sign in sign up
<<
Home , Grigori Perelman, Leslie Greengard, Perceptive Pixel, Warren Weaver

Newsletter Courant Institute of Mathematical Sciences

Departments of and , and the Center for Atmospher e-Ocean Science at Mikhael Gromov Receives the 2009 Abel Prize The Norwegian Academy of Science and Mathematics (2004), the Kyoto Prize in Basic Sciences (2002), and Letters awarded the 2009 Abel Prize to the Balzan Prize (1999). Mikhael Gromov, the Courant Institute’s Jay Gould Professor of Mathematics, “for his According to the Norwegian Academy, Gromov’s work has led to revolutionary contributions to .” “some of the most important developments [in geometry], pr oduc- Gromov will receive the Prize from His ing profoundly original general ideas, which have r esulted in new Majesty, King Harald V of Norway, in Oslo perspectives on geometry and other areas of mathematics.” on May 19th. Courant Director Leslie Greengard said that Gromov “has been an inspiration to colleagues and students here and to Gromov obtained his Masters degree around the world. His unique viewpoint has r evolutionized geome- (1965), his Doctorate (1969) and his Post- try, , and their interplay. The honor is richly doctoral Thesis (1973) from Leningrad deserved.” “The work of Gromov,” writes the Norwegian Photo: Gérard Uferas University. His doctoral advisor was Vladimir Academy, “will continue to be a source of inspiration for many A. Rokhlin. Before joining Courant, Gromov held professorial positions at future mathematical discoveries.” Leningrad University, the State University of New York at Stony Brook, and the Université de Paris VI, and he curr ently also holds a Professorship at the Gromov is the third Courant to receive the Abel Institut des Hautes Études Scientifiques. He has received many other presti- Prize in five years; it was awar ded to Professor Emeritus

gious awards, recently including the János Bolyai Prize fr om the Hungarian in 2005, and to Professor Raghu Varadhan in 2007. Spring/Summer 2009 Volume 6, No. 2 Academy of Sciences (2005), the Frederic Esser Nemmers Prize in The Story of the Poincaré Or when is a Proof a Proof ? by M.L. Ball

This has long been a source of puzzlement to many an under- which among other things implies the Poincaré conjectur e. In this Issue: graduate student; it can also be a deep philosophical question. Here, we take the pragmatic view that a pr oof is truly a proof This was big news in itself, but in November 2002 something 2009 Abel Prize ...... 1 when it is recognized as such by the mathematics community. truly remarkable happened: Grigori Perelman, a widely respected Poincaré Conjecture ...... 1-2 This brings us to the tale of the Poincaré conjectur e, explained Russian mathematician, posted a paper on a pr e-print server. Fifteen Years of CAOS...... 2 with the help of Mathematics Professor . According to Kleiner, “When a mathematician writes a paper, instead of mailing it out to people, he or she now posts it on A Touch of Magic ...... 2 Kleiner joined the Courant Institute this September as a new fac- Arxiv, a central repository of pre-prints, which anyone around the Eric Vanden-Eijnden ...... 3 ulty member. He is originally from Seattle and comes to Courant world can access anytime. Over night, a huge number of people Jack Schwartz ...... 4 by way of Yale, the , and Berkeley. became aware of the fact that Perelman had posted this pre- Benson Fellowship...... 4 print. In it, he developed a number of new tools for studying the Formulated approximately 100 years ago, the Poincaré conjec- and claimed that by using these, he could pr ove the Sudokill...... 5 ture was one of the most famous unsolved pr oblems in mathe- geometrization conjecture. Warren Weaver Hall...... 6 matics. Not only was it a central question in topology , it was a Alumni Spotlight...... 6 question that many very well known mathematicians had tried “This was really an extraordinary development in many respects Thomas Bringley ...... 6 to solve – unsuccessfully. Then in the 1980s came a br eak- because first of all, someone was claiming to pr ove the through. A mathematician named Richard Hamilton introduced geometrization conjecture. Not only that, but since 1994, Donors ...... 7 the Ricci flow, a completely new way to attack the Poincaré con- Perelman had been living in St. Petersburg following a fellowship 2009 Student Prizes ...... 8 jecture. If it was successful, he theorized, it would pr ove not just at Berkeley. He had published essentially nothing and had virtual- the Poincaré conjecture but also the geometrization conjecture, ly withdrawn from the mathematical community. In early 2003,

