$40; expedited delivery to destinations Meetings and Conferences Table of Contents ...... 759 in North America—US$35; elsewhere—US$120. Subscriptions and orders for AMS publications should be addressed to the American Mathematical Society, P.O. Box 845904, Boston, MA 02284-5904 USA. All orders must be prepaid. ADVERTISING: Notices publishes situations wanted and classified advertising, and display advertising for publishers and academic or scientific organizations. Advertising material or questions may be sent to [email protected] (classified ads) or notices-ads@ From the ams.org (display ads). SUBMISSIONS: Articles and letters may be sent to the editor by email at [email protected], by AMS Secretary fax at 314-935-6839, or by postal mail at Department of Mathematics, Washington University in St. Louis, Campus Box 1146, One Brookings Drive, St. Louis, MO American Mathematical Society—Contributions ...... 723 63130. Email is preferred. Correspondence with the managing editor may be sent to [email protected]. For more information, see the section “Reference and Officers of the Society 2010 and 2011 Updates ...... 735 Book List”. NOTICES ON THE AMS WEBSITE: Supported by the Call for Nominations for the George David Birkhoff, Frank AMS membership, most of this publication is freely Nelson Cole, and Levi L. Conant Prizes ...... 736 available electronically through the AMS website, the Society’s resource for delivering electronic prod- ucts and services. Use the URL http://www.ams. Call for Nominations for the Albert Leon Whiteman Memorial org/notices/ to access the Notices on the website. Prize and the AMS Distinguished Public Service Award . . . . . 737 [Notices of the American Mathematical Society (ISSN 0002- 9920) is published monthly except bimonthly in June/July by the American Mathematical Society at 201 Charles Street, Call for Nominations for the 2012 Frank and Brennie Morgan Providence, RI 02904-2294 USA, GST No. 12189 2046 RT****. AMS-MAA-SIAM Prize ...... 738 Periodicals postage paid at Providence, RI, and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248 USA.] Publication here of the Society’s street address and the other information in brackets above is a technical requirement of the U.S. Postal Service. Tel: 401-455-4000, email: [email protected]. © Copyright 2011 by the American Mathematical Society. I thank Randi D. Ruden for her splendid editorial work, and All rights reserved. for helping to assemble this issue. She is essential to everything Printed in the United States of America. The paper used in this journal is acid-free and falls within the guidelines that I do. established to ensure permanence and durability. —Steven G. Krantz Opinions expressed in signed Notices articles are those of Editor the authors and do not necessarily reflect opinions of the editors or policies of the American Mathematical Society. Letters to the Editor

New Bias Discovered: Proc. AMS AMS Rescues Commutative Honoring Professor Chern: Favors Commutative Rings to Algebra—Is Geometry Next? A Bridge Builder between Astronomy My article is meant to confront pre- Nations While there are many issues of inter- I was amazed by the article of conceptions with data. I thank Alex est and concern to both China and the Joseph F. Grcar, “Topical bias in Eremenko for the opportunity to United States, there is one reason for generalist mathematics journals”, explore an example. both countries to celebrate. 2011 is He suggests Proceedings of the Notices 57 (11). the one hundredth anniversary of the AMS (PAMS) favors commutative al- A bias “which seems not to be birth in China of the great Chinese- gebra to subjects including statistics discovered previously” consists in the American mathematician, the late following: of two papers reviewed in because papers of the subjects may Shiing-Shen Chern. Although Chern the Zentralblatt or in Math Reviews, appear in journals of other fields, was born and passed away in China, a paper in pure mathematics is more thus reducing their presence in PAMS. the bulk of his illustrious profes- likely to be published in Proceedings If this were correct, then the same sional career was spent in the United of the AMS than a paper in optics, bias for commutative algebra would States, where he was a professor of statistics, astronomy, or geophysics. be seen at other generalist journals, mathematics, first at the University of In my opinion, this observation is such as Comptes Rendus Mathéma- Chicago and then at the University of California at Berkeley. trivial: just ask any mathematician or tique (C. R. Math). However, C. R. Math publishes commutative algebra Throughout his life Chern did astronomer which of the two papers and statistics in proportions 22 : 262, everything that he could to bring is more likely to appear in Proc AMS. which is roughly the reciprocal of people together. One hopes that both And s/he will give you the right an- 267 : 40 at PAMS. (As in my article, the U.S. and Chinese governments swer without any statistical analysis. papers have primary or secondary will see fit to jointly honor this won- The author does not take into ac- subjects in classes 13 and 62 for derful mathematician and teacher. count an evident thing: Zentralblatt The American Mathematical Society 2000–09.) Thus Eremenko’s interpre- and Math Reviews try to cover not should encourage both governments tation is inconsistent with the data. only mathematics but also other to jointly honor the memory of Shiin- The limitations of his suggestion are areas where mathematics is applied. Shen Chern who was, after all, a vice demonstrated further if he were to By the way, the original name of president of the AMS. try explaining why PAMS favors com- Zentralblatt was Zentralblatt für Personally, I would like to see two mutative algebra to geometry. Mathematik [und ihre Grenzgebiete] new institutes for mathematics— The importance of topical bias is one in the United States and one in which clearly shows the intention to not the cause but the impact. Some- China—emphasizing mathematics cover “boundary areas”. So the set one wrote to me that it is “discrimina- and mathematically related fields of the papers from which the author tory to many mathematicians” if ten- and dedicated to providing research takes his statistics is initially biased: ure committees prefer publications opportunities for both young math- it contains many papers whose pri- in journals that have topical biases. ematicians and for teachers of school mary subject is not mathematics. Another person wrote that PAMS mathematics. Such institutes could A person who wrote a paper in favors the abstract to the concrete, serve as fitting permanent memori- astronomy with some mathematical but “a less monolithic mathematical als to a person whose like we are not content has a choice: to submit it to community is in all of our interests”. likely to see again. an astronomy journal or to a mathe- matical journal. An author of a paper —Joe Grcar —Richard H. Escobales Jr. Canisius College in pure mathematics does not have [email protected] such choice. That’s why mathematical [email protected] journals seem biased towards “pure P.S. There are two minor inaccuracies (Received January 31, 2011) mathematics”. in Eremenko’s letter. My article says biases have not been “discussed” The Law of the Constant Ratio —Alex Eremenko (rather than “discovered”), and my The use of publication and citation Purdue University article does state the full title of databases, namely Web of Science [email protected] Zentralblatt. and Scopus, by funding agencies and governmental institutions around the (Received January 29, 2011) (Received February 3, 2011) world for evaluation of the scientific

MAY 2011 NOTICES OF THE AMS 653 Letters to the Editor performance of countries, universi- The law of the constant ratio for majors prepare a research paper ties, research institutions, and indi- citation counts would also allow cre- and then to present it to the entire viduals, appears as a global trend ation of multidisciplinary rankings department orally. Given his experi- and a global issue. Since this trend based on the h-index using normal- ence with research and his devotion appears to be unavoidable, it is im- ized citation counts. to clarity in presentation of results, portant to have better measures for This is impossible when absolute he took over the seminar with great comparing scientific performance in citation counts are used, since non- success, and with great benefit to different fields of science. normalized citation counts naturally our seniors. A suitable tool for better qualita- result in significant differences in h- It was our privilege here in Moraga tive comparison of scientific per- indices between the fields (http:// to enjoy Henry Helson for a couple formance in different fields of sci- dx.doi.org/10.1038/448737a) of years. ence is the law of the constant ratios (Ball, Ph., Nature 448:2007, 737). —Brother L. Raphael, FSC (http://dx.doi.org/10.1007/ Saint Mary's College s11192-005-0240-0) (Podlubny, I., —Igor Podlubny Moraga, CA 94575 Scientometrics 64(1):2005, 95–99), Technical University [email protected] which says that the ratio of the total of Kosice, Slovakia numbers of citations in any two broad [email protected] (Received February 10, 2011) fields of science remains close to constant. One citation in mathemat- —Katarina Kassayova A Disagreement about Hilbert ics corresponds to five citations in P. J. Safarik University, The review of the book Logicomix in engineering and technology, to eight Kosice, Slovakia the December 2010 issue of Notices citations in biology, to nine citations [email protected] includes (page 1429) a comment on in earth and space sciences, to thir- Hilbert and his son corresponding to teen citations in social and behavioral (Received January 22, 2011) a statement in the book (page 327): sciences, to fifteen citations in chem- “When the boy was diagnosed with A Retired Gentleman istry, to nineteen citations in phys- schizophrenia, at age fifteen, his fa- ics, and to seventy-eight citations After reading the very fine memo- ther sent him off to an asylum, where both in clinical medicine and in bio- rial for Professor Helson in Notices he spent the rest of his life. Hilbert medical research (these nine broad 58(2), I would like to add a personal never visited his son.” fields are taken from the U.S. Na- recollection. This account disagrees with Con- stance Reid’s book, Hilbert, which tional Science Foundation classifica- In 1999 a dapper little gentleman asserts that he entered the insane tion). This approach has already been appeared at the office. I was serving asylum at about age twenty-one (pp. successfully used for compiling the again as chairman at Saint Mary’s 138–139), was released a few years first multidisciplinary list of highly College in Moraga, California, a tiny later (p. 151), and occasionally lived at cited researchers (http://dx.doi. school about twenty minutes from home afterwards (pp. 151, 210, 215). org/10.3152/147154406781775887) Berkeley. (Podlubny, I., and Kassayova, K., Re- He was applying for the position —George Glauberman search Evaluation 15(3):2006, 154– we had posted for a part-time instruc- University of Chicago 162). tor in math. He claimed he was retired [email protected] Based on the same source of from Cal and had seen our opening. Given the disjunction of our scale data (http://www.nsf.gov/ (Received February 11, 2011) statistics/seind04/), we extend from that at Cal, we may conclude the law of the constant ratio to the immediately that money was not the number of articles, too. Namely, one consideration. He was then hired to article in mathematics corresponds fill in temporarily. to three articles in earth and space He came into our department science; to four articles in engineer- and was comfortable at once. He ap- ing and technology, in biology, and peared at our events and many times in chemistry; to five articles in phys- gave the impression that he was a ics; to nine articles in social and junior member at the bottom of the behavioral sciences; to ten articles in ladder—invoking seniority or experi- biomedical research; and to eighteen ence was not his way. He simply liked articles in clinical medicine. being a teacher. This means that quantitative com- As he taught several courses, it parison of researchers working in became apparent to me that this different fields of science can be done extraordinary fellow had a massive by normalizing their correspond- background, a wide acquaintance- ing citation and paper counts with ship, and a remarkable charm. I soon respect to mathematics, and not by put him in charge of our senior semi- using just total counts. nar. This course is meant to help the

654 NOTICES OF THE AMS VOLUME 58, NUMBER 5 A MERICAN MATHEMATICAL SOCIETY

The AMS Book and Journal Donation Program matches donors with academic institutions in countries that have a crucial need for research-level publications to support their mathematics programs. Potential donors are invited to contact the AMS with information about books and primary research journals that they are willing to donate to those libraries. (Please note that textbooks and the Notices or Bulletin are not candidates for this program.) Suitable publications are used to fill existing inquiries, or are listed on our website as an invitation for libraries to request the items. Under this program, donations are shipped not to the AMS but directly to the receiving institutions, and the Society reimburses donors for shipping costs. For more information, see www.ams.org/programs/donations Contact: Membership and Programs Department, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA; telephone: 800-321-4267, ext. 4139 (U.S. and Canada) or 401-455-4139 (worldwide); email: [email protected] Discrete Wavelet Transformations and Undergraduate Education Catherine Bénéteau and Patrick J. Van Fleet

avelet theory was an immensely In much the same way that wavelet theory popular research area in the is the confluence of several mathematical disci- 1990s that synthesized ideas from plines, we have discovered that the discrete wavelet mathematics, physics, electrical en- transformation is an ideal topic for a modern un- Wgineering, and computer science. In dergraduate class—the derivation of the discrete mathematics, the subject attracted researchers wavelet transformation draws largely from calcu- from areas such as real and harmonic analysis, sta- lus and linear algebra, provides a natural conduit tistics, and approximation theory, among others. Applications of wavelets abound today—perhaps to Fourier series and discrete convolution, and the most significant contributions of wavelets can allows near-immediate access to current appli- be found in signal processing and digital image cations. Students learn about signal denoising, compression. As the basic tenets of wavelet theory edge detection in digital images, and image com- were established, they became part of graduate pression, and use computer software in both school courses and programs, but it is only in the derivation and implementation of the dis- the last ten years that we have seen wavelets crete wavelet transformation. In the process of and their applications being introduced into the investigating applications, students learn how undergraduate curriculum. the application often drives the development of The introduction of the topic to undergrad- mathematical tools. Finally, the design of more ad- uates is quite timely—most of the foundational vanced wavelet filters allows the students to gain questions posed by wavelet researchers have been experience “working in the transform domain” answered, and several current applications of wavelets are firmly entrenched in areas of image and provides motivation for several important processing. Several authors [7, 2, 8, 14] have writ- concepts from an undergraduate real analysis ten books in which they present the basic results class. of wavelet theory in a manner that is accessible In what follows, we outline the basic devel- to undergraduates. Others have authored books opment of discrete wavelet transformations and [15, 13, 1, 9] that include applications as part of discuss their connection with Fourier series, con- their presentation. volution, and filtering. In the process, we illustrate the application of discrete wavelet transforma- Catherine Bénéteau is professor of mathematics at the tions to digital images. We next construct one pair University of South Florida. Her email address is of filters that are used by the JPEG2000 image [email protected]. compression standard. We conclude the paper by Patrick J. Van Fleet is professor of mathematics at the University of St. Thomas. His email address is illustrating how wavelet filters are implemented [email protected]. by the JPEG2000 standard. This material is based upon work supported by the Na- Let us begin by discussing the simplest discrete tional Science Foundation under grant DUE-0717662. wavelet transformation.

656 Notices of the AMS Volume 58, Number 5 The Discrete Haar Wavelet Transformation with The discrete Haar wavelet transformation is the ˜ 1 ˜ T ˜T ˜T most elementary of all discrete wavelet transforms (2) WN− 2WN 2 HN/2 GN/2 . = = and serves as an excellent pedagogical tool for the development of more sophisticated discrete What is the advantage of transforming x into a wavelet transformations and their application to and d? The vector a gives us an approximation digital signals or images. of the original vector x, while d allows us to We motivate this transformation as follows: identify large (or small) differences between the Suppose we wish to transmit a list (vector) of pairwise averages and the original data. Identifying large differences might be of interest if we were N numbers, N even, to a friend via the Inter- attempting to detect edges in a digital image, net. To reduce transfer time, we decide to send for example. On the other hand, we might be only a length N/2 approximation of the data. inclined to convert differences that are small One way to form the approximation is to send in absolute value to zero—this action, assuming pairwise averages of the numbers. For example, the original data were largely homogeneous, has T the vector [6, 12, 15, 15, 14, 12, 120, 116] can be the effect of producing a large number of zeros T approximated by the vector [9, 15, 13, 118] . Of in the quantized differences vector d˜. In this course, it is impossible to determine the original case, the modified transform is more amenable to N numbers from this approximation, but if, in data coders in image compression applications. addition, we transmit the N/2 averaged directed Of course, we have no hope of recovering the distances, then our friend could completely recover original vector x from the modified transform, but the original data. For our example, the averaged depending on the application, the sacrifice of loss directed distances are [3, 0, 1, 2]T . of resolution for storage size might be desirable. − − We define the one–dimensional discrete Haar wavelet transformation as the linear transforma- The Two-Dimensional Discrete Haar tion Wavelet Transformation a If we view a grayscale digital image as an M N x , × → d matrix A whose entries are integers between 0 and 255 inclusive, where 0 represents black and 255 where x RN , N even, and the elements of ∈ is white, and integers in between indicate varying a, d RN/2 are ∈ degrees of intensities of gray, then application x2k 1 x2k of the one-dimensional Haar wavelet transform ak − + , ˜ = 2 WM acts on the columns of A. Each column is x2k 1 x2k transformed to a column whose top half gives an dk − − + , = 2 approximation, or blur, of the original column and whose bottom half holds the differences or details where k 1,...,N/2. Given these averages and = in the data. differences, we can recover the original data. We can process the rows of A as well by In matrix form, the transformation can be ˜ ˜ T multiplying WM A by WN . We define the two- expressed as dimensional discrete Haar wavelet transformation ˜ ˜ T of the matrix A to be WM AWN . Of course, both M 1 1 0 0 0 0 2 2 and N must be even integers. An image (stored in   ˜ ˜ ˜ T 1 1 A), WM A, and WM AWN are plotted in Figure 1. 0 0 0 0  2 2  We can better understand the image displayed    .  in Figure 1(c) if we express the two–dimensional  .   .    transformation in block form. Indeed, using (1)  0 0 0 0 1 1   2 2  and (2), we see that W˜N    1 1  =  0 0 0 0  H˜M/2  − 2 2  W˜ AW˜ T A H˜ T G˜T   M N  ˜  N/2 N/2  1 1  = GM/2  0 0 2 2 0 0   −      ˜ ˜T ˜ ˜T  .  HM/2AHN/2 HM/2AGN/2  ..    =  ˜ ˜T ˜ ˜T    GM/2AHN/2 GM/2AGN/2  0 0 0 0 1 1   − 2 2        BV . ˜ = HN/2 HD (1)   It is a straightforward computation to see that if =  G˜  we partition A into 2 2 blocks Aj,k, 1 j M/2,  N/2  × ≤ ≤   1 k N/2, the (j, k) elements of , , , are   ≤ ≤ B V H D

May 2011 Notices of the AMS 657 (a) A (b) W˜320A

˜ ˜ T (c) W320AW512

Figure 1. A 320 x 512 digital grayscale image, the product W˜M A, and the two-dimensional discrete ˜ ˜ T Haar wavelet transformation WM AWN .

constructed using the four values in Aj,k. Indeed, if a b Aj,k , = c d then each (j, k) element of , , , is B V H D a b c d (a c) (b d) + + + + − + 4 4 (a b) (c d) (a d) (b c) + − + + − + , 4 4 respectively. In this way we see that the elements (a) Two iterations of are simply the averages of the elements in the B blocks Aj,k, and the elements in , , and are V H D averaged differences in the vertical, horizontal, and diagonal directions, respectively. If M and N are divisible by 2p, then we can iterate the transformation a total of p times. Figure 1(c) shows one iteration of the discrete Haar wavelet transformation. We can perform a second iteration by applying the two-dimensional discrete Haar wavelet transformation to . Figure 2 shows two B and three iterations of the discrete Haar wavelet transformation applied to A. In applications such (b) Three iterations as image compression, the iterated transformation produces more details portions, and in the case in Figure 2. Multiple iterations of the discrete which the original data are largely homogeneous, Haar wavelet transformation applied to the matrix A from Figure 1(a). then we can expect a large number of near-zero values in the details portions of the iterated transform. These small values can be quantized to zero, and the data coder should be able to Alternatively, we can use the averages portion B compress the modified transform in a highly in applications as well. Suppose we stored a four- efficient manner. iteration version of an image on a web server. Then

658 Notices of the AMS Volume 58, Number 5 Figure 3. The wavelet transform of a digital image of Helaman Ferguson’s Four Canoes is shown at the top left. The portion framed in blue is enlarged and transmitted. Next, the portion of the transform outlined in yellow is transmitted and, with 4 , inverted and enlarged to create the B4 image at top right. This process is repeated for the green,B red, and brown portions of the transform to progressively create a sequence of images whose resolution increases by a factor of two at each step. The original image, outlined in brown, is at bottom right.

4, the fourth iteration averages portion of the We could just as well develop WN via discrete B transform, could serve as a thumbnail image for convolution. the original. If a user requests the original image, Recall that if h and x are bi-infinite vectors, then the convolution of h with x is the bi-infinite we could first transmit 4 and then progressively B send detail portions at each iterative level. The vector y, denoted by y h x, where the nth component, n Z, of the= vector∗ is recipient can apply the inverse transform as detail ∈ portions are received to sequentially produce a yn hkxn k. − = k Z higher-resolution version of the original image. ∈ Figure 3 illustrates the process. If we assume that xn 0 for n < 1 and n > N, = Equation (2) tells us that the discrete Haar where N is an even integer, then we can form WN x wavelet transformation is almost orthogonal. In- by T 1 deed, if we define WN √2W˜N , then W W − , Computing u h x, where the only = N = N • = ∗ nonzero values of h are h0 h1 √2/2. and our transformation is orthogonal. The inverse = = of the transformation now has a simple form, Computing v g x, where the only • nonzero values= of g∗ are g √2/2 and which allows us to easily reconstruct the signal 0 g √2/2. = from its transformed version. 1 Downsampling= − u and v by removing the • odd components of each vector. Relation to Discrete Convolution and Truncating the downsampled vectors ap- Filters • propriately to obtain a and d. We have motivated the construction of WN by The vectors h and g are often called filters. In fact, insisting that WN transform the original data x h and g are special kinds of filters. Let x be a into an averages portion a and details portion d. vector whose elements xk 1, k Z, and suppose = ∈

May 2011 Notices of the AMS 659 k y is a vector whose elements are yk ( 1) , k Z. Then h x √2 x and h y is= the− bi-infinite∈ zero vector.∗ = Thus h is an example∗ of a lowpass filter—it passes low-frequency signals through largely unchanged but attenuates the amplitudes of high-frequency data. In a similar manner we see that g x is the bi-infinite zero vector and g y √2∗y. Here g is an example of a highpass filter∗ —it= allows high-frequency signals to pass largely unchanged but attenuates the amplitudes of low-frequency data. Thus in filtering terms, the discrete Haar wavelet transform is constructed by applying a lowpass filter and a highpass filter to the input data, downsampling both results, and (a) H(ω) then appropriately truncating the downsampled | | vectors. We will learn that all discrete wavelet transforms are built from a lowpass (scaling) filter h and a highpass (wavelet) filter. Fourier series are valuable tools for constructing these filters.

Fourier Series and Discrete Wavelet Transformations A course on discrete wavelet transformations is an excellent venue for the introduction of Fourier series into the undergraduate curriculum. There are two main uses of Fourier series in such a course. We can determine whether a finite-length T filter f [f0, . . . , fL] is lowpass or highpass by = (b) G(ω) plotting the modulus of the Fourier series | | L H(ω) G(ω) ikω Figure 4. The functions H(ω) and G(ω) . F(ω) fke , | | | | = k 0 = and, as we will see later, we can characterize a At the lowest frequency, ω 0, H(0) √2. At (bi)orthogonal discrete wavelet transformation by the highest frequency, ω π=, H(π)| | =0. In the investigating an identity related to the Fourier frequency domain, these two= conditions| | = indicate series of the scaling filter(s). that h is a lowpass filter. In a similar manner, For the discrete Haar wavelet transformation, G(0) 0 and G(π) √2 are conditions that the finite-length filters |imply| that = g is a| highpass| = filter. T For ω R, we use (3) to write T √2 √2 h [h0, h1] , ∈ = = 2 2 H(ω) 2 H(ω π) 2 | | + | + | = T ω ω π T √2 √2 (5) 2 cos2 2 cos2 + 2. g g0, g1 , = = 2 − 2 2 + 2 = In a similar manner, we use (3) and (4) to obtain give rise to the Fourier series (6) G(ω) 2 G(ω π) 2 2 √2 √2 | | + | + | = H(ω) eiω = 2 + 2 and ω (3) √2eiω/2 cos (7) H(ω)G(ω) H(ω π)G(ω π) 0. = 2 + + + = In the next section, we will see that the first √2 √2 G(ω) eiω step in a general strategy for finding longer, more = 2 − 2 sophisticated filters h and g is to find h so that (5) ω (4) √2ieiω/2 sin is satisfied and then make a judicious choice of = − 2 g so that (6) and (7) hold as well. The additional for ω R. To determine the nature of the filter, lowpass conditions H(0) √2 and H(π) 0 we plot∈ H(ω) and G(ω) . Since H(ω) and with our choice of |g ensure| = that the| highpass| = G(ω) are| both| 2π-periodic,| | even functions,| | we conditions G(0) 0, G(π) √2 hold, and in plot| them| on the interval [0, π]. The functions are this way, we| see| that = all| lowpass,| = highpass, and displayed in Figure 4. matrix orthogonality conditions placed on filters

660 Notices of the AMS Volume 58, Number 5 T h and g can be completely characterized using We now set g [h3, h2, h1, h0] . It is straight- = − − Fourier series. forward to show that if (9), (13), (14), and (15) hold, then the highpass conditions (10), (11) are satisfied Daubechies Orthogonal Scaling Filters and Suppose we apply the one-dimensional discrete g2 g2 g2 g2 1 Haar wavelet transformation to the vector v 0 + 1 + 2 + 3 = T = g0g2 g1g3 0. [0, 0, 100, 100] . We obtain the transformed vector + = √2 [0, 100 0, 0]T . The differences portion of the Moreover, we can show that transformed| vector consists only of zeros, missing h0g0 h1g1 h2g2 h3g3 0 the large “edge” between 0 and 100 in v. The + + + = problem is that the Haar scaling/wavelet filter h1g3 h0g2 0 + = pair is too short. Let’s consider longer filter pairs. h3g1 h2g0 0 These filters and the corresponding wavelets were + = discovered by Ingrid Daubechies (see, e. g., [4]). so that WN is an orthogonal matrix. However, there are infinitely many solutions to the system We wish to construct an orthogonal matrix WN that uses longer scaling and wavelet filters. It turns h2 h2 h2 h2 1 out that we need to consider even-length filters, so 0 + 1 + 2 + 3 = T h0h2 h1h3 0 let’s start with a scaling filter h [h0, h1, h2, h3] (16) + = . = T h0 h1 h2 h3 √2 and wavelet filter g [g0, g1, g2, g3] . We insist + + + = = h0 h1 h2 h3 0 that − + − =

(8) H(0) h0 h1 h2 h3 √2 | | = | + + + | = Here is where the Fourier series approach really (9) H(π) h0 h1 h2 h3 0 makes an impact. Daubechies chose to impose the = − + − = and additional condition H′(π) 0. This condition has the effect of “flattening” the= graph of the modulus (10) G(0) g0 g1 g2 g3 0 H(ω) even more at ω π; thus intuitively the = + + + = filter| h| does an even better= job of attenuating (11) G(π) g0 g1 g2 h3 √2 | | = | − + − | = the amplitudes of the high-frequency portions of so that the filters h, g are lowpass and highpass, the input data. If we expand the left-hand side of respectively. H′(π) 0, we obtain the following linear equation We also wish to retain the structure of the = (17) h1 2h2 3h3 0, transformation by suitably truncating two down- − + = sampled, convolution products. In this case, the and we add (17) to our system (16). longer lengths of our filters force us to “wrap” It turns out that there are two real solutions rows at the bottom of each block HN/2, GN/2 of to the system, one of which is a reflection of the matrix WN . For example, in the case in which the other. The solution can be solved by hand N 8, WN takes the form = (see, e. g., [12]) to obtain the Daubechies four-term scaling filter: h3 h2 h1 h0 0 0 0 0  0 0 h3 h2 h1 h0 0 0  1 √3 3 √3 h , h 0 0 0 0 h h h h 0 + 1 +  3 2 1 0  = 4√2 = 4√2    h1 h0 0 0 0 0 h3 h2  3 √3 1 √3 (12) W8   . h2 − , h3 − . =  g3 g2 g1 g0 0 0 0 0    = 4√2 = 4√2  0 0 g g g g 0 0   3 2 1 0  The modulus of H(ω) is plotted in Figure 5.    0 0 0 0 g3 g2 g1 g0    Compare this graph with that of Figure 4.  g g 0 0 0 0 g g   1 0 3 2  In order to construct longer even-length fil-   T ters h [h0, . . . , hL] , L odd, we must write down The wrapping rows cause problems in applications = since it inherently assumes that data are periodic, general orthogonality conditions and lowpass con- but on the other hand, it simplifies our final ditions. We can ensure the orthogonality of WN using the following theorem. requirement that WN be an orthogonal matrix. In this case, we must have ikω Theorem 1. Suppose A(ω) ake and 2 2 2 2 = k Z (13) h0 h1 h2 h3 1 ikω ∈ + + + = B(ω) bke are Fourier series. Then = Z (14) h0h2 h1h3 0. k + = ∈ (18) A(ω) 2 A(ω π) 2 2 It turns out that if real numbers h0, . . . , h3 satisfy | | + | + | = (9), (13), and (14), then (8) holds. We will choose if and only if the positive square root so that (19) akak 2n δ0, n √ − (15) h0 h1 h2 h3 2. k Z = + + + = ∈

May 2011 Notices of the AMS 661 While this derivation of the system is easy to understand, solving it numerically for large filter lengths can be difficult. It should be noted that Daubechies’s classical derivation of these filters is centered around the construction of a trigonometric polynomial that leads to the solution of (18). Particular roots of this polynomial are then used to find a Fourier series H(ω) that solves (23). This process (see [5] or [9]) works well for filters of long length, but the mathematics required to understand it may be better suited for advanced undergraduate or beginning graduate students.

Figure 5. H(ω) for the length four | | Orthogonal Transforms in Applications Daubechies scaling filter. Now that we have the means for constructing or- thogonal filters h, g of any odd length, it is natural to consider the advantages and disadvantages of for n Z, and ∈ their implementation in applications. (20) A(ω)B(ω) A(ω π)B(ω π) 0 Let’s first consider filter length. Certainly, the + + + = if and only if time to compute WN v is inversely proportional to the length of h. On the other hand, it can be (21) akbk 2n 0 − shown [4] that the derivative conditions (23) lead k Z = ∈ to filters g that annihilate (modulo wrapping rows) for all n Z. ∈ data obtained by uniformly sampling a polynomial of degree (L 1)/2. The proof of this theorem is straightforward. − Note that equations (19) and (21) guarantee In image compression we typically transform orthogonality of the matrix WN . the image, then quantize the transform, and finally Suppose H(ω) satisfies (18). If we take encode the result. It can be shown that if the transform is orthogonal, then the error incurred (22) G(ω) eiLωH(ω π), = − + when quantizing the transform coefficients is then G(ω) satisfies (18), and H(ω), G(ω) satisfy exactly the same as the error between the original (20). It is an easy exercise to show that the Fourier image and the compressed image. k Z coefficients of G(ω) are gk ( 1) h1 k, k . There are disadvantages to using orthogonal The condition H (π) 0= leads− naturally− ∈ to the ′ transformations. In lossless image compression, following generalization:= If we want to produce the quantization step is omitted. In this case, we longer scaling filters h, each time we increase the need to use a transformation that maps integers to filter length by two, we require an additional deriv- ative condition at π. For example, the Daubechies integers. It is possible to modify orthogonal trans- scaling filter of length six is, in part, constructed forms (see [3]) and produce integer-to-integer map- pings, but it is easier to modify the biorthogonal by requiring the conditions that H′(π) 0 and = H′′(π) 0. Each time an additional derivative transformations described in the next section. condition= is imposed at π, the modulus of the cor- Unfortunately, the wrapping rows that appear responding Fourier series becomes flatter at the in the WN constructed from Daubechies scaling highest frequency ω π. So the generalderivative and wavelet filters pose a problem in many ap- = conditions are plications. In (12), there is one wrapping row in L 1 each block of the transform. Figure 6 illustrates (23) H(m)(π) 0, m 0,..., − . = = 2 the problem when the discrete Daubechies wavelet 16 We also add the lowpass condition transformation is applied to v R , where vk k, ∈ = k 1,..., 16. The wrapping rows cause the first L = (24) H(0) hk √2 two elements to be combined with the last two el- = = k 0 ements of v to form the last weighted average and = sothat ourgeneralsystemisgivenby(19),(23),and last weighted difference. If the data are periodic, L 2 + this makesperfect sense,but in manysignal/image (24). Daubechies proved that there are M 2⌊ 4 ⌋ = T real-valued scaling filters h [h0, h1, . . . , hL] , L processing applications, the data are not periodic. is odd, that satisfy this system.= Moreover, if we The wrapping row problem, caused by truncating construct G(ω) using (22), then G(0) 0 and downsampled convolution products, is typical in G(π) √2, as desired. = applied mathematics. | | =

662 Notices of the AMS Volume 58, Number 5 Biorthogonal Scaling Filters Fortunately, there is a way to deal with the wrap- ping row problem, and that is to develop filters that are symmetric.

An odd-length filter h is called symmetric if hk = h k, while an even-length filter is called symmetric − if hk h1 k. Daubechies [5] proved that the only = − symmetric, finite length, orthogonal filter is the Haar filter, and we have already discussed some of its limitations. How can we produce symmetric filters while preserving some of the desirable properties of orthogonal filters? These desirable properties are finite length (computational speed), (a) v orthogonality (ease of inverse), and the ability to produce a good approximation of the original data with the scaling filter. Since the inverse need only be computed once, it was Daubechies’s idea to relinquish orthogonality and to construct instead a discrete biorthogonal wavelet transformation. The idea is to construct two sets of filters instead of one. In other words, we construct two wavelet transform matrices W˜N and WN so that 1 T W˜ − W . In block form, we have N = N

H˜N/2 T   T T W˜N W H G (b) W v N = N/2 N/2 16  G˜   N/2    Figure 6. The discrete wavelet transform,   ˜ T ˜ T constructed using the Daubechies length four HN/2HN/2 HN/2GN/2 scaling filter, applied to v.  ˜ T ˜ T  = GN/2HN/2 GN/2GN/2   IN/2 0N/2 . = 0N/2 IN/2 then we can easily verify that G(˜ 0) G(0) 0, G(π)˜ G(π) √2, and = = Let h˜ and h denote two filters and suppose H(ω), = = (29) G(ω)˜ G(ω) G(ω˜ π)G(ω π) 2 H(ω)˜ are the associated Fourier series. We require + + + = both filters to be lowpass so we have H(˜ 0) (30) H(ω)˜ G(ω) H(ω˜ π)G(ω π) 0 H(0) √2 and H(π)˜ H(π) 0. Instead of= + + + = = = = (31) G(ω)˜ H(ω) G(ω˜ π)H(ω π) 0. orthogonality, we insist that the filters satisfy the + + + = T general biorthogonal condition Equation (29) implies that G˜N/2G IN/2, and N/2 = (30), (31), in conjunction with (20) from Theorem 1, (25) H(ω)˜ H(ω) H(ω˜ π)H(ω π) 2. T T establishes H˜N/2G G˜N/2H 0N/2. We can + + + = N/2 = N/2 = also expand the Fourier series in (27) and (28) to Although the filters are no longer orthogonal, they obtain the wavelet filter coefficients are close to orthogonal, and a proof very similar k k ˜ to that of Theorem 1 shows that (25) holds if and (32) g˜k ( 1) h1 k and gk ( 1) h1 k, = − − = − − only if where 1 k ranges over the nonzero indices of − h˜, h. Thus, if we solve (25), we can find all the ˜ (26) hkhk 2n δ0, n, ˜ − filters we need to build WN and WN . Of course k Z = ∈ (25) represents a quadratic system in terms of where n Z. Equation (26) ensures us, if we wrap the scaling filter coefficients, and such systems ∈ ˜ T are difficult to solve. Daubechies’s solution to rows, that HN/2HN/2 IN/2. If we take = this problem was to simply pick the scaling filter (27) G(ω)˜ eiωH(ω π) h˜ and then solve the linear system (25) for the = − + scaling filter h. Moreover, since we have given up (28) G(ω) eiωH(ω˜ π), = − + orthogonality in this new construction, we can

May 2011 Notices of the AMS 663 insist that both scaling filters be symmetric. Let’s look at an example.

Example 1. Suppose we want h˜ to be a symmetric, T length three, lowpass filter h˜ [h˜ 1, h˜0, h˜1] T = − = [h˜1, h˜0, h˜1] . We seek two numbers h˜0, h˜1 so that H(˜ 0) h˜1 h˜0 h˜1 √2 and H(π)˜ h˜1 h˜0 = + +1 = = − + − h˜1 0. The filter h˜ we seek is =

T √2 T [h˜ 1, h˜0, h˜1] [1, 2, 1] . − = 4 To find a symmetric filter h, we must satisfy the biorthogonality condition (25), together with the lowpass constraints H(0) √2 and Figure 7. The modified biorthogonal wavelet = H(π) 0. It turns out that h must have an transformation applied to the vector v from = odd length of 5, 9, 13,.... We choose symmetric Figure 6(a). T h [h2, h1, h0, h1, h2] and use the lowpass condi- = tion H(π) 0 in conjunction with (26) to obtain = the system and

√ √ √ √ √ 3 2 2 2 0 0 0 2 2 h0 2h1 2h2 0 4 4 − 8 − 8 4 − + = √2 √2 3√2 √2 √2  8 4 4 4 8 0 0 0  h h √2 − − 0 1 √ √ √ √ √ + = 0 0 2 2 3 2 2 2 0  − 8 4 4 4 − 8  h1 2h2 0.  √ √ √ √ √  + =  2 0 0 0 2 2 3 2 2  W  − 8 − 8 4 4 4  √2 √2 8  √ √ √  Solving this system gives h , h , and =  2 2 2 0 0 0 0 0  2 8 1 4  4 − 2 4  3√2 = − =  √2 √2 √2  h . We can next use (32) to find the coeffi-  0 0 4 2 4 0 0 0  0 4  −  = √ √ √ cients of the wavelet filters g andg ˜. We have:  0 0 0 0 2 2 2 0   4 − 2 4   √ √ √  ˜g  2 0 0 0 0 0 2 2  g  4 4 − 2  √2   g˜ 1 ˜ 1 T − = 8 It is straightforward to verify that W8− W8 . √2 √2 = g˜0 g0 Note that W˜ and W still have wrapping rows, but = 4 = 4 8 8 3√2 √2 we can exploit the symmetry of the scaling filters g˜1 g1 = − 4 = − 2 to construct a transformation that diminishes the g˜ √2 g √2 2 4 2 4 adverse effects of the wrapping rows. The idea = √2 = g˜3 is quite simple, and we illustrate it now with an = 8 Note that there is some symmetry in the highpass example. filters: g˜k g˜2 k and gk g2 k. Here are exam- Example 2. Consider again the vector v R16 − − = = 30 ∈ ples of the biorthogonal transformation matrices where vk k. We form the vector vp R where = ∈ with N 8. We form the matrices by placing the T = vp [v1, . . . , v16 v15, v14, . . . , v2] . 0th element in the upper left corner of each block = | with positive indexed elements placed consecu- ap We next compute W˜30vp. The periodic na- tively to the right and negative indexed elements dp = placed consecutively to the left with wrapping if ture of vp means that the weighted averages and necessary. differences formed by the wrapping rows use con- secutive elements from v. For example, the first √2 √2 √2 2 4 0 0 0 0 0 4 √2 √2 √2 element of ap is v2 v1 v2 instead of the √2 √2 √2 4 2 4  0 4 2 4 0 0 0 0  + +√2 √2 √2 first element of W˜16, which is v16 v1 v2. √2 √2 √2 4 2 4  0 0 0 4 2 4 0 0  + +   The elements of the transform that do not involve  √2 √2 √2  0 0 0 0 0 4 2 4 wrapping rows are the same as elements in W˜ v. W˜   16 8  √ √ √ √ √  =  2 3 2 2 2 0 0 0 2  We keep the first eight elements of ap and dp and  4 − 4 4 8 8   √2 √2 3√2 √2 √2  concatenate them to form our transform. The re-  0 8 4 4 4 8 0 0   −  sult is plotted in Figure 7. Compare this result to √ √ √ √ √  0 0 0 2 2 3 2 2 2   8 4 − 4 4 8  that plotted in Figure 6(b).  √ √ √ √ √   2 2 0 0 0 2 2 3 2   4 8 8 4 − 4    We can certainly construct biorthogonal filter pairs of different lengths—we can either select h˜, 1Do you see how Pascal’s triangle can be used to generate then set up and solve a linear system for h, or we symmetric, lowpass filters? can use the closed formulas for H(ω)˜ and H(ω)

664 Notices of the AMS Volume 58, Number 5 obtained by Daubechies in [6]. The biorthogonal “reversed”—h is used to build W˜N . For example, filter pair from the above example is particularly the modified transform for vectors of length 8 is: interesting since it plays a significant role in the 3 1 1 0 0 0 1 1 JPEG2000 lossless image compression standard. 4 4 − 8 − 8 4  1 1 3 1 1 0 0 0  Next we present one more modification of the − 8 4 4 4 − 8 transformation from Example 2 to understand  0 0 1 1 3 1 1 0   − 8 4 4 4 − 8  how the discrete biorthogonal wavelet transfor-  1 0 0 0 1 1 3 1   − 8 − 8 4 4 4  W˜8   . mation is used in the JPEG2000 image compression  1 1  =  2 1 2 0 0 0 0 0  standard.  − −   0 0 1 1 1 0 0 0   − 2 − 2   1 1  Discrete Wavelet Transformations and  0 0 0 0 2 1 2 0   − −    JPEG2000  1 0 0 0 0 0 1 1   − 2 − 2  In 1992 JPEG (Joint Photographic Image Experts   Group) became an international standard for com- We use the ideas of Example 2 to further modify pressing digital images. In the late 1990s work the transformation so that it better handles output began to improve the JPEG compression standard, produced by wrapping rows. This modification is ˜ p and a new algorithm was developed. This algo- equivalent to computing W8 to v where rithm uses the biorthogonal wavelet transform 3 1 1 4 2 4 0 0 0 0 0 instead of the discrete cosine transform. Because −  1 1 3 1 1 0 0 0  of patent issues, JPEG2000 is not yet supported − 8 4 4 4 − 8  0 0 1 1 3 1 1 0  by popular web browsers, but it is likely that  − 8 4 4 4 − 8   1 1 5 1  once the patent issues are resolved, JPEG2000 will  0 0 0 0 8 4 8 4  (33) W˜ p  −  . replace JPEG as the most popular standard for 8  1 1  =  2 1 2 0 0 0 0 0  image compression.  − −   0 0 1 1 1 0 0 0   − 2 − 2  The basic JPEG2000 algorithm works as follows.    0 0 0 0 1 1 1 0  Let us assume that we have a grayscale image A.  − 2 − 2    We first subtract 128 from each entry of A. We  0 0 0 0 0 0 1 1   −  apply as many iterations of the modified biorthog-   This modified transform is still invertible, and onal wavelet transformation (see Example 2) as it now does a good job of handling edge effects. we wish (and as possible, depending on the di- However, the coding step of the JPEG2000 al- mensions of the image). The filter pair used in the gorithm works best if the transformation maps discrete biorthogonal wavelet transform depends integers to integers. How can we modify (33) for on whether we choose to perform lossy or loss- general size N so that it maps integers to integers? less compression. In the case of the former, the We could multiply the transformed data by 8, but transformed image is quantized with many ele- that increases the range of the output, which is ments either reduced in magnitude or converted not desirable for coders. The algorithm used by to zero. Of course, once we quantize the trans- JPEG2000 for lossless compression is called lifting formed image, we have no hope of recovering the and is due to Sweldens [11]. original image, but this loss of resolution is not as important as the coder’s ability to compress The Lifting Scheme the quantized transform. In lossless compression, The idea behind lifting is quite simple. For a nice no quantization is performed. In both cases, the tutorial, see [10], and more details are provided in next step is to code the data. JPEG2000 uses an the books [12, 8]. arithmetic coding algorithm known as Embedded To understand how lifting works, we apply (33) Block Coding with Optimized Truncation (EBCOT) Z8 ˜ p to v . The resulting product is W8 v to actually encode the (quantized) transformed ∈ = 1 1 3 1 1 v3 v2 v1 v2 v3 data. This last step is the actual compression step. − 8 + 4 + 4 + 4 − 8 1 1 3 1 1 v1 v2 v3 v4 v5 After transmission of the data, the original image  − 8 + 4 + 4 + 4 − 8  1 1 3 1 1 can be reconstructed by decoding, then applying v3 v4 v5 v6 v7  − 8 + 4 + 4 + 4 − 8   1 1 3 1 1  the inverse transformation as many times as iter- a  v5 v6 v7 v8 v7  (34)  − 8 + 4 + 4 + 4 − 8  , ated. With lossless compression, we can recover 1 1 d =  v1 v2 v3   − 2 + − 2  the image exactly.  1 1   v3 v4 v5   − 2 + − 2  One of the many advantages of JPEG2000 over 1 1  v5 v6 v7  JPEG is its ability to allow the user to perform the  − 2 + − 2   1 1   v7 v8 v7  lossless compression. The biorthogonal filter pair  − 2 + − 2  ˜   for this task is a modified version of the h and h where we have rewritten a1, a4, and d4 so that they from Example 1. The filter h is multiplied by √2/2 display the same symmetry as the other elements and h˜ is multiplied by √2. Moreover, the filters are in the product. Note that the center value of the

May 2011 Notices of the AMS 665 elements of a/(d) are built from the odd (even) transformation that involves rounding! This fi- elements of v. If we form “even” and “odd” vectors nal modification is an important tool used by the T T JPEG2000 image compression standard to perform e [e1, e2, e3, e4] [v2, v4, v6, v8] = = lossless compression. T T o [o1, o2, o3, o4] [v1, v3, v5, v7] , = = We have not discussed in this paper the classi- then cal approach to wavelet theory—the mathematics 1 thereisquite elegant(the books[2, 14, 9]areaimed (35) dk ek (ok 1 ok), at undergraduates). We believe, however, that an = − 2 + − introduction to the discrete wavelet transforma- where k 1, 2, 3, 4 and o : o . The elements of 5 4 tion, with immediate immersion in applications, the top half= of the transformation= can then be is an effective way to introduce students to appli- lifted from d: cations that are ubiquitous in today’s digital age, 1 to hone problem-solving skills, to promote and (36) ak ok (dk dk 1), = + 4 + − improve scientific computing, and to motivate where k 1, 2, 3, 4 and d0 : d1. concepts in upper-level undergraduate courses This method= is computationally= more efficient such as real and complex analysis. than a fast matrix multiplication. Moreover, we can easily modify this transformation so that it References maps integers to integers. Instead of computing [1] E. Aboufadel and S. Schlicker, Discovering the elements of d using (35), we compute d∗, Wavelets, Wiley–Interscience, Hoboken, NJ, 1999. whose elements are [2] A. Boggess and F. J. Narcowich, A First Course in 1 Wavelets with Fourier Analysis, Prentice Hall, Upper (37) dk∗ ek (ok ok 1) Saddle River, NJ, 2001. = − 2 + + [3] A. Calderbank, I. Daubechies, W. Sweldens, and and then compute a∗, whose elements are B.-L. Yeo, Wavelet transforms that map integers to 1 1 integers, Appl. Comp. Harm. Anal. 5, 3 (1998), 332– (38) ak∗ ok (dk∗ dk∗ 1) . 369. = + 4 + − + 2 [4] I. Daubechies, Orthogonal bases of compactly sup- Adding 1/2 to the term above eliminates bias. ported wavelets, Comm. Pure Appl. Math. 41 (1988), Certainly, the elements of a∗ and d∗ are integer- 909–996. valued and only slightly different from those given [5] , Ten Lectures on Wavelets, Society for Indus- by (35), (36), respectively. Moreover, the process trial and Applied Mathematicians, Philadelphia, PA, is completely invertible. Given d∗ and a∗, we can 1992. certainly recover the values ok using (38), and then [6] , Orthonormal bases of compactly supported wavelets II. Variations on a theme, SIAM J. Math. given o and d∗, we can use (37) to recover e. Anal. 24, 2 (1993), 499–519. M. W. Frazier Concluding Remarks [7] , An Introduction to Wavelets Through Linear Algebra, Undergraduate Texts in In this article, we have provided a very brief intro- Mathematics, Springer, New York, NY, 1999. duction to discrete wavelet transformations and [8] A. Jensen and A. la Cour-Harbo, Ripples in Math- have shown how the topic effectively lends itself to ematics: The Discrete Wavelet Transform, Springer, an intriguing undergraduate applied mathematics New York, NY, 2001. course. [9] D. K. Ruch and P. J. Van Fleet, Wavelet Theory: By introducing students to the discrete Haar An Elementary Approach with Applications, Wiley– wavelet transformation, we are able to not only Interscience, Hoboken, NJ, 2009. W. Sweldens construct a matrix representation of a tool used in [10] , Wavelets and the lifting scheme: A 5 minute tour, Z. Angew. Math. Mech. 76 (Suppl. 2) several applications but also provide students with (1996), 41–44. a concrete example of how convolution and Fourier [11] , The lifting scheme: A construction of sec- series can lead to a more general mathematical ond generation wavelets, SIAM J. Math. Anal. 29, 2 model for the construction of more sophisticated (1997), 511–546. scaling and wavelet filters. [12] P. J. Van Fleet, Discrete Wavelet Transformations: The Daubechies filters are better suited for An Elementary Approach with Applications, Wiley– applications, but still suffer from the effects Interscience, Hoboken, NJ, 2008. of truncating infinite convolution products. This [13] J. S. Walker, A Primer on Wavelets and Their Sci- problem leads to the development of biorthogonal entific Applications, 2nd ed., Chapman & Hall/CRC Press, Boca Raton, FL, 2008. scaling filters. Still more modification is needed [14] D. F. Walnut, An Introduction to Wavelet Analysis, to handle boundary effects, and students learn Birkhäuser, Cambridge, MA, 2002. that these modifications are not only tractable [15] M. V. Wickerhauser, Adapted Wavelet Analysis but also lead to the lifting scheme. This compu- from Theory to Software, A K Peters, Wellesley, MA, tational method is not only faster than sparse 1994. matrix multiplication but can also be modified to produce the seemingly impossible invertible

666 Notices of the AMS Volume 58, Number 5 Mathematical Intimidation: Driven by the Data John Ewing

athematicians occasionally worry has checked into our concerns and we shouldn’t about the misuse of their subject. worry. Value-added modeling is promoted because G. H. Hardy famously wrote about it has the right pedigree—because it is based on mathematics used for war in his “sophisticated mathematics”. As a consequence, Mautobiography, A Mathematician’s mathematics that ought to be used to illuminate Apology (and solidified his reputation as a foe of ends up being used to intimidate. When that hap- applied mathematics in doing so). More recently, pens, mathematicians have a responsibility to groups of mathematicians tried to organize a boy- speak out. cott of the Star Wars project on the grounds that it was an abuse of mathematics. And even more Background recently some fretted about the role of mathemat- Value-added models are all about tests—standard- ics in the financial meltdown. ized tests that have become ubiquitous in K–12 But the most common misuse of mathemat- education in the past few decades. These tests have ics is simpler, more pervasive, and (alas) more been around for many years, but their scale, scope, insidious: mathematics employed as a rhetorical and potential utility have changed dramatically. weapon—an intellectual credential to convince Fifty years ago, at a few key points in their educa- the public that an idea or a process is “objective” tion, schoolchildren would bring home a piece of and hence better than other competing ideas or paper that showed academic achievement, usually processes. This is mathematical intimidation. It is with a percentile score showing where they landed especially persuasive because so many people are among a large group. Parents could take pride in awed by mathematics and yet do not understand their child’s progress (or fret over its lack); teach- it—a dangerous combination. ers could sort students into those who excelled The latest instance of the phenomenon is and those who needed remediation; students could valued-added modeling (VAM), used to interpret make plans for higher education. test data. Value-added modeling pops up every- Today, tests have more consequences. “No where today, from newspapers to television to Child Left Behind” mandated that tests in reading political campaigns. VAM is heavily promoted with and mathematics be administered in grades 3–8. unbridled and uncritical enthusiasm by the press, Often more tests are given in high school, includ- by politicians, and even by (some) educational ex- ing high-stakes tests for graduation. With all that perts, and it is touted as the modern, “scientific” accumulating data, it was inevitable that people way to measure educational success in everything would want to use tests to evaluate everything from charter schools to individual teachers. educational—not merely teachers, schools, and Yet most of those promoting value-added entire states but also new curricula, teacher train- modeling are ill-equipped to judge either its ing programs, or teacher selection criteria. Are effectiveness or its limitations. Some of those the new standards better than the old? Are expe- who are equipped make extravagant claims with- rienced teachers better than novice? Do teachers out much detail, reassuring us that someone need to know the content they teach? Using data from tests to answer such questions is part of the John Ewing is president of Math for America. His email current “student achievement” ethos—the belief address is [email protected]. that the goal of education is to produce high test

MAY 2011 NOTICES OF THE AMS 667 scores. But it is also part of a broader trend in mod- things that are not tested (for example, student ern society to place a higher value on numerical engagement and attitude) and concentrating on (objective) measurements than verbal (subjective) precisely those things that are. evidence. But using tests to evaluate teachers, schools, or programs has many problems. (For a Value-Added Models readable and comprehensive account, see [Koretz In the past two decades, a group of statisticians 2008].) Here are four of the most important prob- has focused on addressing the first of these four lems, taken from a much longer list. problems. This was natural. Mathematicians rou- 1. Influences. Test scores are affected by many fac- tinely create models for complicated systems that tors, including the incoming levels of achieve- are similar to a large collection of students and ment, the influence of previous teachers, the teachers with many factors affecting individual attitudes of peers, and parental support. One outcomes over time. cannot immediately separate the influence of a Here’s a typical, although simplified, example, particular teacher or program among all those called the “split-plot design”. You want to test variables. fertilizer on a number of different varieties of 2. Polls. Like polls, tests are only samples. They some crop. You have many plots, each divided cover only a small selection of material from into subplots. After assigning particular varieties a larger domain. A student’s score is meant to to each subplot and randomly assigning levels of represent how much has been learned on all fertilizer to each whole plot, you can then sit back material, but tests (like polls) can be misleading. and watch how the plants grow as you apply the 3. Intangibles. Tests (especially multiple-choice fertilizer. The task is to determine the effect of the tests) measure the learning of facts and pro- fertilizer on growth, distinguishing it from the ef- cedures rather than the many other goals of fects from the different varieties. Statisticians have teaching. Attitude, engagement, and the abil- developed standard mathematical tools (mixed ity to learn further on one’s own are difficult models) to do this. to measure with tests. In some cases, these “intangible” goals may be more important Does this situation sound familiar? Varieties, than those measured by tests. (The father of plots, fertilizer…students, classrooms, teachers? modern standardized testing, E. F. Lindquist, Dozens of similar situations arise in many areas, wrote eloquently about this [Lindquist 1951]; from agriculture to MRI analysis, always with the a synopsis of his comments can be found in same basic ingredients—a mixture of fixed and [Koretz 2008, 37].) random effects—and it is therefore not surprising 4. Inflation. Test scores can be increased without that statisticians suggested using mixed models to increasing student learning. This assertion has analyze test data and determine “teacher effects”. been convincingly demonstrated, but it is widely This is often explained to the public by analogy. ignored by many in the education establishment One cannot accurately measure the quality of a [Koretz 2008, chap. 10]. In fact, the assertion teacher merely by looking at the scores on a single should not be surprising. Every teacher knows test at the end of a school year. If one teacher starts that providing strategies for test-taking can with all poorly prepared students, while another improve student performance and that narrow- starts with all excellent, we would be misled by ing the curriculum to conform precisely to the scores from a single test given to each class. To test (“teaching to the test”) can have an even account for such differences, we might use two greater effect. The evidence shows that these tests, comparing scores from the end of one year effects can be substantial: One can dramatically to the next. The focus is on how much the scores increase test scores while at the same time actu- increase rather than the scores themselves. That’s ally decreasing student learning. “Test scores” the basic idea behind “value-added”. are not the same as “student achievement”. But value-added models (VAMs) are much more This last problem plays a larger role as the stakes than merely comparing successive test scores. increase. This is often referred to as Campbell’s Given many scores (say, grades 3–8) for many Law: “The more any quantitative social indicator students with many teachers at many schools, one is used for social decision-making, the more creates a mixed model for this complicated situa- subject it will be to corruption pressures and tion. The model is supposed to take into account the more apt it will be to distort and corrupt the all the factors that might influence test results— social processes it is intended to measure” [Camp- past history of the student, socioeconomic status, bell 1976]. In its simplest form, this can mean and so forth. The aim is to predict, based on all that high-stakes tests are likely to induce some these past factors, the growth in test scores for people (students, teachers, or administrators) students taught by a particular teacher. The actual to cheat…and they do [Gabriel 2010]. But the change represents this more sophisticated “value- more common consequence of Campbell’s Law added”—good when it’s larger than expected; bad is a distortion of the education experience, ignoring when it’s smaller.

