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Home , Andrew Majda, Lars Ahlfors, Luis Caffarelli, Nevanlinna Prize, Paul Garabedian, Subhash Khot

Spring 2015

Published by the Courant Institue of Mathematical Sciences at University Newsletter

Louis Nirenberg shares 2015 Abel Prize with John Nash Volume 11

p12

p6 Fellowship Established in Perpetuity

p2 p4 The Simplest New Faculty Hard Problem Highlight: Tim Austin

ALSO IN THIS ISSUE:

THE COURANT GLOBAL COMPUTER INSTITUTE WELCOMES PROGRAMMING ROBIN ROY CONTEST p.5 p.9

2015 SPRING PUZZLE: FACULTY HONORS TAKE YOUR SEATS p.10 p.7

STUDENT HONORS , p.11 : AN ILLUSTRATED MEMOIR p.9 The Simplest Hard Problem: on the Unique Games Conjecture by April Bacon

In August 2014, Subhash was awarded the Prize, one of the top honors given by the International Mathematical Union. Subhash received the prize, which is awarded only once every four years, not only for defining the UGC, but also for leading efforts to understand “its complexity

and its pivotal role in the study of efficient The International Mathematical Union approximation of optimization problems.” presented Subhash Khot with its on August 13, 2014 at the International Congress of conference in Long time friend and collaborator Assaf Seoul, Korea. Khot was awarded the Prize Naor (Princeton) traces Subhash’s “pivotal “for his prescient definition of the ‘Unique role” back to his graduate student years Games’ problem, and leading the effort to understand its complexity and its pivotal at Princeton. It was there, under the role in the study of efficient approximation mentorship of his Ph.D. advisor, Sanjeev of optimization problems; his work has led Arora, and another mentor, Johan Håstad to breakthroughs in algorithmic design and approximation hardness, and to new (Royal Institute of Technology in Stockholm), exciting interactions between computational that Subhash quickly found one of the complexity, analysis and geometry.” research agendas that would define the last decade and a half of his scientific career: showing that many computational Photo by Mathieu Asselin. ©NYU Photo Bureau. problems are hard to approximate. The was starting out. I had no fear that, ‘Ah, if I Unique Games Conjecture concerns one propose the conjecture and if it gets quickly When he was seventeen, Subhash Khot such specific problem, and the foundation disproved and turns out to be obviously touched a computer for the first time as a on which Subhash built it came from a wrong, that would be a big embarrassment.’ newly admitted undergraduate student at famous theorem in the 90s called the PCP I was not afraid of any such thing.” the Indian Institute of Technology, Bombay. (Probabilistic Checking of Proofs) Theorem, He arrived at IIT with a mathematical with which Arora and Håstad were both So what is the Unique Games Conjecture? foundation largely acquired through involved. In mathematical terms, according to intensive self-study and the encouragement Subhash, “The problem is about solving a of one exceptional high school teacher and As a graduate student, Subhash “formulated system of linear equations over a large field. headmaster, V. G. Gogate. Just five years later, various ways to strengthen the PCP theorem,” The equations are linear and each equation enrolled in the Ph.D. program at Princeton, says Assaf, and of the three approaches depends on only two variables. So you have a Subhash wrote “On the power of unique Subhash pursued, “two became major bunch of variables and a bunch of equations 2-prover 1-round games,” a paper proposing theorems.” One of these was the “quasi- of this kind and then the conjecture states the Unique Games Conjecture (UGC), which random PCP, which led to a very difficult and that even if we are promised that there is a established a new paradigm in complexity impressive work that involved showing that solution to this system of equations which theory. it’s difficult to partition a graph efficiently … satisfies 99% of the equations, it remains So this is one of the things that he did which computationally difficult to find a solution Now a Professor of at was a success. But then, of course, came the which satisfies even 1% of the equations.” NYU’s Courant Institute for going on nine Unique Games Conjecture … and he quickly years, Subhash appreciates the Institute for realized how important this conjecture is.” Using the UGC, “you can get very precise its integrated and computer approximation thresholds for the science departments, its distinguished “There is no reason why it wasn’t proposed performance of efficient algorithms for faculty, and for how well his life is blended before,” Subhash humbly offers. “Probably seemingly unrelated problems,” says Assaf. with his work. “It’s a place where people because, in some sense, one would need to That is, the UGC has proven to precisely enjoy doing what they are doing. It is kind be … I don’t know what the word is … foolish illuminate the dividing line between of collaborative as opposed to being too enough? I was just a grad student who approximability and inapproximability in a competitive,” he says.