continues on next page (Poincaré Conjecture) continued from page 1 Perelman posted a second pre-print which completed the program he had ERIC VANDEN-EIJNDEN: fairly big molecular systems containing several thousands of atoms for some alluded to in the first paper. This was all rather spectacular.” Fifteen Years of CAOS amount of time,” he said. “We can then try to understand how cer tain molecules evolve in time and how their motion influences their function, for Nevertheless, experts in the field had a gr eat deal of trouble reading Understanding Molecules Through Complex instance. But even with the largest , you can’ t do that by brute Perelman’s papers because they were not written in the traditional format. Simulation and Statistical Mechanics force because the range of spatial- and time-scales involved is way too lar ge, Kleiner says that they could not have been submitted to a r eputable journal and you’re simulating a system that is very, very complicated. And so you and been accepted – there was way too much missing. By and large, they by M.L. Ball need to use the statistical mechanics perspective to develop techniques that were not given serious attention by the experts. accelerate the simulations and permit you to interpr et the results “The Courant Institute is an ideal place for someone like me,” says probabilistically.” Kleiner was an exception. In 2003, at the University of Michigan, he and a Courant Institute Professor Eric Vanden-Eijnden. A citizen of colleague, John Lott, started running a seminar on Per elman’s first paper. This Belgium, Eric earned his B.S., M.S., and Ph.D. in theor etical Eric sees many innovations on the horizon using this appr oach. “The growth produced a set of notes which they then posted on the web; in those notes, from the Université Libre de Bruxelles. “I came here in 1998 right in computing power and recent discoveries in have given they filled in the details of Per elman’s first paper. after finishing my Ph.D., first as a postdoc and then I stayed. Not new food to mathematics,” he explained. “Understanding the structur e and ‘Ocean color’ data east of Tasmania, December 2004, collected by the MODIS only do I like the scientific envir onment here but my family and I functioning of complex macro-molecules provides applied mathematics with What did Perelman himself think of this? According to Kleiner, Perelman was detector on the Aqua satellite. really like living in New York.” enormous challenges but also vast opportunities. To give an example, it is giving a series of lectures at that same year. Kleiner believed that certain proteins – prions, for instance – become lethal on ly and Lott approached him and asked if he intended to r ewrite his pre-prints The Center for Atmosphere Ocean Science (CAOS), an important research initiative when they misfold into a certain shape. If they ar e not in this misfolded and add more detail to make them more readable; his response was that within the Courant Institute, which was created under the leadership of Andy Majda shape, they are actually pretty benign. It is therefore very important to they were written in the best possible way and wer e therefore complete. in 1994, has grown to seven faculty members. The Center brings mathematical understand how folding and particularly misfolding happen since it may approaches to bear on the changes on our global climate and environment, and eventually lead to curing certain diseases.” He continued, “Tackling such studies a vast array of climate issues and phenomena. After finishing their work on Perelman’s first paper, Kleiner and Lott started questions using an applied mathematics perspective is inter esting for writing notes on his second paper, posting those in September 2004. This year CAOS hosted its Tenth Annual Workshop on the topic of “Oceanography at everyone – for mathematicians, it is a way to extend the r ealm of their field During this time there was steadily increasing publicity within the mathe- the Observational and Modeling Frontier: Submesoscale Dynamics.” The workshops by confronting new problems; for chemists and biologists, it is a way to matical community, as well as a lot of perplexity. Kleiner explains, “People provide a unique venue to focus on cutting edge issues in climate science . systematize their approaches using mathematical and computational tools didn’t understand what was going on. The first question they would ask is, The topic of this most recent workshop concerns how the ocean mixes heat, carbon that have proven very successful in many other settings.” ‘Have the Poincaré conjecture, the geometrization conjecture, been and biological traces in a range of scales that are only now beginning to be modeled proven?’ Athough the papers were not that long (approximately 30 pages), and observed. The figure shows ‘ocean color’ data collected by a NASA satellite (the Working in concert with a host of colleagues, Eric focuses in part on there was so much detail missing that it wasn’ t a matter of checking the image is about 20 kilometers across). The colors are not the colors you would see by developing computational tools at Courant which ar e then applied globally. text; you had to take what Per elman described, interpret it, fill in the eye, but represent subtle differences in water color that result from varying A snapshot produced by a computational simulation of an inser tion of a “I don’t work alone – I have many collaborators, not only mathematicians, distributions of biological and chemical elements in the w aters. Plainly, the protein in a lipid bilayer details, and then be confident you did it corr ectly. So they couldn’t be veri- ocean is full of complex fluid dynamical motions (such as vortices and filaments) on fied in the traditional way.” these scales. Understanding and predicting ocean mixing on these scales is essential to improving climate models. Other teams were analyzing Perelman’s papers as well, notably John Morgan “Mathematics is a universal for understanding and Gang Tian, who ultimately produced a book together. “They thanked us The Center is currently housed within the Mathematics Department, but fifteen years after its creation, will become its own department in Fall 2009. I quite generously for having provided the initial set of notes which made it the world around us, and it will be fed b y problems in easier for them to produce their own