668 NOTICES OF THE AMS VOLUME 58, NUMBER 5 The best-known VAM, devised by William Sand- Fortunately, significant help is ers, is a mixed model (actually, several models), available in the form of a relatively which is based on Henderson’s mixed-model new tool known as value-added equations, although mixed models originate much assessment. Because value-added earlier [Sanders 1997]. One calculates (a huge isolates the impact of instruction on computational effort!) the best linear unbiased student learning, it provides detailed predictors for the effects of teachers on scores. information at the classroom level. Its The precise details are unimportant here, but the rich diagnostic data can be used to im- process is similar to all mathematical modeling, prove teaching and student learning. It with underlying assumptions and a number of can be the basis for a needed improve- choices in the model’s construction. ment in the calculation of adequate yearly progress. In time, once teachers History and administrators grow comfortable When value-added models were first conceived, with its fairness, value-added also may even their most ardent supporters cautioned serve as the foundation for an account- about their use [Sanders 1995, abstract]. They ability system at the level of individual were a new tool that allowed us to make sense of educators [Hershberg 2004, 1]. mountains of data, using mathematics in the same And newspapers such as The Los Angeles Times way it was used to understand the growth of crops get their hands on seven years of test scores for or the effects of a drug. But that tool was based students in the L.A. schools and then publish a on a statistical model, and inferences about indi- series of exposés about teachers, based on a value- vidual teachers might not be valid, either because added analysis of test data, which was performed of faulty assumptions or because of normal (and under contract [Felch 2010]. The article explains expected) variation. its methodology: Such cautions were qualified, however, and one can see the roots of the modern embrace of VAMs The Times used a statistical approach in two juxtaposed quotes from William Sanders, known as value-added analysis, which the father of the value-added movement, which rates teachers based on their students’ appeared in an article in Teacher Magazine in the progress on standardized tests from year 2000. The article’s author reiterates the famil- year to year. Each student’s perfor- iar cautions about VAMs, yet in the next paragraph mance is compared with his or her own seems to forget them: in past years, which largely controls for outside influences often blamed for Sanders has always said that scores for academic failure: poverty, prior learn- individual teachers should not be re- ing and other factors. leased publicly. “That would be totally inappropriate,” he says. “This is about Though controversial among teach- trying to improve our schools, not ers and others, the method has been embarrassing teachers. If their scores increasingly embraced by education were made available, it would create leaders and policymakers across the chaos because most parents would be country, including the Obama admin- trying to get their kids into the same istration. classroom.” It goes on to draw many conclusions, including: Still, Sanders says, it’s critical that in- Many of the factors commonly assumed effective teachers be identified. “The to be important to teachers’ effective- evidence is overwhelming,” he says, ness were not. Although teachers are “that if any child catches two very paid more for experience, education weak teachers in a row, unless there and training, none of this had much is a major intervention, that kid never bearing on whether they improved their recovers from it. And that’s something students’ performance. that as a society we can’t ignore” [Hill 2000]. The writer adds the now-common dismissal of any concerns: Over the past decade, such cautions about VAM slowly evaporated, especially in the popular press. No one suggests using value-added A 2004 article in The School Administrator com- analysis as the sole measure of a plains that there have not been ways to evaluate teacher. Many experts recommend that teachers in the past but excitedly touts value- it count for half or less of a teacher’s added as a solution: overall evaluation.

MAY 2011 NOTICES OF THE AMS 669 Nevertheless, value-added analysis of- during the year? (Rule: Include them if fers the closest thing available to an they are in class for 150 or more days.) objective assessment of teachers. And What if we only have a couple years of it might help in resolving the greater test data, or possibly more than five mystery of what makes for effective years? (Rule: The range three to five teaching, and whether such skills can years is fixed for all models.) What’s be taught. the rationale for these kinds of rules? • Class sizes differ in modern schools, The article goes on to do exactly what it says “no and the nature of the model means one suggests”—it measures teachers solely on the there will be more variability for small basis of their value-added scores. classes. (Think of a class of one student.) What Might Be Wrong with VAM? Adjusting for this will necessarily drive teacher effects for small classes toward As the popular press promoted value-added mod- the mean. How does one adjust sensibly? els with ever-increasing zeal, there was a parallel, • While the basic idea underlying much less visible scholarly conversation about value-added models is the same, the limitations of value-added models. In 2003 a there are in fact many models. Do book with the title Evaluating Value-Added Models different models applied to the same for Teacher Accountability laid out some of the data sets produce the same results? problems and concluded: Are value-added models “robust”? The research base is currently insuf- •Since models are applied to longitu- ficient to support the use of VAM for dinal data sequentially, it is essential high-stakes decisions. We have identi- to ask whether the results are consis- fied numerous possible sources of tent year to year. Are the computed error in teacher effects and any attempt teacher effects comparable over suc- to use VAM estimates for high-stakes cessive years for individual teachers? decisions must be informed by an un- Are value-added models “consistent”? derstanding of these potential errors These last two points were raised in a research [McCaffrey 2003, xx]. paper [Lockwood 2007] and a recent policy brief In the next few years, a number of scholarly pa- from the Economic Policy Institute, “Problems pers and reports raising concerns were published, with the Use of Student Test Scores to Evaluate including papers with such titles as “The Promise Teachers”, which summarizes many of the open and Peril of Using Valued-Added Modeling to questions about VAM. Measure Teacher Effectiveness” [RAND, 2004], For a variety of reasons, analyses of “Re-Examining the Role of Teacher Quality in the VAM results have led researchers to Educational Production Function” [Koedel 2007], doubt whether the methodology can and “Methodological Concerns about the Educa- accurately identify more and less ef- tion Value-Added Assessment System” [Amrein- fective teachers. VAM estimates have Beardsley 2008]. proven to be unstable across statistical What were the concerns in these papers? Here models, years, and classes that teachers is a sample that hints at the complexity of issues. teach. One study found that across five • In the real world of schools, data is large urban districts, among teachers frequently missing or corrupt. What if who were ranked in the top 20% of ef- students are missing past test data? fectiveness in the first year, fewer than What if past data was recorded in- a third were in that top group the next correctly (not rare in schools)? What year, and another third moved all the if students transferred into the way down to the bottom 40%. Another school from outside the system? found that teachers’ effectiveness rat- • The modern classroom is more ings in one year could only predict variable than people imagine. What from 4% to 16% of the variation in such if students are team-taught? How do ratings in the following year. Thus, a you apportion credit or blame among teacher who appears to be very inef- various teachers? Do teachers in fective in one year might have a dra- one class (say mathematics) affect matically different result the following the learning in another (say science)? year. The same dramatic fluctuations • Every mathematical model in sociol- were found for teachers ranked at the ogy has to make rules, and they some- bottom in the first year of analysis. This times seem arbitrary. For example, runs counter to most people’s notions what if students move into a class that the true quality of a teacher is

670 NOTICES OF THE AMS VOLUME 58, NUMBER 5 likely to change very little over time and “was surprised and disappointed by her [value- raises questions about whether what is added] results, adding that her students did well measured is largely a “teacher effect” on periodic assessments and that parents seemed or the effect of a wide variety of other well-satisfied” [Felch 2010]. The teacher is made factors [Baker 2010, 1]. to think about why she did poorly and eventually, with the reporter’s help, she understands that she In addition to checking robustness and stability fails to challenge her students sufficiently. In spite of a mathematical model, one needs to check of parents describing her as “amazing” and the validity. Are those teachers identified as superior principal calling her one of the “most effective” (or inferior) by value-added models actually supe- teachers in the school, she will have to change. She rior (or inferior)? This is perhaps the shakiest part of VAM. There has been surprisingly little effort to recants: “If my student test scores show I’m an in- compare valued-added rankings to other measures effective teacher, I’d like to know what contributes of teacher quality, and to the extent that informal to it. What do I need to do to bring my average up?” comparisons are made (as in the LA Times article), Making policy decisions on the basis of value- they sometimes don’t agree with common sense. added models has the potential to do even more None of this means that value-added models are harm than browbeating teachers. If we decide worthless—they are not. But like all mathematical whether alternative certification is better than models, they need to be used with care and a full regular certification, whether nationally board cer- understanding of their limitations. tified teachers are better than randomly selected ones, whether small schools are better than large, How Is VAM Used? or whether a new curriculum is better than an old Many studies by reputable scholarly groups call for by using a flawed measure of success, we almost caution in using VAMs for high-stakes decisions surely will end up making bad decisions that affect about teachers. education for decades to come. This is insidious because, while people debate A RAND research report: The esti- the use of value-added scores to judge teachers, mates from VAM modeling of achieve- almost no one questions the use of test scores ment will often be too imprecise to and value-added models to judge policy. Even support some of the desired inferences people who point out the limitations of VAM ap- [McCaffrey 2004, 96]. pear to be willing to use “student achievement” in the form of value-added scores to make such A policy paper from the Educational judgments. People recognize that tests are an im- Testing Service’s Policy Information perfect measure of educational success, but when Center: VAM results should not serve sophisticated mathematics is applied, they believe as the sole or principal basis for making the imperfections go away by some mathematical consequential decisions about teach- magic. But this is not magic. What really happens is ers. There are many pitfalls to making that the mathematics is used to disguise the prob- causal attributions of teacher effective- lems and intimidate people into ignoring them—a ness on the basis of the kinds of data modern, mathematical version of the Emperor’s available from typical school districts. New Clothes. We still lack sufficient understanding of how seriously the different technical What Should Mathematicians Do? problems threaten the validity of such The concerns raised about value-added models interpretations [Braun 2005, 17]. ought to give everyone pause, and ordinarily they would lead to a thoughtful conversation about the A report from a workshop of the Na- proper use of VAM. Unfortunately, VAM propo- tional Academy of Education: Value- nents and politicians have framed the discussion added methods involve complex sta- as a battle between teacher unions and the pub- tistical models applied to test data of lic. Shouldn’t teachers be accountable? Shouldn’t varying quality. Accordingly, there are we rid ourselves of those who are incompetent? many technical challenges to ascer- Shouldn’t we put our students first and stop taining the degree to which the output worrying about teacher sensibilities? And most of these models provides the desired importantly, shouldn’t we be driven by the data? estimates [Braun 2010]. This line of reasoning is illustrated by a re- And yet here is the LA Times, publishing value- cent fatuous report from the Brookings Institute, added scores for individual teachers by name and “Evaluating Teachers: The Important Role of Value- bragging that even teachers who were considered Added” [Glazerman 2010], which dismisses the first-rate turn out to be “at the bottom”. In an many cautions found in all the papers mentioned episode reminiscent of the Cultural Revolution, above, not by refuting them but by asserting their the LA Times reporters confront a teacher who unimportance. The authors of the Brookings paper

MAY 2011 NOTICES OF THE AMS 671 agree that value-added scores of teachers are bamboozled by the theory behind VAM, and they unstable (that is, not highly correlated year to year) need to speak out forcefully. Mathematical models but go on to assert: have limitations. They do not by themselves convey authority for their conclusions. They are tools, not The use of imprecise measures to make magic. And using the mathematics to intimidate— high-stakes decisions that place so- to preempt debate about the goals of education cietal or institutional interests above and measures of success—is harmful not only to those of individuals is widespread and education but to mathematics itself. accepted in fields outside of teaching [Glazerman 2010, 7]. References To illustrate this point, they use examples such as Audrey Amrein-Beardsley, Methodological concerns the correlation of SAT scores with college success about the education value-added assessment system, or the year-by-year correlation of leaders in real Educational Researcher 37 (2008), 65–75. http:// dx.doi.org/10.3102/0013189X08316420 estate sales. They conclude that “a performance Eva L. Baker, Paul E. Barton, Linda Darling- measure needs to be good, not perfect”. (And as Hammond, Edward Haertel, Hellen F. Ladd, Rob- usual, on page 11 they caution not to use value- ert L. Linn, Diane Ravitch, Richard Rothstein, added measures alone when making decisions, Richard J. Shavelson, and Lorrie A. Shepard, while on page 9 they advocate doing precisely that.) Problems with the Use of Student Test Scores to Evalu- Why must we use value-added even with its im- ate Teachers, Economic Policy Institute Briefing Paper perfections? Aside from making the unsupported #278, August 29, 2010, Washington, DC. http://www. claim (in the very last sentence) that “it predicts epi.org/publications/entry/bp278 more about what students will learn…than any Henry Braun, Using Student Progress to Evaluate Teach- other source of information”, the only apparent ers: A Primer on Value-Added Models, Educational reason for its superiority is that value-added is Testing Service Policy Perspective, Princeton, NJ, 2005. http://www.ets.org/Media/Research/pdf/ based on data. Here is mathematical intimidation PICVAM.pdf in its purest form—in this case, in the hands of Henry Braun, Naomi Chudowsky, and Judith Koenig, economists, sociologists, and education policy eds., Getting Value Out of Value-Added: Report of a experts. Workshop, Committee on Value-Added Methodology Of course we should hold teachers account- for Instructional Improvement, Program Evalua- able, but this does not mean we have to pretend tion, and Accountability; National Research Coun- that mathematical models can do something they cil, Washington, DC, 2010. http://www.nap.edu/ cannot. Of course we should rid our schools of catalog/12820.html Donald T. Campbell incompetent teachers, but value-added models are , Assessing the Impact of Planned an exceedingly blunt tool for this purpose. In any Social Change, Dartmouth College, Occasional Paper Series, #8, 1976. http://www.eric.ed.gov/PDFS/ case, we ought to expect more from our teachers ED303512.pdf than what value-added attempts to measure. Jason Felch, Jason Song, and Doug Smith, Who’s A number of people and organizations are seek- teaching L.A.’s kids?, Los Angeles Times, August 14, ing better ways to evaluate teacher performance 2010. http://www.latimes.com/news/local/ in new ways that focus on measuring much more la-me-teachers-value-20100815,0,2695044. than test scores. (See, for example, the Measures story of Effective Teaching project run by the Gates Trip Gabriel, Under pressure, teachers tamper with Foundation.) Shouldn’t we try to measure long- tests, New York Times, June 11, 2010. http://www. term student achievement, not merely short-term nytimes.com/2010/06/11/education/11cheat. gains? Shouldn’t we focus on how well students are html Steven Glazerman, Susanna Loeb, Dan Goldhaber, prepared to learn in the future, not merely what Douglas Staiger, Stephen Raudenbush, Grover they learned in the past year? Shouldn’t we try to Whitehurst, Evaluating Teachers: The Important distinguish teachers who inspire their students, Role of Value-Added, Brown Center on Education Pol- not merely the ones who are competent? When we icy at Brookings, 2010. http://www.brookings.edu/ accept value-added as an “imperfect” substitute for reports/2010/1117_evaluating_teachers.aspx all these things because it is conveniently at hand, Ted Hershberg, Virginia Adams Simon and Barbara we are not raising our expectations of teachers, we Lea Kruger, The revelations of value-added: An are lowering them. assessment model that measures student growth And if we drive away the best teachers by in ways that NCLB fails to do, The School Admin- using a flawed process, are we really putting our istrator, December 2004. http://www.aasa.org/ SchoolAdministratorArticle.aspx?id=9466 students first? David Hill, He’s got your number, Teacher Magazine, Whether naïfs or experts, mathematicians need May 2000 11(8), 42–47. http://www.edweek.org/ to confront people who misuse their subject to in- tm/articles/2000/05/01/08sanders.h11.html timidate others into accepting conclusions simply Cory Koedel and Julian R. Betts, Re-Examining the because they are based on some mathematics. Un- Role of Teacher Quality in the Educational Production like many policy makers, mathematicians are not Function, Working Paper #2007-03, National Center on

672 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Performance Initiatives, Nashville, TN, 2007. http:// economics.missouri.edu/working-papers/2007/ MATHEMATICS AT THE N ATIONAL S ECURITY A GENCY wp0708_koedel.pdf Daniel Koretz, Measuring Up: What Educational Testing Make a calculated difference Really Tells Us, Harvard University Press, Cambridge, Massachusetts, 2008. with what you know. E. F. Lindquist, Preliminary considerations in objec- tive test construction, in Educational Measurement (E. F. Lindquist, ed.), American Council on Education, Washington DC, 1951. J. R. Lockwood, Daniel McCaffrey, Laura S. Ham- ilton, Brian Stetcher, Vi-Nhuan Le, and Felipe Martinez, The sensitivity of value-added teacher effect estimates to different mathematics achieve- ment measures, Journal of Educational Measurement 44(1) (2007), 47–67. http://dx.doi.org/10.1111/ j.1745-3984.2007.00026.x Daniel F. McCaffrey, Daniel Koretz, J. R. Lockwood, and Laura S. Hamilton, Evaluating Value-Added Models for Teacher Accountability, RAND Corporation, Santa Monica, CA, 2003. http://www.rand.org/ pubs/monographs/2004/RAND_MG158.pdf Daniel F. McCaffrey, J. R. Lockwood, Daniel Koretz, Thomas A. Louis, and Laura Hamilton, Models for value-added modeling of teacher effects, Jour- nal of Educational and Behavioral Statistics 29(1), Spring 2004, 67-101. http://www.rand.org/pubs/ reprints/2005/RAND_RP1165.pdf Tackle the coolest problems ever. RAND Research Brief, The Promise and Peril of Using Value-Added Modeling to Measure Teacher Effective- You already know that mathematicians like complex challenges. ness, Santa Monica, CA, 2004. http://www.rand.org/ But here’s something you may not know. pubs/research_briefs/RB9050/RAND_RB9050.pdf William L. Sanders and Sandra P. Horn, Educational The National Security Agency is the nation’s largest employer of Assessment Reassessed: The Usefulness of Standard- mathematicians. In the beautiful, complex world of mathematics, ized and Alternative Measures of Student Achieve- we identify structure within the chaotic and patterns among ment as Indicators of the Assessment of Educational the arbitrary. Outcomes, Education Policy Analysis Archives, March 3(6) (1995). http://epaa.asu.edu/ojs/article/ Work with the finest minds, on the most challenging problems, view/649 using the world’s most advanced technology. W. Sanders, A. Saxton, and B. Horn, The Tennessee value-added assessment system: A quantitative outcomes-based approach to educational assessment, KNOWINGMATTERS in Grading Teachers, Grading Schools: Is Student Achievement a Valid Evaluational Measure? (J. Mill- Excellent Career Opportunities for Experts in the Following: man, ed.), Corwin Press, Inc., Thousand Oaks, CA, ■ Number Theory ■ Combinatorics 1997, pp 137–162. ■ Probability Theory ■ Linear Algebra ■ Group Theory >> Plus other opportunities ■ Finite Field Theory

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MAY 2011 NOTICES OF THE AMS 673 Remembering Leon Ehrenpreis (1930–2010)

Daniele C. Struppa

Leon Ehrenpreis: A Note on His Mathemat- ical Work Leon Ehrenpreis passed away on August 16, 2010, at the age of eighty, after a life enriched by his passions for mathematics, music, running, and the scriptures. I first met Leon in 1978, when I was a doctoral student under Carlos Berenstein (himself a student of Leon’s), at a time when Carlos had invited him to lecture at the complex analysis seminar at the University of Maryland. I had just begun to attempt my first (of many) readings of his work on the fundamental principle [11] and I was in awe of his presence. And yet, I discovered a gentle human being, with a passion for mathematics and a genuine desire to help the newcomer (me, in that case) to understand its mysteries. Photograph by François Rouvière. What follows in this section is a quick overview Leon explaining his AU-spaces at the 2008 of Ehrenpreis’s work, mostly biased by my own conference held in Stockholm in honor of Jan interest and work on the fundamental principle. Boman’s seventy-fifth birthday. It is of course impossible to pay full tribute to the complexity of Ehrenpreis’s work in such a short note. The subsequent sections are short skill in his willingness to tackle bold generaliza- remembrances, both mathematical and personal, tions, as he extends distribution theory to the of Leon’s life, from some of his friends and case in which Euclidean spaces are replaced by collaborators. locally compact Hausdorff spaces denumerable at Leon Ehrenpreis’s mathematical career started infinity and the derivations ∂/∂x are replaced by with his 1953 dissertation [4], which he wrote while i a countable family of local, closed operators. doing his doctoral work at Columbia University He then plunged immediately into the topics under the guidance of Chevalley. The dissertation, that would become the main drivers for his funda- whose main results later appeared in [8], already mental principle. In an impressive series of papers shows some of Ehrenpreis’s most characteristic from 1954 to 1960, Ehrenpreis addressed the prob- Daniele C. Struppa is chancellor at Chapman University, lem of division in a variety of contexts. Specifically, Orange, CA. His email address is [email protected]. he investigated in [5] the issue of surjectivity of

674 Notices of the AMS Volume 58, Number 5 eetal ucin htaesltoso the May of solutions are that functions ferentiable polynomials let the Now are symbols whose r ibefntoson functions space tiable the on consider class us let introductory any in equations. teach differential we ordinary, of which equations, differential solutions linear coefficients for constant theorem resentation rep- well-known the of generalization far-reaching also in [11]. appeared fact monograph proof important most complete discovered his in whose references and Russian concurrently therein) the was and [28] Ehrenpreis- see Palamodov; and by result of principle independently (this known fundamental became Palamodov what the of 1960 as in of [9] nouncement class larger a considered he where spaces. [7], later such in continued to he on that solutions analysis an exponential [30], on equations results Schwartz the L. extended special of some and theory. of equations case this the convolution of tackled form Ehrenpreis modern [6] In the develop help [27] to Malgrange and [23] Hörmander of those joined results par- Ehrenpreis’s and coefficients equations, differential constant tial linear of of study solvability the the to distributions of theory the appli- of the cation of years heroic the were These functions. space the in and order space coef- the constant in with ficients operators differential partial Carlos’s of honor birthday. in sixtieth Fairfax 2004 in the held at conference Sabadini Irene student and Daniele’s Struppa, Daniele Berenstein, student Carlos Carlos’s student his with Leon Photo by Fabrizio Colombo. ieeta prtr ihcntn coefficients, constant with operators differential nodrt tt t(tlati atclrcase), particular a in least (at it state to order In a as seen be can principle fundamental The an- striking his with culminated this of All 2011 E P eoetesaeo nntl dif- infinitely of space the denote R n D E n let and , F ′ ′ fifiieydifferentiable infinitely of fdsrbtoso finite of distributions of E fifiieydifferen- infinitely of P 1 D,...,P , . . . (D), P 1 , r (D) P , be oie fteAMS the of Notices n . hteeyfunction states every which that theorem, representation the is result on polynomials also the to but related be multiplicities the functions, incorporate somehow must the that derivatives on conditions suitable just growth not Such imposed holomor- place. variety by take the to satisfied on be functions growth the phic must however, of that nature proof, the the conditions of of understanding the crux is complex The several [25]). edition on third variables monograph the fun- in Hörmander’s the and of to [2] in dedicated principle chapters damental the (see, example, reinterpretations and for analysis of subject decades still the is even it announcement, and original Ehrenpreis’s complicated, after quite is theorem the between isomorphism space possible topological is a it obtain that to states roughly principle mental ovlto qain) aifigsm specific some satisfying solu- even equations), (or are equations convolution differential that of functions systems holomorphic of of tions for of spaces holds general fact peculiarity in more but variables a several in not functions problems, phe- is division Hartogs’ of nomenon that study [10] his demonstrated developed of Ehrenpreis had course es- he the arguments in compact By the functions. of using sentially holomorphic removability for the Har- classical singularities on the theorem of proof togs’ elegant and beautiful of systems equations conditions. suitable of differential satisfying coefficient solutions constant of linear spaces to holomorphic philo- for functions of hold that sort extend results could a structural one most that was held years that principle those sophical in work preis’s be to the has course). functions, of above interpreted, generalized suitably stated objects are theorem the spaces representation (when these etc. in functions, holomorphic spaces, Beurling distributions, Schwartz’s includes the where of subvarieties algebraic of sequence V finite varieties certain a of is conditions union growth the on suitable satisfying functions system eylrecaso pcs(htEhrenpreis (what spaces for of holds class it large that called very and equations a differential systems rectangular of to extends actually principle by supported measures bounded { = ab h otipratcneuneo this of consequence important most the Maybe ab h otsrkn uhrsl a his was result such striking most the Maybe Ehren- of most in themes common the of One ti motn opitotta h fundamental the that out point to important is It z (x) f E nltclyuiomspaces uniform analytically : P P P 1 1 n h ulo pc fholomorphic of space a of dual the and (D)f (z) = Q k X = = = k t r oyoil and polynomials are s 1 = = Z V k f Q in k (x) P r E (z) P P exp r (D)f a erpeetdas represented be can = i,x d x) (iz, 0 V } . = ,actgr that category a ), V h ro fthe of proof The o h duality the for V k .Tefunda- The 0. k . where , k (z), P j . k are s { V k } 675 algebraic properties. The paper is beautiful and fifty years. We began as teacher-student when I elegant and shows Ehrenpreis’s talent for simplic- was still doing my undergraduate degree. I heard ity and anticipates the kind of algebraic treatment about a famous, brilliant young mathematician of systems of differential equations that became who was going to give a course entitled Mathe- so important in years to come. matics and the Talmud and I decided to register The interest of Ehrenpreis in removability of for it. After the semester I asked him whether he singularity phenomena is also apparent in another would be willing to write a letter supporting my beautiful series of papers ([12], [13], [14], [15]) application to graduate school, and he told me dealing with elegant and surprising variations on that I would be better off asking a person more the edge-of-the-wedge theorem. familiar with my mathematical abilities. After that I am obviously unable to touch upon all the I did not have much personal contact with Leon important work of Ehrenpreis, but it would be until after I finished my graduate work and our impossible not to mention his interest in the paths crossed again. I was working on problems Radon transform, which absorbed much of his related to compact Riemann surfaces, and we mathematical efforts in the last ten or so years. would meet now and then. Leon was also very His work on this topic culminated in his second much interested in this subject (Ehrenpreis con- monograph [16], in which Ehrenpreis introduces a jecture, Schottky problem) and always expressed generalized definition of the Radon transform in an interest in what I was doing. We even wrote terms of very general geometric objects defined two papers together ([20], [17]), but this is not the on a manifold (what he calls spreads). Just like measure of the influence he had on me. In fact, his previous monograph [11], this more recent my book with Irwin Kra, Theta Constants, Riemann work brings a new and invigorating perspective Surfaces and the Modular Group, [21] grew out of to his subject matter. And as in the case of a conversation with Leon. A visit to New York [11], this work will provide mathematicians with would never be complete without meeting Leon. In ideas and challenges that should keep them busy fact I arrived in New York on August 15 planning for a long time to come. As Ehrenpreis’s former to meet with Leon in the middle of the week to student Carlos Berenstein states in his review [1] discuss my current work, but he passed away on of [16] “[this is] a book that is worth studying, Monday, August 16. Mathematics has lost one of although mining may be a more appropriate word, its finest practitioners. He will be sorely missed as the reader may find the clues to the keys by the mathematical community as both a scholar he’s searching for to open up subjects that are and a gentleman. seemingly unrelated to this book. Thus, one finds at the end that the title is justified.” Takahiro Kawai Hershel Farkas The Fundamental Principle, Hamburger’s Theorem and Date Line A Remembrance When I was a graduate student (late sixties), the Leon Ehrenpreis was one of the leading mathemat- “fundamental principle of Ehrenpreis” [9] was ical figures of the past century. In many areas of really a guiding principle for many young ana- mathematics, specifically differential equations, lysts, including me. It aimed at, and succeeded Fourier analysis, number theory, and geometric in, analyzing general systems of linear differential analysis, his name is a household word. He was a equations with constant coefficients, in the days person who could discuss mathematical problems when a single equation or a determined system from a very wide variety of subfields and directly was the main target of specialists in differential and indirectly had a great influence and impact on mathematicians and mathematics. He had the abil- equations, and the cohomological machinery was ity of getting to the core of a problem and usually not in the toolboxes of most of them. Thus the the ability to give suggestions for possible solu- publication of his book [11] had been yearned for; tions; sometimes he left these for others, worked actually I asked a bookseller to get it by airmail as jointly with other people toward the solution, or soon as it appeared—it was an exceptional case as just solved the problem himself. Ehrenpreis’s di- one U.S. dollar equaled 360 yen in 1970. Unfortu- versity extended way beyond mathematics. He was nately I could not indulge in reading [11] as I had a pianist, a marathon runner, a Talmudic scholar, hoped; in 1970 and 1971 I was totally absorbed in and above all a fine and gentle soul. My personal the collaboration with Sato and Kashiwara to com- association with Leon Ehrenpreis goes back over plete [29], which was a successor to [9] in the sense that it presented the microlocal structure theorem Hershel Farkas is professor of mathematics at the He- brew University of Jerusalem. His email address is Takahiro Kawai is emeritus professor at the Research [email protected]. Institute for Mathematical Sciences, Kyoto University.

676 Notices of the AMS Volume 58, Number 5 May is address mathematics corrections. and email comments useful of for Struppa His C. D. professor University. 1 A&M is [email protected]. Texas Kuchment at Peter has has Leon gone now about being in. one him talking sunk yet that of when not thought believe tense The to past Ehrenpreis. the me use for to hard is It Colleague. and Friend Ehrenpreis—A Leon Kuchment Peter thanks, many Many, Leon! life. daily in of and mathematics effect the to due Kyoto Line. Date in International day the fast the and about the dubious days of was two he date notice that for was to anything reason happened the taken that Another once not I had [19]. he that paper that is our note intellectual cannot I to of I incident led full Weil. which atmosphere and curiosity, warm Hecke theorem the of the forget works expounded related kindly and he and Hamburger’s theorem to relevance its prototype noticed endorse immediately the that explained incidents I of When two impression. note the I sincerity. of memory ending man In this now. kind until continued a has impression was The he that impression such of outcomes Leon. of with example chatting chatting. an were and is I [26] if ideas paper the as The feel in the I browse [11], I of of When pages full Ehrenpreis. Leon is of [11] dreams through book browsing the enjoy occasionally; to Still, continued variety. have characteristic its I coefficients, of equa- point constant generic differential a with at linear necessarily of not system tions, general a for Stockholm the at conference. Boman Jan with Leon Photograph by Yael Ehrenpreis Meyer. mgaeu oP ef,M oiesy and Mogilevsky, M. Deift, P. to grateful am I hsIhv ere uhfo enbt in both Leon from much learned have I Thus the got I Kyoto, in 1973 in Leon met first I When R hlnmccmlxst eni 90 he 1980, in Leon to complexes -holonomic 2011 oie fteAMS the of Notices 1 oeie ikaro o i nahtlseven hotel a in him visits, for would his room I Kansas, during a Wichita, pick run in sometimes me to visited York liked 1970 he when New in also so the inception He its run 2007. since had till he year and that every known runner marathon well avid is It an some music. was or in Talmud, time the mathematics, the or it all activity—be intellectual engaged of was variant brain his that transform. Radon and the on him [16] chapter book privilege with a his Quinto) the to together Todd had with papers (jointly also contributing joint have writing I of email. by and communicating seeing phone and a basis, conferences, regular quite at a other on met each Texas we and visiting Kansas Leon And in years, me twenty holiday. past the a over times like occasion few every feel made met kind time any we any discuss at to mathematics eagerness of abundant his disposition cheerful and unfailing His encounter. first main the of collaboration one our started. how is is This geometry tools. mathematical integral which in tomography, computed I in and working started geometry, just that integral had on at worked me had to Leon unknown time, that, was discovery happy communicated book his I Analysis translating Geometric when while indirectly, him with earlier me proven Sigurdur been met had to my existence also his was (I but there, kind. Arcata Helgason this in of Leon only and experience all Meeting first at not active. old that very who not were still but mortals, flesh Earth, the in mere this existed referred above to least well at corresponded somewhere or semi–gods covers, book to on obviously only which existed Louis luminaries, Lax, other Peter and Ehrenpreis, was Nirenberg, Leon afterward like soon names my emigration that during my did shock and proof truly visit Another constructive first curtain revelation! the iron a being the was all, like outside exist trip of world felt first First the it that very dream. and a my USSR, in was former It the conference outside California. tomography Arcata, and in geometry integral ideas. through wonderful by of rewarded got abundance always one an was one once easy hurdles, minor but an these unusual notations, not preferred and always was Leon terms since It part the detail. in learn in task, to in Zelenko had techniques L. thus We with Leon’s PDEs. work periodic on my 1970s played in late Palamodov, role V. crucial and a and Malgrange fun- papers B. the related by called as books well he the as what since principle, on least damental work at His time, 1970s. long fundamental early very of a for existence solutions) (e.g., results standing vroewoke enErnri realized Ehrenpreis Leon knew who Everyone the from Leon loved I else, everyone like Just the at 1989 in time first the for Leon met I out- Leon’s of some with familiar been have I 2]it usa. Another Russian.) into [22] rusand Groups 677 miles away from the campus, with a sufficiently attractive route to run between the two. So, after his lecture, or just a working day, he would give me his things to take back to the hotel, while he would run. Every time I would meet him after the run, he would have some new ideas (and he had so many great ideas!) about the problem we were working on at the time. Once, when he came back and I was waiting for him in the hotel’s lobby, the receptionist at the front desk asked him: “Did you really run all the way from the campus?” Leon’s reply was: “What else could I do? He refused to give me a ride”—and he pointed at me. I think I lost all the receptionist’s respect at that time.

This was not a one-time event; Leon always liked Photograph by Yael Ehrenpreis Meyer. to crack or to hear a good joke. He was smiling Leon at the Stockholm conference in front of most of the time that I saw him. It was a joy to the Royal Palace. discuss with him not only mathematics, but also religion, music, or anything else. What made this even more enjoyable was that in my experience he he described the big picture, and he illustrated never imposed his opinions, beliefs, or personal his points with examples that brought the ideas problems (and he unfortunately had quite a few) down to earth. Leon’s enthusiasm was contagious, on others. It was relaxing to talk to him. He must and it got even skeptical listeners involved and have been a wonderful rebbe. Over the years, he intrigued. I especially appreciated Leon’s respect became our dear family friend. and concern for the person he was talking with; Leon always liked a good story and had some of he wanted the listener to be as engaged and inter- his own to tell. My favorite, which I tell to students ested as he was. His daughter Yael told me that often, was about him teaching a calculus class he was exactly the same way when he helped her many years ago. As any good teacher would do, he tried to lead his students, whenever possible, with math homework. to the discovery of new things. So, he once said: Leon’s mathematics reflected his emphasis on “Let us think, how could we try to define the unifying principles. In Leon’s book [16] The Uni- slope of a curve?” “What is there to think about?” versality of the Radon Transform, he developed was the reply from one smart student, “it says several overarching ideas and used them to un- on page 52 of our textbook that this is the derstand properties of the transforms, such as derivative.” “Well,” replied Leon, “I haven’t read range theorems and inversion methods. One such till page 52 yet.” The result was that the class overarching idea he defined is the nonparamet- complained to the administration that they were ric Radon transform using spreads (a collection given an unqualified teacher. So much for inspiring of foliations of Euclidean space, the leaves of teaching; it can backfire! which depend on a spread parameter). For the I miss Leon, a great mathematician and human hyperplane transform, the spread is defined by being, and hope that he dwells happily in the a specific hyperplane L0 through the origin (or element of the Grassmannian G(n, n 1), and the house of the Lord forever. − spread variable is a point s in L0⊥: the spread is defined for each L0 by s ֏ s L0. After ten Eric Todd Quinto pages of the book, he is considering+ other mani- folds and spread variables, and he is relating the geometric construction to differential equations A Remembrance and groups. The book draws connections between Before I met Leon Ehrenpreis I was a little ap- several fields, including complex variables, PDE, prehensive. He had theorems named after him, harmonic analysis, number theory, and distribu- and I knew he was a brilliant mathematician. His tion theory—all of which have benefited from his work on existence of solutions to PDEs helped contributions over the years. I remember one talk revolutionize the field, and I wondered what its he gave at Harvard while he was writing the book. creator would be like. Leon immediately put me He pointed to about three hundred pages of notes at ease with his warm enthusiasm and love for on the lectern and told us with a broad smile and mathematics. When we talked about mathematics hearty laugh that he was going to talk about all Eric Todd Quinto is Robinson Professor of Mathematics that. Worried that we would be there for a while, at Tufts University. He email address is todd.quinto@ we laughed a little nervously. However, if I am tufts.edu. remembering right, he covered a lot of material

678 Notices of the AMS Volume 58, Number 5 but ended more or less on time. Peter Kuchment his family, the sorrows were of such immensity and I wrote an appendix to the book, and this, too, that would otherwise crush anyone. But Leon bore was a pleasure. his with unimaginable courage and responsibility. Leon was a rabbi, and some of our most lively Courage that, we dare say, none of us could have conversations occurred when I asked him simple possibly comprehended, let alone mustered. But questions about Jewish law. Leon would launch despite it all, and no matter what transpired, Leon into an energetic description of what the rabbis retainedeverybitof the vitality ofour earlier years. thought about a point and how they resolved His mathematical work continued. His, along with seeming inconsistencies. He always made sure Ahava’s, loving care and unstinting dedication to the conversation was a dialogue and that I was his family continued. His kindness and loyalty to engaged. He cared deeply about Jewish law, and us, his friends, continued. It was who he was. he wanted to share it with me. To think now that this vitality is gone from us I will miss Leon’s theorems and mathematical is very hard to accept. We’ll always cherish our taste, as well as our conversations. His ideas are recollections of him—even as an attempt, however important, but so was his way of communicating illusive, to conjure up a whiff of his vitality. Leon those points and sharing his enjoyment of them. I was one of a kind. We know he is irreplaceable. will miss Leon’s enthusiasm for math and life, his And we miss him. smile, and his menschlichkeit. Alan Taylor Shlomo Sternberg Remembrances of Leon Ehrenpreis A Personal Recollection I first met Leon in the summer of 1966 at an I will leave it to others to describe the extremely AMS summer conference, “Entire Functions and distinguished mathematical career of Leon Ehren- Related Parts of Analysis”, in La Jolla, California. preis. In fact, Leon, Victor Guillemin, and I wrote I had just completed my thesis, which was about one joint paper together [18] of which I am still problems in spaces of entire functions that fit his proud, but this reflects only a very tiny fraction theory of analytically uniform spaces, and I had of his great mathematical achievements. I will studied some of his important papers on division concentrate on the personal. problems and their applications to constant coef- I first met Leon Ehrenpreis in the early 1950s at ficient partial differential operators. So it was very Johns Hopkins University, where I was a student exciting to meet and talk with him. It was also and he an instructor. We became close personal where I had my first encounter with his kindness, friends, and then, when I marriedAviva, he became as he suggested that I apply to spend a postdoc- a close friend of ours, a friendship that lasted from toral year at the Courant Institute, where he was a the time that we were teenagers until his death. professor. It was during that year, 1968-1969, that Thinking back through the years, I can’t recall a sin- I really got to spend a lot of time talking with him gle time, no matter how trying the circumstances and met his student at that time, Carlos Beren- may have been, whether casual or serious, that stein. Thinking back on those times is bittersweet; his voice, his eyes, his whole demeanor conveyed it is sad now because of Leon’s death and doubly less than deep warmth, profound generosity, an so because Carlos is too ill to share memories of optimism, a hopefulness that was pure Leon. that special year. But it also reminds me of this When we were young, “pure Leon” might in- most interesting and fun year of my professional clude a dash of madcap charm, a directness, a life. Carlos was finishing his doctoral thesis at boyish whimsy, a ruefulness, that belied his dis- Courant and helping Leon with the final editing of tinguished mathematical achievements. His style his book on Fourier analysis [11]. Leon had just was not professorial. He was not into style or moved to Yeshiva University in uptown New York image—then or ever. Leon retained and presented City, where he was giving a course on the book. an honesty, a disarming forthrightness, a genuine- Both Carlos and his wife and I and my family ness, a profound generosity and sheer vitality that lived in New York University-owned housing in he carried with him all of his life. He was certainly Greenwich Village, so each Thursday Carlos and I extremely generous to us at crucial junctures in would take the A train uptown to spend the day our lives. with Leon, attending his class and talking about And it was, and is, this vitality that perhaps mathematics. for us best describes Leon. The years passed; life I really saw Leon’s style of doing mathematics transpired with its joys and sorrows. For Leon and in that class. He was always interested in the

Shlomo Sternberg is professor of mathemat- B. Alan Taylor is professor of mathematics at ics at Harvard University. His email address is the University of Michigan. His email address is [email protected]. [email protected].

May 2011 Notices of the AMS 679 680

© C. J. Mozzochi, Princeton, NJ. ai iklti pyis.SvrltmsIheard I was times group Several the (physics). Finkelstein in David Also outstanding mathematicians! an of What group Aumann. Robert Martin and Flatto, Leo Davis, Shapiro, S. Harold Shields, Schwartz, Allen Jacob Rubel, Lee Ehren- Newman, Leon Donald included interacted preis, group who The another. or one mathematicians with year young remarkable a a of was class, there group 1949, that year In the around Michigan. two at for article years colleague his my many in Shields, Allen mentions fact remembering also a [31] York, Shapiro New Harold of under- College that re- remarkable City worth at a class from are Lee graduate came advisor, think Leon my that I from Rubel, learned that I years First, membering. the over Leon Ann visit department. to our Leon and for Arbor visits occasion family family good that a a so always from that suburb, were Detroit was lucky a in Sperka, visit was lived (nee) that I would Ahava Arbor. he wife, Ann when his about in mostly Leon department saw two, our I or was year, year it that and every After think train jogging. I the his and riding in when him especially around always, spent true of I 100% time mathematics the doing some of was to Leon “Edge differential extension equations. partial the coefficient its on constant of and that systems theorem” example, Wedge for much the is work, in view present his is of inquiry of point of style general This this explored. which in functions quasianalytic and series, lacunary boundary problems, general value on of chapters proof contains principle, the fundamental the Fourier presenting contribution, important on most to his view book addition of his in point Indeed, analysis, the analysis. from Fourier analysis of in problem almost at look any the could he in that me interested to seemed It less details. but examples illustrative and in true were theorems that reasons fundamental att asaogtotig ere about learned I things two along pass to want I endsusn ahmtc ihDennis with mathematics discussing Leon ulvnadJh ogna Columbia at Morgan John and Sullivan nvriy 2006. University, oie fteAMS the of Notices References he that will and I him. name. miss team, boyhood greatly my baseball “Alan”, me a called enough always form have to to wanted he children tea that drank worked, many always he we remember that when still fact the much I Like knew but things. I little life, that private in his him I about that to say close cannot personally I was friend. great a mathematical and his suggestions with generous was word He unkind him. an heard from never a I and without face, him his on saw smile never I mathematics. about ing case life. the on professional influence indeed entire profound my is a it had Ehrenpreis So Leon years. that twenty me occupied last have the ques- work for and this from 1988, arose by around that solved tions myself was and question Vogt, inverse Meise, right Giorgi in The the De Hörmander 1973.) by of by given characterization being negative a operators surjective with the [3] in Cattabriga analytic and solved func- real analytic was of real tions space on surjectivity the (The on functions. surjectivity operators of such question in- the of Schwartz as from well been as had list we discussing, that the question inverse that right the me cluded linear told of also theory operators. He differential modern partial 1950s, the coefficient the constant underlie in now Hörmander that in- and by These answered Malgrange, time. questions, Leon, the fundamental at with the them along cluded about knew operators questions he several differential what of list partial a about with back Schwartz Schwartz written Laurent suggestions. had to thesis-problem write for he asking suggested to had led Cheval- ley that that me problems told He on principle. work fundamental the to come Cheval- Claude had of he student ley, a being how, I of him point space asked some the At on functions. differentiable inverse infinitely right linear continuous had a operators differential partial coefficient with con- stant which talked determining of often problem the I about Leon 1970s, in own my the 1970s, on Throughout influential the so work. was in it because sometime part large Leon with versation youths. stimu- talented very these the between about competition and Shields atmosphere lating and Rubel from stories [1] [3] [2] enwsakn a,awy neetdi talk- in interested always man, kind a was Leon con- a of is have I memory vivid second A .A Berenstein A. C. h ao Transform Radon the .Cattabriga L. 1979. York, Amsterdam-Oxford-New Holland, Bj E. J. (2007d:58047). 2019604 islzoiaaiih ieuzoiaderivate a equazioni di analitiche soluzioni di ¨o rk , ig fDffrnilOperators Differential of Rings and eiwof Review , .D Giorgi De E. yL Ehrenpreis, L. by , Volume h nvraiyof Universality The 58 Sull’esistenza , Number , ah Rev. Math. North- , 5 parziali a coefficienti costanti in un qualunque nu- Lipman Bers), pp. 125–132, Academic Press, New mero di variabili, Boll. Un. Mat. Ital. (4) 6 (1972), York, 1974. 301–311. [21] H. M. Farkas and I. Kra, Theta Constants, [4] L. Ehrenpreis, Theory of Distributions in Locally Riemann Surfaces and the Modular Group. An Compact Spaces, Part I, Ph.D. thesis, Columbia Introduction with Applications to Uniformization University, 1953, 122 pp, Proquest LLC. Theorems, Partition Identities and Combinatorial [5] L. Ehrenpreis, Solution of some problems of di- Number Theory, Graduate Studies in Mathematics, vision, I, Division by a polynomial of derivation, 37, American Mathematical Society, Providence, Amer. J. Math. 76 (1954), 883–903. RI, 2001. [6] , Solution of some problems of division, II, [22] S. Helgason, Groups and Geometric Analysis, Division by a punctual distribution, Amer. J. Math. Integral Geometry, Invariant Differential Opera- 77 (1955), 286–292. tors, and Spherical Functions, Pure and Applied [7] , Solution of some problems of division, III, Mathematics, 113, Academic Press, Orlando, FL, Division in the spaces , , A, , Amer. J. Math. 1984. D′ H Q O 78 (1956), 685–715. [23] L. Hörmander, On the theory of general partial [8] , Theory of distributions for locally compact differential operators, Acta Math. 94 (1955), 161– spaces, Mem. Amer. Math. Soc. 21 (1956). 248. [9] , The fundamental principle for linear con- [24] , On the division of distributions by stant coefficient partial differential equations, polynomials, Ark. Mat. 3 (1958), 555–568. Proc. Intern. Symp. Linear Spaces, Jerusalem, 1960, [25] , An Introduction to Complex Analysis in Sev- pp. 161–174. eral Variables, 3rd edition, North-Holland Math- [10] , A new proof and an extension of Har- ematical Library, 7, North-Holland, Amsterdam, togs’ theorem, Bull. Amer. Math. Soc. 67 (1961), 1990. 507–509. [26] T. Kawai, The Fabry-Ehrenpreis gap theorem and [11] , Fourier Analysis in Several Complex Vari- systems of linear differential equations of infinite ables, John Wiley & Sons. Inc., New York, 1970, order, Amer. J. Math. 109 (1987), 57–64. Reprinted by Dover, 2006. [27] B. Malgrange. Existence et approximation des so- [12] , Edge of the wedge theorem for partial lutions des équations aux dérivées partielles et differential equations: Harmonic analysis in Eu- des équations de convolution, Ann. Inst. Fourier clidean spaces (Proc. Sympos. Pure Math., Williams Grenoble 6 (1955-56), 271–355. Coll., Williamstown, Mass., 1978), Part 2, pp. 203– [28] V. P. Palamodov, Linear Differential Operators 212, Proc. Sympos. Pure Math. 35, Amer. Math. with Constant Coefficients, Grundl. d. Math. Wiss., Soc., Providence, RI, 1979. Bd. 168, Springer-Verlag, Berlin-Heidelberg, New [13] , Reflection, removable singularities, and York, 1970. approximation for partial differential equations, I, [29] M. Sato, T. Kawai, and M. Kashiwara, Microfunc- Ann. of Math. (2) 112 (1980), no. 1, 1–20. tions and pseudo-differential equations, Lect. Notes [14] , The edge-of-the-wedge theorem for par- in Math., No. 287, Springer, 1973, pp. 265–529. tial differential equations. Recent developments in [30] L. Schwartz, Théorie générale des fonctions several complex variables (Proc. Conf. Princeton moyenne-periodiques, Ann. of Math. 48 (1947), Univ., Princeton, NJ, 1979), pp. 155–169, Ann. of 857–929. Math. Stud. 100, Princeton Univ. Press, Princeton, [31] H. S. Shapiro, Allen Lowell Shields—Some Rem- NJ, 1981. iniscences, Mathematical Intelligencer 12 (1990), [15] , Reflection, removable singularities, and No. 2, pp. 8–10. approximation for partial differential equations, II, Trans. Amer. Math. Soc. 302 (1987), no. 1, 1–45. [16] , The Universality of the Radon Transform, With an appendix by Peter Kuchment and Eric Todd Quinto, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 2003. [17] L. Ehrenpreis and H. M. Farkas, Some refinements of the Poincare´ period relation, discontinuous groups and Riemann surfaces (Proc. Conf. Univ. Maryland, College Park, MD, 1973), pp. 105–120, Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, NJ, 1974. [18] L. Ehrenpreis, V. W. Guillemin, and S. Stern- berg, On Spencer’s estimate for δ-Poincaré, Ann. of Math. (2) 82 (1965), 128–138. [19] L. Ehrenpreis and T. Kawai, Poisson’s summation formula and Hamburger’s theorem, Publ. RIMS, Kyoto Univ. 18 (1982), 833–846. [20] L. Ehrenpreis, H. Martens, H. M. Farkas, and H. E. Rauch, On the Poincare´ relation, Contribu- tions to analysis (collection of papers dedicated to

May 2011 Notices of the AMS 681 How a Medieval Troubadour Became a Mathematical Figure Michael P. Saclolo

Lyric poetry of the Middle Ages may seem far removed from subgroups of the symmetric group or primi- tive roots of finite fields. However, one piece of medieval poetry has led to work in these mathematical disciplines, namely a sestina written in the Romance language of Old Occitan by a troubadour named Arnaut Daniel:

Lo ferm voler q’el cor m’intra The firm desire that enters no’m pot ies becs escoissendre ni ongla my heart no beak can tear out, no nail de lausengier, qui pert per mal dir s'arma of the slanderer, who speaks his dirt and loses his soul. e car non l’aus batr’ab ram ni ab verga And since I dare not beat him with branch or rod, si vals a frau lai o non aurai then in some secret place, at least, where I’ll have no oncle uncle jauzirai joi, en vergier o dinz cambra I’ll have my joy of joy, in a garden or a chamber.