2 — CIMS Newsletter, Spring 2015 wide class of problems. “In a certain precise, approach and say, I instead want to disprove fundamental problem in cryptography technical sense, Unique Games seems to the UGC and this amounts to coming up called the Shortest Vector Problem in be the simplest really, really hard problem,” with an algorithm for the Unique Games Lattices, and he proved that all kinds of says the IMU. This is because the UGC is problem. The UGC states that the Unique problems in learning theory are intractable hard enough to qualify as a hard problem, Games problem is hard and you disprove … [and] he proved a beautiful theorem just but has a simple enough structure to, as the conjecture by in fact showing that the this fall on a problem called Monotonicity Subhash phrased it, “sit inside of other problem is easy … people attempted to come Testing.” problems.” up with new algorithms and though they didn’t succeed fully, there were some partial Along with collaborator Dana Moshkovitz “Proposing the conjecture itself wasn’t so results which were already new algorithmic (M.I.T.), one major part of Subhash’s much of a big deal,” offers Subhash. “What techniques.” current work is an approach they have followed in the next ten plus years with proposed to prove the Unique Games many developments, I think that was After summing up the many aspects of Conjecture. “We are making what seems the main contribution, a joint effort by the conjecture which Subhash himself has to be a slow and steady progress, but it will several researchers; this was unexpected of “championed and pushed forward,” Assaf probably take a long time,” says Subhash. course.” Over those ten plus years, the UGC says: “And this is not all of his work! This is In the meantime, as the IMU says, “The inspired many new techniques and results just some of it. There are many other things.” Unique Games Conjecture will be driving which are valid whether or not the UGC is For example, “Subhash was the first person research in theoretical computer science true. Through the efforts of Subhash and who proved that it is very hard to solve a for many years to come.” n others, these unexpected benefits came about through approaching the conjecture The graph in different ways—through reductions (i.e. partitioning reducing one problem to another), and problem seeks to through attempting to both prove and partition a given graph into two disprove the UGC. roughly equal parts so as to minimize Reductions from the conjecture are the number of edges cut. Khot's mathematically involved constructions work gives evidence in and of themselves and so, in order to that this problem make use of the conjecture, new tools were might be hard to approximate. needed and therefore discovered in the areas of , isoperimetric inequalities in geometry, and invariance principles in probability. x1 — x7 = 1 1 (mod 17) An instance of the Unique Games x2 — x3 = 13 (mod 17) problem. The Unique Trying to prove the UGC has also had ... Games Conjecture unexpected benefits, “for example, trying .... states that when the modulus (in this case to prove the conjecture actually resulted x7 - x9 = 15 (mod 17) 17) is large, it is hard to in solving an isoperimetric type problem find a good assignment in geometry called constructing foams,” to such a system of Unique Game Problem linear equations. says Subhash. “You could take another

Brittany Shields presents the 2014 Holiday Lecture

This past December, Brittany Shields presented 2014 Holiday Lecture on “The Courant Institute of Mathematical Sciences: A Historical Perspective, 1934-1972.” Shields (who received her M.A. from NYU in 2008) recently earned her Ph.D. from the University of Pennsylvania (2015) with the dissertation, A Mathematical Life: Richard Courant, , and Scientific Diplomacy in Twentieth Century America. The full Holiday Lecture video is now available online, along with past lectures, at http://video.cims.nyu.edu/media/HolidayLectures/

3 New Faculty Highlight: Tim Austin by M.L. Ball

The Clay Institute Fellowship funds Tim Austin and research for five years graduate student Moumanti Podder. Founded in 1998, the Clay Institute supports the international mathematical community by employing research fellows and scholars, and by bestowing research awards in recognition of extraordinary achievement. Once Professor Austin received his graduate degree from UCLA in 2010, recommended him for a Clay fellowship, and auspiciously, he was awarded it—the only one bestowed that year. “It’s a 5-year stipend, which is very generous and very nice,” Tim says. “What’s also really great about it is that you can do your research in any ‘approved’ academic institution you want, or at a place like Microsoft. You then spend your time just thinking about math and talking with Photo by Mathieu Asselin. ©NYU Photo Bureau. colleagues, trying to solve problems.”