account,” Kleiner says. this world for as long as we care to look at them” Then Perelman’s story took an even more unusual twist. In part because of Kleiner and Lott’s notes and the work of Morgan and T ian, Perelman’s work One need spend only a few minutes with Pr ofessor Vanden-Eijnden to but also people in , chemical engineering, and biology departments has become fully appreciated. Indeed, he was awarded the in appreciate his love of mathematics, but in school, he was first attracted to around the world. These collaborations are essential in enabling us to focus 2006, the highest honor a mathematician can r eceive – which he then astrophysics. “Then I discovered statistical mechanics, a way of looking at a on the problems that are of actual interest in material sciences, chemistry, declined. “Which was unheard of!” says Kleiner. “Publicly he said he wanted A very large system from a probabilistic viewpoint,” he said. “In this and molecular biology, and in ensuring that the developed her e to remove himself from the mathematical community because he felt ther e framework, you don’t describe things in detail like you would in classical are useful in real applications.” were certain members who had acted in an unethical way and the communi - Touch mechanics. This is not practical when you look at systems such as, say , a gas ty had not responded appropriately.” of from a microscopic viewpoint. The number of atoms such a gas contains is The techniques Eric described may have significant applications in the futur e just too large and their motion too complicated to focus on each and every in the fields of human health, specifically in the context of drug design. “W e Was Kleiner shocked that Perelman turned down the most prestigious award atom individually. Rather, you must make global statements about the can’t yet say that a new drug is being designed by a pharmaceutical in mathematics? “He’s a very unusual person and his views ar e far from Magic probability of finding atoms here or there and how this probability influences company which was based on first-principle numerical simulation, but it will mainstream,” Kleiner explains. “In his two fairly shor t papers, the number of Photo courtesy of Perceptive Pixel, Inc. the bulk properties of the gas. I really fell in love with that topic and its r oots come. In the same way that numerical simulation helps design airplanes, it fundamentally new ideas that he added to the story easily would have made in probability theory, and that led me here eventually.” will someday help design drugs.” five or six absolutely first rate papers in top jour nals; even if they hadn’t Jeff Han, who founded the high-tech start-up Perceptive Pixel and who developed a solved this incredibly famous and important problem in mathematics, they multi-touch screen while a Research at Courant, is the man behind CNN John As well as teaching and managing a number of students and postdocs, Eric When asked if the world looks to Courant, Eric’s answer was immediate. would still have been an incredible achievement scientifically.” King's "Magic Wall." The seven-and-a-half foot monitor was used by CNN for the 2008 Presidential election coverage, tallying votes, zooming in and out of states, and showing said that he is mostly working on molecular dynamics with applications to “Most definitely. The Institute is very strong overall, and it is ar guably at the molecular biology and material sciences. He explained, “These ar e problems top in applied mathematics—not only because of the r esearch being done For Kleiner, elucidating Perelman’s papers seemed a natural extension of his how swing states could change the election result – all with the touch of a few fingers . “It’s really helping what news production is for,” Han told NYU’s Alumni magazine: “to in which you try to understand certain chemical r eactions or biological here but also because of our very successful graduate and postdoc early interests. “When I was a graduate student at Berkeley , I was drawn to disseminate information, educate the viewer, and break down a complicated thing like processes from first principles, i.e., going all the way down to modeling the programs. You can go into any mathematics department in the country and the Ricci flow because of its mathematical beauty,” he explains, “and then these multiple elections.” motion of the atoms in the molecules involved in these pr ocesses. This is find people who have been graduate students or postdocs her e and after that I didn’t really do anything with it. But because of that time in grad important for understanding the mechanisms essential to the remember it fondly. There is a Courant style of doing applied mathematics school it was easy to pick it up when Per elman’s papers appeared. Since then As Jeremy Bradly of CNN writes, “The inspiration for the multi-touch technology came functioning of your body, such as protein folding. It is also important if you that is exported from here.” I’ve gone in that direction with my research, particularly trying to understand from a decidedly non-digital event: Han was drinking a glass of water. He noticed the way light was interacting with his fingers as he touched the glass , and an ‘Ah ha!’ want to understand basic properties of materials, for instance, how they the Ricci flow with the perspective that it involves both geometry and analy- moment was born that put him straight to work. ” crack under stress, without making constitutive assumptions.” As for the future of applied mathematics? “I am not worried. Mathematics sis. This combination is something the Courant Institute is known for; it’ s a is a universal language for understanding the world ar ound us, and it will be combination of partial differential equations and geometry, and this is one Multi-Touch Screen’s are now also being used by F ox News Channel (who dubbed theirs development and simulation constitute a large part of Eric’ s fed by problems in this world for as long as we car e to look at them,” Eric reason I find it quite exciting to be her e – to develop the par tial differential the “Bill-board” for its user, Bill Hemmer), and ABC, and Perceptive Pixel has clients as various as film production companies and the U.S. military. I work.“With the computer capability we have these days, we can simulate mused, laughing. I equation side of the story. This is a great place to do that.” I