Qan mi soven de la cambra When I am reminded of the chamber on a mon dan sai que nuills hom non intra where I know, and this hurts me, no man enters-- anz me son tuich plus que fraire ni oncle no, they’re all more on guard than brother or uncle-- non ai membre no’m fremisca, neis there’s no part of my body that does not tremble, even l’ongla my nail, aissi cum fai l’enfas denant la verga as the child shakes before the rod, tal paor ai no’l sia trop de l’arma I am that afraid I won’t be hers enough, with all my soul.

Del core li fos non de l’arma Let me be hers with my body, not my soul, e cossentis m’a celat deniz sa cambra let her hide me in her chamber, que plus mi nafra’l cor que colps de verga for it wounds my heart more than blows from a rod car lo sieus sers lai on ill es non intra that where she dwells her servant never enters; totz temps serai ab lieis cum carns et ongla I will always be as close to her as flesh and nail, e non creirai chastic d’amic ni d’oncle and never believe the reproaches of brother and uncle.

Anc la seror de mon oncle Not even the sister of my uncle non amei plus ni tant per aqest’arma did I love more, or as much, by my soul, c’aitant vezis cum es lo detz de l’ongla for as familiar as finger with nail s’a liei plagues volgr’esser de sa cambra I would, if it pleased her, be with her chamber. de mi pot far l’amors q’inz el cor m’intra It can do more as it wills with me, this love that enters mieills a son vol c’om fortz de frevol verga my heart, than a strong man with a tender rod.

Pois flori la seca verga Since the flower was brought forth on the dry rod, Ni d’en Adam mogron nebot ni oncle and from En Adam descended nephews and uncles, tant fin’amors cum cella q’el cor m’intra a love so pure as that which enters non cuig fos anc en cors ni eis en arma my heart never dwelt in body, nor yet in soul. on q’ill estei fors on plaz’ o dins Wherever she stands, outside in the town or inside her cambra chamber, mos cors no’ is part de lieis tant cum ten l’ongla my heart is not further away than the length of a nail.

Michael P. Saclolo is associate professor of mathematics at St. Edwards University. His email address is mikeps@ stedwards.edu.

682 Notices of the AMS Volume 58, Number 5 C’aissi s’enpren e s’enongla For my heart takes root in her and grips with its nail, mos cors e lei cum l’escorss’en la verga hold on like bark on the rod, q’ill m’es de joi tors e palaitz e cambra to me she is joy’s tower and palace chamber, e non am tant fraire paren ni oncle and I do not love brother as much, or father, or uncle; q’en paradis n’aura doble joi m’arma and there’ll be double joy in Paradise for my soul, si ja nuills hom per ben amar lai intra if a man is blessed for loving well there and enters.

Arnautz tramet sa chanson d’ongl’e d’oncle Arnaut sends his song of the nail and the uncle, a grat de lieis que de sa verg’a l’arma to please her who rules his soul with her rod, son Desirat cuit pretz en cambra intra to his Desired, whose glory in every chamber enters.

Note the rearrangement of the final word from related. The troubadours’ northern French-speak- each line of the stanzas to the next. The English ing counterparts are called the trouvères. These translation by Frederick Goldin ([6]) to the right northern poets were influenced by the troubadours of the original illustrates the same phenomenon. and adopted the latter group’s style and themes. Arnaut’s sestina is an example of courtly love The troubadours and the trouvères celebrated poetry. The last three-line stanza unequivocally courtly love. In this highly ritualistic literary tradi- declares the poet’s intention to please his noble tion, full of rules and codes, the object of often lady. What interests us here, however, is how the forbidden desire is an idealized lady of the Court. six six-line stanzas, or sextets, use the same six The poetry composed and performed by the trou- ending words in a permutation given by the cycle badours expresses her unattainability. (124536). The arrangement of the ending words in Arnaut himself was revered as a poet. One of his each sextet corresponds to a power of this cycle, earliest and most prominent admirers was Dante and so if we were to compose a seventh sextet, we Alighieri, the Italian poet and celebrated author of would arrive at one with the original arrangement the Divine Comedy, who lived about a century after of the six ending words. Poets and, lately, math- Arnaut. Dante mentions Arnaut several times in ematicians have been fascinated by this poetic De vulgari eloquentia. He even depicts Arnaut as form, and the desire to generalize it has led to doing penance in Purgatorio in the Divine Comedy, the investigation of the mathematical structures imploring Dante in Occitan not to forget him. involved. Today, our most direct link to courtly love is its long and rich literary tradition. It is an understate- Arnaut Daniel and the Troubadours ment to say that the poetry of the troubadours I begin at the source, the poet. Information about and the trouvères influenced many poetic forms Arnaut's life comes primarily from his Vida. The we enjoy today. Wilhelm discusses sources and Vidas, very short biographical sketches of poet- influences in the introduction to [21]. troubadours in surviving manuscripts of their works (see, for example, [2]), were written primarily The Sestina to promote interest in the troubadours, and there- The poetic form presented earlier is called the ses- fore the information contained therein may not be tina, and Arnaut is credited with its invention ([4]). entirely factual. What is commonly accepted, how- Both Dante and Petrarch composed in the form. ever, is that Arnaut lived in the latter part of the Rudyard Kipling, Ezra Pound, Algernon Charles twelfth century. The Vida tells that he hailed from a Swinburne, and Sir Philip Sidney are among poets castle named Ribérac in the bishopric of Périgueux who composed sestinas in English. Sidney com- in the Dordogne region of France. He was of noble posed an example of a double sestina. birth and presumably had early contact with the As its base, the sestina has the structure of six nobles he would later entertain as a troubadour. sextets followed by a tercet called a tornada or The Vida mentions Arnaut as courting a married an envoi ; the former is an Occitan term meaning noble lady from Gascony, although it quickly “turned” or “twisted”, while the latter is French points out that this forbidden love was believed and means “send-off”. The envoi traditionally in- to have remained unattained. For an extended ac- corporates all six ending words of the sextets. As count of Arnaut’s life, refer to the introduction to previously mentioned, the ending words of each the book edited by James Wilhelm [21]. line of a sextet are rearranged in the subsequent As a troubadour, Arnaut was part of a group of sextet according to the cycle (124536). Of course, musical poets, who entertained courtly audiences any permutation of order six can be used to com- of southern France. Their language of Old Occitan pose a poem that shows a different rearrangement counts modern Provençal as a descendant. Catalan, of the six ending words, while producing the same the language of Catalunya in northern Spain and number of stanzas and lines. But the particular in the Pyrenees region of France, is also closely permutation used by Arnaut inspired poets and

May 2011 Notices of the AMS 683 mathematicians alike. Poets sought either to com- An example is George Pérec’s novel, La Disparition pose in the same style or to develop variations. (translated into English as A Void), a lipogrammatic Mathematicians, instead, posed the question: What novel, redacted without the letter e [9]. Queneau permutations have the “same” properties as the himself played with combinatorial possibilities one used in the sestina? This is the story we are in his collection of sonnets Cent Mille Milliard telling here. de Poèmes (One Hundred Thousand Billion Poems) [10]. For more information on the work of OULIPO, Generalizing the Sestina: the Quenine see, for example, the text translated and edited by Interest in the sestina and the structure pre- Warren Motte [7]. sented by the permutation began among literary Queneau noticed that the spiral representation figures in the twentieth century among lit- can be extended to permutations of a set of any erary figures. According to A. Tavera ([17]), size n. Then he asked which positive integers n give it was Eugène Vinaver, Tavera’s mentor and an order n “spiral” permutation. He determined professor of French at the University of [11], apparently by rote calculation, a list of thirty- Manchester, who made him aware of the one positive integers less than 100 that have this spiral shape of the permutation. To see this, property. Queneau called the generalized sestina number the six ending words of the sextet, top for such n the n-ine. Thus the sestina is the same to bottom, 1 to 6. Now draw an inward “spiral” as a 6-ine, and any one-line poem is degenerately starting from the integer 6 heading towards 1 a 1-ine. The smallest nonadmissible number is then 5, 2, 4, and finally 3 as in Figure 1. The n 4, for the associated permutation that results, = resulting order of the six integers, following the (124), fixes the 3. Later the n-ine became the trajectory of the spiral, is precisely the order of quenine, coined by Roubaud in honor of Queneau. the six ending words in the subsequent strophe. The French word for the sestina is sextine. By analogy one might call the generalization n-ina or quenina in English, but as yet there is no 1 intra established tradition of this convention either in mathematical writing or poetry written in English. 2 ongla The Search for Quenines In this section I shall highlight the various devel- 3 arma opments to find positive integers n that give a generalized sestina, culminating with the defini- 4 verga tive classification. First I shall set up some basic notations and definitions. For x a positive integer, σn is defined by: 5 oncle x/2 if x is even, (1) σn(x) = n (x 1)/2 if x is odd. 6 cambra − − The following terminology related to σn(x) was Figure 1. Spiral representation of a sestina. formalized by Monique Bringer in [2]. The function The six ending words of the strophes of σn(x) is called a spiral permutation. Integers n Arnaut’s sestina are listed in its original order. such that σn(x) is of order n are called admissible. Roubaud also referred to such n as Queneau numbers. A spiral permutation with admissible n The mathematical question arising from the par- is also a quenine or n-ine. In honor of Queneau ticular permutation and its spiral representation and Daniel, Bringer called the cyclic subgroup was taken up by the poet Raymond Queneau and of the symmetric group generated by σn(x) the his colleague, the poet, writer, and mathematician Queneau-Daniel group. Jacques Roubaud. Queneau was a member of the Thus the search for quenines became the search French mathematical society, the Société Mathéma- for admissible n. Moreover, it was the study of tique de France. Moreover, he and Roubaud were the inverse permutation to σn that eventually central figures in the development of OULIPO produced the desired results. Let δn be the inverse (“OUvroir de LIttérature POtentielle”), a literary permutation to σn defined by: movement and association that Queneau and 2x if 2x n, François Le Lionnais founded in 1960. Composed (2) δn(x) ≤ = 2n 1 2x otherwise. of mostly European members, the goal of OULIPO + − is to explore and compose what the group calls As σn is of order n if and only if δn is also of “potential” literature by using constraints drawn order n, finding admissible n by way of δn gives from mathematics and other technical disciplines. the admissible n for σn.

684 Notices of the AMS Volume 58, Number 5 Queneau the orbit of q, a contradiction. Hence 2n 1 must + Queneau apparently did not realize this connec- be prime. tion, at least not in published works (see [11], [12], Bringer also points out that the necessary con- dition that 2n 1 is prime is equivalent to [13]). He recognized early on that not every n is + admissible, citing some basic counterexamples. In Queneau’s prior remark that n is not admissi- ble when n 2xy x y, where x and y are the case of n 4, 7, or 10, for instance, σn fixes at = integers greater= than+ or+ equal to 1. For if 2n 1 least one number. For n 8, σ8 is of order 4. As = were prime, suppose that n 2xy x y have+ for some initial characterization of nonadmissible = + + n, he mentioned the cases in which n 2xy x y noninteger solutions different from x 1 and = + + y (n 1) (which are always solutions),= − then for x, y integers greater than or equal to 1 or if = − + n 2k for k > 1 as examples of such n, since 2n 1 4xy 2x 2y 1 (2x 1)(2y 1). = + = + + + = + + the resulting permutation subgroups are of order 2x 1 and 2y 1 are not equal to 1 (unless n +1) and divide+ 2n 1, which is not possible. less than n. (Consider the orbit of 2 under δn for = + example.) Alas, these conditions do not exhaust Now if n 2xy x y does not have integer solutions, suppose= + that+ 2n 1 is not prime. Then the cases in which n is not admissible. 2n 1 pq for p and q ≠+1 and both odd, i.e., + = p 2p′ 1 and q 2q′ 1. But it follows then that After Queneau = + = + n 2p′q′ p′ q′, which is false, and so 2n 1 Roubaud and his student Bringer continued the must= be prime+ + for n to be admissible. Bringer also+ search for admissible n. In [14] Roubaud was in- remarks that 2n 1 being prime is not sufficient, terested in the various permutations employed by citing a counterexample,+ n 20. the troubadours. In considering the sestina, he Recall that, earlier, Queneau= made the claim attempted to connect the particular permutation that if n 2k, k ≠ 1, then n is not admissible. This used by Daniel to the assonant pairing of end- particular= situation falls under the last item above ing words in the stanzas, reiterating Queneau’s of Bringer’s list of results, but in [2] she includes problem of generalizing the sestina. But it was a separate proof of this case. To see this, note Bringer (in [2]) who took on Queneau’s problem 2 k that σn(2) 1, σn (2) n 2 . It follows that directly and was among the first to characterize k 1 = = = σn + (2) 2. The permutation cycle generated by such admissible and nonadmissible integers n. 2 is of order= k 1, which is strictly less than 2k if Bringer found that a necessary condition for n k ≠ 1. + to be admissible is for 2n 1 to be prime. She + In 1993 Roubaud summarized what was known also found that if 2 is a primitive root of the until that time about the search for quenines or finite field Z/(2n 1)Z (i.e., where 2n 1 is prime), admissible n. In [15] he even proposes extensions + + then n is admissible. (Note: While the mathematics to the quenine. He also attempts to complete that follows in the rest of the article is generally Bringer’s result, stating a seemingly complete accessible, those who would like to read back- characterization of admissible n. He claims that ground and reference materials may look at [5] a necessary and sufficient condition for n to be about finite fields and at classics such as [6], for a admissible is for 2 to be of order n or 2n in the short treatment on symmetric groups, and [4], for multiplicative group of integers modulo 2n 1. a treatment of primitive roots.) The following is Jean-Guillaume Dumas, in [3], points out that this+ is a summary of Bringer’s results, listing conditions not true when n is even, citing the counterexample for both admissible and nonadmissible n. n 8. Also 2 is of order 8 (mod 17). But, as we have= seen, the “octine” is not possible as n 8 Theorem 1 (Bringer). (1) If n is admissible, gives a spiral permutation of order 4. = then 2n 1 is prime. (2) If n and +2n 1 are prime, then n is admis- + From the Middle Ages to the Twenty-First sible. Century (3) If n 2p where p and 4p 1 2n 1 are = + = + prime, then n is admissible. Roubaud was almost correct, and Dumas provided (4) n 2k 1 is not admissible. the solution. In [3] Dumas gives a complete char- (5) n = 4k−is not admissible. acterization of admissible numbers, and therefore = quenines. He even adds to the list started by Que- To show that 2n 1 is prime for n to be ad- neau, naming all quenines under one thousand. + missible, suppose the contrary. Then there exists (For example, the highest admissible n under 1000 a positive integer q > 1 that divides 2n 1. Hence, is n 998. Thus one can compose a poem with + k = if m is in the orbit of q under δn, then m 2 q 998 strophe-ending words permuting “spirally” for ≡ ± (mod 2n 1). This implies that q divides m since 998 stanzas.) Extending Bringer’s work, he investi- + it divides both 2n 1 and 2kq. Therefore the gates the properties of the finite field F , for such + ± p orbit of q only contains divisors of q. But, then, n where p 2n 1 is prime. His characterization 2, . . . , q 1 do not divide q and thus cannot be in of Queneau= numbers+ n is the following: −

May 2011 Notices of the AMS 685 Theorem 2 (Dumas). Let n be an integer such that The characterizations of admissible n obviously p 2n 1 is prime. Then n is admissible if and provide a test of whether a quenine of a certain = + only if: order n exists. At this point there is no way of (1) either 2 is of order 2n (i.e., 2 is a primitive generating such n.

root) of Fp Extensions and Connections (2) or n is odd and 2 is of order n in Zp. There are some very natural ways to extend math- Recall that the first characterization above of ematically the results inspired by the quenine.

admissible n was previously elucidated by Bringer. One generalization to δn, suggested by Roubaud, The following, however, is the entire proof by is to replace multiplication by 2 by any k. Call this

Dumas. permutation δn,k(x), the k-quenines. For example, the 3-quenine has formula: Proof. Beginning with the necessary condition, consider an admissible n. As the order of the 2 in 3x if 3x n, ≤ Fp divides 2n, the number of invertible elements (3) δn,3(x) 2n 1 3x if n < 3x 2n, F =  + − ≤ of p, then 2 can only be of order 2n, n, or strictly 3x (2n 1) otherwise. less than n. Now suppose 2 is of order j < n. Then − +  j j In this case, when n 8, the permutation δ8,3 δn(2) 2 2 2 (mod 2n 1). So there are two = ≡ ± ≡ ± j + is of order 8. Roubaud and Pérec developed an cases to consider. First, if δn(2) 2, then the orbit = of 2 only contains j < n elements, which cannot extension to σn, inspired by the absence of a be true since it is assumed that n is admissible. quenine of order 10 ([15]). The permutation, πn, j is called the p´erecquine after Pérec and is defined Thus, in the other case δn(2) 2. But by defini- j = − by the formula: tion 1 δn(x), so 1 2n 1 2 2, or n 1. ≤ ≤ + − ≤ ≤ But 2 is of order 2 (mod 2(1) 1 3). Therefore, 2x if 2x n, + = if n is admissible, then 2 is of order n or 2n (mod (4) πn(x) ≤ = 2x (n 1) otherwise. 2n 1). But it remains to exclude the instance in − + + which n 2k is even and 2 is of order n (mod As he did with the quenine, Dumas formalizes = 2n 1). But in this case 2k 1 (mod 2n 1). these extensions in [3] and provides analogous + k≡ − k + spiral-like representations for the permutations From here it follows that δn(2) 2 2 2 (mod 2n 1). As k n < n, then as= before ± neither≡ ± involved. With the pérecquine he also characterizes + = 2 situation can exist if n is admissible. all admissible n, finding that πn is of order n if Next, we prove the sufficient condition. Let us and only if 2 is of order n (mod n 1). + call ω the cardinality of the smallest orbit of the Finally, Dumas extends Theorem 2 to all admis-

elements of the set N 1, 2, 3, . . . , n by δn. Now sible n to δn,k and all primitive roots. = { } suppose that u N is of order ω. Now there exists ω ∈ k ω Theorem 4 (Dumas). Let n be an integer such that k such that δn (u) u ( 1) 2 u (mod 2n 1). ≡ ≡ − + p 2n 1 is prime, and let k n. Let Fp be the And, since u is invertible, ( 1)k2ω 1 (mod 2n = + ≤ − ≡ + finite field containing p 2n 1 elements; then δn,k 1). This means that 2ω 1 (mod 2n 1). If 2ω = + ≡ ± + ≡ is of order n if and only if: 1, then ω is greater than the order of 2. Therefore ω n and so ω n for the permutation is at most (1) Either k is of order 2n (i.e., k is a primitive ≥ = F of order n. In the case that 2ω 1, then 2 is of root) in p, or ≡ − F order 2n or an odd n. If 2 is of order 2n, then 2n (2) n is odd and k is of order n in p. n ω ≡ 1 (mod 2n 1). So, 2 + 1, and therefore ω n. − + = = Once more, δn,k is the inverse permutation to If the order of 2 is n with n odd, then (2ω)2 = σn,k. The proof is similar to that of Theorem 2 ( 1)2 1, which means that n divides 2ω. As n is − = except for the condition k n. odd, Gauss’s lemma implies that n divides ω. So ≤ once more, ω n.  Corollary 5. Let n be a positive integer such that = 2n 1 is prime. Then there exists k, 1 k n, such + ≤ ≤ Another characterization of the quenine pro- that δk,n is of order n. vided by Dumas is a corollary to the theorem above. According to Dumas it restates a conjecture by A Connection to Artin’s Conjecture on Primitive Joerg Arndt. Roots Artin’s conjecture states that a positive integer k Corollary 3. Let F be as above. Then n is admis- p that is not a perfect square is a primitive root of sible if and only if: p, for infinitely many primes p. Moreover, the set (1) either 2 is of order 2n in Fp, and n 1 or ≡ of prime numbers p such that k is a primitive root 2 (mod 4), has a positive asymptotic density in the set of F (2) or 2 is of order n in p, and n 3 (mod 4). primes. For example, when k 2 (and, in general, ≡ =

686 Notices of the AMS Volume 58, Number 5 if k ab2 and a is not congruent to 1 (mod 4)), 3. Jean-Guillaume Dumas, Caractérisation des = then the density is Artin’s constant quenines et leur représentation spirale, Math- ématiques et Sciences Humaines 184 (2008), 1 9–23. (5) C : 1 0.373955, 4. G. H. Hardy and E. M. Wright, An Introduction to the = p − p(p 1) ≈ − Theory of Numbers, Oxford University Press, 2008. where the product is taken over all primes includ- 5. R. Lidl and H. Niederreiter, Introduction to Finite ing 2. The conjecture then implies that there are Fields and Their Applications, Cambridge University infinitely many admissible or Queneau numbers n, Press, 1994. 6. Saunders Mac Lane and Garrett Birkhoff, where p 2n 1. Indeed, the sequence of such n = + Algebra, AMS Chelsea, 1999. corresponding to that of primes p for which 2 is a 7. Warren F. Motte (ed.), Oulipo, a Primer of Potential primitive root (sequence A001122 of N. J. A. Sloane Literature, University of Nebraska Press, 1986. of the On-Line Encyclopedia of Integer Sequences) 8. M. Ram Murty, Artin’s conjecture for primitive appears to be a (proper) subset of the set of all roots, Mathematical Intelligencer 10 (1988), no. 4, Queneau numbers. There is a brief treatment of 59–67. Artin’s conjecture in the preface to his collected 9. Georges Pérec, La Disparition, Gallimard, 1989. works [1], while the expository articles by Murty 10. Raymond Queneau, Cent Mille Milliard de Poèmes, Gallimard, 1961. [8] and Stevenhagen [16] trace related history and 11. , Note complémentaire sur la sextine, Subsidia summarize some developments in proving the Pataphysica 1 (1963), 79–80. conjecture. 12. , Batôns, Chiffres et Lettres, Gallimard, 1965. 13. , Letters, Numbers, Forms: Essays 1928–1970, Conclusion University of Illinois Press, 2007. The mathematical ideas inspired by Arnaut’s 14. Jacques Roubaud, Un problème combinatoire posé par la poésie lyrique des troubadours, sestina may not contribute anything to one’s Mathématiques et Sciences Humaines 27 (1969), understanding of courtly love, to the culture 5–12. of the troubadours, or even to the meaning of 15. , N-ine autrement dit quenine (encore), La Arnaut’s poem itself. However, to those who un- Bibliothèque Oulipienne, numéro 66, 1993. derstand the mathematics involved, these results 16. Peter Stevenhagen, The correction factor in inform the reading of the poetry by providing Artin’s primitive root conjecture, Journal de Théorie another dimension to the appreciation of its com- des Nombres de Bordeaux 15 (2003), no. 1, 383–391. A. Tavera D position. Whether or not Arnaut was aware of the 17. , Arnaut aniel et la spirale, Subsidia Pataphysica 1 (1963), 73–78. spiral structure of the permutation employed in the sestina, this structure provided the natural link and spark to mathematical activity. Perhaps we shall never know what inspired Daniel to choose

σn,6 to compose his sestina. His choice, however, inspired modern mathematicians to create and contribute to their own discipline. Now it is the poets’ turn.

Acknowledgments The author would like to thank the facilitators and fellow participants of the MAA Professional Enhancement Program workshop on “Expository Writing to Communicate Mathematics” (June 30– July 3, 2008), where portions of this article began to form. He is especially grateful to fellow work- shop participant Charles Coppin, who read and commented on initial drafts. The author also ap- preciates the guidance, suggestions, and critiques of the editors and reviewers. It was one of the reviewers who made the author aware of the connection to Artin’s conjecture.

References 1. Emil Artin, Collected Papers, Addison-Wesley, 1965. 2. Monique Bringer, Sur un problème de R. Queneau, Mathématiques et Sciences Humaines 27 (1969), 13–20.

May 2011 Notices of the AMS 687 WHATIS... ? an Infra-nilmanifold Endomorphism? Karel Dekimpe

2 Ever since the term “infra-nilmanifold endomor- a linear map lϕ of R that is given by the ma- phism” arose in the 1960s, there has been confusion trix A 2 1 , and ϕ being Anosov is equivalent = 1 1 about its exact meaning, and different authors have to A having no eigenvalues of modulus 1. More used the term to refer to different concepts. Partly generally, if A GL(n, Z), then the linear map n n ∈ because of this confusion, two major results in dy- lϕ : R R determined by A induces a diffeomor- → n n n n namical systems, one on Anosov diffeomorphisms phism ϕ : T T : r Z ֏ lϕ(r) Z on the → + + (1974) and one on expanding maps (1981), turn out n-torus. Such maps, called toral automorphisms, are to be incorrect. prototype examples of infra-nilmanifold automor- With this historical background as motivation, let phisms, which we will describe below. When A has me introduce the reader gradually to the world of no eigenvalue of modulus 1, A is said to be hyper- infra-nilmanifold endomorphisms, starting with one bolic, and the corresponding toral automorphism, of the best known examples, Arnold’s cat map ϕ on which is called a hyperbolic toral automorphism, is the torus T2 R2/Z2. This map is given by an Anosov diffeomorphism. It is easy to construct = Z 2 2 2 2 a hyperbolic matrix A GL(n, ), for any n 2; ϕ : T T : (x, y) Z ֏ (2x y, x y) Z . n ∈ ≥ → + + + + hence any torus T of dimension n 2 admits an ≥ Anosov diffeomorphism. Moreover, by a result of J. Franks, it is known that any Anosov diffeomor- ϕ n → phism ψ on a torus T is topologically conjugate to such a hyperbolic toral automorphism. This means that there exists a hyperbolic toral automorphism ϕ of Tn and a homeomorphism h of Tn such that 1 ψ h ϕ h− . = ◦ ◦ The linear map l can be seen as an automor- In this picture one sees that ϕ stretches any small ϕ phism of the abelian Lie group Rn, leaving Zn invari- rectangle on the torus in one direction and shrinks it ant. Now, Zn is a discrete and cocompact (meaning in the other. In dynamical systems one refers to such that the quotient Rn/Zn is compact) subgroup of a map as an Anosov diffeomorphism. This diffeo- Rn. More generally, let G be any Lie group, and as- morphism exhibits uniformly hyperbolic behavior: sume that lϕ Aut(G) is an automorphism of G, Around any point there are some directions in which ∈ such that there exists a discrete and cocompact sub- the map is expanding and complementary directions group of G, with lϕ( ) . Then the space of right in which it is contracting ([1] contains further de- = cosets G is a closed manifold, and lϕ induces a tails). \ diffeomorphismΓ ϕ : ΓG Γ G : g ֏ lϕ(g). It is an open problem to determine the class of \ → \ If weΓ want this diffeomorphism to be Anosov, l manifolds admitting an Anosov diffeomorphism, ϕ must be hyperbolic. ItΓ is knownΓ thatΓ thisΓ can happen and it is also quite hard to construct examples only when G is nilpotent. So we restrict ourselves to of these mappings. The most obvious method to that case, where the resulting manifold G is said obtain new examples is to generalize Arnold’s cat \ to be a nilmanifold. Such a diffeomorphism ϕ, in- map to higher dimensions. The cat map lifts to duced by an automorphism lϕ, is called a nilmanifoldΓ automorphism and is said to be a hyperbolic nilman- Karel Dekimpe is professor of mathematics at the ifold automorphism, when lϕ is hyperbolic. Just as K.U.Leuven Kulak, Belgium. His email address is in the case of tori, any hyperbolic infra-nilmanifold [email protected]. automorphism is Anosov. Again there is more: by

688 Notices of the AMS Volume 58, Number 5 a result of A. Manning, we know that any Anosov duces a map ϕ on G. This map will no longer be a \ diffeomorphism on a given nilmanifold G is topo- diffeomorphism, but a self-covering. So such a map \ logically conjugate to a hyperbolic nilmanifold auto- ϕ is a self-map of theΓ infra-nilmanifold G that lifts \ morphism on that nilmanifold. Γ to a Lie group automorphism of G, and, moreover, At this point, one might think that the alge- any self-map of G that lifts to an automorphismΓ \ braic approach of finding Anosov diffeomorphisms of G is of this form. M. W. Hirsch was the first per- ends with the class of nilmanifolds. However, there son to use the termΓ infra-nilmanifold endomorphism are manifolds that are not nilmanifolds but are for these maps. However, when using the term infra- finitely covered by a nilmanifold and that also admit nilmanifold endomorphism, most researchers refer Anosov diffeomorphisms obtained in an algebraic to a paper of J. Franks ([3]). It is important to re- way. These manifolds are called infra-nilmanifolds. alize that, although Franks himself attributes the To define such a manifold, one constructs the affine terminology of an infra-nilmanifold endomorphism group Aff(G) of a nilpotent Lie group G as being to Hirsch, the definition used by J. Franks is not con- the semidirect product G ⋊ Aut(G). An element of sistent with the one used by Hirsch, and, in fact, Aff(G) is of the form (g, α), with g G its “trans- Franks’s definition is even mathematically incorrect, ∈ lational part” and α Aut(G) its “linear” part. The causing several researchers to misinterpret this no- ∈ element (g, α) acts on x G by (g, α) x gα(x). tion. However, it is obvious from the rest of Franks’s ∈ = Note that, for G Rn, we recover the usual affine paper that he also intended to use the term infra- = group Aff(Rn). nilmanifold endomorphism for a map ϕ lifting to Let be a torsion-free subgroup of Aff(G) such (and hence induced by) an automorphism as above. that G is a discrete and cocompact sub- These more general infra-nilmanifold endomor- = ∩ groupΓ of G and the index [ : ] is finite. The phisms are also important in dynamical systems: orbitΛ spacesΓ G obtained in this way are the infra- e.g., when lϕ has only eigenvalues of modulus \ nilmanifolds, and each of themΓ isΛ finitely covered > 1, ϕ is an expanding map. As a corollary to his by a nilmanifoldΓ G. The most famous example of famous paper on groups of polynomial growth \ an infra-nilmanifold is, without any doubt, the Klein (1981), M. Gromov proved that any expanding map bottle which has ΛT2 as a double cover. To construct is topologically conjugate to an infra-nilmanifold the Klein bottle, one needs the group Z2 of endomorphism. Unfortunately, this corollary de- = translations, which together with a glide reflection, pended not only on Gromov’s own main result generates the needed group . Λ but also on false results by other researchers, and Now assume that, for a given infra-nilmanifold recently a counterexample to this statement was 1 constructed ([2]). However, again we can consider G, there exists a lϕ AutΓ (G), with lϕ l \ ∈ ϕ− = (where the conjugation is computed inside the the slightly more general class of maps, obtained by taking δ Aff(G), with δ δ and constructing Γaffine group Aff(G)); then again lϕ inducesΓ Γ a ∈ ⊆ diffeomorphism ϕ : G G, now called an the map ψ as above. We say that ψ is an affine \ → \ infra-nilmanifold automorphism. Note that, for endomorphism of the infra-nilmanifold.Γ Γ It turns out 1 that any expanding map is topologically conjugate G, one can see thatΓ lϕ l−Γ lϕ( ), showing ⊆ ϕ = that this new situation is a generalization of the pre- to such an expanding affine endomorphism. We have seen that the class of infra-nilmanifold Λvious one. When lϕ is hyperbolic,Λ the correspondingΛ infra-nilmanifold automorphism is Anosov. For a endomorphisms provides interesting examples long time it was claimed that any Anosov diffeo- of maps, but one should really study the more morphism on an infra-nilmanifold is topologically general class of affine endomorphisms of an conjugate to such a hyperbolic infra-nilmanifold infra-nilmanifold. More evidence for this claim automorphism. (And even more, it is conjectured follows from the fact that any self-map of an infra- that only infra-nilmanifolds admit an Anosov dif- nilmanifold is homotopic to a map induced by feomorphism.) However, as pointed out in [2], there an affine map δ of the corresponding Lie group. do exist Anosov diffeomorphisms on certain infra- So perhaps after more than forty years of lack of clarity about the notion of infra-nilmanifold endo- nilmanifolds that are not of this type. The idea is morphisms, it is time to consider instead what we to look for an element δ (g, lϕ) Aff(G), with = ∈ have referred to here as affine endomorphisms. g ≠ 1 such that δ δ 1 . This δ also induces a − = diffeomorphism ψ : G G : x ֏ glϕ(x), \ → \ Further Reading which is Anosov whenΓ lϕ isΓ hyperbolic. Let us call ψ a (hyperbolic) affineΓ automorphismΓ Γ of theΓ infra- [1] Boris Hasselblatt, Hyperbolic Dynamical Systems, nilmanifold. Some authors, including me, have used Handbook of dynamical systems, Vol. 1A, 239–319, North-Holland, Amsterdam, 2002. the term infra-nilmanifold automorphism to refer to [2] Karel Dekimpe, What an infra-nilmanifold endomor- this more general type of diffeomorphisms. It is an phism really should be..., preprint (18 pages); see open question whether all Anosov diffeomorphisms http://arxiv.org/abs/1008.4500. on an infra-nilmanifold can be obtained in this way. [3] John Franks, Anosov Diffeomorphisms, 1970 Global Up to now, we have discussed only diffeomor- Analysis, Proc. Sympos. Pure Math., Vol. XIV, phisms. However, if G is an infra-nilmanifold and Berkeley, CA, 1968, pp. 61–93, Amer. Math. Soc., \ 1 lϕ Aut(G) is such that lϕ lϕ− , then lϕ still in- Providence, RI. ∈ Γ ⊆ Γ Γ May 2011 Notices of the AMS 689 The Story of Gyrangle

Reza Sarhangi

the MAA booth. One gift from the MAA booth was a folded one-sheet booklet, “A Field Guide to Math on the National Mall”, highlighting mathematical aspects of some interesting sites in the Washing- ton, D.C., area. The sculptor, mathematician, and computer scientist George Hart led a public sculpture barn- raising of his latest work, Gyrangle (Figure 1), at the AMS booth. The 38-inch-high sculpture con- sists of hundreds of laser-cut steel units bolted together in a novel way. To be exact, there are 490 flat or folded hollow equilateral triangles in four Photograph courtesy of George Hart.

Figure 1. Gyrangle.

The first USA Science and Engineering Festival was a call by President Obama to invite the nation to the National Mall in Washington, D.C. for a celebra- tion of science and engineering achievements and their contributions to our society. For two beautiful sunny days, Saturday and Sunday, October 23–24, 2010, thousands of people attended the festival at the National Mall and enjoyed talking to scientists and engineers to learn about their new inventions Figure 2. Gyroid surface. and discoveries. People of all ages played with scientific toys colors. It illustrates a discrete version of the gyroid and machines, and participated in interesting and surface, made entirely from equilateral triangles. exciting activities presented in hundreds of booths The gyroid is a smooth, infinite, triply periodic, located all over the Mall. minimal surface discovered by Alan Schoen in Mathematicians appeared in this national cel- 1970. Channels run through it in many directions ebration by presenting mathematical ideas and and connect at an angle to other channels. The di- activities at several booths, including ones for the rection of connection travels in a spiral along each AMS and the Mathematical Association of America tunnel, giving rise to the name “gyroid”. Figure 2, (MAA). The award-winning mathematics writer downloaded from Wikipedia, illustrates a cubical Ivars Peterson, director of publications and com- portion of the infinite gyroid surface. munications at the MAA, was among the hosts in The gyroid is a smooth surface, but Hart discov- ered a way to triangulate it entirely with equilateral Reza Sarhangi is professor of mathematics at Towson triangles. Both the faces and vertices in the con- University. His email address is [email protected]. struction exhibit a property known as uniformity.

690 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Photographs courtesy of Reza Sarhangi.

Figure 3 (left) George Hart, (right) Annette Emerson and Mike Breen, AMS public awareness officers.

Although the gyroid itself contains no straight show another aspect of mathematics: mathematics lines, Hart’s triangular discretization contains is beautiful! infinite straight lines embedded in various direc- Mathematical sculpture is a rich area of visual tions. It divides all space into two congruent but art that is approached in various ways. Some mirror-image volumes. Another interesting prop- sculptors have no formal background in math- erty is that the faces do not meet edge-to-edge, but ematics, yet their artworks present patterns or instead each triangle shares six half-edges with six structures that make sense to mathematicians. On neighboring triangles. The construction is previ- the other hand, there are mathematicians who use ously unpublished, so the sculpture serves as the techniques from computer science or the arts to first presentation of this discovery. As it illustrates visualize abstract mathematical forms. This gives a gyroid made of triangles, Hart coined the term the public an opportunity to “see” mathematical Gyrangle for it. properties that were previously accessible only to The full infinite surface would be visually repeti- specialized mathematicians. In either approach, tive (and infinitely large) so is not itself suitable sculpture may present harmony and balance in a for a sculpture. Instead, Hart chose a tetrahedral new way and bring an appreciation of mathemat- portion of space as the outer form of the sculpture ics to the public, in a way similar to how we enjoy music and feel its importance in our lives. and inhabited it with the Gyrangle surface as a kind The AMS financially supported the construction of three-dimensional texture. To seal off the edges of this unique piece of mathematical art and do- he introduced a folded triangle unit that closes off nated it to the Department of Mathematics at Tow- the boundary. For visual and mathematical inter- son University, Towson, Maryland. The department est, the 100 pounds of laser-cut steel triangles are is known for educational activities concerning painted in four colors according to the directions mathematical connections to the arts and culture. of their normal vectors. It is one of a series of The president of the Bridges Organization, the au- many sculptures Hart has created for assembly at thor, is a faculty member of this department. The “sculpture barn-raising” events. He prepares the Bridges Organization is a nonprofit organization, components and invites the public to participate which runs the international Bridges conferences in the construction. on mathematical connections in art, music, and During this barn-raising at the Mall, Hart helped science (http://www.BridgesMathArt.org); see hundreds of children and adults screw pieces “Bridges Pécs 2010”, by Paul Gailiunas, Notices, together. At the same time, he continuously February 2011, pages 289–290. These annual answered questions about the mathematics, com- conferences, held in various locations around the puter science algorithms, and fabrication aspects world, attract faculty members from mathematics of the design. The AMS representatives at the booth and science, as well as from the arts, communica- were Annette Emerson and Mike Breen (see the tions, and music. Hart is on the board of directors photo at right in Figure 3). They patiently helped of the Bridges Organization. children successfully fasten screws and connect Hart’s sculptures are recognized around the pieces together, while also answering their very world for their mathematical depth and creative interesting but occasionally difficult questions, use of materials. He is a pioneer in using computer such as “Why are we making this thing?” and “What technology and solid free-form fabrication to cre- is it used for?” The public often sees mathematics ate sculptures. Examples of his artwork can be seen only as something useful, but here the goal was to at major universities, such as the Massachusetts

MAY 2011 NOTICES OF THE AMS 691 AMERICAN MATHEMATICAL SOCIETY COLLECTED PAPERS OF 2011 Abel Prize JOHN Winner! MILNOR Five Volume Set

This set is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefi t from their acquaintance with Milnor’s Photographs courtesy of Reza Sarhangi. mode of thinking and writing. The volumes in Figure 4. Finishing assembly of Gyrangle at this set have been organized by subject. Towson University. Set: Hardcover; List US$361; AMS members US$288.80; Institute of Technology, the University of Califor- Order code MILNORSET nia at Berkeley, and Princeton University. After Items contained in this set are having served as a faculty member at Columbia also available for individual sale: University and Stony Brook University, Hart is now chief of content at the Museum of Mathematics, I. Geometry which will open in New York City in 2012. John Milnor, State University of New York After two days of hard work to assemble Gyran- at Stony Brook, NY gle at the Mall, only two-thirds of the construction A publication of Publish or Perish, Inc. was completed. The partly finished sculpture was 1994; 295 pages; Hardcover; ISBN: 978-0-914098-30-0; List transported to Towson University, where faculty US$59; AMS members US$47.20; Order code MILNOR/1 and students helped to complete it (Figure 4). The sculpture graces the glass lobby of the Department II. The Fundamental Group of Mathematics (Figure 5). John Milnor, Stony Brook University, NY Thank you, George Hart and the American Collected Works, Volume 19; 1995; 302 pages; Hardcover; Mathematical Society, for your great gift to Towson ISBN: 978-0-8218-4875-3; List US$65; AMS members US$52; University! Order code CWORKS/19.2 III. Differential Topology John Milnor, Stony Brook University, NY Collected Works, Volume 19; 2007; 343 pages; Hardcover; ISBN: 978-0-8218-4230-0; List US$69; AMS members US$55.20; Order code CWORKS/19.3 IV. Homotopy, Homology and Manifolds John McCleary, Vassar College, Poughkeepsie, NY, Editor Collected Works, Volume 19; 2009; 368 pages; Hardcover; ISBN: 978-0-8218-4475-5; List US$79; AMS members US$63.20; Order code CWORKS/19.4 V. Algebra Hyman Bass, University of Michigan, Ann Arbor, MI, and T. Y. Lam, University of California, Berkeley, CA, Editors Collected Works, Volume 19; 2010; 425 pages; Hardcover; ISBN: 978-0-8218-4876-0; List US$89; AMS members US$71.20; Order code CWORKS/19.5

www.ams.org/bookstore Photograph courtesy of George Hart. Figure 5. A view of Gyrangle showing some of its hexagonal tunnels.

692 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Report on 2009-2010 Academic Recruitment and Hiring

James W. Maxwell and Colleen Rose

The recent declines in full-time positions under recruitment in mathematics departments continued during the 2009- 2010 academic recruitment cycle. The total number of positions under recruitment by all mathematics departments combined was 1,081. This number is down 26% from the 2008-2009 total and down 46% from the 2007-2008 total. (Note: Throughout this report, the term tenure-track encompasses positions that come with tenure as well as those which provide the option of earning tenure at some point after appointment.)

Figure A.1: Positions Under Recruitment in All Mathematics Departments Combined Annual Recruitment Cycle Annual Recruitment

Number of Positions

The doctoral statistics and biostatistics departments, Group IV, also saw a decline in the level of recruitment, though not as precipitous a decline as for the mathematics departments. Group IV consists of 93 departments and so constitutes a much smaller employment pool than the approximately 1,400 mathematics departments. In 2009 there were approximately 1,800 full-time faculty in Group IV compared to approximately 22,400 full-time faculty in all mathematics departments combined.

Figure A.2: Positions Under Recruitment in Doctoral Statistics and Biostatistics Departments Combined Annual Recruitment Cycle Annual Recruitment

Number of Positions

James W. Maxwell is AMS associate executive director for special projects. Colleen A. Rose is AMS survey analyst.

MAY 2011 NOTICES OF THE AMS 693 2010 Annual Survey of the Mathematical Sciences in the U.S.

Positions Under Recruitment

The percentage decline in positions under recruitment varied significantly among the various reporting groups within the combined mathematics departments. There was a 6% decline for the doctoral mathematics departments combined, a 14% decline for masters mathematics departments (Group M) and a 43% decline for bachelors mathematics departments (Group B). Similarly, the declines in tenure-track positions under recruitment for these same department groupings were 25%, 27%, and 44%, respectively.

Figure A.3: Positions Under Recruitment in All Mathematics Departments by Highest Mathematical Sciences Degree Offered Annual Recruitment Cycle Annual Recruitment

Number of Positions

Figure A.4: Tenure-track Positions Under Recruitment in All Mathematics Departments by Highest Mathematical Sciences Degree Offered Annual Recruitment Cycle Annual Recruitment

Number of Positions

Positions Filled

A total of 960 positions were filled during the 2009-2010 academic cycle for employment beginning in fall 2010 by all mathematics departments combined. This total is down 25% from the 2008-2009 total and down 47% from the 2007-2008 total.

Figure B.1: Positions Filled in All Mathematics Departments Combined Annual Recruitment Cycle Annual Recruitment

Number of Positions

694 NOTICES OF THE AMS VOLUME 58, NUMBER 5 2010 Annual Survey of the Mathematical Sciences in the U.S.

Positions Filled

The situtation for doctoral statistics departments and biostatistics departments combined was much different, as demonstrated by the accompanying figure.

Figure B.2: Positions Filled in Doctoral Statistics & Biostatistics Departments Combined Annual Recruitment Cycle Annual Recruitment

Number of Positions

The decline in positions filled for fall 2010 also varied widely among the various reporting groups within all mathematics departments. For the doctoral mathematics departments combined, the number of positions filled was 458, unchanged from the fall 2009 count but down 29% from the fall 2008 count. For Group M the count was 135, down 11% from fall 2009 and down 51% from the fall 2008 count. For Group B the count was 367, down 45% from fall 2009 and down 59% from fall 2008.

Figure B.3: Positions Filled in Mathematics Departments by Highest Mathematical Sciences Degree Offered Annual Recruitment Cycle Annual Recruitment

0 200 400 600 800 1000 Number of Positions

The total tenure-track positions filled during the 2009-2010 academic cycle by all mathematics departments combined was 479, down 33% from the 2008-2009 total of 710. This total is down 51% from the 2007-2008 figure of 978, the highest total over the past ten years.

MAY 2011 NOTICES OF THE AMS 695 2010 Annual Survey of the Mathematical Sciences in the U.S.

Positions Filled

Figure B.4: Tenure-track Positions Filled in Mathematics Departments by Highest Mathematical Sciences Degree Offered Annual Recruitment Cycle Annual Recruitment

Number of Positions

This survey is part of the Annual Survey of the Mathematical Sciences. All 2010 numbers are estimates based on 721 usable responses from the 1,487 departments that make up the total population of mathematical sciences departments eligible to receive the survey. Since the survey was conducted online, it required that we have a valid email address in our records. This excluded 165 departments from participation in the survey.

The interested reader may view additional details on the results of this survey and prior year trends by visiting the AMS website at www.ams.org/annual-survey. Survey results for the doctoral departments in statistics and biosta- tistics are available there. Group Descriptions Other Information Group I is composed of 48 departments with scores in the 3.00–5.00 range. Group I Public and Group I Survey Response Rates Private are Group I departments at public institutions and private institutions, respectively. Faculty Recruitment & Hiring Response Rates Group II is composed of 56 departments with scores in the 2.00–2.99 range. Department* Number Percent Group III contains the remaining U.S. departments Group I (Public) 19 of 25 76 reporting a doctoral program, including a number of departments not included in the 1995 ranking of Group I (Private) 19 of 23 83 program faculty. Group II 46 of 56 82 Group IV contains U.S. departments (or programs) of Group III 60 of 80 75 statistics, biostatistics, and biometrics reporting a Group IV (Statistics) 36 of 57 63 doctoral program. Group V contains U.S. departments (or programs) in Group IV (Biostatistics) 13 of 35 38 applied mathematics/applied science, operations Group Va 12 of 18 67 research, and management science that report a Group M 105 of 180 58 doctoral program. Group Va Group B 411 of 1014 41 is applied mathematics/applied science; Group Vb, which was no longer surveyed as of * Departments and programs that do not formally "house" faculty and their salaries are excluded from this survey. 1998–99, was operations research and management science. Group M contains U.S. departments granting a master’s Other Sources of Data degree as the highest graduate degree. Group B contains U.S. departments granting a Visit the AMS website at www.ams.org/annual- baccalaureate degree only. survey/other-sources for a listing of additional sources of data on the Mathematical Sciences. Listings of the actual departments which compose these groups are available on the AMS website at www. ams.org/annual-survey/groups_des.