Born in London and raised in Colchester, England, Courant Institute Associate Professor of Tim just finished the five-year fellowship. Mathematics Tim Austin is an ergodic theorist. His research focuses primarily on analysis, The first two years were spent at Brown probability, ergodic theory, metric geometry and geometric group theory. University, primarily because his fiancée, Kathy Smith, was doing a postdoc there. She From Cambridge to Microsoft, In short order, Tim gained admission to was then offered a faculty fellowship at NYU, then to UCLA and Brown, and finally, UCLA’s graduate program and was invited by enabling the couple to move together to New to Courant Terence Tao to be one of his students. “My York in 2012. Before coming to Courant full Even in his early teens, Tim Austin knew original plan was to go to L.A. in mid-August, time, Tim conducted research for Clay during he wanted to study math. “I started to read 2006, but one of the people I applied to work spring semesters, then taught a Courant and popular math and with in the U.S., Yuval Peres, was moving course each fall, which he found to be a good got enthusiastic about it, and very quickly to Microsoft Research, and he offered me a balance. “Some people can just go away and decided that’s what I wanted to do,” says the month’s position as a consulting researcher, do research for 40 hours a week and not do Courant Institute Associate Professor. “My learning about what they do and thinking anything else and be very productive,” Tim family was not especially mathematical. My about some problems,” he explains. “So states. “I was actually starting to go a little parents were actually both librarians, so it before I even showed up at grad school at bit crazy by the end of my time at Brown—a was quite a bookish household. They fully UCLA, I spent July of that year in Redmond, little too much time inside my own head—so supported my interests, but neither of them Washington at the main Microsoft campus. I teaching is a very good outlet for that.” was mathematically inclined at all.” got to know quite a few of the people there— most importantly, Assaf Naor.” Ergodic theory: a branch of dynamical systems After earning his undergraduate degree in pure mathematics from Cambridge While still at UCLA, Tim was invited by As an ergodic theorist, Tim’s work University in 2005, Professor Austin found Professor Naor (now at Princeton) to spend a is concerned with the study of the himself drawn to analysis. “I didn’t have month working with him at Courant, to gain mathematical structures needed to describe a particular subject in mind but I knew I some diversity and to be exposed to a bigger a system in the real world that can exist in wanted to do some kind of analysis, and range of problems. “That initial month was a range of different states, and that changes there were not many people doing really my introduction to Courant,” Tim says. “It its state as time passes according to a fixed crunchy hard analysis in Cambridge,” Tim turned into a long-term collaboration with rule. As he describes it, “Ergodic theory recalls. “When I asked my professors where Assaf, sparked my interest in coming here, studies the questions that concern long run the good analytic people were, they generally and was a chance for me to learn more about averages, or other statistical properties of mentioned places in the U.S., particularly what people are doing at Courant.” these systems. So I look at how the rate, or UCLA, because Terence Tao was there.” some other quantity that answers one of