2 3 “For sheer power and universality Jack’s mind I suspect that among the readers of this newsletter, few are unfamiliar with Sudoku. In had no peer, except for von Neumann.” Memoriam: Jack Schwartz The same cannot be said about Sudokill, a game invented for a graduate class I teach — Peter Lax Sudokill in heuristic problem solving. Sukokill is a two person game which pits player against a strategic variation of Sudoku player in trying to force the other player to violate the Sudoku r ules.

Jack Schwartz, professor at the SETL, whose purpose was to allow the succinct expr ession of algorithms in a form Here's a quick refresher on Sudoku. The goal is to fill a 9 by 9 grid with digits between Courant Institute for forty two close to their mathematical formulation, and thus easier to understand and r eason 1 and 9. Each digit should appear exactly once in each r ow, once in each column, and years and founder of its about. The book Schwartz wrote, On Programming, which collected algorithms by Dennis Shasha, Professor of once in each non-overlapping three by three box starting from the upper left cor ner. Computer Science department, written in SETL from many fields of computer science, had a significant influence on passed away in his Manhattan the design of more recent programming , most notably ABC and Python. home on March 2nd. In his life- time, Professor Schwartz His most widely recognized publication as a mathematician was Linear Operators, In the following example, we use 0 to r epresent a blank. 006000000 How can the row player force a win (i.e., force the column authored more than a dozen a three-volume work co-authored with Neilson Dunford. Published over three 8403x 2000 player to make an illegal move)? books, more than one-hundred decades ago, it continues to be r egarded as the definitive work in the field. 000000007 3 20005074 papers and technical reports, led a variety of research projects, and advised over 704000893 0 60090800 Solution: Suppose the row player puts a 2 on the bot- 006802000 tom row (replacing the C), yielding: fifty Ph.D. students, several of whom became life-long collaborators. Professor Allan Gottlieb, who came to Courant thr ough the advisement of 0 00624000 0 07528600 002030060 Schwartz, states that he owes much of his academic success to the ef forts, the 0 80006701 210900087 5 76149238 Although he was retired when he passed away, Prof. Schwartz never stopped example set, and the help given by Schwartz, whom everyone called Jack. Almost 9 03400080 000403025 8 49372516 working. As Computer Science Professor Bud Mishra, to whom Jack was a men- everyone, that is. For the first few months after he joined Courant, Gottlieb always 0 00704900 000000100 3 21865974 600090000 463791852 tor, remembers, “He never slowed down. He had so many dif ferent interests— called him “Professor Schwartz”— “despite his request and the practice of every- 459000108 then the column player must replace a blank in the same 158624793 and he always saw a role for computing and mathematics in them. He was con- one else, from students, to professors, secretaries, staff, and custodians, to call him column (marked with ys): 792538461 Jack.” Clyde Kruskal, a joint student of Gottlieb and Schwartz’ s, one day asked Consider the lower left box: stantly learning.” 0060y 0000 2 14956387 Gottlieb why he was “being so foolish.” Gottlieb explained as follows: 0 0 0 8403x 2000 9 874136A 5 Two months before his passing, Schwartz decided to lear n about optics, so he 7 0 4 3200y 5074 6 35B 8 7129 got a book on Newton’s optics and Mishra introduced him to Andrew Hicks, who “Ten years previously, while struggling on my math Ph.D. thesis, I hit a pr oblem in 0 0 6 060090800 Then the column player has to move wher e the A is. The 0 0 7 0 00624000 Sudoku rules would suggest replacing the A by a 4 to builds mirrors. Before long, Jack invited Hicks to write a book with him. As Bud functional analysis that I was unable to solve. I went to the library to seek out the 0 8 0 0 02030060 satisfy the constraints within the lower right hand box. But tells, “soon Jack was scanning ever ything 3D in his apartment and making beauti- famous text by Dunford and Schwartz, which I had shamefully never r ead. A trip to that would violate the row constraint, because there is 9 0 3 2 109y 0 087 already a 4 in that row. ful things. From early Roman History to Chinese music—whatever topic you had, the Volume 1 index and then to the page r eferenced gave me exactly the theorem I 000704900 0004y 3025 he had an interest.” needed as well as several corollaries and related results. All this on one page out of 600090000 0000y 0100 459000108 End of Warm-Up: Now it's your turn, but this time 800 in one volume out of thr ee! Such a magnificent edifice could not have been Suppose the column player chooses the one marked by an we’ll favor the column player. Not only was Schwartz constantly learning about very diverse topics, he was constructed by someone named simply ‘Jack.’” Pr ofessor Emeritus Louis Nirenberg upper case Y: We know that of the five zer oes present in the lower left 1. Can the column player force a win in two moves given also teaching them. As Courant Professor Emeritus Peter Lax recalls, “When says of Jack: “he could read mathematics the way I read a novel—for him, reading box, one must be 7 and one must be 8. Because ther e is a 