696 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Book Review At Home with André and Simone Weil Reviewed by Michèle Audin

father was a professor in America, Sylvie studied At Home with André and Simone Weil Sylvie Weil in Paris, which meant, for instance, that at age (English translation of Chez les Weils, translated eleven she took, alone, the “direct” Air France by Benjamin Ivry) flight Chicago-Montréal-Gander-Shannon-Paris. Northwestern University Press, October 2010 US$24.95, 192 pages …and Simone Weil’s Niece ISBN-13: 978-0810127043 And there was an aunt, too, a deceased one: Sylvie was the baby daughter who arrived just This book is about the family of the mathemati- a few months before her aunt, the philosopher cian André Weil (1906–1998), one of the most Simone Weil, who died at age thirty-four. This was influential number theorists in the twentieth cen- another heavy inheritance, inside the Weil family tury. The family consisted of a grandfather and and outside it, as the baby daughter became a little a grandmother (Bernard and Selma Weil), a father girl, then a young woman, looking very much like (André Weil) and a mother (Eveline Weil), a stepson (Alain de Possel), and two daughters (the book’s her aunt—an aunt, who, moreover, was considered author Sylvie and her sister Nicolette). And yes, a saint. The little girl was surely a comfort to her there was an aunt, too, Simone Weil (1909–1943), mourning grandparents, but this heritage must the philosopher. The book tells Sylvie’s story and have been quite a burden for her. A professor of that of her family—of how it was to be André French literature in several American universities Weil’s daughter and Simone Weil’s niece, and of and a writer,1 Sylvie obviously found her own way. how Sylvie made her way, in life and in this family. But she had to learn about and to understand the aunt she so closely resembled, through the André Weil’s Daughter… sometimes difficult relationships in the family. Mathematicians will have no difficulty understand- ing that it was not very easy to be André Weil’s Visiting André Weil in Jail in 1940 daughter: Having a father who was a brilliant and Because he had decided not to serve as a soldier famous mathematician, as well as the main charac- ter in the Bourbaki adventure, complicated Sylvie’s during World War II, André Weil was jailed from efforts to find her own way in life. In addition, he February to May 1940 (this is also the reason had a circuitous career. The daughter of a French that he could not get a position in France after Jewish refugee, Sylvie Weil was born in the United the war and why the life of the Weil family was States in 1942, left for Brazil in 1945, then left geographically so complicated). In his jail cell, he Brazil for Chicago in 1947. She was raised by her worked quite a lot, and he was supported by his parents, of course, but also by her grandparents, in particular by her two grandmothers. While her

Michèle Audin is professor of mathematics at the 1Author of A New York il n’y a pas de tremblements de Institut de Recherche Mathématique Avancée at terre, Le jardin de Dima, Les vendanges de Rachi, among the Université de Strasbourg. Her email address is others, and two novels for young adults translated in the [email protected]. U.S., My Guardian Angel and Elvina’s Mirror.

May 2011 Notices of the AMS 697 Bourbaki friends and by his family, who would of the cover, in which, unfortunately, the siblings visit him, bring him books, and so on.2 André and Simone are pulled apart by the title of Of course, Sylvie, who would be born in 1942, the book. was not present then. But, from a simple sheet of By now it should be clear that this book is not paper on which André’s mother, father, sister, and a biography, neither of André Weil nor of Simone wife had each written a sentence for him, Sylvie Weil. But it does allow us to enter into the Weil is able to reconstitute a portrait of this group home and to have a tactful glance at a few colorful visiting him in his jail cell. She is also able to evoke Jewish ancestors, at Selma and Bernard, at the the different personalities of these four people. privacy of Simone, André, and Eveline—and at This is a beautiful example of the subtle way she Sylvie. conveys delicate things in the book. I hope the readers of the Notices will enjoy, as much as I did, reading this both reserved and Riemann’s Zeta Function intimate account of how it was to be at home with As this is a review for the Notices, let me make it the Weil family. unbalanced and concentrate more on the André References side than on the Simone one. Readers should, of course, not expect to learn any mathematics here. [1] A. Weil, Œuvres scientifiques, Volume I, Springer, However, there is a formula in the book, 1979. [2] , The Apprenticeship of a Mathematician, 1 1 1 1 + + + · · · + + · · · , Birkhäuser, Basel, 1992, translated from the French 2s 3s ns by Jennifer Gage. the definition of the Riemann zeta function, which André Weil wrote on a piece of paper for his daughter when she was learning how to add fractions. This is the only formula in the book, but it signifies his constant interest in Dirichlet series and the Riemann hypothesis. This is another hint about how the book proceeds, by light brush strokes.

The Sugar Bowl One of the themes of the book is the failure of Simone and André Weil to adapt to ordinary life and the real world. Many touching details in the book illustrate this failure. For example, the knowledge of where the sugar bowl was kept in André and Eveline Weil’s house was incompatible with the higher subjects occupying André’s brain. Reading the book, we understand that this was not just absentmindedness, as one might think, but something more profound.

Walks But André Weil was a father, too, and Sylvie recalls quite a few stories about him and their father- daughter relationship. They used to have long walks together, in the Luxembourg Gardens in Paris, in São Paulo, in Chicago, or in Princeton, the little girl with her tall father. And there is also the story of the (adult) daughter accompanying her old father to Japan in 1994, where André Weil would be awarded the Kyoto Prize (together with Akira Kurosawa).

I will not comment on the English translation, by Benjamin Ivry, but let me mention the design

2For André Weil’s 1940 story, see [2]; for the mathematics he made in prison, see the enlightening comments in his complete works [1].

698 Notices of the AMS Volume 58, Number 5 Book Review

The Value of Nothing: A Review of The Quants

Reviewed by David Steinsaltz

The Quants believing that “this Scott Patterson time is different” Crown Business, 2010 [15]. The most re- US$27.00, 352 pages cent round of ex- ISBN-13: 978-0307453372 cuses was pro- vided, if not directly Scott Patterson, former financial journalist for by mathematicians, The Wall Street Journal, has written a book-length then under the ban- love letter to quantitative finance and its practi- ner of mathematics, tioners. To judge by some comments posted on and the crisis that amazon.com and elsewhere, though—“naïve”, ensued was of ter- “mathematically illiterate”, “sensationalism”, rifying proportions. “bumbling idiot”—the love is not requited. Of For this reason alone course, the book is not really about the sort of The Quants would people who write comments on the websites of deserve the attention online retailers. The “quants” of Patterson’s title of the mathemati- are a handful of capitalist potentates, supremely cal community. Few successful and influential practitioners of math- readers will be bored, and most will learn some ematically inspired finance. Putting to one side things that are worth knowing about the world a certain oversensitivity to criticism and the un- and about the place of mathematics in the world. questionably sensationalist subtitle—“How a New This book joins a long list of recent popular Breed of Math Whizzes Conquered Wall Street and or semipopular titles on quantitative finance and Nearly Destroyed It”—many who identify with the its practitioners. It is not the best in all respects, job title “quant” are very far removed from the certainly not as a technical primer. Its approach world of Patterson’s conquering heroes and from can seem infuriatingly nonanalytical and apolitical, Patterson’s enthusiasm for them. While the book even willfully obtuse at times. But it is intelligent makes little pretence of reflecting their careers and serious, by and large, and its relentless focus or their experience, it probably offends by imply- on the look and feel of the rarefied quant world, ing—with little evidence—that the managers and although a limited perspective, is a valuable one, the menials share a unified mathematical culture and one that requires the skills of a talented jour- and mindset. nalist, which Patterson obviously is. But the managers, and their real and perceived The quants, as Patterson describes them, relationship to mathematics, do make an impor- “couldn’t care less about a company’s ‘fundamen- tant story. Economic historians teach us that one tals’, amorphous qualities such as the morale of indispensable ingredient in a financial crisis is its employees or the cut of its chief executive’s jib. an excuse for ignoring the lessons of the past, That was for the dinosaurs of Wall Street […] who for overriding the traditional safeguards, for focused on factors such as what a company actu- ally made and whether it made it well. Quants were David Steinsaltz is University Lecturer in Statistics and Tuto- agnostic on such matters, devoting themselves rial Fellow in Mathematics and Statistics at Worcester College, instead to predicting whether a company’s stock University of Oxford. His email address is steinsal@ would move up or down based on a dizzying array stats.ox.ac.uk.

MAY 2011 NOTICES OF THE AMS 699 of numeric variables.” It’s an old story, actually. stock purchases, futures contracts—differ only in A similar conflict embroiled the earliest attempts, name from gambling. Indeed (see [4, Chapter 3.2]) three centuries ago, to expand the nascent life insurance in the sixteenth and seventeenth probability theory beyond its disreputable origins centuries was often a short-term bet on the life in games of chance. Historian Lorraine Daston of some famous person. Usually the accusation writes, “The mathematicians created a new ap- is lobbed from the left, to be dismissed by the fi- proach to the subject that challenged the previous nanciers as propaganda, ignorant of the vital work practice of risk, legal and otherwise. [ …] It was as performed by capital markets. It is a surprise to see if the jurists and the commercial class they wrote how many of today’s leading financiers—not all of for lived in a world of fine-grained detail where them mathematical types—have come to embody regularities were partial at best […] The mathema- this accusation. “Every day they went head-to-head ticians, in contrast, apparently lived in a world on Wall Street, facing off in a computerized game strictly governed by invariable laws that could be of high-stakes poker in financial markets around expressed as the function of a small number of the globe, measuring one another’s wins and losses variables” [4, Chapter 3.1]. from afar, but here [in their quant poker games] In that twilight struggle, B. Gnedenko has ar- was a chance to measure their mettle face-to-face.” gued [11], the probabilists were routed. From the It is not the least of the paradoxes that Patter- early gambling studies there followed a profusion son’s protagonists eagerly seek risk in gambling, of “papers devoted to applications in various while their core mathematical models presume branches of the natural sciences and public life. that investors pay a premium to dispose of risk. Many of these had so little validity that they were The contradiction does not seem to register on considered ‘mathematically scandalous affairs’. Patterson, who throughout seems entranced by Disenchantment followed and among Western these sharp operators using financial markets as European mathematicians probability theory began a gambling den. to be thought of as some kind of mathematical After probability and compound interest, the entertainment hardly deserving serious attention.” key financial principle underlying the quant mod- Probability’s association with gambling endan- els is arbitrage, the financial perpetual motion gers more than just respectability. Human beings machine generated by price discrepancies. In have natural intuitions about risk that are system- principle, if you find the same asset being sold at atically violated by cards, dice, and roulette wheels. different prices in different markets—Patterson As evolutionary psychologists have remarked, “If uses the example of gold trading for $1,000 in New humans had evolved in casinos where their win- York and $1,050 in London—you can buy in one nings translated into reproductive success, selec- market and sell in the other to generate riskless tion probably would have eliminated the gambler’s profit. Back in the day, you would need to float fallacy” [13]. In the real world, probability theory your gold bricks over the Atlantic, but today the is a specialized adjunct to more natural human only limit on your profits would be the amount of intuitions, not a substitute for them. money you could borrow and the amount of gold In Patterson’s account, modern quantitative you could buy before the New York market raises finance originated with Ed Thorp, a mathematician the price. Statistical arbitrage expands the pos- who applied the Kelly criterion to blackjack in his sibilities, by allowing for randomness. It attempts 1962 book Beat the Dealer before turning the same to extract profits from discrepancies in the future principles to finance in Beat the Market (1967). Pat- expectations of combinations of assets. Patterson terson makes clear (as do other sources) that Thorp is at his best when describing these strategies, both himself has always been the farthest thing from the mechanisms and the psychology that gives a gambler by temperament, but some of his intel- birth to them. These depend, in different ways, lectual heirs revel in high-stakes poker parties and on inefficiencies in pricing mechanisms, creating junkets to Las Vegas casinos. Describing the credit short-term disequilibria that can generate profits derivatives group at Deutsche Bank around 2000, as they reset. Patterson writes “In their downtime, Weinstein’s Unless they don’t. The book is punctuated by traders would randomly bet on just about anything crises, large and small, in which the expectation in sight: a hundred on the flip of a coin, whether fails. A casino owner needs only to pump enough it would rain in the next hour, whether the Dow money through the system and let the law of large would close up or down.” The financial markets numbers take care of the rest. In the financial are “the world’s biggest casino”. While “investors” markets all the “bets” are correlated, in hard-to- put up the money, the quants “place bets”: Bets on estimate ways, and the probabilities are only trade patterns, bets on currency exchange rates, vaguely defined, estimated by analogy with the bets on company growth and defaults, and bets on past. Not to mention that the quant strategies the bets that other traders would make. themselves alter the patterns of the markets. There is nothing new about the accusation that Pumping large quantities of borrowed money financial transactions involving risk—insurance, through these strategies can lead to a meltdown.

700 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Arbitrage is a bit like dumpster diving. Lars • Special privileges. A significant por- Eighner formulated [5] three rules for safely con- tion of quant profits come from their suming discarded comestibles. The third rule: access to information and trades closed answer the question “Why was this discarded?” to ordinary investors. They have top-of- The principle of “efficient markets” says that the-line computer systems for bringing market prices already incorporate all publicly in market information, processing it, available information, so there should not be any and executing trades instantaneously. opportunities for statistical arbitrage. This prin- They work for major international in- ciple need not be true—indeed, there are good vestment banks, or they win preferred- reasons, well discussed in this book, to believe it customer treatment from the banks. is not—but mathematical market models generally They may also profit from inside knowl- depend on it. Thus the computations of quantita- edge of how their own vastly leveraged tive finance are largely based on the principle that trades are moving the markets. Many these computations are a waste of time. Patterson of the most lucrative trades are simply repeatedly circles back to this paradox, which closed to outsiders. Michael Lewis’s The clearly troubles many of the quants. How can Big Short [10] narrates the years-long they consistently beat the market average? Some struggle of investors, who predicted the explanations on offer: collapse of mortgage-backed securities • They’re smarter than other peo- (MBS), to make the necessary contacts ple. This seems to be, unsurprisingly, to sell the MBS short. The big quant their favored explanation. Traders who shops would have made the short sale translate new information into prices in microseconds. can profit, a process that Patterson • They act crazy. Patterson’s quants compares to throwing meat into a cultivate an aura of strangeness. pool full of piranhas. The meat (new Some gamble manically. Many defy information) disappears quickly, but Wall Street dress conventions. They the piranhas (the traders) do get fed. organize company paintball tourna- Now, Patterson describes the quants ments. One rages at bad news and —with some notable exceptions—as destroys computer monitors. One unconcerned with anything so coarse makes a show of busking in a Wall as commerce, but their pattern-seeking Street subway station. They rave about is another way to integrate information, the Truth of “Alpha”.1 including past information and unrec- Patterson describes all this with ognized persistent biases. This could amusement, as some blend of residual earn them a steady profit. math-nerd culture and plutocrat eccen- • Weaker regulatory constraints. If tricity. He never considers its strategic you find a pristine can of soup in value. If Trader A makes a large sale of the dumpster on its sell-by date, you stock Z, he signals that he doesn’t think know why the supermarket couldn’t Z is worth holding at the current price, use it; unconstrained by rigid health causing the price to drop. George Aker- directives, an ordinary person could lof analyzed this problem in his famous be fairly confident that the contents study of the used car market and came are worth having. Retail banks, pension to the conclusion that this information funds, municipal governments, and imbalance—A knows why he sold, but many other institutional investors are B doesn’t—depresses prices and can tightly regulated, forced to make deci- lead to a market-destroying downward sions based on crude categories. Laws spiral. If A appears crazy, or at least constrain the sorts of risks they are al- inscrutable, his trades will have less lowed to take with the funds entrusted influence on the market. Eccentricity to them. By loaning the capital to hedge functions like the poker player’s dark funds or investment banks the regula- glasses. tions vanish, a benefit sometimes called •They’re not. If I were to sell bud- regulatory arbitrage. Considerable get earthquake insurance in Califor- theoretical ingenuity has gone into nia, I could make a fortune—until the producing financial instruments, such earthquake. Economist Joseph Stiglitz as the now infamous auction-rate secu- rities that duplicate traditional bank- 1α is just the intercept term in a linear regression of an ing functions within an unregulated individual asset price against an overall market index, but securities framework, sometimes called the quants, or Patterson, or both, seem to confuse it with “shadow banking”. the cabalistic aleph.

MAY 2011 NOTICES OF THE AMS 701 writes: “In today’s dynamic world, this that yielded the real money.” Thus begins one of market discipline broke down. The the more fascinating vignettes of the book, told financial wizards invented highly risky from the perspective of one Aaron Brown, who was products that gave about normal re- “sick of seeing the same rich kids he’d suckered turns for a while—with the downside at Harvard lord it over the quants in trading-floor not apparent for years. Thousands of games such as Liar’s Poker.” Brown killed the money managers boasted that they game off by spreading a winning strategy among could ‘beat the market’, and there was a his fellow quants. “No longer would they stand ready population of shortsighted inves- at the end of the line and be victimized by the tors who believed them” [17]. [BSDs].”3 As long as high profits over a few In such an environment women can only be years are enough to be labeled a suc- peripheral objects: wives and girlfriends dis- cess, there is an incentive to define the tracting the quants with the blandishments of earthquakes out of the model. Until the forty-bedroom home and hearth; or a secretary, earthquake strikes he’s a genius, and whose firing gives a clue to the mental state of after the quake he still gets to keep his her (male) boss. The one female quant in the book, genius bonus. At the height of the last Kim Elsesser—also, though herself quite senior, crisis one of Patterson’s heroes, Citadel the book’s token representative of nonkingpin Investment chief Ken Griffin, estimated quant-dom—disappears after a few amusing an- that his company had a 55 percent ecdotes “to study gender issues in the workplace chance of surviving [12]. How high do at UCLA”. It hardly surprised me after this to read the annual returns need to be, to be of the recent lawsuit charging persistent gender worth risking everything on a coin flip? discrimination at Goldman Sachs [3] or that the This is not, primarily, a book about math- number of women working in U.S. finance has been ematical models. It includes some nice profiles of dropping steadily [18]. mathematicians and some slightly dodgy accounts The tone shifts in the aftermath of the crash. of random walks and Lévy processes. For all that Skeptical academics take the stage (along with it has to say about mathematical thinking or the the irrepressible and omnipresent Nassim Taleb). application of mathematical models, though, it Paul Wilmott, who wrote back in 2000 about the could be Harry Potter and the Volatility Smile, dangerous misuse of mathematics in finance with BlackBerries instead of wands. It’s all gesture [20], produced with Emanuel Derman a “model- and evocation, as in: “The quants pulled out their ers’ Hippocratic Oath”: five vows of humility, calculators, cracked open their calculus books, and came up with solutions.” Indeed, nearly every concluding with “I understand that my work figure of any significance in the book is referred to may have enormous effects on society and the as a “wizard” or a “whiz”. There is “quant alchemy” economy, many of them beyond my comprehen- and the “dark art of securitization”. sion.” Estimable sentiments, but absent a suitable What we get instead is a psychohistory of unre- educational program, what is it worth to swear an solved adolescent conflict, shading into a pervasive oath to “understand” something? It seems about as sexual menace. “The money was huge, the women effective as combating the modelers’ anglophone were beautiful, and everyone was brilliant and in- parochialism by requiring the vow: “I understand side the secret. […] At Deutsche Bank, risk wasn't Chinese.” [expurgated] managed. Risk was [expurgated]- Has the corner of mathematics called “math- slapped, risk was tamed and told what to do.” The ematical finance” actually influenced financial quants identify the dinosaur traders of Wall Street practice? Haug and Taleb [8] have debunked with all the privileged bullies who humiliated them the mystique of the Black-Scholes-Merton for- on the playground and mocked their mathematical mula, arguing (persuasively, if somewhat interests in high school. They are burning for re- self-contradictorily) that the formula has never venge, and Patterson channels their fantasies into been applied in the real world, that equivalent his narration: “A friend sent Muller congratulatory calculations have been known and applied since flowers for his new job. The bouquet was delivered the dawn of time, and that it is fundamentally to his desk on the trading floor. It was raw meat misleading. Li’s copula formula (which Patterson to the grizzled traders around him: Look at the describes as a phenomenon without really explain- California quant boy and his pretty flowers.”2 In the ing) has been blamed for the collateralized debt 1980s we read, “quants were seen as second-class obligation (CDO) fiasco [19], but it is so banal in citizens at most trading firms, computer nerds itself that it seems more like a decoration than a who didn't have the balls to take the kinds of risks real impetus to the CDO market.

2In this case, though, it is possible to compare Patterson’s 3[BSD] is here a crass expression for the bankers’ ana- dialogue directly to his source. There is evidence of con- tomical endowment that seems to be a term of art in the siderable embellishment. finance world.

702 NOTICES OF THE AMS VOLUME 58, NUMBER 5 It takes more than Hardyan “uselessness” [7] to culture and financial culture” is a chapter in his buy a mathematician a clear conscience these days, book [1]. (An earlier version of this chapter was though. University mathematicians have served the published in the late 1990s.) The traditions and finance industry with a steady stream of students professional ethic of engineering “charges them trained to look past the reality of the world to an with examining painstakingly what will happen in abstract realm of interchangeable entities and to case of an accident, a fracture or conflagration, and accept models axiomatically, without skepticism. to effect a repair.” Engineers, he wrote, plan for the At least as important, we have participated in what inevitability of failure and for its consequences. G. Bowker [2] has termed “legitimacy exchange” Financial engineers don’t install emergency (though with a view to the huge blow suffered by exits, and on the evidence of this book they cannot the reputations of both groups, perhaps it might imagine the need. Is this ostentatious math-nerd be called a “credibility default swap”). The bank’s naïveté genuine or merely a camouflage? Surely, team of MIT Ph.D.s is a token of seriousness, like one thinks, as the disasters and near-disasters the Picasso in the lobby, the marble columns, and pile up, as the difference between brilliance and the expensive wristwatch. In return for lending the bankruptcy is the whim of a single deep-pocketed reputation of their subject, academic mathemati- investor, or a flight to liquidity, or the faith of cians are compensated by sharing the financiers’ creditors, or a government decision to bail out reputation as important people doing important a counterparty or temporarily ban short-selling, work, and the enviable status as a conduit to high- surely they cannot still believe that there is an paying careers, whether or not they also pocketed ineffable truth to the markets, to be captured in consulting fees. probabilistic models and calculated to the fifth Faced with dwindling public esteem, defenders decimal place. It is disappointing that Patterson of quantitative finance have sought to mortgage never poses the question of premeditation. The their intellectual stature for a legitimacy loan people who end up with the billions are portrayed from the engineering profession. Patterson picks as innocent bystanders, just little boys on the up on this, writing “few—aside from zealots such seashore collecting pretty pebbles. We are even as Taleb—were calling for them to be cast out of invited to pity their stressful days and sleepless Wall Street. That would be tantamount to banishing nights during the crash: “A quant nightmare. Mar- civil engineers from the bridge-making profession kets were at the mercy of unruly forces such as after a bridge collapse.” (It is not clear exactly who panicked investors and government regulators.” The mighty quant barons of this story are not, it Patterson is quoting here, but he or his source is must be emphasized, the entire world of quantita- channeling the very similar comments published in tive finance, and one longs for a latter-day quant 2008 by mathematician S. Shreve [16].) M. Hellwig, Max Weber to map the lines of power and the in the course of an otherwise careful analysis of percolation of ideology through the institutions. sources of the crisis [9], averred that “One might Until he or she arrives, Patterson has produced at as well blame the architect of the World Trade least one plausible journalistic portrait of the past Center for not having taken the risk into account few decades of quantitative finance, one that is at that kerosene-filled airplanes might be flown into least consistent with what we see in other recent the building.” As it happens, the lead structural books. It is a picture from outside the mathemati- engineer for the World Trade Center told reporters cal community, and it shows us how, whatever we in 1993 [14] that the towers had been designed to may believe personally, the successes of financial withstand a jet collision. The collapse has since mathematics will be largely privatized, while the been extensively studied as an engineering fail- failures will be hung around all of our necks. ure, but thousands survived because of the safety “Quant alchemy” indeed. By the end, I couldn’t margin that was built into the building. Cranking help thinking of H. G. Wells’s famous takedown the 9/11 metaphor up another notch, David Hand of Winston Churchill after the First World War: has compared bank executives to people who break “He believes quite naïvely that he belongs to a into a 747 cockpit and crash the plane [6]. peculiarly gifted and privileged class of beings to Mathematicians are not engineers, and not whom the lives and affairs of common men are only because one can hardly imagine top civil given over, the raw material of brilliant careers.” engineering academics reacting with nonchalance The quant aristocrats have had their Gallipoli. How if their best graduates were not building bridges will they adapt? How will the mathematical com- but finding bridges prone to collapse so they can munity respond? After the last quant has done his cash in buying insurance on them. Or boasting turn on the economic stage, it now seems hard to of how their elite training and inherent brilliance imagine that anyone will want to erect a statue to enabled them to hoodwink the inspectors into his memory. approving shoddy plans. The engineering analogy was eloquently demolished by Nicolas Bouleau, References financial mathematician and professor at the École [1] Nicolas Bouleau, Mathématiques et risques finan- Nationale des Ponts et Chausées. “Engineering ciers, Odile Jacob, Paris, 2009.

MAY 2011 NOTICES OF THE AMS 703 [2] Geof Bowker, How to be universal: Some cybernetic [12] Sebastian Mallaby, More Money than God, Blooms- strategies, 1943–70, Social Studies of Science 23(1), bury, London, 2010. February 1993, 107–127. [13] Rose McDermott, James H. Fowler and Oleg [3] Andrew Clark, Goldman Sachs hit by lurid allega- Smirnov, On the evolutionary origin of prospect tions of sex discrimination, The Guardian, September theory preferences, Journal of Politics 70(2), April 16, 2010, p. 27. 2008, 335–50. [4] Lorraine Daston, Classical Probability in the Enlight- [14] Eric Nalder, Twin Towers engineered to withstand enment, Princeton University Press, Princeton, 1995. jet collision, Seattle Times, February 27, 1993. [5] Lars Eighner, My daily dives in the dumpster, [15] Carmen M. Reinhart and Kenneth S. Rogoff, This Harper’s, December 1991, 19–22. Time is Different: Eight Centuries of Financial Folly, [6] David J. Hand, Mathematics or mismanagement?: The Princeton University Press, Princeton and Oxford, crash of 2008, Newsletter of the London Mathematical 2009. Society 382, June 2009. [16] Steven Shreve, Don’t blame the quants, Forbes, [7] G. H. Hardy, A Mathematician's Apology, Cambridge October 7, 2008. University Press, 1940. [17] Joseph Stiglitz, Freefall: Free Markets and the [8] Espen Gaarder Haug and Nassim Nicholas Sinking of the Global Economy, Penguin Books, 2010. Taleb, Why we have never used the Black-Scholes- [18] Kyle Stock, Ranks of women on Wall Street thin, Merton option pricing formula. Available at http:// Wall Street Journal, September 20, 2010. papers.ssrn.com/sol3/papers.cfm?abstract_ [19] George Szpiro, Eine falsch angewendete Formel und id=1012075. ihre Folgen, Mitteilungen der Deutschen Mathema- [9] Martin F. Hellwig, Systemic risk in the financial sec- tischen Vereinigung 17(1) (2009), 44–45. tor: An analysis of the subprime-mortgage financial [20] Paul Wilmott, The use, misuse and abuse of crisis, De Economist 157(2) (2009), 129–207. mathematics in finance, Royal Society Philosophical [10] Michael Lewis, The Big Short: Inside the Doomsday Transactions: Mathematical, Physical and Engineering Machine, W. W. Norton & Company, New York, 2010. Sciences 358(1765), January 2000, 63–73. [11] L. E. Maistrov, Probability Theory: A Historical Sketch, Academic Press, New York, 1974.

DOCEAMUS doceamus . . . let us teach Revitalizing the 1960 Mathematics Major

Alan Tucker I entered college around 1960 in a golden era for math major changed, along with an argument for the mathematics major. At that time, 5 percent why it needs to be revitalized. of freshmen expressed an interest in becoming Most United States universities in the 1950s math majors (although only half as many earned had many tenured non-Ph.D. faculty in math- math degrees). Math grads were in demand for ematics, and many offered a dated mathematics new careers in aerospace and other technological curriculum, e.g., a typical junior math course was industries, along with traditional careers in insur- tensor calculus. A dramatic increase in the number ance and teaching. Many of my math major friends of math Ph.D.s was needed both to upgrade the planned to go to medical or law school, as well as quality of faculty and to match the rapid growth graduate school in mathematics or other quanti- of college enrollments. The mathematics major tative disciplines. For many smart freshmen with curriculum required a massive revision to reverse unsure career plans, mathematics was a default the high failure rate in first-year graduate courses major. This piece sketches my reading of why the in Lebesgue integration and such. The proposed Alan Tucker is professor of mathematics at SUNY- solution appeared in Pregraduate Preparation for Stony Brook. His email address is Alan.Tucker@ Research Mathematicians (1963), the first report of stonybrook.edu. the MAA’s new Committee on the Undergraduate

704 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Program in Mathematics (CUPM). The widely ad- as they stuck to their two-courses-per-semester, opted 1965 CUPM report, A General Curriculum for undergraduate-focused tradition. Other public Mathematics in Colleges, presented a gentler version universities followed the Berkeley example, and of the 1963 recommendations with the goal that math- finally the Ivies gave in. Soon all faculty at univer- ematics majors at all institutions should have some sities wanted to be treated like stars with reduced preparation for graduate study in mathematics (it teaching loads. A huge increase in precalculus was assumed that one-third of math majors would and other low-level mathematics enrollments at earn an M.S. in the mathematical sciences). public universities, along with the pressure to get From 1960 to 1965, the number of math bach- research grants, has further diminished the atten- elor’s degrees grew from 11,000 to 20,000, and tion given to math majors over the past forty years. math Ph.D.s from 300 to 700, according to AMS and I believe that research mathematics depart- CBMS survey data. The 1968 NRC COSRIMS report ments will have trouble flourishing, especially predicted 60,000 B.S.s and 2,200 Ph.D.s in math by at public universities, without flourishing math 1975. The bachelors’ number actually decreased, majors. This was a key message in the 1999 AMS dropping to 12,000 by 1980 and staying around Towards Excellence report, which cited examples of there to this day. Ph.D. numbers did grow but more several universities with flourishing math majors. slowly. Many math majors struggled with the more As one model, in the programs cited at UCLA and abstract curriculum, and employers complained Chicago, research faculty collaborate with nonre- that math graduates often seemed ill prepared search faculty or mathematically trained advisors to work on industry’s problems. Further, new to give math majors personal attention. programs in computer science lured away many Mathematics departments cannot compete with potential math majors. Although math majors the natural sciences for resources in research dol- were now better prepared for success in graduate lars. Because regular faculty do limited teaching school, the catholic 1960 image of the math major in calculus-and-below courses, which represent had faded. From 1975 on, only 1 percent of college over 80 percent of math enrollments, mathemat- freshmen expressed an interest in a math major. ics departments cannot count on the huge enroll- Now let me turn to the situation from the fac- ments in these courses to justify their size. Indeed, administrators are increasingly using four-course- ulty viewpoint, based on conversations with my per-semester lecturers, adjuncts, and technology father A. W. Tucker, who was chairman of the to provide cheaper instruction than graduate stu- Princeton Mathematics Department around 1960. dents and instructors—and they often do a better His view of academic life was that he was paid to job; in the process, math teaching assistantships teach but given the free time to do research, which and faculty lines are eliminated. he loved. That was a time when universities had Without meaning to diminish the importance of modest graduate programs and the focus was on research mathematics, I believe that a broad-based, undergraduates; federal support of research was thriving major in a core discipline such as math- just starting. All Princeton faculty, including de- ematics is valued and respected by administrators partment chairs and even the dean of the college, as an important university service to society and taught two courses per semester. One semester its economic well-being. The value of studying each year my father was the lead professor in the mathematics is perhaps more in its mental training big calculus course that most freshmen took. When than its content. The wide-ranging accomplish- I asked him years later when I was a department ments of math majors speak for themselves: from chair why he assumed this extra duty, he looked at economist John Maynard Keynes to biologist Eric me like I was crazy and said, “The most important Lander, who led the Human Genome Initiative, to thing the Princeton Mathematics Department did Jim Simons, professor turned hedge fund guru was to teach freshman calculus, and so as depart- turned philanthropist, and even to basketball star ment chairman it was obvious that I should lead Michael Jordan. that effort.” As chair, he felt it was also his job to Alan Tucker has taught for forty years at SUNY- get to know most of the math majors personally. Stony Brook, where 6 percent of bachelor’s gradu- [For more vignettes about those days, see my per- ates are in mathematics, pure and applied. sonal website: www.ams.sunysb.edu/~tucker.] My father believed that one person could be blamed (or credited) with reorienting university faculty toward graduate students and research— Clark Kerr. In seeking to recruit star faculty from the Ivy League schools to Berkeley, Kerr hit upon the winning strategy of offering reduced teaching loads and little undergraduate teaching. I remem- ber seeing one after another of our faculty neigh- bors get lured away, while my father and the rest of the Princeton administration watched helplessly

MAY 2011 NOTICES OF THE AMS 705 JPBM Communications Award

The 2011 Communications Award of the Joint positive portrayal of the power and fun of math- Policy Board for Mathematics (JPBM) was presented ematics through their hit TV series, Numb3rs. at the Joint Mathematics Meetings in New Orleans, Nicolas Falacci and Cheryl Heuton created the Louisiana, in January 2011. extraordinary TV series Numb3rs, featuring an The JPBM Communications Award is presented FBI agent and his brother, a mathematical genius. annually to reward and encourage journalists and Through its six-season run on CBS, the series fea- other communicators who, on a sus- tured the use of mathematical thinking and model- tained basis, bring mathematical ideas ing to solve crimes. Numb3rs provided the general and information to nonmathemati- public with a glimpse of the mathematical world, cal audiences. JPBM represents the its depth and its power, in a way that connected American Mathematical Society, the with a broad spectrum of viewers. With creativity American Statistical Association, the and cleverness, their work, which includes over Mathematical Association of America, one hundred episodes, made its fans aware of the and the Society for Industrial and Ap- ubiquity of mathematics in their daily lives. plied Mathematics. The award carries [Falacci and Heuton have been recognized by a cash prize of US$1,000. the National Science Board with its Public Service Previous recipients of the JPBM Award, and they are the recipients of the Carl Communications Award are: James Sagan Public Understanding of Science Award.] Gleick (1988), Hugh Whitemore (1990), Ivars Peterson (1991), Joel Schneider Cheryl Heuton and (1993), Martin Gardner (1994), Gina Biographical Sketch Nicolas Falacci Kolata (1996), Philip J. Davis (1997), Nicolas Falacci was born 1959 in Hyannis, Mas- Constance Reid (1998), Ian Stewart sachusetts. He attended the undergraduate film (1999), John Lynch and Simon Singh (special award, program at New York University’s Tisch School 1999), Sylvia Nasar (2000), Keith J. Devlin (2001), of the Arts and received his B.F.A. in 1981. He Claire and Helaman Ferguson (2002), Robert Os- sold his first feature-length screenplay in 1989 serman (2003), Barry Cipra (2005), Roger Penrose to Columbia Pictures and producer Joel Silver. He (2006), Steven H. Strogatz (2007), Carl Bialik (2008), continued writing film projects for various studios George Csicsery (2009), and Marcus du Sautoy and producers, mostly in the science fiction genre. (2010). That same year, while pursuing his favorite pas- The 2011 JPBM Communications Award was time of rock climbing in the Los Angeles area, he presented to Nicolas Falacci and Cheryl Heu- met Cheryl Heuton. Within a couple of years, the ton. The text that follows presents the selection two of them moved to New York City, married, and committee’s citation, a brief biographical sketch, began writing together. and the recipients’ responses on receiving the Cheryl Heuton was born 1957 in Whittier, Cali- award. fornia. She grew up in the north San Diego area and attended the University of California, San Diego. She worked as a reporter for local weekly newspa- Citation pers, then went on to become an editorial writer The 2011 JPBM Communications Award is awarded for the Los Angeles Herald-Examiner and later the to Nicolas Falacci and Cheryl Heuton for their Long Beach Press Telegram. She was nominated

706 NOTICES OF THE AMS VOLUME 58, NUMBER 5 for a Pulitzer Prize for her series of articles about that television audiences would find mathemati- the mentally ill homeless. cians as fascinating as we did. As a writing team, Cheryl and Nick sold their Noting the popularity of crime dramas, specifi- first feature script to Warner Brothers, then went cally the ones based on forensic sciences, we felt on to write film projects for New Line, MGM, Imag- that this type of storytelling could provide the ine, Sony, and HBO. opportunity to contrast and collide the thinking In 2003 they pitched CBS Television an idea for that goes on within a criminal investigation by a television series centered around a mathemati- police detectives with the extreme deductive rea- cian. Production on Numb3rs began in 2004, and soning of a mathematician. Our research led us the show debuted on CBS in January 2005. A rat- to the real-life collision of math and police work: ings success, Numb3rs was renewed for a total of This happened by way of Kim Rossmo, a Canadian six seasons. During those six years, Cheryl and mathematician, homicide detective, and, more Nick worked on the show as executive producers. importantly, one of the pioneers of geographic Each season they wrote and supervised numerous profiling. episodes. The notion of a mathematician solving major In early 2010 Nick directed the 119th and final crime investigations was a reality. We had a strong episode of Numb3rs. The show continues to be suspicion that a lot of other people would be as broadcast in syndication in the United States and in fascinated by this unexpected, yet exciting conflu- numerous foreign countries, including the United ence of disciplines as we were. Kingdom, Germany, Sweden, Australia, Japan, and We are extremely honored to have been selected Brazil. to receive the JPBM Communications Award. Nei- ther of us, obviously, are mathematicians, and Response from Nick Falacci and Cheryl neither of us pursued our careers with any plan to Heuton popularize mathematics on network television. So While we pursued a career in film and television much of what brought Numb3rs to fruition was, writing, we both have a lifelong passion and inter- as mathematicians or cosmologists might say, a est in science. I, specifically, arrived at NYU intent happy coincidence. on achieving a double major in film and…physics. By creating Numb3rs, we have experienced two extremely rewarding accomplishments: the excite- Once I was informed of the required workload, es- ment of creating a successful television drama and pecially the number of math classes I would have the profound satisfaction of introducing an audi- to take, I abandoned my scientific aspirations on ence of ten to twelve million viewers each week the spot and focused my energy on filmmaking. to the elegance and power of mathematics and its Cheryl and I discovered our shared love of sci- direct impact on our daily lives. ence on our first date, when we realized we were We wish to acknowledge our utmost gratitude both tremendous fans of James Burke’s “The and appreciation for the people at CBS who be- Day the Universe Changed”. Though we never lieved in the show from the very beginning; the discussed a specific intention to write about sci- other Numb3rs writers who took on the daunting entists, we found ourselves naturally inclined to task of incorporating mathematics into a crime create characters with backgrounds in engineering, procedural drama week in, week out; our entire math, and science. One of our feature scripts was production staff, who embraced the notion and based on the true story of the Glomar Explorer, an premise of the show; our enthusiastic research- amazing engineering feat by the Navy to salvage a ers and our extraordinarily talented consultants Russian submarine three miles beneath the surface who helped us navigate the world of mathemat- of the ocean. We developed a network television ics; and, of course, Caltech, for its vigorous and series about the extraordinary crash and accident wholehearted support of the show and for making analysts at the National Transportation Safety us welcome on their campus. Board. It was probably only a matter of time before Cheryl and I would be drawn to the world of mathematics and mathematicians. Both long-time skeptics, we were fascinated by the rigorous ratio- nal thinking of mathematicians. We were continu- ally and delightedly surprised by the seemingly endless capacity of mathematics to help mankind understand the nature of the world and fuel the development of technology. With the help of the writing of various authors like John Allen Paulos, we discovered the unique way that mathemati- cians view the world. The more we explored and researched the topic, the more we were convinced

MAY 2011 NOTICES OF THE AMS 707 MAA Prizes Presented in New Orleans

At the Joint Mathematics Meetings in New Orleans, Carl B. Allendoerfer Awards and has been an MAA Louisiana, in January 2010, the Mathematical Asso- Polya Lecturer. He has served as vice president and ciation of America (MAA) presented several prizes. president of MAA. He has also published more than one hundred articles in mathematical journals and Gung and Hu Award for Distinguished other publications. Service The Yueh-Gin Gung and Dr. Charles Y. Hu Award Haimo Awards for Teaching for Distinguished Service to Mathematics is the The Deborah and Franklin Tepper Haimo Awards most prestigious award made by the MAA. It hon- for Distinguished College or University Teaching ors distinguished contributions to mathematics were established in 1991. These awards honor col- and mathematical education, in one particular lege or university teachers who have been widely aspect or many, whether in a short period or over recognized as extraordinarily successful and a career. whose teaching effectiveness has been shown to Joseph Gallian is Distinguished Professor have had influence beyond their own institutions. of Teaching and Professor of Mathematics at the The 2011 Haimo Awards were presented to University of Minnesota, Duluth. His service to Erica Flapan, Karen Rhea, and Zvezdelina mathematics takes form in three major activities: Stankova. his work with Research Experiences for Under- Erica Flapan has been teaching at the collegiate graduates (REUs), his work with Project NExT, and level for more than twenty-five years. She is cur- his service to professional organizations and the rently Lingurn H. Burkhead Professor of Mathemat- mathematical community at large. He was one of ics at Pomona College. Her outstanding teaching the early proponents of undergraduates conduct- was recognized early; she received awards before ing mathematical research, and his REU at Duluth, earning her Ph.D., as a postdoctoral fellow, and which began in 1977, is widely regarded as the as the recipient of the 2005 Irving Foundation premier REU. The quality of the work at his REU is Distinguished Faculty Fellowship for mentor- evidenced by the 150 papers by participants that ing students of color at Pomona and the 2010 grew out of their REU work and that have appeared Southern California–Nevada Section Award for in the Journal of Algebra, Journal of Combinatorial Distinguished College or University Teaching. She Theory, Discrete Mathematics, and others. In 2002 is best known for her dynamic, energetic classes he was recognized by the Council on Undergradu- that foster the participation of all students in the ate Research (CUR) with a Fellow Award given to room. She was co-principal investigator of a grant members who have demonstrated sustained excel- to bridge mathematics and chemistry at Pomona, lence in research with undergraduates. which helped to fund the creation of an Advanced Gallian has been involved with Project NExT Problem Solving course designed to give aspiring since 1994, and became its codirector in 1998, as- chemistry students needed mathematical strength- suming primary responsibility for many parts of ening. Her work in connecting mathematics and the program and participating in developing the chemistry is further illustrated by her widely ac- workshop program. He has coordinated Mathemat- claimed book When Topology Meets Chemistry: A ics Awareness Month twice and served on more Topological Look at Molecular Chirality (Cambridge than forty national committees. He was a member University Press and the Mathematical Associa- of the CUR for eleven years, serving as chair of tion of America, 2000). Flapan teaches in several the mathematics and computer science division summer programs aimed at broadening interest for part of that time. He has served as associate in advanced mathematics among high school and editor of Mathematics Magazine and American undergraduate students and encouraging them Mathematical Monthly and has directed or codi- to pursue graduate degrees. Her colleagues and rected five conferences. He has been a referee for students say that she serves both as a formal and forty journals. informal advisor to many students; she is known as Gallian has received teaching awards from a tireless advocate and strong voice in support of the University of Minnesota Duluth, the Carnegie diversity. Flapan received her B.A. from Hamilton Foundation for the Advancement of Teaching, and College in 1977 and her Ph.D. from the University the Mathematical Association of America (Haimo of Wisconsin at Madison in 1983. Her research Award). He has received the MAA Trevor Evans and interests are in low-dimensional topology and its

708 NOTICES OF THE AMS VOLUME 58, NUMBER 5 applications to chemistry and molecular biology. other cities. She was coeditor of the book A Decade She has recently coauthored a book (with James of the Berkeley Math Circle (American Mathematical Pommersheim and Tim Marks) titled Number Society, 2008). With Paul Zeitz and Hugo Rossi, she Theory: A Lively Introduction with Proofs, Applica- cofounded the Bay Area Mathematical Olympiad, tions, and Stories (John Wiley & Sons, 2010). an annual competition among 250 students from Karen Rhea has been a faculty member in col- forty-five schools in the Bay Area. Several of these leges and universities for about thirty years, the students have gone on to be members of the U.S.A. last decade at the University of Michigan. In 1998, Mathematical Olympiad team. Stankova has been while a professor at the University of Southern actively involved in the U.S. participation in the Mississippi, she was awarded the MAA Louisiana- International Mathematical Olympiad, including as Mississippi Section’s Award for Distinguished an instructor in the training camps of the USAMO. College or University Teaching of Mathematics. Her students at every level are enthusiastic about She is director of the introductory program at her teaching and mentoring, indicating that her Michigan, which serves about 4,500 students an- classes are challenging and fun. They rave about nually in precalculus and the first year of calculus her teaching ability, her enthusiasm for mathemat- and which is widely viewed as one of the most ics, and her capacity to dramatically change their successful programs of its scope in the country. attitudes toward mathematics and their percep- At the beginning of each academic year she runs tions of their own mathematical abilities. Stankova an intense training week for all new instructors in was drawn to mathematics through her Math Circle the introductory program. She has received praise in Bulgaria, and she consequently earned silver for helping instructors find their own voices, and medals at the International Mathematical Olym- she continues to work with them after they leave piads. She completed a B.A./M.A. degree at Bryn the program. Many of the instructors she works Mawr in 1992 and received her Ph.D. in algebraic with go on to become faculty elsewhere, broaden- geometry from Harvard University in 1998. ing her influence on mathematics instruction. Her students say that her enthusiasm and eagerness Chauvenet Prize to teach make class interesting and that she pres- The Chauvenet Prize recognizes a member of the ents the material as clearly as possible. She has MAA who has written an outstanding expository contributed to the general development of the article. First awarded in 1925, the prize is named calculus curriculum and to the discourse on how for William Chauvenet, who was a professor of to teach calculus effectively through her work with mathematics at the United States Naval Academy. the Harvard Calculus Consortium. Not only has Bjorn Poonen of the Massachusetts Institute her work made significant contributions to the of Technology received the 2011 Chauvenet Prize content of the introductory courses at Michigan for his article “Undecidability in number theory”, but it also has contributed to the development of Notices of the American Mathematical Society 55 a calculus curriculum that aims to get students (2008), no. 3, 344–350. Hilbert’s tenth problem (in actively involved in their own learning throughout his famous list of twenty-three problems posed the country. Rhea has given numerous talks and in 1900) asks if there is an algorithm to decide workshops, has served on the MAA Committee whether, for a given polynomial p(x1,…, xn) in n on Professional Development, and was recently variables with integer coefficients, there exist in- appointed to the Committee on the Teaching of tegers a1,…, an such that p (a1,…, an) = 0. Although Undergraduate Mathematics. a proof that no such algorithm exists was found Zvezdelina Stankova’s goals in teaching are in 1970, “Hilbert’s tenth”, with its many ramifica- to develop students’ ability to do independent tions and generalizations, continues to stimulate thinking, no matter what the level of the student, mathematicians today. For example, it is known from the middle and high school students in the that there is no algorithm to decide the existence Math Circles she works with through the senior of integer solutions to integer-coefficient polyno- undergraduate mathematics majors of Mills Col- mial equations in eleven variables, but what about lege and the University of California, Berkeley. As a just two variables? We don’t know yet. Poonen’s full-time faculty member at Mills College, Stankova masterful exposition strikes a perfect balance has also taught one course per year at the Univer- between technicality (for the experts) and accessi- sity of California, Berkeley, for eleven years, and, bility (for the rest of us). His story involves Turing in 1998, she founded the Berkeley Math Circle, machines, quantum computers, Diophantine sets, a weekly program for fifty Bay Area middle and undecidability, prime-producing polynomials, high school students. She has been the Berkeley and the Riemann hypothesis. It is a treat to find Math Circle’s director and a frequent lecturer since such a diversity of ideas wrapped up neatly into the beginning. In addition, she has been directly a single fascinating package. Poonen received his involved in the creation of Math Circles in seven A.B. in mathematics and physics from Harvard more cities in the United States and Canada and University in 1989 and his Ph.D. in mathematics has contributed to the creation of Circles in twelve from the University of California, Berkeley, in 1994.

MAY 2011 NOTICES OF THE AMS 709 He taught at Berkeley until 2008, then moved to David P. Robbins Prize MIT. His research focuses on number theory and This prize was established in memory of David P. algebraic geometry, and he has also worked in Robbins by members of his family. Robbins, who combinatorics, probability, and computer science. died in 2003, received his Ph.D. in 1970 from MIT. He is the founding managing editor of Algebra and He was a long-time member of the Institute for Number Theory. Defense Analysis Center for Communication Re- search and a prolific mathematician whose work Euler Book Prize (much of it classified) was in discrete mathemat- The Euler Book Prize is given to the author(s) of an ics. The prize is for a paper with the following outstanding book about mathematics. Mathemati- characteristics: it shall report on novel research cal monographs at the undergraduate level, histo- in algebra, combinatorics, or discrete mathematics ries, biographies, works of mathematical fiction, and shall have a significant experimental compo- and anthologies are among those types of books nent, and it shall be on a topic which is broadly accessible and shall provide a simple statement of eligible for the prize. The prize was given for the the problem and clear exposition of the work. This first time in 2007, the 300th anniversary of the prize is awarded every three years. birth of Leonhard Euler. The 2011 David P. Robbins Prize was awarded Timothy Gowers has been awarded the 2011 to Mike Paterson, Warwick University; Yuval Euler Book Prize for his editorial work on The Peres, Microsoft Research, University of Wash- Princeton Companion to Mathematics (Princeton ington, University of California, Berkeley; Mikkel University Press, 2008). The book is a vast com- Thorup, AT&T Labs; Peter Winkler, Dartmouth pendium of mathematical information in the form College; and Uri Zwick, Tel Aviv University, for of essays by experts on a wide variety of fields, their innovative work on two papers: “Overhang”, in most cases bringing the reader up to date on American Mathematical Monthly 116, January developments in recent decades in a way that 2009, and “Maximum Overhang”, American Math- nonexperts can understand and appreciate. The ematical Monthly 116, December 2009. The two Committee understood that the book is the work papers together solve, to within a constant fac- of many, but singled out Gowers because of his tor, the classic problem of stacking blocks on a extraordinary achievement in putting this whole table to achieve the maximum possible overhang, volume together (over 1,000 pages of text) and also i.e., reaching out the furthest horizontal distance for writing a beautiful 76-page introduction, as well from the edge of the table. The January paper was written by Paterson and Zwick, and the December as 68 of the 288 individual entries. The organiza- paper was written by all five authors. The January tion is thematic, with sections on the origins of paper proves the surprising result that n blocks modern mathematics, mathematical concepts, the can be (cunningly) stacked using suitable coun- various branches of the subject, the big problems, terbalancing to achieve an overhang proportional biographical essays, and a section on the influence to n (1/3). (Many people have assumed that the of mathematics on other fields. The book has overhang of about log n, given by the standard something for everyone who has any interest in calculus exercise, is optimal.) The December paper mathematics. Many sections can be read with great gave a complementary argument, showing that benefit and considerable pleasure by mathematical an overhang proportional to n(1/3) is, in fact, amateurs and students. Overwhelmed as we are in the largest possible for any balanced stack. The the twenty-first century by the enormous size of papers describe an impressive result in discrete mathematics, the professional mathematician can mathematics; the problem is easily understood benefit from finding out what colleagues are doing and the arguments, despite their depth, are easily in branches of mathematics that did not exist when accessible to any motivated undergraduate. many of us were in school. Anyone who wonders Certificates of Meritorious Service about “mirror symmetry”, “quantum groups”, Each year the MAA presents Certificates of Meri- “vertex operator algebras”, “automorphic forms”, torious Service for service at the national level or or “Ricci flow”, topics referred to in the current for service to a section of the MAA. Those honored mathematical literature or even in the newspapers, in 2011 are: Joseph Gallian (University of Minne- can find help here. Gowers’s early research was in sota, Duluth), North Central Section; John Hagood the geometry of Banach spaces. He solved several (Northern Arizona University), Southwest Section; old problems in the area, some posed by Banach Allen Hibbard (Central College, Pella, Iowa), himself. More recently, he has worked in addi- Iowa Section; Joseph Malkevitch (York College, tive combinatorics: his new proof of Szemerédi’s CUNY), Metro New York Section; Jenny McNulty theorem has been particularly influential. In 1996 (University of Montana), Pacific Northwest Section; he was awarded a European Mathematical Society and Gerald Porter (University of Pennsylvania), prize, and he received a Fields Medal in 1998. Eastern Pennsylvania and Delaware Section.