4 — CIMS Newsletter, Spring 2015 these questions, could be computed in terms trying that, and it doesn’t work. Then what kind of research they do. Everyone of something else. I ask more ‘pure’ questions something comes along and I think, ‘Oh has their own specialties, but it’s very about sub-classifying the possible structure that’s an interesting idea…I’m not quite natural to talk to people whose interests of systems within some large class, according sure what that does,’ and I keep it in the are perhaps quite far from your own, to try to what kinds of behavior they exhibit—or back of my mind.” to find something in common or just chat even better, generating a smaller list which for general interest,” he says. “This forces effectively captures all the possibilities.” Then four weeks later, he says, as he is you to examine whether what you’re doing lying in bed or riding on the bus, he will is interesting.” “Let me say two things about examples of suddenly realize that that was the very probability-preserving systems,” said Tim. idea he needed. “I don’t even remember An additional benefit of Courant’s “Historically, the examples that gave rise to having the idea,” Tim says. “Only much tradition of interdisciplinary interaction, the modern theory are models of the solar later do I realize the problem was already Tim adds, is the fact that “because you system and of the motion of the particles of solved and I just didn’t notice it, which get to learn about more diverse things, gas in a box. However, there are also simpler is very annoying actually, because it might help you decide on some new abstract examples that play an important probably during those four weeks, I tried direction of research. You can tap into the role in the theory as objects of comparison. a whole load of other things and got quite knowledge of your colleagues regarding Two of the most important of these are a rigid frustrated and didn’t need to.” some problem or dead end that might rotation of the points around a circle, and arise. For instance, if I discover that I need the progression of a sequence of ‘pure noise’ The Courant Institute: an to know about subject X while working random bits by one time-step.” interdisciplinary network of on Y,” he says, “I know who to go to about collaborators X. These are all very positive benefits. It’s A knack for solving problems but not Tim has been at the Courant Institute for quite a lovely place, indeed.” n knowing he’s solved them two and a half years, and the collaborative “I don’t think I’ve ever had a moment where atmosphere and easily approachable I have an idea and immediately know, ‘This faculty have been a pleasure, he says. is the idea that will solve the problem,’ Tim “Courant has supported me very reveals. “Rather, what has happened several generously. It also has this nice bent that times is that I’m bumbling along trying this, people are not very rigidly classified by

The Courant Institute Welcomes Robin Roy

Research on Alzheimer’s Disease and the Aging Brain at Columbia, Director of Development for Basic Sciences and Graduate Medical Education at Mt. Sinai Medical Center, and Associate Dean for Development and External Affairs for Columbia’s Mailman School of Public Health. She comes to us from Barnard College, where she served as Senior Associate Director of Development.

Robin has an M.B.A. in Marketing from Columbia and an A.B. in English and M.A. in Musicology from Smith College. Her numerous achievements include developing a case statement for basic science research and managing the development program for the 10 basic science departments and three translational research institutes at Mt. Sinai, spearheading the reorganization of the Advisory Board for the Columbia School of Public Health, and negotiating and securing

Photo by Mathieu Asselin. ©NYU Photo Bureau. a $22 million gift from a Public Health school alumnus. She is a two time CASE (Council for Advancement and Support of Education) We are delighted to welcome Robin Roy as Director of Development, Circle of Excellence award winner. Courant/Global Public Health, Science and Technology. Robin has a strong and successful background in development for basic science, Welcome, Robin! n having served as Director of Development for the Taub Institute for