0060y 0000 the following board? (Here the column player can begin by moving anywhere.) Jack switched from mathematics to the computer science depar tment, he mathematics was just easy.” 7 in the third column and the seventh (from the top) row, 8403x 2000 the only legal place for a 7 is to the right of the 6, yielding: told that when he first came to the Courant Institute, he looked at our 3200y 5074 815349267 Bulletin and decided to give all the courses listed ther e.” When Lax asked if Nirenberg recalls a story about a visit Peter Lax made to Schwartz at Stanfor d. 0 0 0 060090800 7 A 4 B 51893 000624000 Schwartz had fulfilled his resolution, he said yes. “Surely,” Lax replied, “there When they met, Jack looked frantic, and said to Peter: “Did you bring something to 7 0 4 396872415 0 0 6 002030060 147528639 must have been some subjects about which you knew very little.” “In those read? I read the Cornflakes box three times!” 0 0 7 2109y 0087 C 82936DE1 cases,” answered Jack, “I took out of the library the two or thr ee leading 0 8 0 0004Y 3025 963F 17GH I books on the subject and read them.” “Everyone was astonished by [Jack’s] brilliance,” says Nirenberg, of the talk given by 9 0 3 0000y 0100 231J 8 K 956 678195324 Schwartz and Dunford at the Institute. “He knew so much and was so clear .” 000704900 Now the row player must move in one of the positions L 5 92M 3 17N Schwartz made major contributions to a wide range of ar eas: spectral theory of 670090000 marked with a z: 459000108 linear operators, von Neumann algebras, macroeconomics, the mathematics of “More than anything,” Mishra recalls of him, “he had a lot of fun. Jack was always 0060y 0000 2. Here's a harder one. Can the column player for ce a win By contrast, the following would be illegal: in three moves given the following? (Again the column quantum field theory, parallel computation, computer time-sharing, high-level having fun.” 8403x 2000 player can begin by moving anywhere.) 3200y 5074 programming languages, compiler optimization, transformational programming, 0 0 0 060090800 7 A 581329B computational logic, motion planning in robotics, and multimedia. Schwartz is survived by his third wife, Diana, his daughters, Abby Schwar tz 7 0 4 000624000 CD14765EF 0 0 6 of Manhattan and Rachel Fainman of W innipeg, Manitoba, and his sister, 002030060 34G 259H 17 0 0 7 In high-level language programming, Schwartz designed a new language called Judith Dunford. I 2109y 0087 914587326 0 8 0 zzz4 Y 3 z 25 I 57362J 49 9 0 3 0000y 0100 6239417KL 070704900 13269847M 600090000 Toward the end of the game, the following rules pr ove Joann Benson received her M.A. in in 1976 fr om Hunter College N 8 OP25931 459000108 important: if there are no blanks in the column wher e the New Joann and Stan where she worked under an NSF grant in computer aided instruction. Fr om row player last moved, then the column player may move Q 7913R 862 because then there would be two 7s in the same r ow. anywhere. Likewise, if there are no blanks in the row where there she moved on to Pan Am W orld Airlines. She decided to be a full time the column player last moved, the r ow player may move Here's an invitation. If you can pr oduce a four move forced Benson Fellowship in homemaker when their third daughter came along. The Bensons have thr ee In Sudokill, players alternate moves where a move consists anywhere. win on a board initially having more blanks than assignments, please send it to me at [email protected]. daughters, Gianna, Bridget, and Linda Fé. of replacing a blank by a number. The first player is called the row player, and the second is the column player. Also, please play Sudokill at Yu Yiwen’s website: Mathematics Initially, the row player can make any legal Sudoku move. Warm-up: Suppose it is the row player's move in the http://homepages.nyu.edu/~yy497/projects/showcase/Sudok Subsequently, the column player must move in the same following situation (where letters represent blanks): illWebGame This year, Mr. Benson is completing his M.A. in Art at Califor nia State column as the last move of the r ow player and the row A generous gift from Joann and Stan Benson has enabled the University Northridge. His paintings span a wide variety of subjects and player must move in the same r ow as the last move of the 576149238 creation of this new fellowship. column player. If a player makes an illegal Sudoku move, 849372516 media, from abstract and representational paintings to computer art and oil then that player loses. 321865974 stains on natural wood. His online gallery can be viewed at For the solution email: Mr. Benson, M.S. ‘75, met Mrs. Benson at W arren Weaver Hall during a If we represent blanks as 0s or letters, if the r ow player 463791852 [email protected] http://home.earthlink.net/~stansart/. moves where there is an x: 158624793 high school summer course on FOR TRAN at NYU. After graduating from 792538461 Courant, Mr. Benson worked for Pfizer, Inc, a pharmaceutical company, for By establishing this student fellowship at Courant, the Bensons ar e pleased 214956387 19 years in various senior management positions. Mr. Benson then served as to be able to help provide a Courant student with the same type of 9874136A 5 635B 871C 9 Senior Vice President, Sales and Marketing, of Amgen, Inc., a biotechnology opportunity that led to their success. I company, from 1995 to 2001.