710 NOTICES OF THE AMS VOLUME 58, NUMBER 5 AWM Awards Given in New Orleans

The Association for Women in Mathematics (AWM) returned to the Mathematical Olympiad Summer presented three awards at the Joint Mathematics Program as a grader and also served as a grader Meetings in New Orleans, Louisiana, in January for the Mathematical Olympiad of Central America 2011. and the Caribbean. In 2010 Gong served as one of the coaches for the USA team for the Girls’ Math- Shafer Prize ematical Olympiad in China. Five of the eight girls The Alice T. Schafer Prize for Excellence in Math- on the team won gold medals, and the head coach ematics by an Undergraduate Woman was estab- describes Gong as “a young lady with a great heart, lished in 1990. The prize is named in honor of thoughtful and gentle”, who pushed the students Alice T. Schafer, one of the founders of AWM and with “acute mathematical insights and inspiring one of its past presidents. Schafer passed away in personality”. Her mentors describe a remarkable September of 2009. young mathematician, exceptionally talented and The 2011 Schafer Prize was awarded to Sherry original, with one commenting she is already Gong of Harvard University. A senior, her perfor- “comparable to some of the best mathematical mance in her classes has been outstanding. She minds I know”. began with Harvard’s famous problem-solving class, in which she achieved a score above 100, and Louise Hay Award since her sophomore year she has taken numerous Established in 1991, the Louise Hay Award for graduate mathematics courses, earning A’s in all of Contributions to Mathematics Education recog- them. Her recommenders were universally amazed nizes outstanding achievements in any area of by her ability to master sophisticated mathematics mathematics education. Louise Hay was widely rapidly, whether in a class or independently mas- recognized for her contributions to mathematical tering background for a research project. Gong has logic and her devotion to students. been involved in four different research projects The 2011 award was presented to Patricia and is the author or coauthor of three papers. She Campbell of the University of Maryland, College spent summer 2008 at the Duluth REU researching Park, in recognition of her leadership and contri- cyclotomic polynomials; her paper was published butions in research, teaching, and service to math- in the Journal of Number Theory. In 2009 she ematics education. Throughout her career, she has worked with a group at MIT that did research on engaged and challenged her students, university computing the dimension of the space of charac- colleagues, professional colleagues, school admin- ters of the Lie algebra of Hamiltonian vector fields istrators, and classroom teachers to advance the on a symplectic vector space; their work will be teaching of mathematics. As a leader in the field published shortly. She and an economist have of mathematics education, Campbell is esteemed published a paper in Integers on congruence condi- especially for her contributions to the teaching and tions characterizing primes. Most recently she did learning of mathematics in urban settings and for research on periodic cyclic cohomology of group working in schools that serve predominately mi- algebras of torsion free groups at Vanderbilt. As a nority populations from low-income backgrounds. high school student, Gong medaled repeatedly in She has worked in schools to improve student the International Mathematical Olympiad, winning learning for two decades. From 1989–1997, she led a gold medal in 2007. After entering college, she Project IMPACT, a professional development effort

MAY 2011 NOTICES OF THE AMS 711 that demonstrated the feasibility of school-wide advanced PDEs. She ably identifies research topics mathematics reform, supplementing summer pro- that match the students’ interests and abilities. fessional development with in-school mathematics Especially noteworthy is her encouragement of stu- specialists in order to increase achievement in dents whose potential had previously gone unno- schools with predominately minority populations. ticed, even by the students themselves. The results She has collaborated in developing the MARS bear witness to the strength of Hughes’s belief in Project (Mathematics: Application and Reasoning her students, to the force of her personality, and to Skills), which has addressed a complex set of prob- the contagious quality of her enthusiasm for math- lems in Baltimore public schools, targeting poor ematics. Particularly stunning are the accounts of student achievement through system-wide teacher students who began college convinced they were development in mathematics. With Campbell as “bad at mathematics”, but who were charmed by the principal investigator, the MARS Project was Hughes into taking calculus with her. They take awarded a five-million-dollar grant through the more mathematics, still not convinced of their own NSF Local Systemic Initiative program. abilities but warming to the subject. The students Through her current research, Campbell con- end up majoring in mathematics, doing a research tinues to pursue her efforts to ensure quality project, and proceeding to graduate programs and education for all children. As part of the research careers in mathematics. The overall numbers are component of the Mid-Atlantic Center for Math- striking, and the mathematics program at Bryn ematics Teaching and Learning, she leads a re- Mawr has flourished in the time Hughes has been search project that is poised to assess the impact there, with large increases in majors. of Grade 4–8 teachers’ knowledge of mathematics Hughes has brought her knowledge of how to and mathematics pedagogy on student achieve- encourage young women in mathematics to the ment. Her current work in the area of mathematics national level. She has served AWM in many ways, leadership at the elementary level builds on her including as president in 1987–88. She has also prior efforts and her evaluation of the work and served often as organizer, panelist, and speaker role of elementary mathematics specialists and will in activities aimed at increasing the participa- contribute significantly to the research in this area. tion of women and minorities in mathematics. After having identified the challenges that some She has been a member of the board of directors of young women face, especially minority women, the National Council of Teachers of Mathematics Hughes began programs to help negotiate crucial and has served many roles within the organization. transitions, the first one being from undergradu- As a teacher, mentor, and colleague, she has gained ate course work to the math major. In 1998 she the appreciation of her students and colleagues for and Sylvia Bozeman of Spelman College created her commitment, skill, and energy for the cause of the ongoing EDGE program, which addresses the mathematics education and for challenging them transition from college to graduate school with to think more deeply about the tough issues they marked success. must confront.

M. Gweneth Humphreys Award for Mentorship of Undergraduate Women in Mathematics This award is named for M. Gweneth Humphreys (1911–2006). Humphreys graduated with honors in mathematics from the University of British Co- lumbia in 1932, earning the prestigious Governor General’s Gold Medal at graduation. After receiving her master’s degree from Smith College in 1933, Humphreys earned her Ph.D. at age 23 from the University of Chicago in 1935. She taught math- ematics to women for her entire career. This award, funded by contributions from her former students and colleagues at Randolph-Macon Woman’s College, recognizes her commitment to and her profound influence on undergraduate students of mathematics. The inaugural award was presented to Rhonda Hughes of Bryn Mawr College in recognition of her outstanding mentoring of undergraduate women in mathematics. Hughes is a dedicated and motivating teacher at all undergraduate levels, from basic calculus to

712 NOTICES OF THE AMS VOLUME 58, NUMBER 5 2011 Mathematics Programs That Make a Difference

Each year, the AMS Committee on the Profession The selection committee for the 2011 Mathe- (CoProf) selects outstanding programs to be des- matics Programs That Make a Difference consisted ignated as Mathematics Programs That Make a of: Matthias Heinkenschloss, Bryna Kra, Susan Difference. For 2011 the programs honored are the Loepp (chair), Rick Miranda, Richard Tapia, and Center for Women in Mathematics at Smith Eric Tchetgen Tchetgen. College and the Department of Mathematics Below are CoProf’s citations, followed by brief de- at North Carolina State University. scriptions of the programs prepared by Notices staff. CoProf created the Mathematics Programs That Make a Difference designation in 2005 as a way to bring recognition to outstanding programs that Center for Women in Mathematics, successfully address the issue of underrepresented Smith College groups in mathematics. Each year CoProf has iden- Citation tified two exemplary programs that: 1. aim to bring more individuals from underrep- Be it resolved that the American Mathematical resented minority backgrounds into some portion Society and its Committee on the Profession rec- of the pipeline beginning at the undergraduate ognize the Center for Women in Mathematics and level and leading to an advanced degree in math- the Center’s Postbaccalaureate Program, Smith ematics or retain them in the pipeline; College, for its significant efforts to encourage 2. have achieved documentable success in doing women to continue in the study of mathematics. so; and The program’s supportive and encouraging 3. are replicable models. environment has resulted in remarkable suc- Previously designated Mathematics Programs cess. Talented undergraduate women, who have That Make a Difference are: the graduate program discovered their passion for mathematics late in at the University of Iowa and the Summer Institute their undergraduate careers or after they have in Mathematics for Undergraduates/Research obtained a degree in a field other than mathemat- Experience for Undergraduates at Universidad de ics, are recruited for the program. The program’s Puerto Rico, Humacao (2006); Enhancing Diversity participants take courses, attend weekly colloquia, in Graduate Education (EDGE) and the Mathemati- and participate in research projects, resulting in cal Theoretical Biology Institute (2007); the Math- a valuable and effective community experience. ematics Summer Program in Research and Learning Graduates of the program are accepted for and (Math SPIRAL) at the University of Maryland and succeed in mathematics graduate programs at an the Summer Undergraduate Mathematical Science astonishingly high rate. The program has made a Research Institute at Miami University (Ohio) remarkable contribution to the national effort to (2008); the Department of Statistics at North Caro- produce more women Ph.D.s in the mathematical lina State University and the Department of Math- sciences. ematics at the University of Mississippi (2009); The AMS commends the members of the Depart- the Department of Computational and Applied ment of Mathematics at Smith College for their Mathematics at Rice University and the Summer high level of commitment and their successful Program in Quantitative Sciences, Harvard School efforts to improve the diversity of the profession of Public Health (2010). of mathematics in the United States.

MAY 2011 NOTICES OF THE AMS 713 Program Description Smith College who want to spend one or both After earning a bachelor’s degree in theater, with semesters of their junior year in a mathematically a minor in mathematics, at Smith College in 2005, intense environment. The NSF grant provides Samantha Oestreicher spent two years working in financial aid to participants who are U.S. citizens the costume shop in a college theater department or permanent residents. In addition, the center and freelancing in costuming and backstage work hosts an annual conference called Women in in theaters in New England. Fast-forward to the Mathematics in New England (WIMIN). In 2009 the fall of 2010, and she is starting her third year of conference was one of the Regional Undergraduate graduate school in mathematics at the University Mathematics conferences sponsored by the Math- of Minnesota. Her performance is outstanding: ematical Association of America and attracted 105 she passed her preliminary examinations early, participants and twenty-four student talks. Most of participates actively in a research seminar, and the center’s postbaccalaureate students attend the is an exemplary teaching assistant. She held an Joint Mathematics Meetings, the Joint Statistical internship at Los Alamos National Laboratory and Meeting, and/or the Hudson River Undergraduate now has a research assistantship on a grant from Mathematics Conference. the National Science Foundation (NSF). The center is well integrated into the Smith Col- That Oestreicher made her way back to math- lege mathematics department and capitalizes on ematics and then excelled so quickly is an indica- some of the department’s assets, such as the Math tion of her talent and motivation. Helping that Forum, a welcoming and comfortable space where talent to flower and that motivation to strengthen students and teachers gather for conversation, was the postbaccalaureate program at the Cen- study, and relaxation, as well as tea and cookies. ter for Women in Mathematics at Smith College. At the same time, the center has had a positive, re- Founded in 2007 with funding from the NSF, the center serves women who discover their desire vitalizing influence on the department. By bringing to do mathematics only after having exited the together a group of active, serious, and motivated traditional educational track and who need to women, the center inspires Smith mathematics build up or refresh their backgrounds to be able majors and increases the level of activity in the to enter graduate school. “If it wasn’t for Smith’s department. The center has fostered a vertically program and the NSF funding, then I would never integrated community that is developing into a have made it as far as I have,” Oestreicher said. focal point for women mathematicians in New “Smith’s program gave me a totally fresh start and England. It is also having a national impact, as the opportunity to do math for a living.” other departments around the country establish The center’s postbaccalaureate program, the programs emulating those at the Smith center. first in mathematics in the United States, attracts Data about the center’s students demonstrate students from all over the country. In this one- its success. By the fall of 2010, twenty-four women year program, students take upper-level courses had completed the postbaccalaureate program. Of in the Smith mathematics department and also those, seventeen entered graduate school in the have the opportunity to take courses at Amherst, mathematical sciences immediately after complet- Hampshire, and Mount Holyoke colleges and the ing the program, and five will have entered after University of Massachusetts at Amherst. In addi- brief deferrals; almost all of these students went tion, the center designed two special courses for to Group I or II departments. Only one student has the students. The first, Dialogues in Mathematics, dropped out of the graduate program. Ten new introduces the students to the culture and pro- students joined the program in the fall of 2010. fession of mathematics through various means: The September 2007 issue of the Notices carried meetings with colloquium speakers to talk about an Opinion column by the directors of the then mathematics and mathematical careers, prepa- newly created Center for Women in Mathematics. ration for the GRE examination, discussions of The final paragraph of their piece captures well the strategies for graduate school, and examination of philosophy behind the center: “Yes, we marvel at issues pertinent to the mathematical community. the prodigies whose unwavering interest and apti- In the other course, the Advanced Mathematics Seminar, the students work in small groups with tude in mathematics are evident from the start. But faculty, generally on a research topic. The topics we must also open our minds to the vast numbers have included graph theory, combinatorics, and of students—women and minorities (and others computational geometry, as well as biological and from all walks of life)—who can be mathematicians medical applications of mathematics. The center’s but may not make that choice until late in their NSF grant provides tuition and a living stipend for college careers or after.” some of the postbaccalaureate students who are U.S. citizens or permanent residents. Program directors: Ruth Haas and Jim Henle Among the center’s other activities is a Junior Website: http://www.math.smith.edu/ Program for undergraduate women from outside center

714 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Department of Mathematics, NC State might very well be the top producer in North Carolina State University the nation: In the same nine-year time period as above, twenty-six mathematics doctorates were Citation awarded to female African-Americans by Group I Be it resolved that the American Mathematical Soci- and II departments, and six, or nearly a quarter, ety and its Committee on the Profession recognize earned their degrees at NC State. the Department of Mathematics, North Carolina What accounts for this achievement? One fac- State University, for its significant efforts to en- tor is the department’s commitment, starting courage students from underrepresented groups more than a decade ago, to recruiting domestic to continue in the study of mathematics. students into its graduate program. Today 96 per- The department’s exceptional commitment to cent of its graduate students are U.S. citizens or its students includes early research opportunities, permanent residents (and 49 percent are women). financial support provided by grant funding, and One of the strategies the department uses is an extraordinary faculty mentoring. In addition, the annual recruiting weekend, in which students are department offers impressive undergraduate pro- invited to the campus to learn about the graduate grams and postdoctoral opportunities. Since 1999 program. Through its long-standing contacts with the department has produced almost 13 percent of historically black colleges and universities, the all African-American Ph.D.s nationally. The depart- department identifies strong African-American ment at North Carolina State University has made, applicants, encourages them to apply, and invites and continues to make, a remarkable contribution them to the recruiting weekend. to the national effort to produce more minority Another factor is the substantial support the Ph.D.s in the mathematical sciences. department offers to students. An S-STEM grant The AMS commends the members of the De- from the National Science Foundation provides partment of Mathematics at North Carolina State financial support for all of the department’s University for their high level of commitment and African-American students during the first two their successful efforts to improve the diversity of years in graduate school. For students whose back- the profession of mathematics in the United States. grounds need additional shoring up, extra mentor- Program Description ing is available. In addition, the department has a In how many different ways can a mathematics Research Experience for Early Graduate Students department succeed? Count the successes of the (REG) program, which provides stipends for first- Mathematics Department at North Carolina State and second-year graduate students to work with University, and you will have a good approxima- faculty on summer research projects. Unlike other tion. The recipient of last year’s AMS Award for graduate students, S-STEM students are eligible for an Exemplary Program or Achievement in a Math- two summers of REG participation. ematics Department, NC State has excelled in just A third factor in the department’s success lies about everything mathematics departments do. in the broad and flexible nature of its graduate This time, the department was chosen for the program. Students have a wide variety of research Programs That Make a Difference distinction for areas to choose from, and many opportunities are one particular achievement: its extraordinary available to work on interdisciplinary problems record in serving students who have traditionally with researchers in other university departments, been underrepresented in mathematics, especially in industry, and in government laboratories. The African-Americans. mathematics department wanted the structure of The numbers speak for themselves. According its qualifying examinations to reflect the increas- to the Annual Survey of mathematics departments ingly interdisciplinary nature of mathematical re- that the AMS and collaborating organizations pre- search, so it created a set of fifteen examinations, pare each year, Group I and II mathematics depart- and each student must complete three of them. ments produced seventy-three African-American The final, and perhaps most important, fac- Ph.D.s during the academic years 1999–2000 to tor is the faculty’s commitment to students. The 2008–2009 (this counts U.S. citizens only). Nine department’s success with students from under- of these seventy-three, or 12.3 percent, graduated represented groups is not due to outsized efforts from the NC State mathematics department. And by a small number of faculty members. Indeed, NC State is not an enormous producer of math- the thirteen African-Americans who received their ematics Ph.D.s overall; in that period, it accounted Ph.D.s in the department during the academic for just 2 percent of the total number of Ph.D.s years 1999–2000 to 2010–2011 were spread among produced by Group I and II departments. NC State’s twelve different advisors. impressive record has continued, with a total of The department’s commitment to underrepre- four additional African-Americans receiving their sented students does not stop with the graduate Ph.D.s in the department in the 2009–2010 and program. The department stands out nationally 2010–2011 academic years. When it comes to as a predominantly white institution in which a female African-American Ph.D.s in mathematics, large number of African-Americans earn bachelor’s

MAY 2011 NOTICES OF THE AMS 715 degrees in mathematics. Alongside its Research Helminck was interviewed for an article in the Experiences for Undergraduates program, the de- Notices. Asked how the department managed to partment has started REU+, which is geared toward achieve so much, he replied: “You have to cre- students from historically black colleges and uni- ate a culture in which people believe this is the versities. At the postdoctoral level, the department right direction for the department so that there has spearheaded a new national program called is broad faculty participation. You start with a the Alliance for Building Faculty Diversity in the few people and you show that a program is suc- Mathematical Sciences, which offers postdoctoral cessful, then one by one you have faculty start to fellowships to new Ph.D.s from traditionally under- participate…They can totally change their minds.” represented groups. Fellows will typically spend two years in one of the alliance institutions and Department head: Loek Helminck one year in an NSF-funded mathematics institute. Website: http://www.math.ncsu.edu After NC State was chosen for the AMS Ex- emplary Program Award, department head Loek

2011 Award for an Exemplary Program or Achievement in a Mathematics Department

The Award for an Exemplary Program or Achieve- Citation ment in a Mathematics Department was estab- The American Mathematical Society is pleased lished by the AMS Council in 2004 and was given to recognize the undergraduate Math Center at for the first time in 2006. The purpose is to rec- the University of Arizona with the 2011 Award ognize a department that has distinguished itself for an Exemplary Program or Achievement by a by undertaking an unusual or particularly effective Mathematics Department. The Math Center is a program of value to the mathematics community, national leader in the effort to recruit, mentor, and internally or in relation to the rest of society. graduate undergraduate math majors, especially Departments of mathematical sciences in North those students from backgrounds traditionally underrepresented in mathematics. Since 2004 the America that offer at least a bachelor’s degree in Math Center has mathematical sciences are eligible. Through the • increased the total number of majors by 69 generous support of an anonymous donor, the percent, from 281 to 474, award carries a cash prize of US$5,000. • increased the total number of female majors The award is presented by the AMS Council act- by 72 percent, from 102 to 175, ing on the recommendation of a selection commit- • increased the total number of majors from tee. For the 2011 award, the members of the selec- underrepresented minority groups by 125 per- tion committee were: Carlos Castillo-Chavez, Amy cent, from 48 to 108, with the result that about Cohen (chair), William Jacob, and Philip Kutzko. 25 percent of math majors at the University of The previous recipients of the award are Harvey Arizona come from these groups. Mudd College (2006), the University of California, This impressive achievement comes about not as Los Angeles (2007), the University of Iowa (2008), a result of any substantial change in the structure the University of Nebraska, Lincoln (2009), and of the math major but rather by the tireless recruit- ment activities of the Center, the range of activities North Carolina State University (2010). and opportunities provided to UA math majors, The recipient of the 2011 Award for an Exem- and the collegial and welcoming environment plary Program or Achievement in a Mathematics created by the Center. Recruiting is done on a per- Math Center at the Univer- Department is the sonal basis. There is a yearly high school calculus sity of Arizona. What follows is the selection class visitation project in which a team consisting committee’s citation.

716 NOTICES OF THE AMS VOLUME 58, NUMBER 5 of a faculty member, a graduate student, and an undergraduate student visits AP calculus classes at About the Cover local high schools. There is an MAA-[Mathematical Wavelets in image compression Association of America] funded five-day calcu- lus workshop for incoming students enrolled in This month’s cover was inspired by the article calculus. And, perhaps most remarkably, there “Discrete wavelet transformations and under- is the personal effort of Professor William Vélez, graduate education”, by Catherine Bénéteau Associate Head for Undergraduate Affairs for the and Patrick Van Fleet. The February 2008 issue UA Math Department, who has, for the last fifteen of the Notices contained an article by David years, conducted a program of making twenty-min- Austin on the JPEG format, including at the ute individual appointments with every minority end a few remarks about the newer JPEG2000 student enrolled in calculus. Once a student be- specification, which is based on wavelets. This comes a math major, the Center offers a variety of month’s cover illustrates what the first step in programs, ranging from a substantial undergradu- a simple wavelet compression would be like, ate research program to a highly popular math club when applied to Austin’s cover for the 2008 to encourage and support the student’s progress issue. The effect is much like one of the figures toward success. Finally, a concerted effort is made in the article by Bénéteau and Van Fleet. to ensure that the student is informed of the In making the cover, we considered several full range of opportunities available in academe, sophisticated options, but in the end chose to government, and industry to someone with apply Haar wavelets for a simple visual effect. computational skills. Indeed, since 2007 the pro- Wavelets are complicated, and it would have gram has broadened its scope to target students been almost impossible to make a single cover in other fields who might be interested in a double image that showed clearly something more major, thus increasing the fraction of double ma- subtle. There is no natural way to interpret jors from 30 percent to 40 percent over the last differences of colors graphically. Magnitudes three years. The numbers show that this program in the difference images have been shifted and is succeeding: over the last two years, about a magnified in order to make the process more quarter of UA math majors have gone on to gradu- visible, and this has introduced some appar- ate programs, and almost 20 percent have gone ently random noise. into middle and high school teaching. As further Although in the end we didn’t use anything evidence of this success, the May 2010 outstand- fancy, we found the book Ripples in Mathemat- ing undergraduate researcher and the December ics, listed in the Bénéteau and Van Fleet article, 2010 outstanding graduating senior in the College as well as the article “Factoring wavelet trans- of Science were both math majors. forms into lifting steps” by Ingrid Daubechies The small numbers of women and minorities and Wim Sweldens (Journal of Fourier Analysis at all levels in our profession, together with an and Applications, 1998), to be valuable guides increasing alienation of all U.S. students from the to the lifting algorithm. mathematical sciences, is well documented and is cause for concern both on moral and on practical —Bill Casselman grounds. In that context, the Math Center at the Graphics Editor University of Arizona stands out both as an ex- ([email protected]) ample of what can be done and as a model of what must be done, the very definition of an exemplary program.

MAY 2011 NOTICES OF THE AMS 717 Arizona’s Math Center Wins AMS Award

Allyn Jackson

Just take one more math course: That’s what Wil- about a calculus problem… I told her liam Velez tells as many students as he can. He this happened all the time. doesn’t say this only to those who might major —Jonathan Cain, mathematics major, in mathematics. And he doesn’t say it only to class of 2011 students he meets in person. Velez, a professor of mathematics and director of the University of In terms of space and budget, the Math Center Arizona’s Math Center, sends out email messages is nothing glorious. It’s a big room on the second to, for example, all students who got an A or B in floor of the mathematics building, outfitted with precalculus in the previous semester, maybe 150 blackboards, several tables, and plenty of chairs. students in all. He congratulates them on their There is a small office for the coordinator of the success, explains why mathematics is useful in center, Laurie Varecka, a former graduate student many professions, and repeats the mantra: Just in the department who has taught beginning take one more math course. He doesn’t get many courses there and used to coordinate the teaching immediate responses. “But four months later,” he assistant program. Asked about how the center is says, “I’ll get a message from one of the students funded, department head William McCallum says saying, ‘I enjoyed that math course, can I come with a chuckle, “It doesn’t really have any funding.” and talk to you?’” The center has no outside grants; it is supported This high-tech yet personalized recruitment entirely by the mathematics department budget, of students has become the hallmark of the Math mainly through dedicated staff and faculty time. Center. As the focal point for the undergraduate It has a small pot of money for things like pizza mathematics major at Arizona, the center has for students after talks sponsored by MathCats, grown organically as an expression of how the the club for undergraduate mathematics majors. mathematics department sees its mission within The Math Center was started around twenty the university. When the center gets students to years ago by an adjunct faculty member, Robin Steinberg (now at Pima Community College), who take more mathematics, it can count on excellent was given the task of looking after the depart- instruction delivered by a faculty committed to un- ment’s majors. A few years later, McCallum became dergraduate education. The Math Center’s impact director of the center. “I had been making noises in is reflected in an arresting statistic: the number the department about how we needed to do some- of mathematics majors at Arizona has more than thing much more systematic and organized for the doubled since 2004. For its dedication to students math majors, that we should really create a home and its outstanding success in increasing the for them,” McCallum said. “And I was rewarded number of mathematics majors at the University by being given the job of doing that!” He began to of Arizona, the Math Center was awarded the 2011 develop the center as a place where mathematics AMS Award for an Exemplary Program or Achieve- majors could drop in to ask questions and get ment in a Mathematics Department. advice. The idea was to supplement the guidance Tables, Chairs, and a Killer Database of faculty advisors—who see advisees perhaps once a semester—by providing contact on a day- We usually gather in the Math Center to-day basis and help with things like navigating to do homework in groups. My musi- the university bureaucracy. The center became a cian girlfriend came there one time and forum where students could gather and talk to was shocked to find a group of real each other or to professors who passed through. It analysis students (myself included) built a small library of mathematics books for stu- yelling, screaming, and throwing things dents to peruse, and it began holding events, such as celebrations of Mathematics Awareness Month. Allyn Jackson is senior writer and deputy editor of the In August 2003 Velez was appointed Associate Notices. Her email address is [email protected]. Head for Undergraduate Programs and thereby

718 NOTICES OF THE AMS VOLUME 58, NUMBER 5 director of the Math Center. He brought with him his long experience and successful track record in recruiting and mentoring mathematics students, particularly those from minority groups that are underrepresented in the field. The center director- ship gave him a platform from which to greatly expand his recruitment work—and it gave him the time to do it: With release time from the depart- ment, he teaches only one course per year. Around the same time that he started as director, the de- partment had decided to create a database to get a better picture of the population of math majors— the number of minority students, the number of Photo courtesy of the Dept. Mathematics, University of Arizona. women students, the number of freshmen, how many and which courses they took, what grades Associate professor and faculty advisor they received, and so forth. The Math Center built Ted Laetsch conversing with a group of this database, which has become central to Velez’s undergraduate math majors. recruitment efforts. Much of the information was available within the mathematics department, but department puts on undergraduate education. By at some point the Math Center was also able to tap early 2011 the number of majors had more than into an extensive data system run centrally by the doubled, to just over 600. The number of female university. “We can mine the university data to an majors also doubled, from about 100 to about extent unthinkable before,” Velez said. 200. But perhaps most impressive of all is the As an example of what he is able to do with the increase in the number of majors from underrep- database, he described a project he carried out in resented minority groups: In 2004 there were 48 December 2010. He went through the database such majors, and by early 2011 the number had to identify students who had gotten As or Bs in risen to 125, an astounding 160 percent increase. second-semester calculus. He then made a list of Today about 20 percent of math majors at the which ones had not subsequently enrolled in a University of Arizona come from these groups. math course. He sent out email messages to each The department also has about 600 math minors. of those students, encouraging them to continue These results came about not through changes in taking math and suggesting what courses they the major program but rather through the Math might take next. Projects such as this—zeroing Center’s systematic recruitment, which sends the in on a particular set of students and crafting an message that mathematics welcomes many kinds email suited to their situation—are of course very of people with diverse interests and goals. time-consuming. Velez is setting them up to run automatically in the future. Inviting Students into Mathematics One much larger such mailing has been auto- The Math Center provides support to all mated and has run for the past few years. For this undergraduate math majors at the UA. mailing, the Math Center obtains the names and From the moment I set foot on campus email addresses of all students who have been ac- during orientation to my junior year cepted to the University of Arizona, about 4,000 in college, I have always felt the pres- or 5,000 students. In March each year it sends ence of the mathematics community messages to these individuals suggesting that they on campus. study mathematics and explaining the value of the mathematics major. The messages include a link to —Lynette Guzman, mathematics major, the “Math Moments” posters on the AMS website. class of 2012 In addition, for the past couple of years, Velez has Born in Tucson to parents who were natives of added a “hook” to the message: He offers to send a Mexico, Velez received his degrees at the Uni- document called “Resources for Calculus Students” versity of Arizona. When he joined the Arizona that he wrote a few years back. Originally intended mathematics department as a faculty member for minority students, the document is now given in 1977, he was the only Chicano—and he is still to all calculus students at Arizona. This hook does the only one (though there are now two Hispanic not elicit a great number of replies, but enough faculty members). In the late 1980s he started to students have responded that Velez is convinced notice the small number of mathematics majors his message is being read. coming from minority groups underrepresented in A few statistics bear out the success of the mathematics—there was perhaps one such student Math Center’s approach. In 2004 the department graduating every other year. And this was in Ari- had 281 mathematics majors—already a respect- zona, a state with a large population of Chicanos, able number that points to the emphasis the Hispanics, and Native Americans. Velez began

MAY 2011 NOTICES OF THE AMS 719 departments don’t understand how mathematics has invaded all of the sciences,” he says. “This opens opportunities for math majors to go to graduate school in other areas… . Also, mathemati- cians don’t understand what students can do with a math major when they enter the workforce. This prevents mathematicians from being more aggres- sive in recruiting and advising students.’’ An active member and former president of SACNAS (Society for the Advancement of Chicanos and Native Americans in Science), Velez has lec- tured widely on undergraduate education, mentor- ing, and increasing diversity in mathematics and science. He has also written many articles on these

Photo courtesy of the Dept. Mathematics, University of Arizona. subjects, including several for the Notices (the most Jaron Gubernick, president of the under- recent was “Not business as usual’’, an Opinion col- graduate mathematics club MathCats, juggling umn in the May 2003 issue). He has received many at an event sponsored by the Math Center. honors for his work mentoring students, including the President’s Award for Excellence in Science, directly contacting students from these groups Mathematics and Engineering Mentoring in 1997. and encouraging them to take mathematics. For A Committed Department the last fifteen years he has made twenty-minute individual appointments with every minority stu- The Math Center builds our community dent enrolled in calculus. and makes people come together… . As Velez takes the issue of underrepresented students, we look past the competition minorities very personally. “I am part of the Chi- we have with each other and realize cano community here,” he says. “I interact with that we are all there for the same rea- this community a lot. It’s impressive, the clever- son and that we can realize our goals ness of these people to survive. If we could tap together. that cleverness and entice children to come into mathematics, we would see wonderful mathemati- — Jonathan Cain, mathematics major, cians.” At the same time, this community is belea- class of 2011 guered by social problems such as drugs, violence, Last fall Math Center coordinator Laurie Varecka and poor schools. To mathematicians who might was making a course substitution for a math major be moved to help such students, these problems who was to graduate at the end of the year, and can seem like insurmountable obstacles. But stu- she decided to check his completed degree require- dents who make it to the university have passed ments. She noticed that he was missing one credit the first hurdle, Velez says. What they need is ex- in one area. “That would have been enough to pre- plicit encouragement—an “invitation”, as he puts vent him from graduating,” she says. She quickly it—to come into mathematics and to learn that it got in touch with him. As it turned out, he was is a fulfilling and valuable area to study. He took doing his independent study with a departmental on the directorship of the Math Center as a way to faculty advisor, who was very willing to be flexible institutionalize his concern for minority students. and increase the number of hours for the course “When I retire, I don’t want concern for minority to help the student graduate on time. “That’s the students to retire with me,” he says. kind of thing that makes me happy, when we are In fact, Velez’s brand of “aggressive advising” able to catch things like that and help students,” works for all students, not just those from under- she says. Such mindfulness shows students the represented minorities, as is evident from the 50 Math Center is there for them and will go the extra percent increase in the total number of math ma- mile to help them succeed. “A lot of the work [of jors one year after he became director of the Math the Math Center] is just keeping track of the stu- Center. He believes mathematics faculty need to dents,” McCallum says. “Laurie sends out emails be much more proactive in conveying to students with events they might be interested in. When the the excitement of mathematics and the career op- times of the year arrive when students are sup- portunities the major opens up. “How do students posed to register for classes, she makes sure that know there is a math major if we don’t tell them?” they meet their advisors. A lot of it is just paying he asks. In addition, he notes, the prevailing attention and making them feel that someone is attitude in many departments is that the mathemat- interested in their welfare.” ics major has one goal only: to prepare students This attention starts early, with an orientation for graduate school in mathematics. Velez thinks session for freshman and transfer math majors, that that attitude must change. “Mathematics held the Saturday before classes begin. At the

720 NOTICES OF THE AMS VOLUME 58, NUMBER 5 session, students learn about the math major and development. Some faculty members—including the options within it and also find out about re- McCallum, Velez, and Deborah Hughes Hallett— sources available through the Math Center. Over have made significant contributions to undergrad- lunch the students can have informal conversa- uate education at the national level. McCallum was tions with McCallum, Varecka, Velez, and the other on the AMS Committee on Education from 2002 faculty members who attend. As students progress through 2008 and served as chair for five years; through the major, they benefit from a department Hughes Hallett also served on that committee from in which attention to undergraduate education is 2008 through 2010. the norm. They also have many opportunities to The department also has a strong commitment work with department faculty on “research expe- to improving precollege mathematics educa- rience” projects, for which research assistantship tion. This shows in small ways, such as visits by support is available. In fact, Velez says that there department faculty to high school classrooms are more faculty willing to do research with under- in Tucson, and in much larger and more formal graduates than there are undergraduates wishing structures, such as the Institute for Mathematics to do research. Many math majors participate in and Education. Funded primarily by the univer- research experience programs in other disciplines, sity, with additional support from the NSF and such as biology, chemistry, and geosciences, where private foundations, the institute was started by their mathematical skills are very useful. In addi- McCallum in 2006; the current director is faculty tion, students can count on help from the Math member Joceline Lega. It sponsors a variety of Center in finding summer internships and other local, national, and international projects designed opportunities to gain professional experience. to promote collaborations that aim to improve How does the department inspire in its faculty mathematics education, mainly at the precollege such devotion to students? As department head, level. The department’s Center for Recruitment McCallum has been asked this question, particu- and Retention of Mathematics Teachers recruits larly during site visits for the department’s two undergraduates into the education option of the VIGRE grants from the National Science Founda- mathematics major. It also supports beginning tion. “I don’t think anybody in the department teachers by pairing them with mentors who are thinks that anything special is going on to make senior teachers and by sending undergraduates that happen,” he said. “It’s just part of the culture.” out into the schools to work as tutors. When he visits other mathematics departments, he The educational activity in the department, realizes that often there is much more distance paired with its strong research profile, make for a between faculty and students and much less unique atmosphere that is especially inviting to in- attention paid to undergraduates. “And I think, dividuals interested in both teaching and research. gee, how did that happen?” he says. The Arizona “There is no division really,” McCallum says. “Some department had an exceptional dedication to people are focusing their energies more on their undergraduates when McCallum first joined the research, obviously, and some people are focusing faculty in 1987. “A culture like that, once estab- their energies more on educational activities. But lished, is self-maintaining because it attracts fac- you can move back and forth between those two, ulty who like that culture,” he remarks. “It’s not and you don’t get labeled particularly that you are that every single faculty member in the department one or the other. That appeals to me personally, is totally devoted to undergraduates, and that is because that is what I’ve done in my career.” not necessary to have the right culture. You just In the middle of all of this activity stands the need enough.” Math Center, the linchpin of a vibrant and success- Nevertheless, there are some specific programs ful department. Much of the center’s success is due in the department that nurture that culture. One to Velez’s zeal for recruiting; Varecka’s thorough is a program of “teaching postdocs”—postdoctoral and thoughtful approach and the structure of the positions for people who have Ph.D.s in mathemat- center are also key. But a large part of its success is ics but who are primarily interested in teaching ca- the climate in the department. Velez notes that the reers. “They contribute tremendously to the life of Exemplary Program Award was given to the Math the department, and specifically to the educational Center, not to him personally. “It is the resources environment for the undergraduates,” McCallum the department has invested in the major program says. Another program, called Undergraduate that has allowed me to do the things I have done,” Teaching Assistantships (UTA), gives math majors he says. “My job is to bring the students in the who are interested in teaching careers opportuni- door. If I didn’t have the support of gifted teachers ties to work with faculty on instructional and cur- on the faculty, we could not keep these students ricular issues and perhaps even to teach a course. as majors. I am part of an unusual department.” “It’s sort of the analogue for teaching of a research experience,” McCallum explains. The UTA program dovetails nicely with the department’s long tradition of devoting thought to the undergraduate curriculum and course

MAY 2011 NOTICES OF THE AMS 721 Do the Math

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See our E-Books at press.princeton.edu American Mathematical Society—Contributions

Dear Friends and Colleagues,

During 2010 your generous contributions helped the Society and our profession in many ways. Thank you for your support.

In 2010, the Epsilon Fund, the endowment whose income supports the Young Scholars program, stands at a level where it can annually provide grants to support ten separate programs that touch ap- proximately 600 talented and highly motivated mathematics students every year. We are very grateful for the numerous individual contributions indicated in the following pages. We continue to place a very high priority on supporting the programs that bring mathematically talented high school students together and introduce them to mathematical research.

The Centennial Fellowships continue to play a key role in supporting outstanding young mathemati- cians, from three to twelve years beyond the doctorate. These fellowships are funded by contributions from mathematicians throughout the world.

Your contributions to the General Fund support many aspects of the Society’s mission, including pro- grams for mathematicians in the developing world, public awareness, advocacy for the profession, and support of mathematicians just beginning their careers in research.

Your generosity allows the Society to carry out all these programs and demonstrates that the math- ematics community cares deeply about our profession. Thank you.

Donald E. McClure Executive Director

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].

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

MAY 2011 NOTICES OF THE AMS 723 AMS Contributions

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 : Maurice Auslander - Anonymous Charles A Cole, Jr, by Nancy Cole Bluford Charles A Cole, Jr, by Margo Halsted Charles A Cole, Jr, by Phoebe Olcott Richard J Maher, PhD by Patrick Maher Gifts were made in honor of the following: J E Marsden by Stuart S. Antman Dr George Andrews by Kenneth I. Gross Vincent O McBrien by Joseph W. Paciorek Sue Caplan by Lisa Wade Professor Irving Reiner by Irma M. Reiner Gloria Cook by Lisa Wade Arnold Ross by Manuel P. Berriozabal the recognition Marriott received from INFORMS as a Franz Alice T Schafer by Richard D. Schafer Edelman Award finalist by Marriott International Richard Schelp by Richard J. Fleming Leo Schneider by Susan Schwartz Wildstrom Sanford Segal by Dona Davidson Frederick Bodo Strauss by Delmar L. Boyer Kathryn B Toll - Anonymous Louis W Tordella by Charles A. Cole

Contributors to the AMS During 2010 * 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 ε Murray Marvin Stokely III Matching gift from Oracle ε* Rupert D. Boswell Jr. ε* Albert W. Currier Matching gift from John Corporation ε* Aldridge K. Bousfield * Charles W. Curtis ASSOCIATES Wiley & Sons, Inc. Karen Vogtmann and John * Delmar L. Boyer ε* Everett C. Dade (Gifts of $5,000 and above) * Alexander H. Weintraub Smillie * Louis R. Bragg ε* David B. Damiano Alan & Katherine Stroock Fund ε* Susan Schwartz Wildstrom ε* Justin Clement Walker ε* David M. Bressoud ε* Robert J. Daverman ε* Adrian David Banner Anonymous (5) * Steven H. Weintraub ε W. Dale Brownawell * Ronald W. DeGray * Stephen S. Bullock * Morris Jack DeLeon ε* William Craig * Richard E. Williamson ε ε Robert Bumcrot * Guy M. De Primo ε Savage Charitable Fund of SPONSORS * Jay A. Wood ε ε ε Tsu C. Wu ε* James E. Burke ε Michael E. Detlefsen the Community Foundation (Gifts of $500 and above) of Broward Anonymous (3) ε* Donald L. Burkholder ε* Robert L. Devaney A&J Brodkey Philanthropic * Robert and Maria W Steinberg ε* Thomas R. Butts ε* Charles R. Diminnie Fund Anonymous (3) PATRONS ε* Robert Calderbank * James A. Donaldson M. Salah Baouendi and Linda ε Andy Carter and Diane L Her- ε* Loyal Durand (Gifts of $100 and above) ASSOCIATES Preiss Rothschild rmann ε* Peter L. Duren ε* Henrik Bresinsky ε William Abikoff ε* Jairo A. Cavalcante ε John W. Duskin Jr. (Gifts of $1,000 and above) Nancy Cole Bluford ε Yousef Alavi ε* Nathaniel Chafee * Elmer Eisner * John S. Alin ε* Joan S. Birman ε Earl F. Ecklund Jr. ε Jagdish Chandra ε Gérard G. Emch ε Felix E. Browder * Stephen P. Gill Amna Sobyan Al-Jihany ε Chao-Ping Chang ε* Jessie Ann Engle Robert L. Bryant ε* Anne H. Allen ε ε* Kenneth I. Gross ε Ruth M. Charney ε Mats Engwall Karl E. Byleen Frank W. Anderson ε* Bill Hassinger Jr. ε* Concordia C. Chen * John C. Fenley Roger Chalkley * George E. Andrews Richard V. Kadison ε ε* Richard C. Churchill ε* Aurino Ribeiro Filho Richard A. Cleveland ε* Kenneth I. Appel * Stuart Citrin * Gerald B. Folland ε Joseph Kist ε ε * John B. Conway ε* Richard A. Askey ε Robert A. Clark ε* Paul Fong ε* Maria Margaret Klawe ε* John H. Ewing ε Walter O. Augenstein ε Wil Clarke ε* Richard L. Gantos ε* Robert V. Kohn ε Ronald L. and Fan Chung Theodore J. Barth ε John Coffey ε* Anthony A. Gioia ε* Gary J. Kurowski Graham ε Jürgen O. Batt ε* Daniel I. A. Cohen ε* Milton Alfred Glass ε David B. Massey ε George F. Haddix * Frances B. Bauer ε Charles A. Cole ε* Richard P. Goblirsch ε* James W. Maxwell * Carl E. Harrell ε Horst Behncke ε* Paul Dana Cole ε* Martin Golubitsky and Bar- M. Susan Montgomery ε Denis A. Higgs ε* Steven R. Bell ε* Peter S. Constantin bara Lee Keyfitz * Walter V. Petryshyn * John M. Hosack ε ε* Alan E. Berger ε* Arthur H. Copeland Jr. ε Richard J. Greechie Ivan P. Polonsky * Phyllis & Donald Kahn Philan- ε ε* Manuel P. Berriozabal ε Douglas L. Costa ε Peter H. Greene thropic Fund ε* Richard M. Schoen ε George Berzsenyi * Louis J. Cote * Wilfred Martin Greenlee ε* George F. Leger ε* Abdulalim A. Shabazz ε* Marilyn S. Bickel ε* Lenore J. Cowen & William * Richard K. Greicar ε Marriott International * Keith Paul Smith ε* Richard L. Bishop Bogstad * Seymour Haber ε Donald E. McClure ε Louis Solomon ε Terrence Paul Bisson ε * Michael G. Crandall ε* Peter Hagis Jr. ε Vaughan R. Pratt ε* Joel H. Spencer ε* Peter B. Bjorklund Annalisa Crannell ε Richard M. Hain ε* Samuel Murray Rankin III * Ronald J. & Sharon M. Stern ε* S. Elwood Bohn ε Henry Crapo Heini Halberstam * Norton Starr ε* Margaret W. Taft ε Leonard John Borucki ε* Ernest S. Croot III * C. P. Harakis

724 NOTICES OF THE AMS VOLUME 58 NUMBER 5 AMS Contributions

ε* David Harbater Yasuhiro Morita ε* Howard G. Tucker ε Armen Bagdasaryan ε* Barry W. Brunson ε Mikihiro Hayashi ε* Joseph R. Morris ε* Jean E. de Valpine ε Paul M. Bailyn Billy F. Bryant ε* William S. Heck ε* Robert A. Morris ε* R. Lee Van de Wetering ε* Joni E. Baker ε Clifford M. Bryant Jr. ε Patricia Hersh ε* Thomas W. Mullikin ε David A. Vogan Jr. ε* Kirby A. Baker ε Nicholas P. Buchdahl ε* Gerald A. Heuer ε* Albert A. Mullin ε* Dan-Virgil Voiculescu ε Robert S. Baker ε* Joseph T. Buckley * Gloria C. Hewitt ε* Bruno L. Nachtergaele ε* David B. Wales ε* William R. Ballard ε Daniel Buehler ε Theodore W. Hildebrandt ε Kuniaki Nakamitsu ε Homer F. Walker * Carlo Bardaro ε Ioan Sebastian Buhai ε William R. Hintzman ε* Nobuo Nobusawa ε Frederick Walters ε* Julio Edgardo Barety * Daniel Willis Bump ε* Samuel S. Holland Jr. ε Sunsook Noh ε* Hans Ulrich Walther Bruce H. Barnes ε Lutz Bungart ε* Raymond T. Hoobler M. Frank Norman ε* Evelyn K. Wantland Britt William Barrett ε* Adam Buraczewski * Henry C. Howard ε* Hajimu Ogawa ε Roger P. Ware ε* Jose Barros-Neto ε Almut Burchard ε* Tiao-Tiao Hsu ε* Takashi Ono * Frank W. Warner III ε David J. Barsky ε R. B. Burckel ε* James G. Huard ε Zbigniew Opalka ε* William Edwun Warren ε* Karl F. Barth * Krzysztof Burdzy * Joseph A. Hughes ε Donald S. & Shari Ornstein ε* Cary H. Webb ε* Alexander Barvinok ε Anne M. Burns ε* George W. Hukle * Robert Osserman * Lloyd R. Welch ε* Hyman Bass ε* Ralph Stevens Butcher ε* Craig L. Huneke ε* Scott C. Otermat Ellen Westheimer Patricia Bauman ε* Robert Lawrence Byrom ε* Walker E. Hunt ε* Joseph W. Paciorek James V. Whittaker ε* J. Thomas Beale ε* Luciano Caccianotti Sufian Y. Husseini * Jingyal Pak Brian D. Wick ε* Homer F. Bechtell ε* Rotraut C. Cahill ε* Franklin T. Iha Hiram Paley ε* Clinton Curtis Williams ε* Edward Beckenstein M. Carme Calderer Yulij Sergeevich Ilyashenko * Henry J. Passerini Ruth J. Williams and J William ε* David S. Becker ε James J. Callahan ε* I. Martin Isaacs ε Charles M. Patton Helton * Eric D. Bedford ε* James C. Cantrell * William H. Jaco ε* Alexander Perlin ε George Washington Wimbush ε* John A. Beekman ε Sylvain E. Cappell Hervé M. Jacquet ε* Mollie Pflumm ε* Scott A. Wolpert ε James C. Beidleman ε* Corrado Cardarelli Robert R. Jensen ε Gilles Pisier ε* Alan C. Woods ε* Wolfgang Bell IV ε* Jon F. Carlson Richard P. Jerrard ε Vera S. Pless ε* Bostwick F. Wyman ε David P. Bellamy ε* David W. Carter ε* Henry Price Kagey ε Dirk Arnold Plummer PE ε* Tatsuhiko Yagasaki Richard G. Belshoff ε Joao Bosco Carvalho ε* Daniel S. Kahn John William Poduska Sr. ε* Masayuki Yamasaki Katalin A. Bencsáth ε* James R. Case ε Joji Kajiwara ε Aleksey Popelyukhin ε* Michael Yanowitch ε Julius S. Bendat ε* Erio A. Castagnoli ε* Herbert M. Kamowitz * James V. Ralston ε Ann Yasuhara ε James W. Benham ε German Tellez Castillo ε* Julian R. Karelitz ε* Ravi K. Ramakrishna ε Sam Wayne Young ε* Carlos Benítez ε Thomas E. Cecil ε Herbert E. Kasube ε* M. M. Rao Michel M. Zarka * Georgia Benkart ε* Gulbank D. Chakerian ε* Victor J. Katz ε Wayne Mark Raskind ε Thomas Zaslavsky ε Sterling K. Berberian ε Richard A. Champion Jr. ε* Harry Kesten ε Michael Reid ε Tien Yu Zhao ε* George M. Bergman ε Weita Chang ε* Allan M. Kirch William H. Reid Anonymous (42) Salvatore D. Bernardi ε Paul Jackson Channell ε* Joseph P. Kirley ε* Bruce Reznick ε Christopher Bernhardt ε Jeff Cheeger ε* Julia F. Knight ε* Tong-Shieng Rhai FRIENDS ε Swanhild Bernstein ε* Kwan-Wei Chen ε* George H. Knightly ε Barbara Slyder Rice ε* James S. Bethel ε Herman Chernoff (Gifts of less than $100) ε Yasuo Komori ε Norman J. Richert ε* Gerhard Betsch ε* Theodore S. Chihara ε Heinz J. König ε* Marc A. Rieffel ε* Ian M. Aberbach ε* Nicholas J. Bezak * Choong Yun Cho ε* Antoni A. Kosinski ε* James B. Robertson ε* Clarence M. Ablow ε* Gautam Bharali ε Jaigyoung Choe ε Zdislav V. Kovárˇík ε Charles D. Robinson ε* William P. Abrams ε Daniel C. Biles ε Junesang Choi ε* Ralph M. Krause ε* Vijay K. Rohatgi ε* Colin C. Adams ε* Louis J. Billera ε* Jal R. Choksi Hsu-Tung Ku ε Mario Rosati ε* William W. Adams * Martin Billik ε* Demetrios Christodoulou ε* Nosup Kwak ε* Robert A. Rosenbaum ε* Winfred P. Adams ε Katalin Bimbó ε Lung Ock Chung Michael T. Lacey ε* Sharon Cutler Ross ε* Jeffrey D. Adler ε David Samuel Bindel ε* William A. Clee * Jeanne LaDuke ε Hugo Rossi ε* T. M. G. Ahsanullah ε* Jerome Blackman ε Philip A. Cobb ε* Joseph A. Langsam * Richard L. Roth ε* Tadashi Aikou David E. Blair ε* James A. Cochran ε* Walter R. Lawson ε Christel Rotthaus ε* Michael I. Aissen ε J. A. Rod Blais * John C. Cock * Peter D. Lax * Herman Rubin ε* Ethan J. Akin ε Albert A. Blank ε* James Wesley Cogdell Earl E. Lazerson ε* Bernard D. Rudin ε* Peter Albers ε* John D. Blanton ε* Amy Cohen ε Robert N. Leggett Jr. ε* David Ryeburn ε Daniel Alexander ε Robert J. Blattner ε* Frederick R. Cohen ε* Joan R. Leitzel ε G. Thomas Sallee * Kenneth S. Alexander ε* David S. Bloom ε* Donald L. Cohn ε* Manoel Jose M. S. Lemos ε Daniel Saltz ε* Roger K. Alexander Theodore S. Bolis ε* George Cole ε* H. W. Lenstra * Paul T. Schaefer ε Stephanie B. Alexander ε* Francis Bonahon ε Vincent E. Coll Jr. ε D. J. Lewis Richard D. Schafer ε* Gerald L. Alexanderson ε David B. Bond ε* Daniel Comenetz ε* H. L. Lewis * Mark Schroder ε* M. Kursheed Ali ε* Joseph E. Bonin ε Jack Frederick Conn ε* William James Lewis * Cedric F. Schubert ε Krishnaswami Alladi ε William M. Boothby ε* Frank F. Connor ε* Robert J. Lipshutz * Stuart A. Seligson ε Alexander Anthony Am- ε D. David Bourland III * Thomas A. Cootz ε* Walter L. Lok ε* George H. Senge brioso ε* Ward D. Bouwsma ε* Heinz O. Cordes Warren S. Loud ε* Norman E. Sexauer ε* Vrege Jolfai Amirkahanian ε Paul J. Bowron ε Steve A. Corning * Albert T. Lundell ε* Freydoon Shahidi ε Fredric Davis Ancel ε Mike Boyle * Thomas Carney Corrigan ε* Russell D. Lyons ε* Yuzi Shimizuike ε Donald W. Anderson ε Sylvia T. Bozeman ε* James P. Cossey Patrick Maher ε Kenichi Shiraiwa ε* Joel H. Anderson ε* John S. Bradley ε Matthys Coster ε Mark Mahowald ε* Stanley R. Shubsda Jr. ε* Michael T. Anderson ε* Richard C. Bradley * Ovidiu Costin ε Michael Makkai ε Stephen Kurt Shultz ε* Susan Andima ε* Steven B. Bradlow ε* Malcolm A. Coulter * J. J. Malone ε* Allan J. Silberger ε* Peter P. Andre ε* Alberto Branciari Lawrence J. Crone ε * Joseph S. Mamelak ε David B. Singmaster ε* Philip M. Anselone ε Fred Brauer ε* Donald L. Curlovic Joseph F. Manogue ε* John R. Smart ε* Peter H. Anspach ε* George U. Brauer ε Philip C. Curtis Jr. ε* Edward Manougian ε* Colin Smith * Stuart S. Antman John C. Breckenridge ε* James N. Damon ε* Eugene A. Margerum ε* Wilbur L. Smith ε Enrico Arbarello Stewart Brekke ε* Martin P. Dana ε* Greg Marks ε* Stephen E. Spielberg ε* Myla M. Archer ε David W. Bressler Donald A. Darling ε* Thomas J. Marlowe Jr. ε* Olaf P. Stackelberg ε* Richard F. Arenstorf ε Carl M. Brezausek George Dassios ε Wallace S. Martindale III ε* Ivar Stakgold ε Martin Argerami ε James G. Bridgeman ε* Boris A. Datskovsky ε Howard Masur ε Richard P. Stanley * Martin Arkowitz ε* Joseph Edward Brierly ε Dona Davidson * Jacob R. Matijevic * Clarence F. Stephens Joseph Robert Armstead * Judith E. Broadwin ε Chandler Davis ε James P. McKeon ε Glenn H. Stevens ε* Thomas E. Armstrong ε* Jerald S. Brodkey * Donald M. Davis ε* T. G. McLaughlin ε* Lawrence D. Stone ε* Jonathan W. Aronson ε* Edgar H. Brown Jr. ε* Martin D. Davis ε* Robert C. McOwen ε* Richard W. Sullivan ε Kendall E. Atkinson ε Gordon E. Brown ε* Paul L. Davis Morris J. Meisner ε* Keith A. Taylor ε* Joel Avrin * Kenneth S. Brown ε* Jane M. Day ε* Richard C. Metzler ε* Edward C. Thoele ε Scott E. Axelrod ε* Lawrence G. Brown ε* Anthony T. Dean ε* Ernest A. Michael ε Erik G. F. Thomas ε Christine W. & Raymond G. ε Richard J. Brown ε Djairo G. De Figueiredo Gary R. Miller ε* Robert J. Thompson Ayoub ε Richard K. Brown ε Percy Alec Deift Catherine Ann Miner ε* John A. Thorpe ε* Sebastian Baader ε* Andrew M. Bruckner ε Frederik Michel Dekking ε Martin James Mohlenkamp ε John Torquato ε* Kiyoshi Baba ε* Paulo Brumatti ε* Aristide Deleanu * Cathleen S. Morawetz ε Ralph P. Tucci ε* Richard J. Bagby ε Robert R. Bruner ε* Peter Der

MAY 2011 NOTICES OF THE AMS 725 AMS Contributions

ε* John E. Derwent ε Skip Garibaldi ε John J. Hirschfelder ε Nigel J. Kalton ε* Gerald M. Leibowitz * Dennis DeTurck * Howard Garland ε Ronald Hirshon Soji Kaneyuki ε* James I. Lepowsky Emeric Deutsch ε James George Marcel Gatheral ε* Friedrich E. P. Hirzebruch ε Eberhard Kaniuth ε* Steven C. Leth ε Raoul A. De Villiers ε Eberhard G. P. Gerlach ε* Peter David Hislop ε* Richard A. Kanner Edward L. Lever ε* Paul F. J. Dhooghe ε* Hillel H. Gershenson ε* Arthur M. Hobbs ε* Stanley Kaplan Bernard W. Levinger ε Beverly E. J. Diamond ε* Murray Gerstenhaber ε* Jonathan P. E. Hodgson ε* Luise-Charlotte Kappe ε* Michael David Levy Meighan Irene Dillon ε* Joseph L. Gerver ε* Helmut H. W. Hofer ε Martin Lewis Karel ε* George M. Lewis ε Gerald P. Dinneen ε D. Ghisa ε* Michael E. Hoffman ε Vladislav Kargin ε Roger T. Lewis ε* Dragomir Zˇ. Djokovic´ ε Peter Gibbs ε Detlev W. Hoffmann ε* Johan Karlsson ε* Frederick W. Leysieffer ε Heinz Deitrich Doebner ε Richard M. Gillette ε Charles S. Holmes ε Guido Karrer ε Liangpan Li ε* Boro Doering ε Adam Ginensky ε* Philip John Holmes ε* Brian J. Kasper Yanyan Li ε* Pierre E. Dolbeault Ross B. Gingrich ε* Roger H. Homer ε Martin D. Kassabov * Jaung Liang ε* James P. Donaly * Vladimir Gisin ε Jennifer L. Hopkins ε Shunji Kawamoto ε* Zvie Liberman ε* Jim Douglas Jr. * James G. Glimm ε Jim E. Hoste ε Kiran S. Kedlaya Stephen Lichtenbaum ε* Ronald G. Douglas ε J. D. Goddard ε Fredric T. Howard ε Edward L. Keenan ε* Elliott H. Lieb ε Karl Heinz Dovermann * Kazimierz A. Goebel ε Everett W. Howe ε* John F. Kellaher ε* Shen Lin ε* Alex J. Dragt ε Michel X. Goemans ε* J. S. Hsia ε Thomas W. Kellar ε* Peter A. Linnell ε* Ronald Lewis Drake ε Abraham Goetz ε* Pao-sheng Hsu ε* Edward L. Keller ε* Sally Irene Lipsey ε* Alexander N. Dranishnikov ε* Valentina Gogovska Robert Hubata ε* Wayne G. Kellner ε William G. Lister ε* Arthur A. Drisko ε* Robert Gold ε Archibald Perrin Hudgins ε* John B. Kelly ε Andrew C-F Liu ε* Bruce K. Driver ε Seth I. Goldberg ε* Denise Huet ε Stan Kelly-Bootle ε* Ming Chit Liu * Thomas L. Drucker Dorian Goldfeld ε* George A. Hufford ε Daniel C. Kemp ε* Tsai-Sheng Liu ε James S. Dukelow Jr. ε* William Mark Goldman ε* Anne Hughes ε Efim Khalimsky * George W. Lofquist ε Steve N. Dulaney ε* Daniel A. Goldston ε* Mark E. Huibregtse ε* Dmitry Khavinson ε* Charles J. Lombardo ε Stephen C. Dumars ε* Martin Golubitsky Gustavus E. Huige Andrei Khruzin * John M. Long ε* William Dart Dunbar Jr. ε* José Luis Gómez Pardo ε* Birge K. Huisgen-Zimmer- ε Michael K. H. Kiessling ε* William C. Lordan * Kanat Durgun ε Xianghong Gong mann Henry H. Kim * Michael P. Loss ε Timothy R. Eaton ε Lidia Gonzalez ε* James E. Humphreys Tatsuo Kimura ε László Lovász ε* Patrick Barry Eberlein ε* Kenneth R. Goodearl ε* Thomas W. Hungerford * Wilfred M. Kincaid ε* Sylvia Chin-Pi Lu ε* Allan L. Edmonds ε* Roe W. Goodman ε* Karen C. Hunt ε* Brendan King ε Tsu-Ming Lu ε* William I. Eggers ε Basil Gordon * Beryl E. Hunte ε Alexander A. Kirillov Sr. ε* Jonathan D. Lubin ε* Gertrude Ehrlich ε Carolyn S. Gordon ε James F. Hurley ε Ellen E. Kirkman ε R. Duncan Luce ε Sylvan H. Eisman ε* Yasuhiro Goto ε* Michael G. Hurley Paul O. Kirley ε Sorin Lugojan ε G. Griffith Elder ε* Claude Goutier ε* Taqdir Husain ε* Jan Kisyn´ski ε* Norman Y. Luther ε* Joanne Elliott ε* David J. Grabiner Joan P. Hutchinson ε Phyllis M. Kittel Zinaida A. Lykova ε* Steven P. Ellis ε* Sidney W. Graham Francesco Iachello ε* Peter H. Kleban ε Gregory D. Lyng ε* Richard S. Elman ε* Kevin A. Grasse Masao Igarashi Benjamin G. Klein ε Michael C. Mackey ε Hans P. Engler ε* Larry K. Graves ε* Tom Ilmanen ε* Israel Kleiner ε Manohar L. Madan ε* Philip G. Engstrom ε* James A. Green ε Ettore Ferrari Infante ε Stanislav V. Klimenko ε James Joseph Madden ε Kumar Eswaran ε William L. Green ε Hiroshi Inoue ε* Marvin I. Knopp ε* Adolf G. Mader ε* Edward R. Fadell ε* Curtis Greene ε* Arnold J. Insel ε K. R. K. Knorr * Mehran Mahdavi Barbara T. Faires ε* Frederick P. Greenleaf ε* Lynne Kamstra Ipina ε Hai-Ping Ko ε* Joseph Malkevitch ε Carl Faith * Stanley J. Greif * Ron Irving ε* Tsuyoshi Kobayashi ε Salvador Malo ε Bruno Farina ε* Phillip A. Griffith ε* Richard E. Isaac ε Richard M. Koch ε Michael Maltenfort * Amassa C. Fauntleroy Alain A. Grigis * Godfrey L. Isaacs ε* Yoshiharu Kohayakawa * Alfred P. Maneki ε Ruth G. Favro ε* Helmut Groemer ε Masanori Itai ε* János Kollár ε John L. Manferdelli ε* Solomon Feferman ε* Leonard Gross ε* Noboru Ito ε* Sundaresan Kondagunta ε* Jason Manning ε* Mark E. Feighn ε* Edward H. Grossman ε* N. M. Ivochkina ε Eric J. Kostelich ε Pauline Mann-Nachbar ε Paul Feit ε Robert Andrew Grossman ε* Eric Robert Jablow ε* Adnah G. Kostenbauder ε* Margaret O. Marchand ε Arnold D. Feldman ε Edward A. Grove * William Burkley Jacob Bryna Kra ε* Stefano Marchiafava ε* Norman Feldman Gerd Grubb ε* William Araujo Jacques ε* Jurg Kramer ε* Murray Angus Marshall ε Vincent J. Ferlini ε* Juan Mateos Guilarte ε* John Antone Jaksich Lawrence Kramer ε Nathaniel F. G. Martin ε* José Humberto Ferreira Rosa ε Craig R. Guilbault ε David M. James ε Helen F. Kriegsman ε Thomas Harry Martin ε* Ian M. Ferris ε* Victor W. Guillemin ε Jan Janas ε Nell Stevenson Kroeger ε* Samuel Masih ε* Gary A. Feuerbacher ε* Richard K. Guy * James Jantosciak ε* Gary R. Krumpholz ε Attila Máté Maurice C. Figueres ε* Petros Hadjicostas ε* Herbert Jarszick ε* Wei-Eihn Kuan ε* Jerold C. Mathews ε Benjamin Fine ε* Gerhard E. Hahne ε* Trevor M. Jarvis ε Sharon Kunoff ε George Douglas Matthews ε* Carlos E. Finol ε* Ruth M. Hailperin ε Charles H. Jepsen ε* Masatake Kuranishi ε* Stephen B. Maurer ε William T. Fishback ε* Andras Hajnal ε David Jerison ε* Robert P. Kurshan ε John Patterson Mayberry ε* Benji N. Fisher ε* Douglas F. Hale ε * Eugene C. Johnsen Leong-Chuan Kwek ε* Raymond A. Mayer Jr. ε* Uri Fixman ε* Alfred W. Hales * Trygve Johnsen ε* Jean Pierre Lafon * Michael J. McAsey ε Harley Flanders ε* Brian C. Hall ε Bradford W. Johnson ε Marwan Lahoud ε* Gregory L. McColm ε* Richard J. Fleming ε Timothy Hall ε Charles N. Johnson ε Kee Y. Lam * Robert M. McConnel ε* Julie A. Fondurulia Margo Halsted ε* Dale Martin Johnson ε* John Patrick Lambert ε Thomas McConnell ε S. Ashby Foote ε John L. Hank ε* David Copeland Johnson ε William A. Lampe ε* Robert A. McCoy ε* David Ford ε Heiko Harborth * David L. Johnson ε* Peter S. Landweber ε* Thomas L. McCoy ε John Michael Fox ε* Beverly Bailey Hargraves ε* Donald G. Johnson ε Leo J. Lange ε* Marjorie Frost McCracken ε* Deborah S. Franzblau ε Andrew William Harrell Gerald W. Johnson ε* Carl E. Langenhop ε John G. McDonald ε* Michael W. Frazier ε* Edmund O. Harriss ε Theodore D. Johnson ε* David C. Lantz ε* O. Carruth McGehee ε Stephen H. Friedberg ε Akio Hattori Eleanor Green Jones * Arnold Lapidus ε Richard J. McGovern ε* Merwyn M. Friedman ε Jane M. Hawkins ε James P. Jones ε* Michel L. Lapidus ε* William D. McIntosh ε* Jurg M. Frohlich ε* Leo Hellerman ε Kathryn A. Jones David R. Larson ε John K. McIver ε* Bent Fuglede ε* Simon Hellerstein ε* William B. Jones ε* George Laush ε* Thomas G. McKay * Hisanori Fujita ε* John P. Hempel Mattias Jonsson ε* Lorraine D. Lavallee ε* Robert W. McKelvey ε* William R. Fuller Sr. ε* Francis McVey Henderson ε* Troels Jorgensen ε* John W. Lawrence ε James G. McLaughlin ε* John D. Fulton ε* Carsten Hennig ε* Virginia V. Jory ε* H. Blaine Lawson Jr. ε Robert F. McNaughton Jr. ε* William Fulton ε* James B. Herreshoff ε Seva Joukhovitski ε* Robert F. Lax Gerald M. McNerney ε B. A. Fusaro ε Eric H. Herrin ε* Joaquim J. A. Judice ε James W. Lea Jr. George Joseph McNinch Chihchy Fwu ε Troy L. Hicks ε Winfried Just ε Ian J. Leary * Raymond Mejia William E. Gabella Takeyuki Hida * Manjunatha Prasad K ε Carl W. Lee ε* Anders Melin ε Marvin C. Gaer ε* Yasunari Higuchi ε* Jeffry N. Kahn ε* John M. Lee ε Louis C. Mello ε Fernando Galaz-Fontes ε* Hugh M. Hilden ε* Yûichirô Kakihara ε Ke-Seung Lee ε* José M. R. Méndez-Pérez ε Jean H. Gallier ε* Shirley A. Hill ε Agnes M. Kalemaris ε* Kotik K. Lee ε Nadine L. Menninga ε* Joseph M. Gani ε* Nancy Hingston ε Albert Kasangu Kalinde * J. Larry Lehman ε* Bruce Mericle

726 NOTICES OF THE AMS VOLUME 58, NUMBER 5 AMS Contributions

ε* Jorma K. Merikoski ε Donald A. Patterson ε Roger D. Rosenkrantz Emilio del Solar-Petit ε James Vickers ε* Jean-Pierre G. Meyer ε Nicholas J. Patterson ε Kenneth A. Ross ε Bruce Michael Solomon ε* Jose L. Viviente ε William A. Michael ε* Walter M. Patterson III * Adrian S. Roth ε Boris Solomyak ε* Michael Voichick ε* John J. Michels ε* Sandra O. Paur ε Mitchell J. Rothstein ε Sung Yell Song Paul S. Voigt ε* Marvin V. Mielke ε* Lawrence E. Payne James Rovnyak ε* Linda R. Sons ε* Paul A. Vojta ε* Ellen Rammelkamp Miller ε Roberto Peirone ε* Virginia G. Rovnyak ε Andrea Sorbi Emil J. Volcheck Jack M. Miller Stephen Pennell William W. Rowell * Michael J. Sormani ε ε ε ε Hans W. Volkmer * John W. Pennisten * James Samuel Royer * Kenneth S. Miller ε ε ε Sergio Spagnolo Lisa Wade ε Russell G. Miller ε* Juan C. Peral ε* Daniel Ruberman ε Ralf J. Spatzier ε Daniel F. Waggoner * Stephen S. Miller ε* Peter Perkins * Joachim H. Rubinstein ε Birgit Speh ε William M. Wagner ε* Thomas Len Miller ε* Sanford Perlman ε* Wolfgang M. Ruess ε Alan P. Sprague * Jonathan M. Wahl ε* William David Miller ε Peter A. Perry ε Robert S. Rumely ε Emily H. Sprague ε Masato Wakayama ε* Kenneth C. Millett ε* William G. Pertusi ε* William H. Rupley ε David A. Sprecher * Nolan R. Wallach ε Dionyssios Mintzopoulos * Charles Samuel Peskin ε Bernard Russo ε David H. Spring ε ε* Norman D. Mirsky ε Holger P. Petersson ε* Cihan K. Saclioglu ε Thirumalai P. Srinivasan Lawrence J. Wallen ε* Michał Misiurewicz ε* John W. Petro ε* Héctor N. Salas * Ross E. Staffeldt ε* John Thomas Walsh ε Guido Mislin Carl Stuart Pettis ε* Habib Salehi ε Saul Stahl ε James Robert Ward Jr. ε* Theodore Mitchell ε* Jonathan Pila ε* Laurent Saloff-Coste ε* Friedemann W. Stallmann * Seth L. Warner ε William J. Mitchell Anand Pillay ε Raimundo J. B. de Sampaio ε* William L. Stamey ε* Bette L. Warren ε Itaru Mitoma ε* Steven Pincus ε* Jose Luis Sanchez Palacio ε Mildred L. Stancl ε Lawrence C. Washington ε* Lothrop Mittenthal ε* Sergio Plaza ε* Robert W. Sanders ε Paul H. Stanford ε* Arthur G. Wasserman ε Felipe Montes ε Paul P. Pollack * Angel San Miguel ε* Lee James Stanley Robert H. Wasserman ε Peter L. Montgomery ε* Harriet S. Pollatsek ε Jose Cloves Verde Saraiva ε Christopher W. Stark ε* Michiaki Watanabe * Barbara B. Moore * John A. Poluikis * Donald E. Sarason Russell Lynn Stead ε ε ε ε ε Shôji Watanabe Florian Pop C. Sauerbier ε* Richard A. Moore ε ε ε Leon Steinberg * William C. Waterhouse ε W. Keith Moore Robert Michael Porter * Stanley A. Sawyer ε David R. Steinsaltz ε* David S. Watkins ε* Frank Morgan ε Richard C. Potter Karen Saxe Ellen M. Stenson ε* Mark E. Watkins ε* Larry J. Morley Keith W. Powls ε* Juan Jorge Schäffer ε Petr ˇSteˇpánek ε* David L. Webb * L. E. Morris ε Stanley Preiser * Gideon Schechtman ε John Colin Stillwell ε Elias Wegert * John A. Morrison ε* Martin E. Price ε Jeffrey H. Schenker ε* Paul K. Stockmeyer * Hans F. Weinberger ε* Joseph G. Moser ε* David S. Protas ε* John F. Schmeelk ε William G. Stokes ε ε* Marvin G. Mundt ε* Józef H. Przytycki ε* Markus Schmidmeier ε Gunter H. Stolz ε* Joel L. Weiner ε Grattan P. Murphy ε Eric L. Pugh ε* Maria Elena Schonbek ε H. A. Stone ε* Michael I. Weinstein ε* Alexander Nagel ε* Loki Der Quaeler ε Richard M. Schori ε Orlin Tsankov Stoytchev ε David M. Wells ε* Kazumi Nakano David Quesada * John Schue ε* Emil J. Straube ε Greg Wene ε Kanji Namba ε Eric Todd Quinto George W. Schueller ε* Walter A. Strauss ε John C. Wenger ε Takao Namiki ε* Paul H. Rabinowitz ε Alan Schumitzky ε Volker Strehl ε* Henry C. Wente ε Isaac Namioka ε* Andrew J. Radcliffe ε* Charles Freund Schwartz ε* Gerhard O. Strohmer ε John Wermer James B. Nation ε* Louis B. Rall * Gerald W. Schwarz ε* Daniel W. Stubbs ε Elisabeth M. Werner ε Manmath Nayak Dinakar Ramakrishnan Willi Schwarz ε Garrett James Stuck ε* John E. Wetzel * Melapalayam S. Ramanujan Richard J. Schweickert ε Jan V. Neerven ε ε ε* Kelly John Suman ε* Brian Cabell White * Joseph Neggers * George N. Raney * Eric Schweitzer Patrick Suppes ε ε ε ε ε* Charles M. White ε Philip C. Nelson * R. Michael Range ε* Ridgway Scott ε* Andrew V. Sutherland ε Tad P. White ε* Csaba Nemethi ε* Salvatore Rao ε* Warner Henry Harvey Scott III ε* William J. Sweeney ε Alan Dean Wiederhold ε* Umberto Neri ε* Louise Arakelian Raphael ε* Eira J. Scourfield ε* Roman Sznajder ε* Roger A. & Sylvia Margaret ε* Christoph J. Neugebauer ε Douglas C. Ravenel ε Christoph J. Scriba ε Kazuaki Taira Wiegand ε Siegfried F. Neustadter ε* S. W. Rayment ε* Robert T. Seeley ε* Lajos F. Takács * Susan Gayle Williams James A. Nickel ε Rolando A. Rebolledo ε* George F. Seelinger ε Yoshinori Takei ε Charles K. Williamson ε* Lance W. Nielsen ε* David E. Reese ε Jan Segert ε Shigeo Takenaka ε Louis Nirenberg ε Eugenio Regazzini ε* Howard A. Seid ε* Yoshihiro Tanaka ε* John R. Willis ε* Togo Nishiura ε Irma M. Reiner ε* George Seifert ε Daniel Joseph Tancredi * Robert Lee Wilson ε Zbigniew H. Nitecki ε* John H. Reinoehl ε Leon H. Seitelman ε* Daniel Louis Tancreto ε Samuel Ronald Windsor ε* Scott R. Nollet Jean N. Renault ε* George B. Seligman ε* Elliot A. Tanis ε* Eric J. Wingler Rutger Noot ε Michael Bela Revesz ε Roel H. G. Sergeant ε James S. Tanton ε F. Wintrobe ε* Eric A. Nordgren ε* Robert J. Reynolds ε* Francesco Serra Cassano Leon H. Tatevossian ε* Bettina Wiskott ε Phil Novinger Charles W. Rezk ε* Richard J. Shaker ε* James J. Tattersall ε* Louis Witten ε James E. Nymann ε Henry Crawford Rhaly Jr. * Patrick Shanahan ε* S. James Taylor Stephen Wollman ε* Andrew P. Ogg * Martin G. Ribe ε* Priti Shankar ε Zachariah C. Teitler ε* Stephen D. Wolthusen Phoebe Olcott * Stephen J. Ricci * Henry Sharp Jr. Chuu-Lian Terng ε ε John W. Wood ε Mogens Norgaard Olesen Horst P. Richter * Ching-Kuang Shene ε* Paul M. Terwilliger ε Nick John Wood ε Paul D. Olson ε* Benjamin Rickman ε* John C. Shepherdson ε John Alexander Thacker ε* George V. Woodrow III ε* Frank W. J. Olver ε Ronald Edgar Rietz ε Richard B. Sher ε Edward Linus Thome ε Alun Wyn-Jones ε* Peter J. Olver ε Alcibiades Rigas ε Michael Sherbon * Daniel B. J. Tomiuk ε* Hiroyoshi Yamaki ε* John Arthur Oman ε Robert D. Rigdon ε Amin Shokrollahi ε* Andre Toom Deane Yang ε* Philip J. O’Neil * Jose Rio ε* Steven E. Shreve Craig A. Tracy ε * Fawzi M. Yaqub * Barrett O’Neill ε Thomas W. Rishel ε* David S. Shucker ε* Charles R. Traina * Yoshitsugu Oono ε Joel W. Robbin ε* Stuart J. Sidney ε* Selden Y. Trimble V ε Mitsuru Yasuhara ε Edward T. Ordman ε Alain M. Robert Martha J. Siegel ε Spiros P. Tsatsanis ε* Suresh Yegnashankaran ε* Peter P. Orlik ε* Anne Drinkwater Roberts ε Daniel S. Silver ε Tamotsu Tsuchikura ε* J. Michael Yohe Bent Orsted ε Joel L. Roberts ε Joseph H. Silverman ε* Kazô Tsuji ε* Donald F. Young ε* Mason S. Osborne ε* Joseph B. Roberts ε* Anastasios Simalarides ε* Joann Stephanie Turisco ε Gabjin Yun ε* James M. Osterburg ε Lois J. Roberts ε* Patrick J. Sime Helene R. Tyler ε* Charles T. Zahn ε* Michio Ozeki ε Paul C. Roberts * Yakov G. Sinai ε* Johan Tysk ε V. E. Zakharov ε* Judith A. Packer Margaret M. Robinson ε* Hardiv H. Situmeang * Yasushi Unai Unai ε Jean-Claude Zambrini Fotios C. Paliogiannis ε Tom Roby ε* Man-Keung Siu ε Harald Upmeier ε* François Zara John H. Palmieri Pedro Martins Rodrigues * Walter S. Sizer * John A. W. Upton ε ε ε ε ε Jose Zero ε Taxiarchis Papakostas John Roe ε Christopher Skinner ε Wilfredo O. Urbina ε* David E. Zitarelli ε Kyoo-Hong Park ε* David E. Rohrlich ε David L. Skoug ε* Johannes A. Van Casteren ε Paul Zorn ε Elwood G. Parker ε* Judith Roitman ε Michael Slattery ε Jan Harm Van der Walt ε Steven M. Zucker ε* Thomas H. Parker ε Dale P. O. Rolfsen ε* Richard A. Smith ε* H. N. Van Eck ε* Paul F. Zweifel ε* Alberto Parmeggiani ε* Guillermo Romero Melendez * Joel A. Smoller ε Aernout C. D. Van Enter ε Paul J. Zwier ε Walter R. Parry ε Nicholas J. Rose ε* Timothy Law Snyder ε* A. H. Van Tuyl Anonymous (277) ε* Donald S. Passman ε* David Rosenberg ε William M. Snyder Jr. ε Alphonse Thomas Vasquez ε* John J. Pastor ε* Jonathan M. Rosenberg ε Robert I. Soare ε Juan L. Vazquez

MAY 2011 NOTICES OF THE AMS 727 Mathematics People

Clay Mathematics Institute (CMI). He received his M.Sc. at Butcher Receives Inaugural the University of Bonn in 2010 under the supervision of Jones Medal Michael Rapoport and is currently working on his Ph.D. thesis at Bonn. His major interest is arithmetic geometry, John Butcher of the University of Auckland, New Zea- and he is working on the bad reduction of Shimura variet- land, has received the inaugural Jones Medal for lifetime ies and the Langlands program. achievement in the mathematical sciences. The prize ci- Clay Research Fellows are appointed for terms ranging tation reads in part: “John Butcher is without doubt one from two to five years; graduating doctoral students and of the leading world experts on numerical methods for mathematicians within three years of receiving the doc- the solution of ordinary differential equations (ODEs), toral degree are eligible for the fellowships. The primary and the world expert on Runge-Kutta methods. … The selection criteria for the fellowship are the exceptional entire subject today is organized around the concept of quality of the candidate’s research and the candidate’s B-series, named after John, the expansion of the integra- promise to become a mathematical leader. tor as a power series in the time step, with coefficients that are polynomial in the Runge-Kutta coefficients and in —From a CMI announcement the vector field appearing in the ODE and its derivatives: these appear in certain combinations known as elementary differentials of the vector field which are represented as Mazzucato Awarded Michler rooted trees.” The Jones Medal is named for Vaughan Jones and was Prize established by the Royal Society of New Zealand. It will Anna Mazzucato of Pennsylvania State University has be awarded biennially for lifetime achievement in pure been awarded the 2011 Ruth I. Michler Memorial Prize or applied mathematics or statistics by a person with by the Association of Women in Mathematics (AWM). She substantial connections to New Zealand. was honored for her “wide range of mathematical talents”. Her research involves the analysis of partial differential —From a Royal Society of New Zealand announcement equations, particularly those arising from continuum me- chanics of deformable solids and incompressible fluids, and associated inverse problems. In 1994 she earned her Polterovich Awarded Coxeter- Laurea (B.S./M.S.) in mathematical physics at Universitá James Prize degli Studi di Milano. She received her Ph.D. in mathemat- ics at the University of North Carolina, Chapel Hill, in 2000, Iosif Polterovich of the University of Montreal has been where she studied the Navier-Stokes and other nonlinear awarded the 2011 Coxeter-James Prize of the Canadian evolution equations under the direction of Michael Taylor. Mathematical Society (CMS). He was recognized for his The Michler Prize grants a midcareer woman in aca- work in spectral geometry, as well as his contributions to demia a residential fellowship in the Cornell University isospectral domains with mixed boundary conditions, the mathematics department without teaching obligations. asymptotics of eigenvalues of the Laplacian, and isoperi- metric inequalities for eigenvalues. —From an AWM announcement The prize was named after geometer Donald Coxeter and Ralph Duncan James, both former presidents of the CMS. It recognizes young mathematicians who have made Spohn Awarded Heineman outstanding contributions to mathematical research. Prize —From a CMS announcement Herbert Spohn of the Technical University of Munich has been awarded the 2011 Dannie Heineman Prize for Mathematical Physics. He was honored for his “seminal Scholze Awarded 2011 Clay contributions to nonequilibrium statistical mechanics as Research Fellowship exemplified by his exact solutions of growth models and stationary states of open systems. Combining mathemati- Peter Scholze of the University of Bonn has been cal rigor with physical insight, his work elucidates the awarded a five-year Clay Research Fellowship by the transition from microscopic to macroscopic behavior.”

728 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Mathematics People/Mathematics Opportunities

The prize carries a cash award of US$10,000 and is pre- and computational contributions to discrete optimiza- sented in recognition of outstanding publications in the tion”; Daphne Koller, professor of computer science, field of mathematical physics. The prize was established Stanford University, “for contributions to representation, in 1959 by the Heineman Foundation for Research, Edu- inference, and learning in probabilistic models with ap- cational, Charitable, and Scientific Purposes, Inc., and is plications to robotics, vision, and biology”; Terrence J. administered jointly by the American Institute of Physics Sejnowski, Francis Crick Professor and director of the (AIP) and the American Physical Society (APS). The prize Computational Neurobiology Laboratory, Salk Institute for is presented annually. Biological Studies, La Jolla, California, “for contributions to artificial and real neural network algorithms and applying —From an APS announcement signal processing models to neuroscience”; and Mihalis Yannakakis, Percy K. and Vida L. W. Hudson Professor of Computer Science, Columbia University, “for contri- National Academy of butions to algorithms and computational complexity.” Engineering Elections —From an NAE announcement The National Academy of Engineering (NAE) has elected sixty-eight new members and nine foreign associates. Among them are four whose work involves the mathemati- cal sciences. They are: William J. Cook, Chandler Family Chair Professor in Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, “for theoretical Mathematics Opportunities

NSF Postdoctoral Research International Mathematics Fellowships Competition for University The National Science Foundation (NSF) awards Mathemati- Students cal Sciences Postdoctoral Research Fellowships (MSPRF) for appropriate research in areas of the mathematical The Eighteenth International Mathematics Competi- sciences, including applications to other disciplines. tion (IMC) for University Students will be held July 28 Awardees are permitted to choose research environments through August 3, 2011, at American University in that will have maximal impact on their future scientific Blagoevgrad, Bulgaria. Participating universities are development. Awards are made in the form of either invited to send several students and one teacher; indi- Research Fellowships or Research Instructorships. The vidual students are welcome. Students completing their Research Fellowship option provides full-time support for first, second, third, or fourth years of university educa- any eighteen academic-year months in a three-year period, tion are eligible. The competition will consist of two in intervals not shorter than three consecutive months. sessions of five hours each. Problems will come from The Research Instructorship option provides a combina- the fields of algebra, analysis (real and complex), geom- tion of full-time and half-time support over a period of etry, and combinatorics. The working language will be three academic years, usually one academic year full time English. See the website http://www.imc-math.org. and two academic years half time. Under both options, the uk/ or contact John Jayne, University College London, award includes six summer months; however, no more Gower Street, London WC1E 6BT, United Kingdom; tele- than two summer months of support may be received in phone: +44-20-7679-7322; email: [email protected]. any calendar year. Under both options, the stipend support —John Jayne for twenty-four months (eighteen academic-year months University College London plus six summer months) will be provided within a forty- eight-month period. The deadline for proposals is October 19, 2011. See http://www.nsf.gov/pubs/2008/nsf08582/nsf08582. htm.

—From an NSF announcement

MAY 2011 NOTICES OF THE AMS 729 Inside the AMS

Epsilon Awards for 2010 AMS Holds Workshop for The AMS Epsilon Fund for Young Scholars was estab- Department Chairs lished in 1999 to provide financial assistance to summer The AMS held its annual workshop for department chairs programs in the United States and Canada for mathemati- prior to the Joint Mathematics Meetings in New Orleans, cally talented high school students. These programs have Louisiana, in January 2011. This one-day session is de- provided mathematically talented youngsters with their signed in a workshop format to stimulate discussion and first serious mathematical experiences. The name for the allow the sharing of ideas and experiences among attend- fund was chosen in remembrance of the late Paul Erdo˝s, ing department chairs, which allows attendees to address who was fond of calling children “epsilons”. departmental challenges from new perspectives. The The AMS has chosen ten summer mathematics pro- 2011 workshop was led by Timothy Hodges, University of grams to receive Epsilon grants for activities in the sum- Cincinnati; John Meakin, University of Nebraska-Lincoln; mer of 2011. The grants will support program expenses Helen Roberts, Montclair State University; and Stephen and student scholarships and, in some cases, scholarships Robinson, Wake Forest University. only. The programs were chosen on the basis of math- Workshop sessions have included a range of issues facing departments, including planning and budgeting, ematical excellence and enthusiasm. Award amounts were personnel management, assessment, outreach, faculty governed by the varying financial needs of each program development, communications, and departmental leader- and totaled US$100,000. ship. This year’s workshop focused on leading a depart- The 2011 grants are awarded to: All Girls/All Math, ment in challenging times, assessment, new approaches University of Nebraska, Lincoln; Canada/USA Mathcamp, to nonmajor mathematics classes, and faculty evaluation Reed College, Portland, Oregon; Lamar Achievement in as an opportunity. Mathematics Program (LAMP), Lamar University, Beau- The 2011 workshop was the largest ever for the AMS, mont, Texas; MathPath, Colorado College, Colorado with sixty department chairs and leaders from across the Springs; PROMYS, Boston University; PROTaSM (Puerto country attending. Rico Opportunities for Talented Students in Mathematics), —Anita Benjamin University of Puerto Rico, Mayagüez Campus; Research AMS Washington Office Science Institute, Massachusetts Institute of Technology; Ross Mathematics Program, The Ohio State University; Texas State Honors Summer Math Camp, Texas State Uni- From the AMS Public versity, San Marcos; Young Scholars Program, University of Chicago. Awareness Office The grants for summer 2011 are paid for by the AMS Epsilon Fund for Young Scholars. The AMS Epsilon Fund Ph.D. + epsilon for Young Scholars has been funded by contributions of The AMS has launched a blog, Ph.D. AMS members and friends; the goal of the endowment + epsilon, written by Adriana Salerno, assistant professor at Bates College. is to provide at least US$100,000 in support each sum- As an early-career mathematician, mer. For further information about the Epsilon Fund for she will blog about her experiences Young Scholars, visit the website http://www.ams.org/ and challenges. The AMS invites other giving-to-ams/ or contact [email protected]. early-career mathematicians to fol- Information about how to apply for Epsilon grants is low the blog and share comments available at http://www.ams.org/employment/ at http://www.ams.org/blog/ epsilon.html. A fairly comprehensive listing of summer Adriana Salerno phdplus/. programs for mathematically talented high school students (including those with and without Epsilon grants) is available American Association for the Advancement of at http://www.ams.org/employment/mathcamps.html. Science Annual Meeting The AMS Public Awareness Office ran the Who Wants to —AMS Development Office Be a Mathematician game during Family Science Days and

730 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Inside the AMS hosted an exhibit at the 2011 meeting of the American Francis U. Williamson, of France, died on January 8, Association for the Advancement of Science in Washing- 2011. Born on June 20, 1938, he was a member of the ton, D.C., February 17–21. See descriptions of some of Society for 27 years. the events related to mathematics that took place at the A. Wayne Wymore, of Tucson, Arizona, died on Febru- meeting at http://www.ams.org/meetings/aaas2011. ary 24, 2011. Born on February 1, 1927, he was a member of the Society for 58 years. 2011 Mathematical Art Exhibition album The fifty-eight works in the 2011 Mathematical Art Exhi- bition, held at the Joint Mathematics Meetings, are in an Correction album on Mathematical Imagery. The works include digital Reference [17] in the January 2011 Notices article “Real prints, origami, crochet, jewelry, and sculpture; the images face of János Bolyai” omitted the name of one of the au- may be sent as e-postcards. See http://www.ams.org/ thors of the cited article. The reference should have read: mathimagery. E. Kiss and J. Sandor, On a congruence by János Bolyai connected by pseudoprimes, Mathematica Pannonia, 15(2) Deaths of AMS Members (2004), 283–288. —Notices staff Hugh N. Albright, professor, LaSalle University, died on February 24, 2011. Born on February 27, 1928, he was a member of the Society for 40 years. Winifred A. Asprey of Poughkeepsie, New York, died on October 19, 2007. Born on April 8, 1917, she was a member of the Society for 61 years. Thierry E. Aubin, of Paris, France, died on March 21, 2009. Born on May 6, 1942, he was a member of the Society for 29 years. John E. Brothers, professor, Indiana University, died on November 15, 2010. Born on July 6, 1937, he was a member of the Society for 47 years. Elizabeth H. Cuthill, of Solomons, Maryland, died on January 11, 2011. Born on October 16, 1923, she was a member of the Society for 62 years. AMERICAN MATHEMATICAL SOCIETY David F. Dawson, of Denton, Texas, died on Febru- ary 7, 2011. Born on September 16, 1926, he was a member TEXTBOOK of the Society for 59 years. Introduction to Denis A. Higgs, of Toronto, Canada, died on Febru- Representation ary 25, 2011. Born on May 6, 1932, he was a member of Theory the Society for 41 years. Greg Hjorth, professor, University of Melbourne, Pavel Etingof, Oleg died on January 13, 2011. Born on June 14, 1963, he was Golberg, Sebastian a member of the Society for 18 years. Hensel, Tiankai Liu, Jaroslav Jezek, professor, Charles University, died Alex Schwendner, on February 13, 2011. Born on March 5, 1945, he was a Dmitry Vaintrob, and member of the Society for 33 years. Elena Yudovina George E. Lang, professor, Fairfield University, died on May 9, 2007. Born on June 29, 1942, he was a member withwith historicalhistorical interludesin by Slava of the Society for 38 years. Gerovitch, Massachusetts Institute of Gerard McDonald, professor, Loyola University Technology, Cambridge, MA of Chicago, died on September 18, 2010. Born on Novem- The goal of this book is to give a “holistic” ber 27, 1946, he was a member of the Society for 31 years. introduction to representation theory Ernst Snapper , professor, Dartmouth College, died Student Mathematical Library, Volume 59; 2011; on February 5, 2011. Born on December 2, 1913, he was a approximately 232 pages; Softcover; ISBN: 978-0-8218- member of the Society for 69 years. 5351-1; List US$42; AMS members US$33.60; Order Alfred J. van der Poorten, of Australia, died on code STML/59 October 9, 2010. Born on May 16, 1942, he was a member of the Society for 41 years. Thomas Williams , of Mt. Joy, Pennsylvania, died on www.ams.org/bookstore September 30, 2010. Born on October 24, 1937, he was a member of the Society for 12 years.

MAY 2011 NOTICES OF THE AMS 731 Reference and Book List

The Reference section of the Notices Keck 568, 500 Fifth Street, NW, Wash- Associateship Programs, National is intended to provide the reader ington, DC 20001; telephone 202- Research Council, Keck 568, 500 Fifth with frequently sought information in 334-2760; fax 202-334-2759; email Street, NW, Washington, DC 20001; an easily accessible manner. New [email protected]. telephone 202-334-2760; fax 202- information is printed as it becomes May 1, 2011: Applications for 334-2759; email [email protected]. available and is referenced after the National Academies Christine Mirza- October 1, 2011: Applications for first printing. As soon as information yan Graduate Fellowship Program AWM Travel Grants. See http:// is updated or otherwise changed, it for fall 2011. See http://sites. www.awm-math.org/travelgrants. will be noted in this section. nationalacademies.org/PGA/ html#standard. policyfellows/index.htm. October 1, 2011: Nominations for Contacting the Notices May 1, 2011: Applications for the 2012 Emanuel and Carol Parzen The preferred method for contacting AWM Travel Grants. See http:// Prize. Contact Thomas Wehrly, De- the Notices is electronic mail. The www.awm-math.org/travelgrants. partment of Statistics, 3143 TAMU, editor is the person to whom to send html#standard. Texas A&M University, College Sta- articles and letters for consideration. May 15–June 15, 2011: Submis- tion, Texas 77843-3143. Articles include feature articles, me- sion period for DMS Workforce Pro- October 19, 2011: Proposals for morial articles, communications, gram in the Mathematical Sciences. NSF Postdoctoral Research Fellow- opinion pieces, and book reviews. See http://www.nsf.gov/funding/ ships. See “Mathematics Opportuni- The editor is also the person to whom pgm_summ.jsp?pims_id=503233. ties” in this issue. to send news of unusual interest August 1, 2011: Applications November 1, 2011: Applications about other people’s mathematics for August review for National for November review for National research. Academies Research Associateship Academies Research Associateship The managing editor is the person Programs. See the National Acad- Programs. See the National Acad- to whom to send items for “Math- emies website at http://sites. emies website at http://sites. ematics People”, “Mathematics Op- nationalacademies.org/PGA/RAP/ nationalacademies.org/PGA/RAP/ portunities”, “For Your Information”, PGA_050491 or contact Research PGA_050491 or contact Research “Reference and Book List”, and “Math- ematics Calendar”. Requests for Where to Find It permissions, as well as all other inquiries, go to the managing editor. A brief index to information that appears in this and previous issues of the Notices. The electronic-mail addresses are AMS Bylaws—November 2009, p. 1320 [email protected] in the AMS Email Addresses—February 2011, p. 326 case of the editor and notices@ AMS Ethical Guidelines—June/July 2006, p. 701 ams.org in the case of the managing AMS Officers 2010 and 2011 Updates—May 2011, p. 735 editor. The fax numbers are 314- AMS Officers and Committee Members—October 2010, p. 1152 935-6839 for the editor and 401- 331-3842 for the managing editor. Conference Board of the Mathematical Sciences—September 2010, p. 1009 Postal addresses may be found in the masthead. IMU Executive Committee—December 2010, page 1488 Information for Notices Authors—June/July 2010, p. 768 Upcoming Deadlines Mathematics Research Institutes Contact Information—August 2010, April 30, 2011: Nominations for p. 894 AWM Gweneth Humphreys Award. National Science Board—January 2011, p. 77 See www.awm-math.org, telephone New Journals for 2008—June/July 2009, p. 751 703-934-0163, or email awm@awm- NRC Board on Mathematical Sciences and Their Applications—March math.org. 2011, p. 482 May 1, 2011: Applications for NRC Mathematical Sciences Education Board—April 2011, p. 619 May review for National Acad- emies Research Associate- NSF Mathematical and Physical Sciences Advisory Committee—February ship Programs. See the National 2011, p. 329 Academies website at http:// Program Officers for Federal Funding Agencies—October 2010, sites.nationalacademies. p. 1148 (DoD, DoE); December 2010, page 1488 (NSF Mathematics Education) org/PGA/RAP/PGA_050491 or con- Program Officers for NSF Division of Mathematical Sciences—Novem- tact Research Associateship Pro- ber 2010, p. 1328 grams, National Research Council,

732 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Reference and Book List

Associateship Programs, National Penguin, reprint edition, August Isaac Newton on Mathematical Research Council, Keck 568, 500 Fifth 2010. ISBN 978-01431-173-77. Certainty and Method, by Niccolò Street, NW, Washington, DC 20001; The Calculus of Friendship: What a Guicciardini. MIT Press, October 2009. telephone 202-334-2760; fax 202- Teacher and Student Learned about ISBN-13: 978-02620-131-78. 334-2759; email [email protected]. Life While Corresponding about Math, *Le Operazioni del Calcolo Logico, December 21, 2011: Nominations by Steven Strogatz. Princeton Uni- by Ernst Schröder. Original German for the Schauder Medal. Contact Lech versity Press, August 2009. ISBN-13: version of Operationskreis des Logik- 978-0691-13493-2. (Reviewed June/ Gorniewicz, manager of Schauder kalkuls and Italian translation with July 2010.) Center, [email protected]. commentary and annotations by Da- The Calculus of Selfishness, by Karl vide Bondoni. LED Online, 2010. ISBN Book List Sigmund. Princeton University Press, 978-88-7916-474-0. January 2010. ISBN-13: 978-06911- The Book List highlights books that Logicomix: An Epic Search for Truth, 427-53. by Apostolos Doxiadis and Christos have mathematical themes and are The Clockwork Universe: Isaac aimed at a broad audience potentially Papadimitriou. Bloomsbury USA, Newton, the Royal Society, and the September 2009. ISBN-13: 978-15969- including mathematicians, students, Birth of the Modern World, by Edward 145-20. (Reviewed December 2010.) and the general public. When a book Dolnick. Harper, February 2011. ISBN- Loving + Hating Mathematics: Chal- has been reviewed in the Notices, a 13: 978-00617-195-16. (Reviewed lenging the Myths of Mathematical Life, reference is given to the review. Gen- April 2011.) by Reuben Hersh and Vera John-Steiner. erally the list will contain only books Complexity: A Guided Tour, by Princeton University Press, January 2011. Melanie Mitchell. Oxford University published within the last two years, ISBN-13: 978-06911-424-70. Press, April 2009. ISBN-13: 978- though exceptions may be made in The Math Book: From Pythagoras to 01951-244-15. (Reviewed April 2011.) cases where current events (e.g., the the 57th Dimension, 250 Milestones in The Cult of Statistical Significance: death of a prominent mathemati- the History of Mathematics, by Clifford How the Standard Error Costs Us cian, coverage of a certain piece of A. Pickover. Sterling, September 2009. Jobs, Justice, and Lives, by Stephen T. mathematics in the news) warrant ISBN-13: 978-14027-579-69. Ziliak and Deirdre N. McCloskey, drawing readers’ attention to older A Mathematician’s Lament: How University of Michigan Press, Febru- books. Suggestions for books to School Cheats Us Out of Our Most Fas- ary 2008. ISBN-13: 978-04720-500-79. include on the list may be sent to cinating and Imaginative Art Form, by (Reviewed October 2010.) [email protected]. Paul Lockhart. Bellevue Literary Press, Duel at Dawn: Heroes, Martyrs, and *Added to “Book List” since the April 2009. ISBN-13:978-1-934137- the Rise of Modern Mathematics, by list’s last appearance. Amir Alexander. Harvard University 17-8. Apocalypse When?: Calculating Press, April 2010. ISBN-13: 978- Mathematicians: An Outer View How Long the Human Race Will Sur- 06740-466-10. (Reviewed November of the Inner World, by Mariana Cook. vive, by Willard Wells. Springer Praxis, 2010.) Princeton University Press, June 2009. June 2009. ISBN-13: 978-03870-983- Euler’s Gem: The Polyhedron For- ISBN-13: 978-06911-3951-7. (Reviewed 64. mula and the Birth of Topology, by August 2010.) *At Home with Andre and Simone David S. Richeson. Princeton Univer- Mathematicians Fleeing from Nazi Weil, by Sylvie Weil. (Translation of sity Press, September 2008. ISBN-13: Germany: Individual Fates and Global Chez les Weils, translated by Benjamin 978-06911-267-77. (Reviewed Decem- Impact, by Reinhard Siegmund- Ivry.) Northwestern University Press, ber 2010.) Schultze. Princeton University Press, October 2010. ISBN 978-08101-270- The Grand Design, by Stephen July 2009. ISBN-13: 978-06911- 43. (Reviewed in this issue.) Hawking and Leonard Mlodinow. 4041-4. (Reviewed November 2010.) The Best Writing on Mathematics: Bantam, September 2010. ISBN-13: A Motif of Mathematics: History and Application of the Mediant and 2010, edited by Mircea Pitici. Prince- 978-05538-053-76. the Farey Sequence, by Scott B. ton University Press, December 2010. Here’s Looking at Euclid: A Surpris- Guthery. Docent Press, September ISBN-13: 978-06911-484-10. ing Excursion through the Astonish- 2010. ISBN-13:978-4538-105-76. The Black Swan: The Impact of the ing World of Math, by Alex Bellos. Mrs. Perkins’s Electric Quilt: And Highly Improbable, by Nassim Nicho- Free Press, June 2010. ISBN-13: 978- 14165-882-52. Other Intriguing Stories of Mathemati- las Taleb. Random House Trade Pa- Hidden Harmonies (The Lives and cal Physics, Paul J. Nahin, Princeton perbacks, second edition, May 2010. Times of the Pythagorean Theorem), University Press, August 2009. ISBN-13: ISBN-13: 978-08129-738-15. (First by Robert and Ellen Kaplan. Blooms- 978-06911-354-03. edition reviewed March 2011.) bury Press, January 2011. ISBN- Naming Infinity: A True Story of Bright Boys: The Making of Infor- 13:978-15969-152-20. Religious Mysticism and Mathemati- mation Technology, by Tom Green. *Hot X: Algebra Exposed, by Danica cal Creativity, by Loren Graham and A K Peters, April 2010. ISBN-13: 978- McKellar. Hudson Street Press, Au- Jean-Michel Kantor. Belknap Press 1-56881-476-6. gust 2010. ISBN 978-15946-307-05. of Harvard University Press, March *The Calculus Diaries: How Math How to Read Historical Mathematics, 2009. ISBN-13: 978-06740-329-34. Can Help You Lose Weight, Win by Benjamin Wardhaugh. Princeton Nonsense on Stilts: How to Tell Sci- in Vegas, and Survive a Zombie University Press, March 2010. ISBN-13: ence from Bunk, by Massimo Pigliucci. Apocalypse, by Jennifer Ouellette. 978-06911-401-48. University of Chicago Press, May

MAY 2011 NOTICES OF THE AMS 733 Reference and Book List

2010. ISBN-13: 978-02266-678-67. 2011. ISBN 978-03074-533-89. (Re- (Reviewed April 2011.) viewed in this issue.) *Number Freak: From 1 to 200— Recountings: Conversations with The Hidden Language of Numbers MIT Mathematicians, edited by Joel Revealed, by Derrick Niederman. Peri- Segel. A K Peters, January 2009. ISBN- gee Trade, August 2009. ISBN-10: 13: 978-15688-144-90. 03995-345-98. Roger Boscovich, by Radoslav *Numbers: A Very Short Introduc- Dimitric (Serbian). Helios Publishing tion, by Peter M. Higgins. Oxford Uni- Company, September 2006. ISBN-13: versity Press, February 2011. ISBN 978-09788-256-21. 978-0-19-958405-5. The Shape of Inner Space: String Numbers Rule: The Vexing Math- Theory and the Geometry of the Uni- ematics of Democracy, from Plato to the verse's Hidden Dimensions, by Shing- Present, by George G. Szpiro. Princeton Tung Yau (with Steve Nadis). Basic University Press, April 2010. ISBN-13: Books, September 2010. ISBN-13: 978-06911-399-44. (Reviewed January 978-04650-202-32. (Reviewed Febru- 2011.) ary 2011.) The Numerati, by Stephen Baker. The Solitude of Prime Numbers, Houghton Mifflin, August 2008. ISBN- by Paolo Giordano. Pamela Dorman 13: 978-06187-846-08. (Reviewed Books, March 2010. ISBN-13: 978- 06700-214-82. (Reviewed September October 2009.) 2010.) Our Days Are Numbered: How Solving Mathematical Problems: A Mathematics Orders Our Lives, by Personal Perspective, by Terence Tao. Jason Brown. Emblem Editions, April Oxford University Press, September 2010. ISBN-13: 978-07710-169-74. 2006. ISBN-13: 978-0199-20560-8. (Re- Perfect Rigor: A Genius and the viewed February 2010.) Mathematical Breakthrough of the The Strangest Man, by Graham Century, by Masha Gessen. Houghton Farmelo. Basic Books, August 2009. Mifflin Harcourt, November 2009. ISBN-13: 978-04650-182-77. ISBN-13: 978-01510-140-64. (Re- Street-Fighting Mathematics: The viewed January 2011.) Art of Educated Guessing and Oppor- Pioneering Women in American tunistic Problem Solving, by Sanjoy Mathematics: The Pre-1940 Ph.D.’s, Mahajan. MIT Press, March 2010. by Judy Green and Jeanne LaDuke. ISBN-13: 978-0262-51429-3. AMS, December 2008. ISBN-13: 978- Survival Guide for Outsiders: How 08218-4376-5. to Protect Yourself from Politicians, Plato’s Ghost: The Modernist Trans- Experts, and Other Insiders, by Sher- formation of Mathematics, by Jeremy man Stein. BookSurge Publishing, Gray. Princeton University Press, Sep- February 2010. ISBN-13: 978-14392- tember 2008. ISBN-13: 978-06911- 532-74. 361-03. (Reviewed February 2010.) Symmetry: A Journey into the Pat- Probabilities: The Little Numbers terns of Nature, by Marcus du Sau- That Rule Our Lives, by Peter Olofs- toy. Harper, March 2008. ISBN: 978- son. Wiley, March 2010. ISBN-13: 978- 00607-8940-4. (Reviewed February 04706-244-56. 2011.) Problem-Solving and Selected Top- Symmetry in Chaos: A Search for ics in Number Theory in the Spirit Pattern in Mathematics, Art, and Na- of the Mathematical Olympiads, by ture, by Michael Field and Martin Michael Th. Rassias. Springer, 2011. Golubitsky. Society for Industrial The AMS provides down- ISBN-13: 978-1-4419-0494-2. and Applied Mathematics, second revised edition, May 2009. ISBN-13: loadable pdf fi les of posters *Proofiness: The Dark Arts of Math- ematical Deception, by Charles Seife. 978-08987-167-26. promoting awareness of Viking, September 2010. ISBN 978- Teaching Statistics Using Base- mathematics, programs, and 06700-221-68. ball, by James Albert. Mathematical services to post in common Proofs from THE BOOK, by Martin Association of America, July 2003. ISBN-13: 978-08838-572-74. (Re- areas, classrooms, and offi ces. Aigner and Günter Ziegler. Expanded fourth edition, Springer, October viewed April 2010.) 2009. ISBN-13: 978-3-642-00855-9. What’s Luck Got to Do with It? The Visit ams.org/posters for *The Quants: How a New Breed of History, Mathematics and Psychology more information. Math Whizzes Conquered Wall Street of the Gambler’s Illusion, by Joseph and Nearly Destroyed It, by Scott Mazur. Princeton University Press, Patterson. Crown Business, January July 2010. ISBN: 978-069-113890-9.