4 5 The Courant Institute recognizes with gratitude the following alumni, Alumni Spotlight faculty, and friends who have made gifts for Academic Year 2008-2009:

Sashi Reddi, M.S. in Computer Science ‘90, Liliana X. Aguas Mou-Ta Chen Michael John Goetz Julian D. Laderman Grant Parker James K. Steadman Courant Institute; Ph.D. ‘93, Wharton School of Sait Z. Aksoy Alexey Chentsov Aaron Goldenberg Arnold Lapidus Patricia R. Peeler William H. Stechmann Danielle Choi Stephen H. Gomory Irene Huen Lee Christopher Cates Pennock Alan H. Stein Business, The University of Pennsylvania Silvio J.Anichini Ethan Aranov Edwin Myung Choi Jesse D. Goodman Kristin Lee MaryBeth Perdue Marsha E. Stein Janis Elia Archer Lydia F.Cipriani Robert B. Gordon Claudia Leme Luke Peterson Gladys Cohen Steinberg Sashi Reddi is founder and chairman of AppLabs, the Julius A.Archibald, Jr. Richard J. Cole Dmitry Goykhman George F.Lenz Frederick C. Phillips Joseph Steinberg world’s largest independent testing, quality Annabel Armour Diana M. Collins Arvin Grabel Marlene Ader Lerner Evan C. Picoult Paul P.Stepanczuk Gordon A.Assing John A. Cook Samuel M. Graff Peter V.Lessek William Pierce Julie V.Stern management and certification solutions company. He is also the founder Jeffrey M. Bachrach Julia E. Corwin Barry Granoff Brian R. Lessing Kevin J. Pluck Kristin L. Stevens and chairman of FXLabs, a leading developer of high quality game pr oducts Paul M. Bailyn Lois Corwin Daniel Greenberg Bernard W.Levinger K. J. Polansky Cheryl Sylivant for PC’s and Videogame consoles. A serial entrepreneur, Sashi had Jonathan J. Baker Robyn Cutler Jonathan Christopher Gruhl Arieh Listowsky Julian F.Prince Brian Tajlili Bernard C. Baldwin Marie E. Cyborski Milton Halem Ryan Cutrone Littlewood Vicki and Joe Pung Alice Takhtajan previously started two other companies: EZPower Systems and iCoop. Paul L. Benninghoff Paul Vartan Czkwianianc Lisa M. Hamilton Walter Littman Paul H. Rabinowitz Jean Taylor Neil E. Berger Amnon Dalcher David Kenric Hammond Charles A. Loesch Matthew L. Rajpolt Maja-Lisa Wessman Thomson “AppLabs was started when I realized that with an increasing number of Edward A. Berndt Teymour T.Darkhosh Richard D. Hannes Tara & Patrick Lohr-Bringley Prashanth Ravishankar Charles Tier organizations automating their business processes, there was a growing Eli Bernstein Florin David Caitlin Harren Kevin Lookis Gina Ricci Lu Ting Frances C. Bernstein Raymond P.de Lacaze Keith Harrow Cheng Ly Charles Wesley Rice Stephen J.Tobon need for the companies to test the ef ficiency of their software and IT Herbert J. Bernstein Barbara De Ramona Madeline Trieger Harrow Donald I. MacDavid John M. Rinzel Sarah Tolan systems,” says Sashi. “And I found that they pr efer to engage the services Michael E. Bernstein Linda Brand Debord Miriam Hausman Charles G. Major Francis J. Rivieccio Serdar Topak of an independent testing and quality management company for an Geoffrey C. Berresford Sidney P.Diamond Brian T.Hayes Edward Man Daniel Robinson Carol Topping Helen Beylkin Pisheng Ding David Hertzberg Douglas D. Mandell Christopher J. Rohner Wai Hon Tsui unbiased appraisal.” AppLabs is backed by Sequoia Capital, which invested Lucy Biederman Leslie M. Donahu Theodore Hiebert Telly Mavroidis Alan S. Rojer Selim Tuvi around $23m in AppLabs. Daria J. Bielecki Michael Aaron Dooley Yehuda Hilewitz Anne-Claire McAllister Nicholas J. Rose Julius J.Vandekopple Photos: Annemarie Poyo Furlong Malcolm R. Billings Robert E. Dowd Harry Hochstadt Victor S. McBarnette Joshua S. Rosenblatt Charles A. von Urff Nurit Binenbaum Jan S. Edler Brian P.Hotaling Corey McCaffrey Junhua Wang FXLabs is the leading end-to-end game development company in India, and John P. Sabini Albert A. Blank Blaine M. Edmundson Jessica M. Houssian Donald J. McCarthy Robert L. Sachs Donald R.Warren Warren Weaver Hall has its head office in Hyderabad, India. It takes advantage of multi-shor e Rachel Joy Blumberg Matthew Edmundson Gary Houston Brian J. McCartin Jeffrey S. Saltzman Henry Weinberg development, and uses its own IP, to develop games with Indian content Richard Boykin Thomas J. Emerson Hongfei Huang Morris J. Meisner Murray Schechter Michael H.Weinstein both for the Indian market as well as a wider inter national market. Craig Seth Brass Raymond Stuart Ennis Carol Hutchins Gerardette Melyon Lorin Schneider Abraham S.Weishaus In 1965 Warren Weaver Hall was given a Bard Award for excellence Marian Woertz Brawer Mark E. Epstein Barry E. Jacobs Arthur S. Menikoff Edmond Schonberg Alan A.Weiss in New York Architecture by the City Club of New York. While the Mitchell Bressack William C. Erb Caitlin R. Jenkins Margaret Ellen Meurer Sara Wernick Schonwald Bonita Katz Weiss building’s exterior, designed by Warner, Burns, Toan & Lunde, Its recent game based on a Bollywood movie has become the biggest Jessica Brier Tanya N. Erlach Theodore J. Johnson Rita S. Miller Patricia Schulman Burton Wendroff Robert C. Brigham Renee Faibish Charles S. Kahane Stanislav Miltchev Mintchev Jonathan Schwartz Maria G.Westdickenberg remains the same as it was nearly for ty five years ago, its interior has selling videogame ever in India. Cheryl M. Bringley Michael B. Fein Laurence S. Kaplan Eric L. Mokole Bernard D. Seckler Preston Whiteway recently undergone substantial renovation. Over the past two years, James Bringley Ramon Fernandez Marina Talbot Michael Katz Raymond Enrique Moradel Evelyn Mehler Seckler Michael Williams floors two through five have seen significant changes, including five “When I joined Courant for a Master’s in 1987, that was my first time in Jenny Marie Bringley Norman J. Finizio Robert F.Kelly Carlos Julio Moreno Thomas I. Seidman Richard F.Williams new classrooms, new conference rooms, and a new computer lab. the US. A lot of my views on what is possible have been shaped by my Joanne Bringley Thomas R. Flack Eric Y.Kemperman Alexander T.Mourtos Mary Shafran Patricia Williamson initial experiences interacting with some gr eat minds at Courant inter-mixed Joseph E. Bringley Jeanne T.Flannery Barbara Keyfitz Jill Schellabarger Mueller Arnold Shak Thomas P.Witelski The new second floor computer lab consolidates the two pr evious Robert P.Bringley Bernard A. Fleishman Madan R. Khatri Sarah Muller Harold D. Shane Wai Kin Wong fifth floor labs into one space. The lab comprises two r ooms, with life in the East V illage. It was a strange but potent combination of Trinity Broderick Andrew B. Flint Suzanne M. Khuns Neeta S. Nabar Michael J. Shelley Shao A. Wu separated by a pane of glass, and has a total of 33 workstations. experiences that got me thinking out of the box on what I could do with Robert F.Brodsky Daniel B. Forger, Jr. Hui K. Kim Brooke L. Nagel Seymour Sherman Deborah Wylie my life,” says Sashi. Ryan H. Brothers Richard Foy. Mary K. Klein Assaad Youssef Nasr David A. Shulman Jiazhao Jessie Xu Some other special features included in the renovations are raised Cheryl Lynn Bruce Jill Pernick Friedman Paula Shafran Koerte Joshua N. Newman Ilya Shutman Michael Yanowitch classroom seating on the second floor, to allow for a better view of Gail Besdine Bukiet Mitchell R. Friedman Mark Kollar Joyce A. Newman Bertram Siegel Chee Yap the board, and a “Smart Board” – an interactive white board. Sashi received his BTech (Bachelor of Science) degree in Computer Science Ana Calcatin Mark D. Galit Christof Samuel Konig Stuart B. Newman Carole E. Siegel Ephraim Zakry Mariellen Gallagher Susan L. Korn Louis Nirenberg Renovations on the remaining floors (six through nine) are expected from the Indian Institute of Technology in Delhi, and after ear ning his Maria Calle Barry M. Singer Joseph W.Zalewski Paul J. Capobianco Ron Gallagher Evan M. Korth Barbara J. O’Donnell Robert A. Smith Anthony J. Zeppetella Master’s in Computer Science at Courant, he ear ned his Ph.D. from The to be completed by the end of 2010. I Rohan Nandakumar Denise M. Gargan Lucien F. Kraner Rhoda Lee Okunieff John M. Snygg Jun Zhang Wharton School of Business, The University of Pennsylvania. I Chandorkar Bijoy M. George Herbert C. Kranzer Enlin Pan Meredith N. Springer Wei F.Zheng Muhammad Abid Abbas Jacob Gilbert Sam Krinsky Ming Pan Joan Low Stachnik Chaudhry William Gleason Marvin S. Kruger Antonio Paras Vladimir G. Stanishev