734 NOTICES OF THE AMS VOLUME 58, NUMBER 5 From the AMS Secretary

Officers of the Society 2010 and 2011 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. large of the Council, the last year of Colloquium Editorial Committee 2010 Paul J. Sally Jr. 2/05–1/12 the present term is listed. Rebecca F. Goldin Journal of the AMS Editorial Council Bryna Kra Committee Irena Peeva Karl Rubin 8/09–1/14 President Joseph H. Silverman Mathematical Reviews Editorial George E. Andrews 2/09–1/11 Sarah J. Witherspoon Eric M. Friedlander 2/11–1/13 Committee 2011 President Elect Ronald M. Solomon 2/10–1/13 Aaron Bertram Eric M. Friedlander 2/10–1/11 Mathematical Surveys and William A. Massey Monographs Editorial Committee Immediate Past President Panagiotis E. Souganidis George E. Andrews 2/11–1/12 Ralph L. Cohen 2/09–1/13 Michelle L. Wachs Mathematics of Computation Vice Presidents David Wright Sylvain Cappell 2/10–1/13 Editorial Committee 2012 Barbara Lee Keyfitz 2/11–1/14 Chi-Wang Shu 2/02–1/12 Alejandro Adem Frank Morgan 2/09–1/12 Proceedings Editorial Committee Richard Hain Bernd Sturmfels 2/08–1/11 Ken Ono 2/10–1/14 Jennifer Schultens Secretary Transactions and Memoirs Editorial Janet Talvacchia Robert J. Daverman 2/99–1/13 Committee Christophe Thiele Associate Secretaries Robert Guralnick 2/05–1/13 2013 Georgia Benkart 2/10–1/12 Board of Trustees Michel L. Lapidus 2/02–1/12 Matthew Ando Matthew Miller 2/05–1/13 Estelle Basor George E. Andrews (ex officio) 2/09– Steven Weintraub 2/09–1/13 Patricia Hersh 1/11 Tara S. Holm John B. Conway 2/01–1/11 Treasurer John M. Franks (ex officio) 2/99–1/12 John M. Franks 2/99–1/11 T. Christine Stevens Eric M. Friedlander (ex officio) 2/11– Jane M. Hawkins 2/11–1/13 Members of Executive 1/13 Associate Treasurer Committee Mark Green 2/10–1/15 John M. Franks 2/11–1/12 Members of the Council, as provided Jane M. Hawkins (ex officio) 2/11–1/13 Linda Keen 2/09–1/11 for in Article 7, Section 4 (last sen- William H. Jaco 2/11–1/16 tence), of the Bylaws of the Society. Linda Keen 2/99–1/11 Ronald J. Stern 2/09–1/14 Karen Vogtmann 2/08–1/13 Ruth M. Charney 2/07–1/11 Carol S. Wood 2/02–1/12 Ralph L. Cohen 2/11–1/15 Craig L. Huneke 2/08–1/12 Bryna Kra 2/10–1/14 Joseph H. Silverman 2/09–1/13

MAY 2011 NOTICES OF THE AMS 735 AMERICAN MATHEMATICAL SOCIETY Call for NOMINATIONS

The selection committees for these prizes request nominations for consideration for the 2012 awards, which will be presented at the Joint Mathematics Meetings in Boston, MA, in January 2012. Information about these prizes may be found in the November 2009 issue of the Notices, pp. 1326–1345, and at http://www.ams.org/prizes-awards.

GEORGE DAVID BIRKHOFF PRIZE. The George David Birkhoff Prize is awarded jointly by the AMS and SIAM for an outstanding contribution to applied mathematics in its highest and broadest sense. The award was first made in 1968 and now is presented every third year.

FRANK NELSON COLE PRIZES. The Frank Nelson Prizes are now presented at three-year intervals for outstanding contributions in algebra and number theory published in the preceding six years. The award in January 2012 will be the Frank Nelson Cole Prize in Algebra.

LEVI L. CONANT PRIZE. The Levi L. Conant Prize, first awarded in January 2001, is presented annually for an outstanding expository paper published in either the Notices or the Bulletin of the American Mathematical Society during the preceding five years.

Nominations for all prizes should be submitted to the secretary, Robert J. Daverman, American Mathematical Society, 238 Ayres Hall, University of Tennessee, Knoxville, TN 37996-1320. Include a short description of the work that is the basis of the nomi- nation, with complete bibliographic citations when appropriate. A brief curriculum vitae should be included for the nominee. The nominations will be forwarded by the secretary to the appropriate prize selection commttee, which, as in the past, will make final decisions on the awarding of these prizes.

Deadline for nominations is June 30, 2011. AMERICAN MATHEMATICAL SOCIETY Call for

NOMINATIONS The selection committees for these prizes request nominations for consid- eration for the 2012 awards, which will be presented at the Joint Mathematics Meetings in Boston, MA, in January 2012. Information about past recepients of these prizes may be found in the November 2009 issue of the Notices, pp. 1326–1345 and at http://www.ams.org/prizes-awards.

ALBERT LEON WIHTEMAN MEMORIAL PRIZE

The Albert Leon Whiteman Memorial Prize now is awarded every third year, for notable exposition on the history of mathematics. The ideas expressed and understandings embodied in that exposition should reflect exceptional math- ematical scholarship.

DISTINGUISHED PUBLIC SERVICE AWARD

This award was established by the AMS Council in response to a recommenda- tion from its Committee on Science Policy. The award is presented to a research mathematician who made a distinguished contribution to the profession in the preceding five years. The US$4,000 prize is awarded every two years.

Nominations should be submitted to the Secretary, Robert J. Daverman, American Mathematical Society, 238 Ayres Hall, Department of Mathematics, University of Tennessee, Knoxville TN 37996-1320. Include a short description of the work that is the basis of the nomination, with complete bibliographic citations when appropriate. A brief curriculum vita of the nominee also should be included. The nominations will be forwarded by the Secretary to the appropriate prize selection committee, which will make final decisions on the awarding of these prizes.

Deadline for nominations is June 30, 2011. The prize is awarded each year to an undergraduate student (or students having submitted joint work) for outstanding research in mathematics. Any student who is an undergraduate in a college or university in the United States or its possessions, or Canada or Mexico, is eligible to be considered for this prize.

The prize recipient’s research need not be confined to a single paper; it may be contained in several papers. However, the paper (or papers) to be considered for the prize must be submitted while the student is an undergraduate; they cannot be submitted after the student’s graduation. The research paper (or papers) may be submitted for consideration by the student or a nominator. All submissions for the prize must include at least one letter of support from a person, usually a faculty member, familiar with the student’s research. Publication of research is not required.

The recipients of the prize are to be selected by a standing joint committee of the AMS, MAA, and SIAM. The decisions of this committee are final. The 2012 prize will be awarded for papers submitted for consideration no later than June 20, 2011, by (or on behalf of) students who were undergraduates in December 2010.

Questions may be directed to: Nominations and submissions Barbara T. Faires should be sent to: Secretary Morgan Prize Committee Mathematical Association of America c/o Robert J. Daverman, Secretary Westminster College American Mathematical Society New Wilmington, PA 16172 238 Ayres Hall Department of Mathematics Telephone: 724-946-6268 University of Tennessee Fax: 724-946-6857 Knoxville, TN 37996-1320 Email: [email protected] 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 2011 * 2–6 Advanced Course on Krein-de Branges Spaces of Entire Func- computed to be useful, there is a need to develop efficient algorithms tions and Old and New Spectral Problems, Centre de Recerca that address dynamic risk measures in both the objective function Matemàtica, Bellaterra, Barcelona, Spain. and the constraints. This calls for new methods of ADT. It also calls Scientific committee: Hakan Hedenmalm, Nikolai Makarov, Joaquim for new methods for modeling constraints in a dynamic setting in a Ortega-Cerdà, Mikhail Sodin. practically useful manner and for ways to understand the interplay Information: http://www.crm.cat/acdebrange. among risk measures, problem formulation, and computational trac- tability. There is a further need to develop optimization techniques * 7–8 Southeast Geometry Conference, University of South Carolina, and algorithms for computing risk measures, and to understand the Columbia, South Carolina. limitations that existing optimization algorithms impose on the vi- Description: The 21st annual Southeast Geometry Conference will ability of a risk measure when efficiency in computing is important. feature 50-minute talks on topics including geometric analysis and Consequently, the WS will also focus on practically useful modeling extremization problems. Young researchers and grad students are techniques and efficient algorithmic approaches for incorporating especially encouraged to participate in the conference, which will in- risk measures in the constraints and/or objective function. clude a poster session. If you plan to attend the conference, please let Organizers: Melike Baykal-Gursoy, Rutgers University; gursoy@ the organizers know for planning purposes. Some NSF support will rci.rutgers.edu; David Brown, Duke University, dbbrown@ be available for graduate students, postdocs, and junior researchers. duke.edu; Aleksandar Pekec, Duke University, [email protected]; Local Organizers: Ralph Howard (USC), Thomas Ivey (College of Andrzej Ruszczynski, Rutgers University, rusz@business. Charleston). Confirmed Speakers: Jacob Bernstein (Stanford), Jason rutgers.edu; Dharmashankar Subramanian, IBM Watson Labs, Cantarella (UGA), John Pardon (Princeton), Ray Treinen (Kansas [email protected]. State). Sponsors: DIMACS Special Focus on Algorithmic Decision Theory Information: http://www.math.sc.edu/~howard/SEGC2011/. and The Homeland Security Center for Command, Control, and * 9–13 DIMACS/CCICADA Workshop on Risk-Averse Algorithmic Interoperability Center for Advanced Data Analysis (CCICADA). Decision Making, DIMACS Center, CoRE Building, Rutgers Univer- Presented under the auspices of the Special Focus on Algorithmic sity, Piscataway, New Jersey. Foundations of the Internet and the Center for Dynamic Data Analy- Short Description: Properly assessing riskiness of available options sis (DyDAn). is central to decision making under uncertainty. Measures of risk Local Arrangements: Workshop Coordinator, DIMACS Center, are often important in the context of solving dynamic optimization [email protected], 732-445-5928. problems. This workshop will concentrate on recent work developing Deadlines: Pre-registration deadline: May 2, 2011. alternative measures and their properties, especially in the context Information: http://dimacs.rutgers.edu/Workshops/ of dynamic optimization. Since a risk measure has to be efficiently RiskMeasures/.

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

MAY 2011 NOTICES OF THE AMS 739 Mathematics Calendar

* 10–14 Riemannian Geometry and Applications “RIGA” 2011, Uni- Description: May 23–24 will be devoted to stochastic methods in versity of Bucharest, Faculty of Mathematics and Computer Science, financial models, May 23–27 to stochastic analysis, random fields Bucharest, Romania. and other applications than finance. Description: This is the third Conference Riemannian Geometry and Information: http://mathaa.epfl.ch/prob/ascona/2011/ Applications “RIGA”, which is devoted to geometry of Riemannian index.html. and pseudo-Riemannian manifolds, submanifold theory, structures * 26–29 Waterloo Workshop in Computer Algebra, WWCA 2011 on manifolds, complex geometry and contact geometry, Finsler, La- Celebrating Herbert S. Wilf’s 80th birthday, W80, Wilfrid Laurier grange and Hamilton geometries, applications to other fields. University, Waterloo, Ontario, Canada. Organizing committee: Ion Mihai (University of Bucharest), Adela Description: The event features 27 Invited Speakers. Mihai (University of Bucharest), Radu Miron (Romanian Academy), Information: http://www.cargo.wlu.ca/W80. Valentin Vlad (Romanian Academy). Invited speakers: Alfonso Carri- azo (University of Seville), Bang-Yen Chen (Michigan State University), June 2011 Franki Dillen (Katholieke Universiteit Leuven), Leopold Verstraelen * 6–8 Perspectives in Mathematics and Life Sciences, Fundación (Katholieke Universiteit Leuven). Euroárabe (C/San Jerónimo 27), Granada, Spain. Information: http://fmi.unibuc.ro/ro; fmi.unibuc.ro/ro/ Coordinator: Juan Soler. manifestari. Organizing Committee: Juan J. Nieto, Juan Calvo, Óscar Sánchez, * 16–18 Fifth International Conference on Recent Advances in Ap- José L. López, Tomás Alarcón. plied Dynamical Systems, Shanghai Normal University, Shanghai, Scientific Committee: Ángel Calsina, Carmen Cadarso, Manuel People’s Republic of China. Doblaré, Miguel A. Herrero, Ángel Sánchez, Juan Soler. Description: This is part of a conference series co-organized by Zhe- Speakers: Bascompte, Jordi; Bellomo, Nicola; Beresticky, Henri; Ber- jiang Normal University, Shanghai Normal University and Guangzhou lyand, Leonid; Carleton, Alan; Caselles, Vicent; Cuesta, José; Deco, University, chaired by Professor Jibin Li (ZJNU), Maoan Han (SHNU) Gustavo; Degond, Pierre; Frangi, Alejandro; García Ojalvo, Jordi; Gre- and Jianshe Yu (GZU), and the previous conferences have been held nier, Emmanuel; Jabin, Pierre-Emmanuel; Meinhardt, Hans; Mimura, in Jinhua (2005, 2007, 2010), Guangzhou (2009). Masayasu; Perthame, Benoit; Ruíz i Altaba, Ariel. Scientific Committee Co-Chairs: Shui-Nee Chow (Georgia Institute Information: http://www.ugr.es/~kinetic/biomat. of Technology, USA), Peter Bates (Michigan State University, USA). Organizing Committee: Honorary Chair: Benyu Guo (Shanghai * 8–9 Workshop on “Numerical knots: models & simulations”, Cen- Normal University, China), Chair: Maoan Han (Shanghai Normal Uni- tro di Ricerca Matematica “Ennio De Giorgi”, Collegio Puteano, Piazza versity, China), Co-Chairs: Jibin Li (Zhejiang Normal University and dei Cavalieri 3, 56126 Pisa, Italy. KUST, China) Jianshe Yu (Guangzhou University, China). Description: In this workshop we will focus on modeling open and Information: http://jxshix.people.wm.edu/ closed chains in a variety of biological and physical contexts, on the 2011shanghai/. analysis of the topological, geometric, and other properties of the * 16–20 Ramification in Algebra and Geometry at Emory, Emory modeled chains. Examples include lattice models, wormlike chains, University, Atlanta, Georgia. ideal knots, shape and scale of knotting, localization, constrained Description: This conference is primarily focused on the interaction environments, and knot energies with applications to DNA, proteins, between algebra and geometry within the following thematic areas: viral capsids and polymer melts. The arithmetic of linear algebraic groups and homogeneous spaces, Plenary Speakers: Jason Cantarella, UG, Athens, USA; Cristian Mi- cohomological invariants, essential dimension, division algebras and cheletti, SISSA, Trieste, Italy; Enzo Orlandini, INFN, IT; Eric Rawdon, the Brauer group, Chow groups and motivic decomposition, generic STU, St. Paul, USA; Rob Scharein, SFSU, San Francisco, USA; Doros Galois extensions, and Brauer-Manin obstructions. Theodorou, NTUA, Athens, Greece; Mariel Vazquez (to be confirmed), Information: http://www.mathcs.emory.edu/RAGE/. SFSU, San Francisco, USA; Peter Virnau, UM, Mainz, Germany. Short Talks: Eleni Panagioutou, NTUA, Athens, Greece; Luca Tubiana, * 18–19 Workshop on “Entanglement and linking”, Centro di Ricerca SISSA, Trieste, Italy; Christos Tzoumanekas (to be confirmed), NTUA, Matematica “Ennio De Giorgi”, Collegio Puteano, Piazza dei Cavalieri Athens, Greece; Guillaume Witz (to be confirmed), EPFL, Lausanne, 3, 56126, Pisa, Italy. Zwitzerland. Description: This workshop will be mainly devoted to differential Thematic Workshop Conveners: Ken Millett, Eric Rawdon, Rob geometric, topological and hydrodynamical aspects of ordinary and Scharein (to be confirmed). higher-order linking, braiding and their asymptotic versions (helicity Contact: email: [email protected]. (This event is part of and its higher order analogues); integral formulae for higher order linking numbers and the quest for generalized “helicity bounds the intensive research period “Knots Applications”). energy” results and generalizations of Whitehead products, link- Information: http://www.crm.sns.it/event/206/. homotopy invariants of links and the homotopy invariants of as- * 13–15 The Mathematics of Porous Media, Radisson Blu Resort, sociated maps to configuration space, with applications to magne- Split, Croatia. tohydrodynamics of plasmas, vortices, and relaxations of braided Description: The aim of this International Conference is to celebrate magnetic fields. the 60th birthday of Professor C. J. (Hans) van Duijn. With his work, Invited Speakers: P. Akhmetiev, Izmiran, Russia; M. Berger, Exeter started in the 70s, Hans has essential and pioneering contributions Univ., United Kingdom; G. Hornig, Dundee Univ., United Kingdom; to the Mathematics of Porous Media. He is still an active researcher C.-C. Hsieh, Academia Sinica, TPE; L. Kauffman, Univ. Illinois, Chi- in this field, in spite of taking the lead of the Eindhoven University cago, USA; R. Komendarczyk, Tulane Univ., USA; M. Lefranc, Lille of Technology in the past seven years. The programme will consist of Univ., France; J. Parsley, Wake Forest Univ., USA; R. Ricca, Univ. keynote lectures, two lectures dealing with aspects of the scientific Milano-Bicocca, Italy. work of C. J. van Duijn, shorter lectures (by invitation) and poster Short Talks: A. Benvegnù, Univ. Verona, Italy; F. Maggioni, Univ. Ber- presentations. The number of participants is limited to 35. At the gamo, Italy; C. Shonkwiler, Haverford College, USA. moment no parallel sections are planned. We address the invitation * 23–27 7th conference on Stochastic Analysis, Random Fields to participate in this conference to the friends and colleagues of of and Applications, Centro Stefano Franscini (Monte Verita), Ascona, Hans van Duijn, but further to all younger researchers and Ph.D. stu- Switzerland. dents who work in this exiting field or want to learn more about it.

740 NNOTICESOTICES OFOF THETHE AMSAMS VOLUME 58, NUMBER 51 Mathematics Calendar

Information: http://www.am.uni-erlangen.de/ annual meeting, to discuss very recent developments in the field. modeling-simulation-optimization/mpm2011.html. It consists of a single track of invited talks, which are scheduled to * 13–16 Poisson Geometry and Applications, Figueira da Foz, Por- leave ample time for discussion and interaction among the partici- tugal. pants. To encourage participation of students and junior research- Description: The aim of the conference is to bring together research- ers, no registration fee is charged, and financial support is available. ers working in Poisson geometry and related topics (like integrable The workshop features a poster session. systems, geometric mechanics and quantization). Deadline: For poster abstract submissions and applications for Invited speakers: J. Cariñena (Zaragoza), M. Crainic (Utrecht), I. Cruz travel support is March 15, 2011. (Oporto), D. Iglesias-Ponte (La Laguna), Y. Kosmann-Schwarzbach Information: http://www.math.uwaterloo.ca/~mip2011. (Paris), C. Laurent-Gengoux (Coimbra), R. Loja Fernandes (Lisbon), * 20–24 2011 Casablanca International Workshop on Mathematical C. M. Marle (Paris), J. C. Marrero (La Laguna), E. Martinez (Zaragoza), Biology, University Hassan II, Casablanca, Morocco. F. Petalidou (Thessaloniki), T. Ratiu (Lausanne), V. Rubtsov (Angers), Description: This workshop intends to bring together expert re- F. Schätz (Lisbon), M. Stiénon (Penn-State Univ.), P. Xu (Penn-State searchers from around the world to exchange ideas and share their Univ.), M. Zambon (Madrid). research results about all aspects of Mathematical Biology in general Registration: To register please follow the instructions in the con- and the use of optimal control theory in biology and medicine in ference website: http://www.mat.uc.pt/~poissonga/ (click particular. This meeting also intends to promote and explore new on the link “On-line registration” in the left side menu). Please send collaborations among the international scientific community and your questions or comments to: [email protected]. in particular, researchers in Africa and Morocco. The workshop will Information: http://www.mat.uc.pt/~poissonga/. include nine plenary talks by leading researchers in mathematical * 14–23 Advanced Course on Dynamical Systems, Centre de Recerca biology, parallel sessions of invited and contributed talks, a gradu- Matemàtica, Bellaterra, Barcelona, Spain. ate students and postdoctoral fellows poster session and an expert Scientific committee: George Elliott, Andrew S. Toms. panel to discuss current problems and future directions in math- Information: http://www.crm.cat/acdynamical. ematical modeling of biological processes. Information: http://sites.google.com/a/asu.edu/ * 15–16 Workshop on “DNA knots”, Centro di Ricerca Matematica cicwmb/. “Ennio De Giorgi”, Collegio Puteano, Piazza dei Cavalieri 3, 56126 Pisa, Italy. * 21–24 Summer School Geodesic Flow, Negative Curvature and Description: Viruses pack DNA very tightly in capsids; upon release Isomorphism Conjectures, Georg-August Universität, Göttingen, and circularization in the globular phase, the DNA knots produced Germany. can inform about the packing geometry. DNA is also packed very Description: School (for graduate students) on geodesic flow in nega- tightly in eukaryotic chromosomes, and some DNA knotting and link- tive curvature (broadly defined) and its applications. Second part of ing may be present in the chromosome organization.This workshop the school on the Farrell-Jones isomorphism conjecture (one of the will have talks discussing various aspects of DNA knotting and the applications) and more general aspects of geometric group theory. relationship of knotting to biological understanding. Speakers: Patrick Eberlein (University of North Carolina), Wolfgang Plenary Speakers: Javier Arsuaga, SFSU, San Francisco, USA; Dorothy Lück (Bonn), Romain Tessera (Lyon). Buck, Imperial College London, UK; Isabel Darcy, Univ. Iowa, USA; Information: http://www.uni-math.gwdg.de/geoflow. Cristian Micheletti, SISSA, Trieste, Italy; Andrzej Stasiak, Univ. Laus- * 26–July 1 II Jaen Conference on Approximation Theory, Computer anne, Switzerland; De Witt Sumners, Florida State Univ., USA; Mariel Aided Geometric Design, Numerical Methods and Applications, Vazquez (to be confirmed), SFSU, San Francisco, USA. Ubeda, Jaen, Spain. Short Talks: Marco Baiesi (to be confirmed), Univ. Padova, Italy; Description: The objective of this conference is to provide a useful Mauro Mauricio, Imperial College London, United Kingdom; Angelo and nice forum for researchers in the subjects to meet and discuss. Rosa (to be confirmed), IIT, Genova, Italy; Luca Tubiana, SISSA, Tri- In this sense, the conference programs have been designed to keep este, Italy; Karin Valencia, Imperial College London, United Kingdom. joined the group during five days with a program full of scientific Thematic Workshop Conveners: D. Buck, C. Micheletti, D. Sumners and social activities. The Conference will take place in Úbeda, a (to be confirmed). World Heritage Site. Contact: email: [email protected] (This event is part of the Invited speakers: Allan Pinkus, Technion, Israel; Francisco Marcel- intensive research period “Knots and Applications”). lán, Universidad Carlos III de Madrid, Spain; Hrushikesh N. Mhaskar, Information: http://www.crm.sns.it/event/207/. California State University, USA; Igor Shevchuk, University of Kyiv, * 15–18 International Conference on Mathematical Methods and Ukraine; Kirill A. Kopotun, University of Manitoba, Canada; Ronald Models in Biosciences (BIOMATH 2011), Bulgarian Academy of DeVore, Texas A&M University, USA; Tom Lyche, University of Oslo, Sciences, Sofia, Bulgaria. Norway; Zeev Ditzian, University of Alberta, Canada. We invite you to Description: The conference is devoted to recent research in biosci- contribute a talk or a poster. We provide the possibility of organizing ences based on applications of mathematics as well as mathematics minisymposia on subjects of current interest. The conference will be applied to or motivated by such applications. It is a multidisciplinary dedicated to Prof. Dany Leviatan on the occasion of his retirement. meeting forum for researchers who apply mathematical tools and Information: http://www.ujaen.es/revista/jja/jca/. methods of analysis to the study of phenomena in the broad fields * 27–July 1 3rd Workshop on Fluids and PDE, University of Campi- of biology, ecology, medicine, biotechnology and bioengineering. nas, Campinas, SP Brazil. Advanced mathematical tools relevant to deal with life science prob- Description: This is the third edition in a series of workshops lems are also welcome. Contributed talks in any of these fields are aimed at fostering collaboration among the growing community of invited for presentation at the conference. researchers working in Brazil on mathematical fluid mechanics, in Abstract deadline: April 30, 2011. particular on the incompressible Navier-Stokes and Euler equations, Information: http://www.biomath-bg.eu. as well as stimulating further collaboration with the international * 20–23 2011 Workshop on Mixed Integer Programming (MIP2011), community. This edition of the workshop will feature a series of tu- University of Waterloo, Waterloo, Ontario, Canada. torial lectures (the first day) aimed at graduate students and young Description: The Mixed Integer Programming (MIP) workshop series researchers, followed by specialized seminars by leading experts in brings together the integer optimization research community in an the field. There is space for contributed short talks as well as poster

MAY 2011 NOTICES OF THE AMS 741 Mathematics Calendar

presentations. Register at the website; to submit an oral communi- Topics: Classical and quantum integrable systems, Symmetries of cation or a poster and to apply for funding the registration must be Differential equations, Variational methods, Evolution equations, received no later than May 27th, 2011. Geometric methods in Classical Mechanics, Poisson and Symplec- Information: http://www.ime.unicamp.br/~fluid/WFEDP3. tic Geometry. Information: http://www.sigmaphi2011.org/ July 2011 events-detail.aspx?IDEvento=35. * 4–8 2011 Taiwan International Conference on Geometry: Special * 12–13 Workshop on “Topological dynamics in physics and biol- Lagrangians and Related Topics, Department of Mathematics, Na- ogy”, Centro di Ricerca Matematica “Ennio De Giorgi”, Collegio Pu- tional Taiwan University, Taipei, Taiwan. teano, Piazza dei Cavalieri 3, 56126 Pisa, Italy. Description: This conference will start a series of bi-yearly interna- Description: With this workshop we shall investigate the role of tional conferences on differential geometry in Taiwan. An important topological properties of knot theory in some physical and biologi- area in geometry will be specified as the main theme each time. Our cal systems, by exploring how topological invariants influence and purpose is to create a discussion and interaction platform in the constrain the dynamics and the energy minimization of physical chosen area, and at the same time to foster future cooperations and systems, from optics to polymer physics, from magnetic and nem- introduce new people into the field. Additional short courses may atic systems to soap films. also be arranged around the same time as the conference. Invited Speakers: Dorothy Buck, Imperial College, UK; Tetsuo De- Topic: Special Lagrangians and Related Topics will include special guchi, Ochanumizu Univ., Japan; Mark Dennis, Bristol Univ., UK; Lagrangians, Lagrangian mean curvature flow, J-holomorphic curve Giovanni Dietler, EPFL, Switzerland; Ray Goldstein (to be confirmed), techniques for Lagrangians, and the calibrated geometries in general. Cambridge Univ., UK; Cristian Micheletti, SISSA, Trieste, Italy; Michael The tentative topic for 2013 is “Geometry and General Relativity.” Monastyrsky, ITEP, Federal Republic of Russia; Enzo Orlandini, INFN, Information: http://www.tims.ntu.edu.tw/workshop/ Padova, Italy; Adriana Pesci (to be confirmed), Cambridge Univ., UK; Default/index.php?WID=111. Andrzej Stasiak, Univ. Lausanne, Switzerland; De Witt Sumners, * 6–8 DIMACS Workshop on Competitive Algorithms for Packet Florida State Univ., USA. Scheduling, Buffering and Routing in the Internet, DIMACS Cen- Contact: email: [email protected]. (This event is part of ter, CoRE Building, Rutgers University Piscataway, New Jersey. the intensive research period “Knots and Applications”). Description: The Internet employs the store-and-forward packet Information: http://www.crm.sns.it/event/221/. switching paradigm, where packets are forwarded in a hop-by- * 18–22 Infinity Conference, Centre de Recerca Matemàtica, Bellat- hop manner toward their destinations, and are stored at each erra, Barcelona, Spain. intermediate router until they can be sent to the next intermedi- Scientific committee: Sy Friedman, John Baldwin, Maria Luisa Bonet, ate router, chosen according to the routing policy. The main ad- Juan Carlos Martínez, Michael Rathjen. vantage of the packet switching paradigm is the ability to share Information: http://www.crm.cat/cinfinity. a common infrastructure for multiple connections using statisti- * 24–29 ICDEA2011: 17th International Conference on Difference cal multiplexing, which allows one to create networks at much Equations and Applications, Université du Québec à Trois-Rivières, lower cost with greater throughput, flexibility, and robustness. Québec, Canada. In this workshop we will consider optimization problems under Description: The conference is organized by the Department of various parameters that arise in the design and management of Mathematics and Computer Science and the Department of Physics packet networks, and the algorithms to solve them together with of the Université du Québec à Trois-Rivières (UQTR), under the aus- their competitive analysis. We are interested in algorithms that per- pices of the International Society of Difference Equations (ISDE). The form the various tasks needed in a packet network, such as routing, purpose of the conference is to bring together experts and students buffering or scheduling. We are interested both in work that focuses in the theory and applications of difference equations and discrete on a single component of the network, such as a single buffer or dynamical systems. a single switch (router), and in work that considers the network as Plenary speakers: Will be experts chosen from the many areas of a whole, such as work on routing or the interaction of the routing difference equations as well as experts in discrete dynamical sys- and scheduling decisions. Finally, we are interested both in work tems and their interplay with nonlinear science. Contributed talks that uses “classical” competitive analysis, and in work that suggests in any area of difference equations are welcome. methods to render the worst case approach of competitive analysis Scientific Committee: George Sell (chair), Saber Elaydi, Jean Mawhin, less worst-case oriented. Linda Allen, and Adel Antippa. Organizers: Alex Kesselman, Google; Alex Lopez-Ortiz, University Local organizing committee: Adel Antippa (chair), Louis Marchildon of Waterloo, alopez-ou at waterloo.ca; Yishay Mansour, Tel (chair), Ismaïl Biskri (chair), Boucif Amar Bensaber, Pierre Bénard, Aviv University; Adi Rosen, CNRS, Paris. Jean-Sébastien Boisvert, Jérémie Gobeil, Alain Goupil, Jérémie Ma- Deadlines: Pre-registration deadline: June 29, 2011. thieu, Mhamed Mesfioui, Sébastien Tremblay. Information: http://dimacs.rutgers.edu/Workshops/ Information: For more information please contact Dr. Adel An- Packet/. tippa (email: [email protected]) or visit http://www. * 9–10 Directions in Matrix Theory 2011, Department of Mathemat- icdea2011.org. ics, University of Coimbra, Portugal. * 24–30 Dynamical models in life sciences, University of Evora, Description: This workshop aims to be a forum of discussion of Evora, Portugal. frontline areas of Matrix Theory and its Applications. The work- Description: The aim of this summer school is to bring together shop will bring together renowned researchers of diverse fields specialists and students in mathematics, biology, physics and engi- fostering the exchange of experiences and insights from different neering with a common goal: the better understanding of the math- perspectives. ematics behind life sciences and the better understanding of life Information: http://www.mat.uc.pt/~cmf/Directions2011/ sciences using a deeper knowledge of mathematics. This will be a DMT2011.htm. joint event of the Portuguese Centro Internacional de Matem·tica, * 11–15 Workshop in Mathematical Physics, Agia Napa, Cyprus. the European Society for Mathematical and Theoretical Biology and Description: Part of Sigma Phi International Conference in Statisti- the European Mathematical Society in the historical city of Evora, cal Physics. Portugal, providing the perfect environment for the interaction

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between senior scientists in the field and students. It will consist Mathematics, Vladivostok, vice-chairman); Frederic Cohen (Roches- of 7 mini-courses aimed to Ph.D. students and junior post-docs, in ter University, USA); Mikiya Masuda (Osaka City University, Japan); mathematics, biology and related areas. Taras Panov (Moscow State University); Iskander Taimanov (Sobo- Information: http://c3.glocos.org/ssmtb/. lev Institute of Mathematics); Alexander Podgaev (Pacific National * 25–29 NSF-CBMS Regional Research Conference, Mathematical University). Epidemiology and its Applications, East Tennessee State Univer- Important dates: Deadline for registration: April 30, 2011. Deadline sity, Johnson City, Tennessee. for submission of abstracts: May 30, 2011. Recommended arrival Description: Carlos Castillo-Chavez and Fred Brauer will give ten day: September 4, 2011. September 5–10, 2011: Conference. keynote lectures, and there will be breakout sessions and formation Information: See http://iam.khv.ru/ttaf-2011/ of working groups. A poster session will also be held for participants the1st_announcement.htm. to display their work. Full support will be offered to between 35 and * 11–15 Israeli-Polish Mathematical Meeting, University of Łódz´, 40 participants. See webpage for more details. Poland. Information: http://www.etsu.edu/cas/math/cbms.aspx. Description: Israeli-Polish Mathematical Meeting is a joint initiative August 2011 of the Polish Mathematical Society (PTM) and Israel Mathematical Union (IMU). The main purpose of the conference is to stimulate the * 18–20 The First Strathmore University Mathematics Conference. exchange of new ideas in all aspects of mathematics. Mathematicians “Strengthening Mathematics Research, Applications and Educa- tion in Africa”, Strathmore University, Nairobi, Kenya. from other countries are also cordially invited to participate. The Description: The Centre of Advanced Research in Mathematical Sci- meeting program will cover many topics pertaining to mathematical ences (CARMS) of Strathmore University will hold its “First Interna- research conducted in Israel and Poland. The meeting will consist tional Conference in Mathematical Sciences”. of plenary lectures, thematic sections and other informal scientific Theme: “Strengthening Mathematics Research, Applications and discussions and social activities as well. All the talks will be in Eng- Education in Africa”. The first morning of the conference will also lish. The meeting will be hosted by the University of Łódz´, Faculty serve as a launch for CARMS. The theme of the launch is “The Role of Mathematics and Computer Science, Łódz´, Poland. The confer- of Mathematics and Statistics in Vision 2030, Kenya”. The conference ence will start in the morning of Monday, September 12, 2011 and will feature plenary sessions, invited speakers, poster presentations, end in the afternoon of Thursday, September 15, 2011. and be preceded by workshops. The five proposed workshops cover Information: http://imuptm.math.uni.lodz.pl. a wide area of interests. The main objective of this conference is to * 12–16 Satellite Meeting Unravelling and Controlling Discrete Dy- provide a forum for researchers, educators, students and industries namical Systems, Vienna, Austria. interested in mathematical sciences. This process will involve local, Description: The Satellite Meeting Unravelling and Controlling Dis- regional and international mathematicians. crete Dynamical Systems is organized during the 8th European Con- Information: http://www.strathmore.edu/maths/. ference on Complex Systems (ECCS). * 31–September 3 XX International Fall Workshop on Geometry Goals: Are fourfold: foster the interest in discrete dynamical sys- and Physics, Instituto de Ciencias Matemáticas, ICMAT (CSIC-UAM- tems; communicate the most recent advances on the means to quan- UC3M-UCM), Madrid, Spain. titatively grasp and control discrete dynamical systems; perpetuate Description: The Fall Workshops on Geometry and Physics have been the dynamical systems point of view on the intriguing dynamics of held yearly since 1992, and bring together Spanish and Portuguese cellular automata; gain insight into the dynamics of models based geometers and physicists, along with an ever increasing number of upon discrete modelling paradigms. participants from outside the Iberian peninsula. The meetings aim Deadline: For abstract submission: May 10, 2011. to provide a forum for the exchange of ideas between researchers Information: http://www.disdysys.ugent.be/. of different fields in differential geometry, applied mathematics and physics, and always include a substantial number of enthusiastic October 2011 young researchers amongst the participants. * 7–9 ICMA2011: The Third Conference on Mathematical Modeling Program: Includes: Mini courses: Alberto Ibort (Univ. Carlos III), and Analysis of Populations in Biological Systems, Trinity Univer- Franco Magri (Univ. Milano Bicocca). sity, San Antonio, Texas. Invited speakers: Mauro Carfora (Univ. Pavia), Piotr T. Chrusciel This conference will build upon the success of the (Univ. Vienna), Marisa Fernández (Univ. PaÌs Vasco), Gary Gibbons Description: (Univ. Cambridge), Janusz Grabowski (Polish Academy of Sciences), previous two conferences that were held on the campuses of the Renate Loll (Utrecht Univ.), Patrizia Vitale (Naples Univ.). University of Arizona in 2007 and University of Alabama Huntsville Registration/Deadline: The on-line registration will be opened on in 2009. Furthermore, the proceedings of ICMA I were published in March 1, 2011. two issues of the Journal of Biological Dynamics and one issue in the Information: http://www.icmat.es/congresos/xxifwgp/. Journal of Difference equations. The proceedings of ICMA II will be published in two issues of the Journal of Biological Dynamics. The September 2011 main focus of this conference will be on ecology and evolution. In ad- * 5–9 AGMP&MP2 Summer School: Mathematical Topics in Quan- dition, there will be a focus on ecological and evolutionary problems tum Mechanics and Quantum Information, Tjärnö, Sweden. in related fields, such as environmental science, epidemiology, etc. Description: The aim of the Summer School is to introduce Ph.D. We will invite researchers working on model derivation and analysis, students and junior researchers of mathematical and physical spe- data testing, and model simulations in these fields. cialities to mathematical methods of quantum mechanics and quan- Scientific Committee: Chris Cosner, Jim Cushing (chair), Maia Mart- tum information. cheva, Gail Wolkowicz, and Sebastian Schrieber. Information: http://www.agmp.eu/3q11/. Organizing Committee: Saber Elaydi (chair), Jim Cushing, Jia Li, * 5–10 Toric Topology and Automorphic Functions, Pacific National David Ribble, Peter Olofsson, and Cabral Balreira. University, Khabarovsk, Russia. Information: For more information contact Dr. Saber Elaydi, Confer- Program Committee: Victor Buchstaber (Steklov Mathematical ence Director (email: [email protected]) and visit http:// Institute, Moscow, chairman); Mikhail Guzev (Institute of Applied web.trinity.edu/x8339.xml.

MAY 2011 NOTICES OF THE AMS 743 Mathematics Calendar

* 10–14 AIM Workshop: Weighted singular integral operators and Information: http://aimath.org/ARCC/workshops/ non-homogenous harmonic analysis, American Institute of Math- hyperbolicpoly.html. ematics, Palo Alto, California. January 2012 Description: This workshop, sponsored by AIM and the NSF, will focus on recent developments on weighted inequalities for singular * 4–7 Joint Mathematics Meetings, Boston, Massachusetts. integral operators and the connection with questions in geometric Information: http://www.ams.org/meetings/national/ measure theory and PDEs. jmm/2138_intro.html. ∗ Information: http://aimath.org/ARCC/workshops/ * 23–27 AIM Workshop: Set theory and C -algebras, American In- singularintops.html. stitute of Mathematics, Palo Alto, California. Description: This workshop, sponsored by AIM and the NSF, will be * 24–26 Algebra Geometry Mathematical Physics, University of ∗ Haute Alsace, Mulhouse, France. devoted to applications of set theory to C -algebras. Main topics: Include, but are not limited to: Deformation theory and Information: http://aimath.org/ARCC/workshops/ quantization, Hom-algebras and n-ary algebraic structures, Hopf settheorycstar.html. algebra, quantum algebra, Integrable systems, Jet theory and Weil March 2012 bundles, Lie theory and applications, Noncommutative and nonasso- * 3–4 AMS Western Section Meeting, University of Hawaii, Honolulu, ciative algebra, Representation theory, Number theoretical methods Hawaii. in string theory, Quantum geometry, Spectral and computational Information: http://www.ams.org/meetings/sectional/ methods for Maxwell equations, Ternary algebras and applications. sectional.html. Information: http://www.agmp.eu/mul11/. * 10–11 AMS Southeastern Section Meeting, University of South * 24–28 AIM Workshop: The Kardar-Parisi-Zhang equation and Florida, Tampa, Florida. universality class, American Institute of Mathematics, Palo Alto, Information: http://www.ams.org/meetings/sectional/ California. sectional.html. Description: This workshop, sponsored by AIM and the NSF, will be devoted to the study of the the Kardar-Parisi-Zhang equation and * 12–16 AIM Workshop: Classifying fusion categories, American universality class. Institute of Mathematics, Palo Alto, California. Description: This workshop, sponsored by AIM and the NSF, will be Information: http://aimath.org/ARCC/workshops/ devoted to the classification problem for fusion categories, includ- kpzequation.html. ing those with additional structure, e.g., ribbon and modular fusion * 31–November 4 AIM Workshop: Geometry of large networks, categories. More specifically, we will focus on the development American Institute of Mathematics, Palo Alto, California. and application of both theoretical and computational techniques Description: This workshop, sponsored by AIM and the NSF, is de- for classifying fusion categories that are “small” in various senses. voted to geometric models of large networks. It intends to bring to- Information: http://aimath.org/ARCC/workshops/ gether mathematicians, computer scientists, and engineers. fusioncat.html. Information: http://aimath.org/ARCC/workshops/ * 17–18 AMS Eastern Section Meeting, George Washington University, largenetworks.html. Washington, District of Columbia. November 2011 Information: http://www.ams.org/meetings/sectional/ sectional.html. * 7–11 AIM Workshop: The Klein project, American Institute of Math- ematics, Palo Alto, California. * 30–April 1 AMS Central Section Meeting, University of Kansas, Description: This workshop, sponsored by AIM and the NSF, will be Lawrence, Kansas. devoted to the development of the Klein Project, specifically to the Information: http://www.ams.org/meetings/sectional/ preparation of “vignettes” that characterise important ideas within sectional.html. the field of the mathematical sciences using specific examples. Information: http://aimath.org/ARCC/workshops/ kleinproject.html. The following new announcements will not be repeated until the criteria in the next to the last paragraph at the bottom * 17–18 Jornadas de Criptografía (Spanish Cryptography Days), of the first page of this section are met. Murcia, Spain. Description: As part of the activities of the Centenary of the Real May 2012 Sociedad Española de Matemáticas the Algebra Group of Murcia * 20–2 7th European Conference on Elliptic and Parabolic Problems, organize the Jornadas de Criptografía SCD2011 with the aim of Gaeta, Italy. bringing together researchers in cryptography, including mathemati- Description: Besides Elliptic and Parabolic issues, the topics of cians and computer scientists, as well as industrial and government the conference include Geometry, Free Boundary Problems, Fluid organizations interested in new developments and applications of Mechanics, Evolution Problems in general, Calculus of Variations, cryptography. Homogenization, Control, Modeling and Numerical Analysis. In ad- Information: http://www.um.es/docencia/jsimon/ dition to the plenary talks parallel sessions and minisymposia will CongresoCripto/CryptographyMeeting.html. be organized. December 2011 Information: http://www.math.uzh.ch/gaeta2012. * 5–9 AIM Workshop: Stability, hyperbolicity, and zero localization of functions, American Institute of Mathematics, Palo Alto, Califor- nia; Description: This workshop, sponsored by AIM and the NSF, will be devoted to the emerging theory of stability and hyperbolicity of functions, in particular the cases of polynomials and analytic func- tions of one or several variables.