List includes companies providing matching gifts for their employees. To find out whether your employer sponsors matching gifts, please visit: www.matchinggifts.com/nyu. You may make an online gift to the Courant Institute by visiting www.nyu.edu/giving.

In Memoriam: unbounded domains. The latter won a student paper prize fr om SIAM. Tom’s Corporations & Foundations THE DIRECTOR’S CIRCLE The Generosity of Friends Thomas Bringley work was characterized by physical and analytical insight, technical brilliance, (1981-2008) AccountNet Inc. The Director’s Circle is the Courant Institute’s giving society for those making Your donations to the Courant Annual Fund are more important and tremendous originality.” Adobe Systems Inc. a contribution of $1,000 or more for a given fiscal year. Members receive than ever.This unrestricted income is supporting students and their Advantage Testing,Inc. special invitations as guests of the Director to events of interest throughout the conference travel, and is enhancing the activities of our student AT&T Foundation year, with complimentary access extended where applicable.Additionally, those clubs including the cSplash and WinC outreach programs. In April, Thomas Tyler Bringley, beloved student and A conference was held in Tom’s memory on March 28th, 2009, with eight Axa Foundation giving at the $5,000 level and above qualify for membership in the various cSplash hosted 250 local high-school students to the Institute for an friend, passed away on June 22, 2008 after a speakers discussing problems related to Tom’s mathematical interests, and Joan and Joseph Birman Foundation university-wide giving societies. introductory math day and in March, the Women in Computing student Albert A. Blank Revocable Trust group’s outreach day was attended by 230 New York area high school long battle with cancer. Tom “was a superb including a talk by Charlie Peskin on Tom’s doctoral thesis, “Analysis of the Chalkstream Capital Group, L.P. Members of the Director’s Circle girls.The Annual Fund is also providing matching funds to secure grants student and colleague,” says Courant Director Immersed Boundary Method for Stokes Flow.” A. Robert Cyborski TTEE Steve Allen & Caroline Philip Greenwald Kevin P. Scherer* from other sources, is allowing Courant to invite distinguished speakers Edition One Group for both technical and public lectures, is assisting with furnishing the Leslie Greengard, “who continued to excel in Thompson Norman Grossman* Mark Spitznagel Fidelity Charitable Gift Fund Ernest Battifarano Ruth Shor newly renovated floors in Warren Weaver Hall, including providing Since his passing, Tom’s wife, Krista, his family, and his colleagues and Jefferson Young Han* his coursework and research despite the most Google Inc. Joan S. Birman Alexander Eugene Hasha Lawrence Sirovich furniture for Ph.D. student offices, and is creating improved public adverse of circumstances.” friends have raised funds to create the Thomas Tyler Bringley Memorial W.W.Grainger Inc. Joseph Paschal Brooks Frank Hoppensteadt Carole Hochman spaces in both Warren Weaver Hall and the Broadway building. Gaurdian Life Insurance Co. of America Scholarship, which will support the work of a Ph.D. student studying applied Marshall Butler David G. Korn Sirovich IBM Corporation Philippe G. Charles Cathleen S. Morawetz Edward T.Vanvliet In September 2009, we will have our second Director's Circle dinner in Tom arrived at the Institute in the Fall of mathematics at the interface of many disciplines, guiding applications in Giving Campaign Timothy S. Choate* Eileen Rodriguez Otto Benjamin S.White recognition of donors at the $1,000 and above level, with a special talk 2003, after undergraduate work at Duke in medicine and biology. The Scholarship has over 150 donors to date, fr om Mostyn Foundation Inc. Edwin and Danielle Choi Jonathan Otto Robert A.Young by Raghu Varadhan,Abel Prize Winner.We invite you to join this g roup Non Nobis Solum Foundation with a $1,000 or higher donation to the Courant Annual Fund. math and physics, and completed his Ph.D. her e in May 2008. According individuals from Rochester to Chicago to Califor nia. Glen de Vries* Sashi P.Reddi Charles M. Zegar* G. S. Schwartz & Co. Inc. Carol Ann Fugosich Jeffrey M. Rosenbluth* to his advisor, Charlie Peskin, Tom’s work at Courant involved two Sealed Air Corporation Leslie Greengard Jeffrey Saltzman All donations great and small are essential in continuing to help provide Tom was an exemplary student and a very kind individual, and he is missed Transparent Materials LLC support for a truly extraordinary range of scientific and educational research projects: “one of these solved a 50-year old myster y on the Zegar Family Foundation *NYU President’s Society Members — gifts of $5,000 and abov e. initiatives. mechanism of valveless pumping, and the other intr oduced and greatly by his family, and his many friends at the Courant Institute. I validated a new immersed boundary method for Stokes flow on

6 7 2009 Courant Institute Student Pr izes Stay Connected to the Institute

Henning Biermann Award Harold Grad Memorial Prize Keep in touch with colleagues and friends via two new Piotr Mirowski Afshin Rostamizadeh web resources: There are several groups related to the Courant Institute on LinkedIn.com, a career networking Sandra Bleistein Prize Moses A. Greenfield site, namely, an all-inclusive Courant Network, an Alumni Antonina Mitrofanova Research Award group, and a Mathematics in Finance group. Sukbin Lim Ignacio Rodriguez Also, University Development and Alumni Relations pro- vides VioletNet, (violetnet.nyu.edu) a searchable directory Wilhelm Magnus Memorial Prize Hollis Cooley Prize of all NYU Alumni and an “interactive community designed Karol Koziol Michael Damron especially for NYU alumni.” Diogo Arsénio Janet Fabri Prize Please keep us updated on your address and phone num- Raia Hadsell Bella Manel Prize ber. Email [email protected]. Lin Li Kurt O. Friedrichs Prize Paul Hand Matthew Smosna Prize Your News in the CIMS Manda Wilson Newsletter Max Goldstein Award Matthew Nolin The Courant Institute invites all Alumni to keep colleagues and friends up-to-date on life events. All items submitted (such as career achievements and family milestones) will be considered for publication in the Newsletter or online. Please send the details to [email protected].

To join our community of Courant donors, please visit the new NYU online giving page at www.nyu.edu/giving or contact Cheryl Sylivant at [email protected] or call 212 998 3321.

NEW YORK UNIVERSITY Courant Institute of Mathematical Sciences Warren Weaver Hall 251 Mercer Street New York, NY 10012