744 NNOTICESOTICES OFOF THETHE AMSAMS VOLUME 58, NUMBER 51 Classified Advertisements

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ALABAMA discipline and in multidisciplinary initia- CHILE tives. Documentation of such success SHELTON STATE COMMUNITY COLLEGE should include a record of publication PONTIFICIA UNIVERSIDAD CATOLICA in both mathematics and a multidisci- Department of Mathematics DE CHILE plinary application area and examples Instructor, Mathematics of collaboration and program building. Departamento de Matemticas Shelton State Community College is ac- Special emphasis will be placed on ap- The Department of Mathematics invites cepting applications for: Instructor, Math- plied analysis and scientific computation. applications for three tenure-track posi- ematics. For Information, visit http:// Areas of particular interest are multiscale tions at the assistant professor level www.sheltonstate.edu, or call the modeling and simulations as well as un- beginning either March or August 2012. Office of Human Resources at 205-391- certainty analysis. Applicants should have a Ph.D. in math- 2272 EOE Additional information can be obtained ematics, proven research potential either by contacting the search committee chair, in pure or applied mathematics, and Dr. Jay R. Walton ([email protected]. a strong commitment to teaching and edu). research. The regular teaching load for TEXAS Individuals wishing to be considered for assistant professors consists of three this position should send a copy of their one-semester courses per year, reduced TEXAS A&M UNIVERSITY CV and a letter of interest to: to two during the first two years. The an- Senior Faculty Position in Applied and Dr. Jay R. Walton, Chair nual salary will be US$45,000 (calculated Computational Mathematics IUMRI Mathematics Search Commit- at the current exchange rate of 500 chilean tee pesos per dollar). As part of Texas A&M University’s recogni- Department of Mathematics Please send a letter indicating your main tion of the increasing importance of the 3368 TAMU research interests, potential collaborators modeling and computational sciences, Texas A&M University in our department (http://www.mat. http:// the Department of Mathematics ( College Station, Texas 77843-3368 puc.cl), detailed curriculum vitae, and www.math.tamu.edu) is recruiting for Electronic submissions will also be ac- three letters of recommendation to: a senior faculty position in applied and cepted and should be sent to: jwalton@ Director Departamento de Matem- computational mathematics. This position math.tamu.edu, with IUMRI Mathematics ticas, is one of three new senior lines dedicated Position in the Subject Line. Additional Pontificia Universidad Catolica de to computational science that were cre- information and letters of reference will Chile, ated as part of an initiative led by the be solicited after a preliminary review. Av. Vicua Mackenna 4860 Santiago, Institute for Applied Mathematics and Review of the applicant pool will begin Chile; Computational Science (http://iamcs. April 1, 2011. Start dates are flexible, and fax: (56-2) 552-5916; tamu.edu). Considerable startup funding the position will remain open until filled. email: [email protected] is available. Texas A&M University is an Equal Op- Computational science has become For full consideration, complete applica- portunity Employer and has a policy of inherently multidisciplinary. As a result, tion materials must arrive by June 30, being responsive to the needs of dual- successful candidates for this position 2011. career couples. 000027 should be able to demonstrate a strong 000031 record of research accomplishments and leadership both within the mathematics

Suggested uses for classified advertising are positions available, books or June 28, 2011; October 2011 issue–July 28, 2011; November 2011 issue–August lecture notes for sale, books being sought, exchange or rental of houses, 30, 2011; December issue–September 28, 2011. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, age, The 2011 rate is $3.25 per word. No discounts for multiple ads or sex, race, religion, or national origin. “Positions Available” advertisements from institutions outside the U.S. cannot be published unless they are the same ad in consecutive issues. For an additional $10 charge, an- accompanied by a statement that the institution does not discriminate on nouncements can be placed anonymously. Correspondence will be these grounds whether or not it is subject to U.S. laws. Details and specific forwarded. wording may be found on page 667 (vol. 56). Advertisements in the “Positions Available” classified section will be set Situations wanted advertisements from involuntarily unemployed math- with a minimum one-line headline, consisting of the institution name above ematicians are accepted under certain conditions for free publication. Call body copy, unless additional headline copy is specified by the advertiser. toll-free 800-321-4AMS (321-4267) in the U.S. and Canada or 401-455-4084 Headlines will be centered in boldface at no extra charge. Ads will appear worldwide for further information. in the language in which they are submitted. Submission: Promotions Department, AMS, P.O. Box 6248, Providence, There are no member discounts for classified ads. Dictation over the Rhode Island 02940; or via fax: 401-331-3842; or send email to [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 2011 billed upon publication. issue–April 28, 2011; August 2011 issue–May 27, 2010; September 2011 issue–

MAY 2011 NOTICES OF THE AMS 745 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 R. Plymen, Geometric structure in the representation theory of reductive p-adic groups II; B. Casselman, The construction of Geometry Hecke algebras associated to a Coxeter group; J. Hakim and J. M. Lansky, Distinguished supercuspidal representations of SL2; J.-L. Kim and J.-K. Yu, Twisted Levi sequences and explicit types on Sp4; F. Murnaghan, Regularity and distinction of supercuspidal Harmonic Analysis representations; M. Nevins, Patterns in branching rules for irreducible representations of SL2(k), for k a p-adic field; R. Portilla, on Reductive, p-adic Parametrizing nilpotent orbits in p-adic symmetric spaces; S. Spallone, An integration formula of Shahidi; M. H. Weissman, Groups Managing metaplectiphobia: Covering p-adic groups. Robert S. Doran, Texas Christian Contemporary Mathematics, Volume 543 University, Ft. Worth, TX, Paul J. June 2011, 277 pages, Softcover, ISBN: 978-0-8218-4985-9, Sally, Jr., University of Chicago, LC 2011000976, 2010 Mathematics Subject Classification: 22E50, IL, and Loren Spice, Texas 11F70, 22E35, 20G25, 20C33, 20G40, 20G05, AMS members Christian University, Ft. Worth, US$79.20, List US$99, Order code CONM/543 TX, Editors

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Representations of Reductive, p-adic Introduction to Groups, which was held on January 16, 2010, in San Francisco, Representation California. One of the original guiding philosophies of harmonic analysis on Theory p-adic groups was Harish-Chandra’s Lefschetz principle, which Pavel Etingof, Massachusetts suggested a strong analogy with real groups. From this beginning, Institute of Technology, the subject has developed a surprising variety of tools and applications. To mention just a few, Moy-Prasad’s development of Cambridge, MA, Oleg Golberg, Bruhat-Tits theory relates analysis to group actions on locally finite Sebastian Hensel, Universität polysimplicial complexes; the Aubert-Baum-Plymen conjecture Bonn, Germany, Tiankai Liu, relates the local Langlands conjecture to the Baum-Connes Massachusetts Institute of conjecture via a geometric description of the Bernstein spectrum; Technology, Cambridge, MA, the p-adic analogues of classical symmetric spaces play an essential role in classifying representations; and character sheaves, originally Alex Schwendner, Two Sigma developed by Lusztig in the context of finite groups of Lie type, also Investments, New York, NY, have connections to characters of p-adic groups. Dmitry Vaintrob, Harvard The papers in this volume present both expository and research University, Cambridge, MA, and articles on these and related topics, presenting a broad picture Elena Yudovina, University of of the current state of the art in p-adic harmonic analysis. The Cambridge, United Kingdom; concepts are liberally illustrated with examples, usually appropriate with historical interludes by for an upper-level graduate student in representation theory or number theory. The concrete case of the two-by-two special linear Slava Gerovitch, Massachusetts group is a constant touchstone. Institute of Technology, Contents: P. N. Achar and C. L. R. Cunningham, Toward a Mackey Cambridge, MA formula for compact restriction of character sheaves; J. D. Very roughly speaking, representation theory studies symmetry in Adler, S. DeBacker, P. J. Sally, Jr., and L. Spice, Supercuspidal linear spaces. It is a beautiful mathematical subject which has many characters of SL over a p-adic field; A.-M. Aubert, P. Baum, and 2 applications, ranging from number theory and combinatorics to

746 Notices of the AMS Volume 58, Number 5 New Publications Offered by the AMS geometry, probability theory, quantum mechanics, and quantum partition via shifting; Good triangulations and meshing; field theory. Approximating the Euclidean traveling salesman problem (TSP); Approximating the Euclidean TSP using bridges; Linear The goal of this book is to give a “holistic” introduction to programming in low dimensions; Polyhedrons, polytopes, and representation theory, presenting it as a unified subject which linear programming; Approximate nearest neighbor search in low studies representations of associative algebras and treating the dimension; Approximate nearest neighbor via point-location; The representation theories of groups, Lie algebras, and quivers as Johnson-Lindenstrauss lemma; Approximate nearest neighbor special cases. Using this approach, the book covers a number of (ANN) search in high dimensions; Approximating a convex body by standard topics in the representation theories of these structures. an ellipsoid; Approximating the minimum volume bounding box of Theoretical material in the book is supplemented by many problems a point set; Coresets; Approximation using shell sets; Duality; Finite and exercises which touch upon a lot of additional topics; the more metric spaces and partitions; Some probability and tail inequalities; difficult exercises are provided with hints. Miscellaneous prerequisite; Bibliography; Index. The book is designed as a textbook for advanced undergraduate and Mathematical Surveys and Monographs, Volume 173 beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of July 2011, approximately 358 pages, Hardcover, ISBN: 978-0-8218- abstract algebra. 4911-8, LC 2011002940, 2010 Mathematics Subject Classification: Contents: Introduction; Basic notions of representation theory; 68U05, 68W25; 68P05, 52Cxx, AMS members US$78.40, List US$98, General results of representation theory; Representations of Order code SURV/173 finite groups: Basic results; Representations of finite groups: Further results; Quiver representations; Introduction to categories; Homological algebra; Structure of finite dimensional algebras; References for historical interludes; Bibliography; Index. Geometry and Topology Student Mathematical Library, Volume 59 August 2011, approximately 232 pages, Softcover, ISBN: 978-0-8218- 5351-1, 2010 Mathematics Subject Classification: 16Gxx, 20Gxx, Grassmannians, AMS members US$33.60, List US$42, Order code STML/59 Moduli Spaces and Vector Bundles David A. Ellwood, Clay Applications Mathematics Institute, Cambridge, MA, and Emma Previato, Boston University, MA, Geometric Editors

Approximation This collection of cutting-edge articles Algorithms on vector bundles and related topics originated from a CMI workshop, held in October 2006, that brought Sariel Har-Peled, University of together a community indebted to the pioneering work of P. E. Illinois at Urbana-Champaign, IL Newstead, visiting the United States for the first time since the 1960s. Moduli spaces of vector bundles were then in their infancy, Exact algorithms for dealing with but are now, as demonstrated by this volume, a powerful tool in geometric objects are complicated, hard symplectic geometry, number theory, mathematical physics, and to implement in practice, and slow. Over algebraic geometry. In fact, the impetus for this volume was the last 20 years a theory of geometric to offer a sample of the vital convergence of techniques and approximation algorithms has emerged. fundamental progress, taking place in moduli spaces at the outset These algorithms tend to be simple, fast, and more robust than their of the twenty-first century. exact counterparts. This volume contains contributions by J. E. Andersen and N. L. This book is the first to cover geometric approximation algorithms Gammelgaard (Hitchin’s projectively flat connection and Toeplitz in detail. In addition, more traditional computational geometry operators), M. Aprodu and G. Farkas (moduli spaces), D. Arcara and techniques that are widely used in developing such algorithms, A. Bertram (stability in higher dimension), L. Jeffrey (intersection like sampling, linear programming, etc., are also surveyed. cohomology), J. Kamnitzer (Langlands program), M. Lieblich Other topics covered include approximate nearest-neighbor (arithmetic aspects), P. E. Newstead (coherent systems), G. Pareschi search, shape approximation, coresets, dimension reduction, and and M. Popa (linear series on Abelian varieties), and M. Teixidor i embeddings. The topics covered are relatively independent and are Bigas (bundles over reducible curves). supplemented by exercises. Close to 200 color figures are included These articles do require a working knowledge of algebraic in the text to illustrate proofs and ideas. geometry, symplectic geometry and functional analysis, but should Contents: The power of grids—closest pair and smallest appeal to practitioners in a diversity of fields. No specialization enclosing disk; Quadtrees—hierarchical grids; Well-separated pair should be necessary to appreciate the contributions, or possibly to decomposition; Clustering—definitions and basic algorithms; On be stimulated to work in the various directions opened by these complexity, sampling, and ε-nets and ε-samples; Approximation path-blazing ideas; to mention a few, the Langlands program, via reweighting; Yet even more on sampling; Sampling and stability criteria for vector bundles over surfaces and threefolds, the moments technique; Depth estimation via sampling; linear series over abelian varieties and Brauer groups in relation to Approximating the depth via sampling and emptiness; Random arithmetic properties of moduli spaces.

May 2011 Notices of the AMS 747 New AMS-Distributed Publications

This item will also be of interest to those working in algebra and geometry of biharmonic maps; G. Calvaruso, Constructing metrics algebraic geometry. with prescribed geometry; J. Bolton and L. Fernández, On the regularity of the space of harmonic 2-spheres in the 4-sphere; Titles in this series are co-published with the Clay Mathematics S. Heller, Conformal fibrations of 3 by circles; K. Leschke, Institute (Cambridge, MA). S Harmonic map methods for Willmore surfaces; F. Mercuri, Contents: J. E. Andersen and N. L. Gammelgaard, Hitchin’s S. Montaldo, and I. I. Onnis, Some remarks on invariant surfaces projectively flat connection, Toeplitz operators and the asymptotic and their extrinsic curvature; P. Baird, E. Loubeau, and C. Oniciuc, expasnion of TQFT curve operators; M. Aprodu and G. Farkas, Harmonic and biharmonic maps from surfaces; J. Jost and F. M. Koszul cohomology and applications to moduli; D. Arcara and ¸Sim¸sir, Non-divergence harmonic maps; R. Slobodeanu, A note on A. Bertram, Reider’s theorem and Thaddeus pairs revisited; higher-charge configurations for the Faddeev-Hopf model; J. Q. Ge L. Jeffrey, Intersection pairings in singular moduli spaces of and Z. Z. Tang, A survey on the DDVV conjecture; G. Bande and bundles; J. Kamnitzer, The Beilinson-Drinfeld Grassmannian and A. Hadjar, On the characteristic foliations of metric contact pairs; symplectic knot homology; M. Lieblich, Arithmetic aspects of C.-L. Bejan, A note on η-Einstein manifolds; M. I. Munteanu and moduli spaces of sheaves on curves; P. E. Newstead, Existence of A. I. Nistor, Minimal and flat surfaces in H2 × R with canonical α-stable coherent systems on algebraic curves; G. Pareschi and M. coordinates; R. C. Voicu, Ricci curvature properties and stability Popa, Regularity on abelian varieties III: Relationship with generic on 3-dimensional Kenmotsu manifolds; S. Gudmundsson and vanishing and applications; M. Teixidor i Bigas, Vector bundles on M. Svensson, On the existence of harmonic morphisms from reducible curves and applications. three-dimensional Lie groups. Clay Mathematics Proceedings, Volume 14 Contemporary Mathematics, Volume 542 June 2011, 180 pages, Softcover, ISBN: 978-0-8218-5205-7, 2010 May 2011, approximately 281 pages, Softcover, ISBN: 978-0-8218- Mathematics Subject Classification: 13D03, 14D20, 14F22, 14H60, 4987-3, LC 2011000414, 2010 Mathematics Subject Classification: 14K10, 22E57, 47B35, 53B10, 53D30, 57R56, AMS members US$44, 53-06, 53-XX, 58Exx; 15A45, 35-XX, 49S05, 57R17, 58D10, 81T20, List US$55, Order code CMIP/14 AMS members US$79.20, List US$99, Order code CONM/542

Harmonic Maps and Differential Geometry New AMS-Distributed E. Loubeau, Université de Bretagne, Brest, France, and Publications S. Montaldo, University of Cagliari, Italy, Editors

This volume contains the proceedings of a conference held in Cagliari, Italy, from Algebra and Algebraic September 7–10, 2009, to celebrate John C. Wood’s 60th birthday. Geometry These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of An Introduction to harmonic maps by J. C. Wood, open the proceedings. These are Groups and Lattices followed by a mix of surveys on Professor Wood’s area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Finite Groups and Positive Kähler manifolds and the DDVV conjecture, as well as several Definite Rational Lattices research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, Robert L. Griess, Jr., University contact pairs, prescribed Ricci curvature, conformal fibrations, of Michigan, Ann Arbor, MI the Fadeev-Hopf model, the compact support principle and the curvature of surfaces. Rational lattices occur throughout This item will also be of interest to those working in analysis. mathematics, as in quadratic forms, sphere packing, Lie theory, and integral Contents: J. C. Wood, Thirty-nine years of harmonic maps; A. Gerding, F. Pedit, and N. Schmitt, Constant mean curvature representations of finite groups. Studies of high-dimensional surfaces: An integrable systems perspective; J. C. Wood, Explicit lattices typically involve number theory, linear algebra, codes, combinatorics, and groups. This book presents a basic introduction constructions of harmonic maps; P. Baird and M. Wehbe, Discrete to rational lattices and finite groups and to the deep relationship harmonic map heat flow on a finite graph; G. Bande and between these two theories. D. Kotschick, Contact pairs and locally conformally symplectic structures; E. Musso, Congruence curves of the Goldstein-Petrich Robert L. Griess, Jr. is a professor of mathematics at the University flows; H. Ma and Y. Ohnita, Differential geometry of Lagrangian of Michigan. His various honors include a Guggenheim Fellowship, submanifolds and Hamiltonian variational problems; L. Ornea and an invited lecture at the International Congress of Mathematicians, M. Verbitsky, A report on locally conformally Kähler manifolds; membership in the American Academy of Arts and Sciences, and the M. Rigoli, M. Salvatori, and M. Vignati, k-Hessian differential 2010 AMS Leroy P. Steele Prize for his seminal construction of the inequalities and the compact support principle; H. Urakawa, The Monster group.

748 Notices of the AMS Volume 58, Number 5 New AMS-Distributed Publications

A publication of International Press. Distributed worldwide by the General Interest American Mathematical Society. Contents: Introduction; Bilinear forms, quadratic forms and their isometry groups; General results on finite groups and invariant lattices; Root lattices of types A, D, E; Hermite and Minkowski Tantrasa˙ngrahaof functions; Constructions of lattices by use of codes; Group N¯ılakanthaSomay¯aj¯ı theory and representations; Overview of the Barnes-Wall lattices; Construction and properties of the Barnes-Wall lattices; Even K. Ramasubramanian, ITT unimodular lattices in small dimensions; Pieces of eight; References; Bombay, Powai, India, and M. S. Index; Appendix A: The finite simple groups. Sriram, University of Madras, International Press Chennai, India February 2011, 251 pages, Softcover, ISBN: 978-1-57146-206-0, It is truly remarkable that N¯ılakanthaand 2010 Mathematics Subject Classification: 11H56, 20C10, 20C34, Copernicus, contemporaries living 4000 20D08, AMS members US$44, List US$55, Order code INPR/95 miles apart, should have independently made profound revisions to the classical epicyclic models of the planetary system at the same time. Here, Lectures on Gaussian for the first time, Westerners can read N¯ılakantha’sgreat work, Integral Operators and the Tantrasa˙ngraha, and learn the mathematical principles of Indian astronomy in their most developed form. This work has a Classical Groups major place in the canon of the history of science, enlarging our Yurii A. Neretin, University of worldwide view of the landmark human discoveries. Vienna, Austria – David Mumford Tantrasa˙ngraha, composed in 1500 CE by the renowned Kerala This book is an elementary self-contained astronomer N¯ılakanthaSomay¯aj¯ı,ranks along with Aryabhat¯ıya¯ of introduction to some constructions of Aryabhata¯ and Siddh¯anta´siromani of Bh¯askar¯ac¯aryaas a seminal representation theory and related topics work that significantly influenced further work on astronomy in of differential geometry and analysis. India. This text introduces a major revision of the traditional Topics covered include the theory of various Fourier-like integral planetary models, leading to a unified theory of planetary latitudes operators such as Segal–Bargmann transforms, Gaussian integral and a better formulation of the equation of center for the interior operators in L2 and in the Fock space, integral operators with planets (Mercury and Venus) than was previously available. theta-kernels, the geometry of real and p-adic classical groups and Several important innovations in mathematical technique are also symmetric spaces. included in Tantrasa˙ngraha, especially related to the computation The heart of the book is the Weil representation of the symplectic of accurate sine tables, the use of series for evaluating the sine group (real and complex realizations, relations with theta-functions and cosine functions, and a systematic treatment of the problems and modular forms, p-adic and adelic constructions) and related to the diurnal motion of the celestial objects. The spherical representations in Hilbert spaces of holomorphic functions of trigonometry relations presented in the text—applied to a variety of several complex variables. problems such as the computation of eclipses and elevation of Moon’s cusps—are also exact. This book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. This edition of Tantrasa˙ngraha will appeal to historians of Prerequisites are standard university courses in linear algebra, astronomy as well as those who are keen to know about the actual functional analysis, and complex analysis. computational procedures employed in Indian astronomy. All 432 verses have been translated into English and supplemented with A publication of the European Mathematical Society (EMS). detailed explanations through the use of mathematical equations, Distributed within the Americas by the American Mathematical tables, and figures. Society. A publication of Hindustan Book Agency. Distributed on an Contents: Gaussian integral operators; Pseudo-Euclidean exclusive basis by the AMS in North America. Online bookstore geometry and groups U(p, q); Linear symplectic geometry; The rights worldwide. Segal–Bargmann transform; Gaussian operators in Fock spaces; Gaussian operators. Details; Hilbert spaces of holomorphic Contents: Mean longitudes of planets; True longitudes of planets; functions in matrix balls; The Cartier model; Gaussian operators Gnomonic shadow; Lunar eclipse; Solar eclipse; Vyat¯ıp¯ata; over finite fields; Classical p-adic groups. Introduction; Weil Reduction to observation; Elevation of lunar horns; Appendices: representation over a p-adic field; Addendum; Bibliography; Representation of numbers; Spherical trigonometry; Coordinate Notation; Index. systems; Solution of the ten problems: A couple of examples from Yuktibh¯as¯a; Derivation of the maximum declination of the EMS Series of Lectures in Mathematics, Volume 13 Moon; The traditional Indian planetary model and its revision by February 2011, 571 pages, Softcover, ISBN: 978-3-03719-080-7, N¯ılakantha;Glossary; Bibliography; Index; Index of half-verses. 2010 Mathematics Subject Classification: 22-02, 22E46, 53C35, Hindustan Book Agency 22E50, 47G10, 32M15, 51N30, 14K25, 47B50, AMS members US$62.40, List US$78, Order code EMSSERLEC/13 February 2011, 642 pages, Hardcover, ISBN: 978-93-80250-09- 0, 2010 Mathematics Subject Classification: 01A32, 85-03, AMS members US$65.60, List US$82, Order code HIN/48

May 2011 Notices of the AMS 749 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.

Hector Ceniceros, University of California Santa Bar- Las Vegas, Nevada bara, Immersed boundaries in complex fluids. Tai-Ping Liu, Stanford University, Hilbert’s sixth prob- University of Nevada lem.

April 30 – May 1, 2011 Special Sessions Saturday – Sunday Advances in Modeling, Numerical Analysis and Compu- tations of Fluid Flow Problems, Monika Neda, University Meeting #1071 of Nevada, Las Vegas. Western Section Arithmetic Dynamics, Arthur Baragar, University of Associate secretary: Michel L. Lapidus Nevada, Las Vegas, and Patrick Ingram, University of Announcement issue of Notices: February 2011 Waterloo. Program first available on AMS website: March 17, 2011 Computational Algebra, Groups, and Applications, Ben- Program issue of electronic Notices: April 2011 jamin Fine, Fairfield University, Gerhard Rosenberger, Issue of Abstracts: Volume 32, Issue 3 University of Hamburg, Germany, and Delaram Kahrobaei, City University of New York. Deadlines Computational and Mathematical Finance, Hongtao Yang, University of Nevada, Las Vegas. For organizers: Expired Discrete Dynamical Systems in Graph Theory, Combi- For consideration of contributed papers in Special Ses- natorics, and Geometry, Eunjeong Yi and Cong X. Kang, sions: Expired Texas A&M University at Galveston. For abstracts: Expired Extremal Combinatorics, Jozsef Balogh, University of California San Diego, and Ryan Martin, Iowa State Uni- The scientific information listed below may be dated. versity. For the latest information, see www.ams.org/amsmtgs/ Flow-Structure Interaction, Paul Atzberger, University sectional.html. of California Santa Barbara, and Hector D. Ceniceros, University of California Santa Barbara. Invited Addresses Geometric Group Theory and Dynamics, Matthew Day, Elizabeth Allman, University of Alaska, Evolutionary Danny Calegari, and Joel Louwsma, California Institute of trees and phylogenetics: An algebraic perspective. Technology, and Andy Putman, Rice University. Danny Calegari, California Institute of Technology, Geometric PDEs, Matthew Gursky, Notre Dame Univer- Stable commutator length in free groups. sity, and Emmanuel Hebey, Université de Cergy-Pontoise.

750 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Meetings & Conferences

Knots, Surfaces and 3-manifolds, Stanislav Jabuka, Swa- Katrin Wehrheim, Massachusetts Institute of Technol- tee Naik, and Chris Herald, University of Nevada, Reno. ogy, Title to be announced. Lie Algebras, Algebraic Transformation Groups and Representation Theory, Andrew Douglas and Bart Van Special Sessions Steirteghem, City University of New York. Analysis, Probability, and Mathematical Physics on Frac- Multilevel Mesh Adaptation and Beyond: Computational tals (Code: SS 10A), Luke Rogers, University of Connecti- Methods for Solving Complex Systems, Pengtao Sun, Uni- cut, Robert Strichartz, Cornell University, and Alexander versity of Nevada, Las Vegas, and Long Chen, University Teplyaev, University of Connecticut. of California Irvine. Difference Equations and Applications (Code: SS 1A), Nonlinear PDEs and Variational Methods, David Costa Michael Radin, Rochester Institute of Technology. and Hossein Tehrani, University of Nevada, Las Vegas, Gauge Theory and Low-dimensional Topology (Code: SS and Zhi-Qiang Wang, Utah State University. 7A), Weimin Chen, University of Massachusetts-Amherst, Partial Differential Equations Modeling Fluids, Quansen and Daniel Ruberman, Brandeis University. Jiu, Capital Normal University, Beijing, China, and Jiahong Geometric Aspects of Analysis and Measure Theory Wu, Oklahoma State University. (Code: SS 9A), Leonid Kovalev and Jani Onninen, Syracuse Recent Advances in Finite Element Methods, Jichun Li, University, and Raanan Schul, State University of New University of Nevada, Las Vegas. York at Stony Brook. Recent Developments in Stochastic Partial Differential Geometric and Algebraic Topology (Code: SS 15A), Boris Equations, Igor Cialenco, Illinois Institute of Technology, Goldfarb and Marco Varisco, University at Albany, SUNY. and Nathan Glatt-Holtz, Indiana University, Bloomington. Geometric Structures on Manifolds with Special Holo- Set Theory, Douglas Burke and Derrick DuBose, Uni- nomy, and Applications in Physics (Code: SS 16A), Tamar versity of Nevada, Las Vegas. Friedmann, University of Rochester, Colleen Robles, Topics in Modern Complex Analysis, Zair Ibragimov, Texas A&M University, and Sema Salur, University of California State University, Fullerton, Zafar Ibragimov, Rochester. Urgench State University, and Hrant Hakobyan, Kansas Geometry of Arithmetic Groups (Code: SS 11A), Mladen State University. Bestvina, University of Utah, and Ken Brown, Martin Kassabov, and Tim Riley, Cornell University. Kac-Moody Lie Algebras, Vertex Algebras, and Related Ithaca, New York Topics (Code: SS 14A), Alex Feingold, Binghamton Uni- Cornell University versity, and Antun Milas, State University of New York at Albany. September 10–11, 2011 Mathematical Aspects of Cryptography and Cyber Se- curity (Code: SS 8A), Benjamin Fine, Fairfield University, Saturday – Sunday Delaram Kahrobaei, City University of New York, and Meeting #1072 Gerhard Rosenberger, Passau University and Hamburg Eastern Section University, Germany. Associate secretary: Steven H. Weintraub Multivariable Operator Theory (Code: SS 13A), Ronald Announcement issue of Notices: June 2011 G. Douglas, Texas A&M University, and Rongwei Yang, Program first available on AMS website: July 28, 2011 State University of New York at Albany. Program issue of electronic Notices: September 2011 Parabolic Evolution Equations of Geometric Type (Code: Issue of Abstracts: Volume 32, Issue 4 SS 4A), Xiaodong Cao, Cornell University, and Bennett Chow, University of California San Diego. Deadlines Partial Differential Equations of Mixed Elliptic- For organizers: Expired Hyperbolic Type and Applications (Code: SS 3A), Marcus For consideration of contributed papers in Special Ses- Khuri, Stony Brook University, and Dehua Wang, Univer- sions: May 24, 2011 sity of Pittsburgh. For abstracts: June 29, 2011 Representations of Local and Global Groups (Code: SS 12A), Mahdi Asgari, Oklahoma State University, and Birgit The scientific information listed below may be dated. Speh, Cornell University. For the latest information, see www.ams.org/amsmtgs/ Set Theory (Code: SS 2A), Paul Larson, Miami University, sectional.html. Ohio, Justin Moore, Cornell University, and Ernest Schim- merling, Carnegie Mellon University. Invited Addresses Species and Hopf Algebraic Combinatorics (Code: SS Mladen Bestvina, University of Utah, Title to be an- 6A), Marcelo Aguiar, Texas A&M University, and Samuel nounced. Hsiao, Bard College. Nigel Higson, Pennsylvania State University, Title to Symplectic Geometry and Topology (Code: SS 5A), Tara be announced. Holm, Cornell University, and Katrin Wehrheim, Massa- Gang Tian, Princeton University, Title to be announced. chusetts Institute of Technology.

MAY 2011 NOTICES OF THE AMS 751 Meetings & Conferences

New Developments in Graph Theory (Code: SS 10A), Winston-Salem, Joshua Cooper and Kevin Milans, University of South Carolina, and Carlos Nicolas and Clifford Smyth, Univer- North Carolina sity of North Carolina at Greensboro. Noncommutative Algebra (Code: SS 5A), Ellen E. Kirk- Wake Forest University man and James J. Kuzmanovich, Wake Forest University. September 24–25, 2011 Nonlinear Boundary Value Problems (Code: SS 9A), Maya Chhetri, University of North Carolina at Greensboro, and Saturday – Sunday Stephen B. Robinson, Wake Forest University. Meeting #1073 Nonlinear Dispersive Equations (Code: SS 4A), Sarah Southeastern Section Raynor, Wake Forest University, Jeremy Marzuola, Univer- Associate secretary: Matthew Miller sity of North Carolina at Chapel Hill, and Gideon Simpson, Announcement issue of Notices: June 2011 University of Toronto. Program first available on AMS website: August 11, 2011 Recent Advances in Infectious Disease Modeling (Code: Program issue of electronic Notices: September 2011 SS 8A), Fred Chen and Miaohua Jiang, Wake Forest Uni- Issue of Abstracts: Volume 32, Issue 4 versity. Symmetric Functions, Symmetric Group Characters, Deadlines and Their Generalizations (Code: SS 3A), Sarah Mason, For organizers: Expired Wake Forest University, Aaron Lauve, Loyola University- For consideration of contributed papers in Special Ses- Chicago, and Ed Allen, Wake Forest University. sions: June 7, 2011 For abstracts: August 2, 2011

The scientific information listed below may be dated. Lincoln, Nebraska For the latest information, see www.ams.org/amsmtgs/ sectional.html. University of Nebraska-Lincoln

Invited Addresses October 14–16, 2011 Benjamin B. Brubaker, Massachusetts Institute of Friday – Sunday Technology, Square ice, symmetric functions, and their connections to automorphic forms. Meeting #1074 Shelly Harvey, Rice University, Title to be announced. Central Section Allen Knutson, Cornell University, Title to be an- Associate secretary: Georgia Benkart nounced. Announcement issue of Notices: August 2011 Seth M. Sullivant, North Carolina State University, Title Program first available on AMS website: September 1, 2011 to be announced. Program issue of electronic Notices: October 2011 Special Sessions Issue of Abstracts: Volume 32, Issue 4 Algebraic and Geometric Aspects of Matroids (Code: SS Deadlines 1A), Hoda Bidkhori, Alex Fink, and Seth Sullivant, North Carolina State University. For organizers: Expired Applications of Difference and Differential Equations to For consideration of contributed papers in Special Ses- Biology (Code: SS 2A), Anna Mummert, Marshall University, sions: June 28, 2011 and Richard C. Schugart, Western Kentucky University. For abstracts: August 23, 2011 Combinatorial Algebraic Geometry (Code: SS 6A), W. Frank Moore, Wake Forest University and Cornell Univer- The scientific information listed below may be dated. sity, and Allen Knutson, Cornell University. For the latest information, see www.ams.org/amsmtgs/ Extremal Combinatorics (Code: SS 7A), Tao Jiang, Miami sectional.html. University, and Linyuan Lu, University of South Carolina. Geometric Knot Theory and its Applications (Code: SS Invited Addresses 12A), Yuanan Diao, University of North Carolina at Char- Lewis Bowen, Texas A&M University, Title to be an- lotte, Jason Parsley, Wake Forest University, and Eric nounced. Rawdon, University of St. Thomas. Emmanuel Candes, Stanford University, Title to be an- Low-Dimensional Topology and Geometry (Code: SS 13A), Shelly Harvey, Rice University, and John Etnyre, nounced (Erdo˝s Memorial Lecture). Georgia Institute of Technology. Alina Cojocaru, University of Illinois at Chicago, Title Modular Forms, Elliptic Curves, and Related Topics to be announced. (Code: SS 11A), Matthew Boylan, University of South Caro- Michael Zieve, University of Michigan, Title to be an- lina, and Jeremy Rouse, Wake Forest University. nounced.

752 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Meetings & Conferences

Special Sessions Program first available on AMS website: September 8, 2011 Algebraic Geometry and Graded Commutative Algebra Program issue of electronic Notices: October 2011 (Code: SS 8A), Susan Cooper and Brian Harbourne, Uni- Issue of Abstracts: Volume 32, Issue 4 versity of Nebraska-Lincoln. Deadlines Algorithmic and Geometric Properties of Groups and Semigroups (Code: SS 10A), Susan Hermiller and John For organizers: Expired Meakin, University of Nebraska-Lincoln. For consideration of contributed papers in Special Ses- Association Schemes and Related Topics (Code: SS 1A), sions: July 5, 2011 Sung Y. Song, Iowa State University, and Paul Terwilliger, For abstracts: August 30, 2011 University of Wisconsin, Madison. Asymptotic Behavior and Regularity for Nonlinear Evo- The scientific information listed below may be dated. lution Equations (Code: SS 4A), Petronela Radu and Lorena For the latest information, see www.ams.org/amsmtgs/ Bociu, University of Nebraska-Lincoln. sectional.html. Coding Theory (Code: SS 7A), Christine Kelley and Judy Invited Addresses Walker, University of Nebraska-Lincoln. Computational and Applied Mathematics (Code: SS 13A), Graeme Milton, University of Utah, Title to be an- Ludwig Kohaupt, Beuth University of Technology Berlin, nounced. Germany, and Yan Wu, Georgia Southern University. Lei Ni, University of California San Diego, Title to be Continuous and Numerical Analysis in the Control of announced. PDE’s (Code: SS 9A), George Avalos, Mohammad Ram- Igor Pak, University of California Los Angeles, Title to maha, and Daniel Toundykov, University of Nebraska- be announced. Lincoln. Monica Visan, University of California Los Angeles, Dynamic Systems on Time Scales with Applications Title to be announced. (Code: SS 3A), Lynn Erbe and Allan Peterson, University Special Sessions of Nebraska-Lincoln. Extremal and Probabilistic Combinatorics (Code: SS Celestial and Geometric Mechanics (Code: SS 5A), Len- 5A), Stephen Hartke and Jamie Radcliffe, University of nard Bakker and Tiancheng Ouyang, Brigham Young Nebraska-Lincoln. University. Invariants in Knot Theory and Low-dimensional To- Commutative Algebra (Code: SS 3A), Chin-Yi Jean Chan, Central Michigan University, and Lance E. Miller and Amu- pology (Code: SS 14A), Mark Brittenham, University of rag K. Singh, University of Utah. Nebraska-Lincoln, and Robert Todd, University of Ne- Electromagnetic Wave Propagation in Complex and braska at Omaha. Random Environments (Code: SS 4A), David Dobson, Uni- Local Commutative Algebra (Code: SS 11A), H An- versity of Utah, and Peijun Li, Purdue University. anthnarayan, University of Nebraska-Lincoln, Inês B. Geometric Evolution Equations and Related Topics Henriques, University of California Riverside, and Hamid (Code: SS 2A), Andrejs Treibergs, University of Utah, Salt Rahmati, Syracuse University. Lake City, Lei Ni, University of California San Diego, and Matrices and Graphs (Code: SS 12A), In-Jae Kim, Min- Brett Kotschwar, Arizona State University. nesota State University, Adam Berliner, St. Olaf College, Geometric, Combinatorial, and Computational Group Leslie Hogben, Iowa State University, and Bryan Shader, Theory (Code: SS 1A), Eric Freden, Southern Utah Univer- University of Wyoming. sity, and Eric Swenson, Brigham Young University. Quantum Groups and Representation Theory (Code: SS 2A), Jonathan Kujawa, University of Oklahoma, and Natasha Rozhkovskaya, Kansas State University. Recent Progress in Operator Algebras (Code: SS 6A), Port Elizabeth, Allan P. Donsig and David R. Pitts, University of Nebraska- Lincoln. Republic of South Salt Lake City, Utah Africa Nelson Mandela Metropolitan University University of Utah November 29 – December 3, 2011 October 22–23, 2011 Tuesday – Saturday Saturday – Sunday Meeting #1076 Meeting #1075 First Joint International Meeting between the AMS and the Western Section South African Mathematical Society. Associate secretary: Michel L. Lapidus Associate secretary: Matthew Miller Announcement issue of Notices: August 2011 Announcement issue of Notices: June 2011

MAY 2011 NOTICES OF THE AMS 753 Meetings & Conferences

Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Honolulu, Hawaii Issue of Abstracts: Not applicable Deadlines University of Hawaii For organizers: See the information at http://www.nmmu. March 3–4, 2012 ac.za/sams-ams2011/ssprop.htm For consideration of contributed papers in Special Ses- Saturday – Sunday sions: To be announced For abstracts: To be announced Meeting #1078 Western Section The scientific information listed below may be dated. Associate secretary: Michel L. Lapidus For the latest information, see www.ams.org/amsmtgs/ Announcement issue of Notices: March 2012 internmtgs.html. Program first available on AMS website: To be announced Invited Addresses Program issue of electronic Notices: To be announced Mark J. Ablowitz, University of Colorado, Title to be Issue of Abstracts: To be announced announced. James Raftery, University of Kwazulu Natal, Title to Deadlines be announced. For organizers: August 3, 2011 Daya Reddy, University of Cape Town, Title to be an- For consideration of contributed papers in Special Ses- nounced. sions: To be announced Peter Sarnak, Princeton University, Title to be an- For abstracts: To be announced nounced. Robin Thomas, Georgia Institute of Technology, Title to be announced. Amanda Weltman, University of Cape Town, Title to Tampa, Florida be announced. University of South Florida

Boston, March 10–11, 2012 Massachusetts Saturday – Sunday John B. Hynes Veterans Memorial Conven- Meeting #1079 tion Center, Boston Marriott Hotel, and Southeastern Section Boston Sheraton Hotel Associate secretary: Matthew Miller Announcement issue of Notices: To be announced January 4–7, 2012 Program first available on AMS website: To be announced Wednesday – Saturday Program issue of electronic Notices: March 2012 Meeting #1077 Issue of Abstracts: To be announced Joint Mathematics Meetings, including the 118th Annual Meeting of the AMS, 95th Annual Meeting of the Math- Deadlines ematical Association of America, annual meetings of the For organizers: August 10, 2011 Association for Women in Mathematics (AWM) and the For consideration of contributed papers in Special Ses- 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 with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Associate secretary: Michel L. Lapidus The scientific information listed below may be dated. Announcement issue of Notices: October 2011 For the latest information, see www.ams.org/amsmtgs/ Program first available on AMS website: November 1, 2011 sectional.html. Program issue of electronic Notices: January 2012 Issue of Abstracts: Volume 33, Issue 1 Special Sessions Deadlines Discrete Models in Molecular Biology (Code: SS 1A), Ales- sandra Carbone, Université Pierre et Marie Curie and Labo- For organizers: Expired For consideration of contributed papers in Special Ses- ratory of Microorganisms Genomics, Natasha Jonoska, sions: To be announced University of South Florida, and Reidun Twarock, Uni- For abstracts: September 22, 2011 versity of York.

754 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Meetings & Conferences Washington, District Rochester, New York of Columbia Rochester Institute of Technology September 22–23, 2012 George Washington University Saturday – Sunday

March 17–18, 2012 Meeting #1082 Saturday – Sunday Eastern Section Associate secretary: Steven H. Weintraub Meeting #1080 Announcement issue of Notices: To be announced Eastern Section Program first available on AMS website: To be announced Associate secretary: Steven H. Weintraub Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Deadlines Program issue of electronic Notices: March 2012 For organizers: February 22, 2012 Issue of Abstracts: To be announced For consideration of contributed papers in Special Ses- sions: To be announced Deadlines For abstracts: To be announced For organizers: August 17, 2011 For consideration of contributed papers in Special Ses- New Orleans, sions: To be announced For abstracts: To be announced Louisiana Tulane University Lawrence, Kansas October 13–14, 2012 University of Kansas Saturday – Sunday

March 30 – April 1, 2012 Meeting #1083 Southeastern Section Friday – Sunday Associate secretary: Matthew Miller Meeting #1081 Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Central Section Program issue of electronic Notices: October 2012 Associate secretary: Georgia Benkart Issue of Abstracts: To be announced Announcement issue of Notices: To be announced Deadlines Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced For organizers: March 13, 2012 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: August 31, 2011 For consideration of contributed papers in Special Ses- Akron, Ohio sions: To be announced University of Akron For abstracts: To be announced October 20–21, 2012 The scientific information listed below may be dated. Saturday – Sunday For the latest information, see www.ams.org/amsmtgs/ Meeting #1084 sectional.html. Central Section Special Sessions Associate secretary: Georgia Benkart Announcement issue of Notices: To be announced Combinatorial Commutative Algebra (Code: SS 1A), Program first available on AMS website: To be announced Christopher Francisco and Jeffrey Mermin, Oklahoma Program issue of electronic Notices: To be announced State University, and Jay Schweig, University of Kansas. Issue of Abstracts: To be announced

MAY 2011 NOTICES OF THE AMS 755 Meetings & Conferences

Deadlines Deadlines For organizers: March 22, 2012 For organizers: April 1, 2012 For consideration of contributed papers in Special Ses- For consideration of contributed papers in Special Ses- sions: To be announced sions: To be announced For abstracts: To be announced For abstracts: To be announced Tucson, Arizona Chestnut Hill, University of Arizona, Tucson Massachusetts October 27–28, 2012 Boston College Saturday – Sunday April 6–7, 2013 Meeting #1085 Saturday – Sunday Western Section Eastern Section Associate secretary: Michel L. Lapidus Associate secretary: Steven H. Weintraub Announcement issue of Notices: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Issue of Abstracts: To be announced

Deadlines Deadlines For organizers: March 27, 2012 For organizers: September 6, 2012 For consideration of contributed papers in Special Ses- For consideration of contributed papers in Special Ses- sions: To be announced sions: To be announced For abstracts: To be announced For abstracts: To be announced

The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ Ames, Iowa sectional.html. Iowa State University Invited Addresses Ken Ono, Emory University, Title to be announced April 27–28, 2013 (Erdo˝s Memorial Lecture). Saturday – Sunday Central Section Associate secretary: Georgia Benkart San Diego, California Announcement issue of Notices: To be announced Program first available on AMS website: To be announced San Diego Convention Center and San Program issue of electronic Notices: April 2013 Diego Marriott Hotel and Marina Issue of Abstracts: To be announced

January 9–12, 2013 Deadlines Wednesday – Saturday For organizers: September 27, 2012 Joint Mathematics Meetings, including the 119th Annual For consideration of contributed papers in Special Ses- Meeting of the AMS, 96th Annual Meeting of the Math- sions: To be announced ematical Association of America, annual meetings of the For abstracts: To be announced Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the The scientific information listed below may be dated. winter meeting of the Association for Symbolic Logic (ASL), For the latest information, see www.ams.org/amsmtgs/ with sessions contributed by the Society for Industrial and sectional.html. Applied Mathematics (SIAM). Associate secretary: Georgia Benkart Special Sessions Announcement issue of Notices: October 2012 Operator Algebras and Topological Dynamics (Code: Program first available on AMS website: November 1, 2012 SS 1A), Christopher Francisco and Jeffrey Mermin, Program issue of electronic Notices: January 2012 Oklahoma State University, and Jay Schweig, University Issue of Abstracts: Volume 34, Issue 1 of Kansas.

756 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Meetings & Conferences

Program first available on AMS website: November 1, 2013 Alba Iulia, Romania Program issue of electronic Notices: January 2013 Issue of Abstracts: Volume 35, Issue 1 June 27–30, 2013 Thursday – Sunday Deadlines First Joint International Meeting of the AMS and the Ro- For organizers: April 1, 2013 manian Mathematical Society, in partnership with the For consideration of contributed papers in Special Ses- “Simion Stoilow” Institute of Mathematics of the Romanian Academy. sions: To be announced Associate secretary: Steven H. Weintraub For abstracts: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Tel Aviv, Israel Issue of Abstracts: Not applicable June 16–19, 2014 Deadlines Monday – Thursday For organizers: To be announced Associate secretary: Michel L. Lapidus For consideration of contributed papers in Special Ses- Announcement issue of Notices: To be announced sions: To be announced Program first available on AMS website: To be announced For abstracts: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced

Riverside, California Deadlines University of California Riverside For organizers: To be announced For consideration of contributed papers in Special Ses- November 2–3, 2013 sions: To be announced Saturday – Sunday For abstracts: To be announced Western Section Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced Program first available on AMS website: To be announced San Antonio, Texas Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Henry B. Gonzalez Convention Center and Grand Hyatt San Antonio Deadlines For organizers: April 2, 2013 January 10–13, 2015 For consideration of contributed papers in Special Ses- Saturday – Tuesday sions: To be announced Joint Mathematics Meetings, including the 121st Annual For abstracts: To be announced Meeting of the AMS, 98th Annual Meeting of the Math- ematical Association of America, annual meetings of the Association for Women in Mathematics (AWM) and the Baltimore, Maryland National Association of Mathematicians (NAM), and the Baltimore Convention Center, Baltimore winter meeting of the Association of Symbolic Logic, with Hilton, and Marriott Inner Harbor sessions contributed by the Society for Industrial and Ap- plied Mathematics (SIAM). January 15–18, 2014 Associate secretary: Steven H. Weintraub Wednesday – Saturday Announcement issue of Notices: October 2014 Joint Mathematics Meetings, including the 120th Annual Program first available on AMS website: To be announced Meeting of the AMS, 97th Annual Meeting of the Math- Program issue of electronic Notices: January 2015 ematical Association of America, annual meetings of the Issue of Abstracts: Volume 36, Issue 1 Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the Deadlines winter meeting of the Association for Symbolic Logic, with sessions contributed by the Society for Industrial and Ap- For organizers: April 1, 2014 plied Mathematics (SIAM). For consideration of contributed papers in Special Ses- Associate secretary: Matthew Miller sions: To be announced Announcement issue of Notices: October 2013 For abstracts: To be announced

MAY 2011 NOTICES OF THE AMS 757 Meetings & Conferences Seattle, Washington San Diego, California Washington State Convention & Trade San Diego Convention Center Center and the Sheraton Seattle Hotel January 10–13, 2018 January 6–9, 2016 Wednesday – Saturday Joint Mathematics Meetings, including the 124th Annual Wednesday – Saturday Meeting of the AMS, 101st Annual Meeting of the Math- Joint Mathematics Meetings, including the 122nd Annual ematical Association of America, annual meetings of the Meeting of the AMS, 99th Annual Meeting of the Math- Association for Women in Mathematics (AWM) and the ematical Association of America, annual meetings of the National Association of Mathematicians (NAM), and the Association for Women in Mathematics (AWM) and the winter meeting of the Association of Symbolic Logic, with National Association of Mathematicians (NAM), and the sessions contributed by the Society for Industrial and Ap- winter meeting of the Association of Symbolic Logic, with plied Mathematics (SIAM). Associate secretary: Matthew Miller sessions contributed by the Society for Industrial and Ap- Announcement issue of Notices: October 2017 plied Mathematics (SIAM). Program first available on AMS website: To be announced Associate secretary: Michel L. Lapidus Program issue of electronic Notices: To be announced Announcement issue of Notices: October 2015 Issue of Abstracts: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: January 2016 Deadlines Issue of Abstracts: Volume 37, Issue 1 For organizers: April 1, 2017 For consideration of contributed papers in Special Ses- Deadlines sions: To be announced For organizers: April 1, 2015 For abstracts: To be announced For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announced Atlanta, Georgia Hyatt Regency Atlanta and Marriott At- lanta Marquis

January 4–7, 2017 Wednesday – Saturday Joint Mathematics Meetings, including the 123rd Annual Meeting of the AMS, 100th 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 of Symbolic Logic, with sessions contributed by the Society for Industrial and Ap- plied Mathematics (SIAM). Associate secretary: Georgia Benkart Announcement issue of Notices: October 2016 Program first available on AMS website: To be announced Program issue of electronic Notices: January 2017 Issue of Abstracts: Volume 38, Issue 1

Deadlines For organizers: April 1, 2016 For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announced

758 NOTICES OF THE AMS VOLUME 58, NUMBER 5 Meetings and Conferences of the AMS

Associate Secretaries of the AMS Eastern Section: Steven H. Weintraub, Department of Math- Western Section: Michel L. Lapidus, Department of Math- ematics, Lehigh University, Bethlehem, PA 18105-3174; e-mail: ematics, University of California, Surge Bldg., Riverside, CA [email protected]; telephone: 610-758-3717. 92521-0135; e-mail: [email protected]; telephone: Southeastern Section: Matthew Miller, Department of Math- 951-827-5910. ematics, University of South Carolina, Columbia, SC 29208-0001, Central Section: Georgia Benkart, University of Wisconsin- e-mail: [email protected]; telephone: 803-777-3690. Madison, Department of Mathematics, 480 Lincoln Drive, Madison, WI 53706-1388; e-mail: [email protected]; telephone: 608-263-4283.

The Meetings and Conferences section of the Notices April 6–7 Chestnut Hill, Massachusetts p. 756 gives information on all AMS meetings and conferences approved by press time for this issue. Please refer to the page April 27–28 Ames, Iowa p. 756 numbers cited in the table of contents on this page for more June 27–30 Alba Iulia, Romania p. 757 detailed information on each event. Invited Speakers and November 2–3 Riverside, California p. 757 Special Sessions are listed as soon as they are approved by the cognizant program committee; the codes listed 2014 are needed for electronic abstract submission. For some January 15–18 Baltimore, Maryland p. 757 meetings the list may be incomplete. Information in this Annual Meeting issue may be dated. Up-to-date meeting and conference June 16–19 Tel Aviv, Israel p. 757 information can be found at www.ams.org/meetings/. 2015 Meetings: January 10–13 San Antonio, Texas p. 757 2011 Annual Meeting April 30–May 1 Las Vegas, Nevada p. 750 2016 September 10–11 Ithaca, New York p. 751 January 6–9 Seattle, Washington p. 758 September 24–25 Winston-Salem, North Annual Meeting Carolina p. 752 2017 October 14–16 Lincoln, Nebraska p. 752 January 4–7 Atlanta, Georgia p. 758 October 22–23 Salt Lake City, Utah p. 753 Annual Meeting 2018 November 29– Port Elizabeth, Republic p. 753 January 10–13 San Diego, California p. 758 December 3 of South Africa Annual Meeting

2012 Important Information Regarding AMS Meetings January 4–7 Boston, Massachusetts p. 754 Potential organizers, speakers, and hosts should refer to Annual Meeting page 100 in the January 2011 issue of the Notices for general March 3–4 Honolulu, Hawaii p. 754 information regarding participation in AMS meetings and March 10–11 Tampa, Florida p. 754 conferences. March 17–18 Washington, DC p. 755 Abstracts March 30–April 1 Lawrence, Kansas p. 755 Speakers should submit abstracts on the easy-to-use interac- September 22–23 Rochester, New York p. 755 tive Web form. No knowledge of is necessary to submit October 13–14 New Orleans, Louisiana p. 755 an electronic form, although those who use may submit October 20–21 Akron, Ohio p. 755 abstracts with such coding, and all math displays and simi- October 27–28 Tucson, Arizona p. 756 larily coded material (such as accent marks in text) must be typeset in . Visit http://www.ams.org/cgi-bin/ 2013 abstracts/abstract.pl. Questions about abstracts may be January 9–12 San Diego, California p. 756 sent to [email protected]. Close attention should be paid to specified deadlines in this issue. Unfortunately, late abstracts Annual Meeting cannot be accommodated.

Conferences: (see http://www.ams.org/meetings/ for the most up-to-date information on these conferences.) June 12–July 2, 2011: Mathematics Research Research Communities, Snowbird, Utah. (Please see http://www.ams.org/ amsmtgs/mrc.html for more information.) July 4–7, 2011: von Neumann Symposium on Multimodel and Multialgorithm Coupling for Multiscale Problems, Snowbird, Utah. (Please see http://www.ams.org/meetings/amsconf/symposia/symposia-2011 for more information.) July 24–29, 2011: Conference on Applied Mathematics, Modeling, and Computational Science, Waterloo, Canada (held in cooperation with the AMS).

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