5 Paul Garabedian Fellowship Established in Perpetuity

The Paul the direction his advisor, . elliptic, partly hyperbolic. They accomplished Garabedian He spent ten years at Stanford, with one this by introducing complex coordinates. Fellowship in intervening year at Berkeley, before James This was so sophisticated a mathematical Mathematics Stoker convinced Paul to move to the idea that the aerodynamic community was or Computer Courant Institute. unable to comprehend it; therefore they Science ignored it. Finally a mathematically minded has been In 1964 Paul published Partial Differential aerodynamicist in Canada tested the airfoil in established Equations, a seminal text used worldwide a wind tunnel and found the flow to be indeed in memory even half a century after its publication. free of shocks. After that, aerodynamicists of Professor He advised twenty-seven Ph.D. students. pounced on the Garabedian-Korn design.” The Emeritus Paul Garabedian. One of the From 1972-1978 he served as Director of resulting airfoils increased lift, fuel efficiency, outstanding mathematicians of his the Courant Mathematics & Computing and speed. This discovery revolutionized the time, Paul spent 51 years of his career Laboratory of the US Department of industry and influences much of commercial at NYU’s Courant Institute, from 1959 Energy and was Director of the Division aircraft design today. The research resulted until his death in 2010. The Fellowship of Computational Fluid Dynamics from in three books written by Paul and his team has been established by his wife Lynnel 1978 until his death. He was a member and was acknowledged with a NASA Public Garabedian, with a generous $250,000 gift. of the National Academy of Sciences, the Service Group Achievement Award in 1976 and The Fellowship will support students at American Academy of Arts & Sciences, Certificate of Recognition in 1980. the Courant Institute “who are members and a fellow of SIAM and the American of groups traditionally underrepresented Physical Society. Among his many honors, Advancements in cleaner and in post-graduate programs in science Paul received the Boris Pregel Award safer energy and mathematics, such as women and from the New York Academy of Sciences, Paul worked on problems related to magnetic minorities.” AMS’s Birkhoff Prize, SIAM’s Theodore von fusion—a way to generate carbon-free power Karman Prize, and the National Academy and avoid the risks associated with nuclear Acting Director Michael Shelley said: “The of Sciences Award in Applied Mathematics energy—on and off for a period of forty-plus Institute is deeply grateful to Lynnel for this and . years. “He was very much interested in trying gift that will support exceptional students to find a way to develop magnetic fusion,” says through the years, in memory of Paul and The Bieberbach Conjecture Courant Professor Emeritus Harold Weitzner, his remarkable scientific legacy.” One of Paul’s earliest significant “because he considered it socially desirable.” contributions was related to the celebrated After years of fusion work, Paul developed As a pure mathematician, Paul made Bieberbach Conjecture, which he worked sophisticated models. The result of Paul’s work fundamental contributions to the theory on at Stanford along with Max Schiffer. with his research group was the NSTAB suite of of partial differential equations and to the “Their approach was to use the calculus computer codes. The ideas and computations theory of functions of a complex variable. of variations,” says Peter Lax in the above from these codes enabled others to develop the During the 1950s Paul was a pioneer in mentioned AMS Notices. “The formulas code which is now the standard for designing the use of computing to solve important involved in this research were formidable.” scientific and engineering problems. His Paul’s contribution was an important step work as an applied mathematician has had on the road to the conjecture itself being a major impact on modern aircraft design proved 30 years later, in 1985. and on the design of fusion reactors. “With much outstanding mathematics one can A lasting impact on aircraft design imagine the work having been done by a In the 1970s advances in aircraft design number of mathematicians,” says Courant were allowing planes to fly to nearly the Professor Emeritus Peter Lax in the March speed of sound. Airflow over the wings 2014 Notices of the American Mathematical would increase to supersonic speeds and Society’s memorial article for Paul. “Not generate shock waves which caused a so with most of Paul’s accomplishments; greater drag on the airplane. Along with his outlook was unique. He will be David Korn, a former Ph.D. student, Paul Peter Lax and Paul Garabedian (1968) with remembered for a long time.” used mathematics and numerical methods the CDC (Control Data Center) 6600, the to design airfoils for planes “that carry third in a line of supercomputers which were After receiving his B.A. from Brown (1946) shockless transonic flows,” says Peter Lax housed and operated in the basement of the Institute’s Warren Weaver Hall. Paul served Paul began his studies at Harvard, receiving in the AMS Notices. “This required solving as Director of the Courant Mathematics & his M.A. (1947) and then Ph.D. (1948) under partial differential equations that are partly Computing Laboratory from ’72-’78.

6 — CIMS Newsletter, Spring 2015 stellarators (machines for producing PUZZLE SPRING 2015 controlled fusion reactions in plasma), such as the large “heliotron” stellarator in Japan and a large new stellarator in Germany. “So this was a major contribution to the field,” Take Your Seats says Harold. by Dennis Shasha and Richard Cole

Paul worked tirelessly up until his death. A popular logic game involves His last paper, “The DEMO Quasisymmetric figuring out an arrangement of Stellarator,” written with his former student people sitting around a circular Geoffrey McFadden (NIST), was published table based on hints about, say, their just four months before he died. During the relationships. In this puzzle, we aim last months of his life, Paul continued to to determine the smallest number come to Warren Weaver Hall regularly. There, of hints sufficient to specify an he could be heard singing the praises of arrangement unambiguously. For Lynnel, his wife of 43 years, who graciously example, suppose we must seat Alice, attended to all the practicalities of their lives Bob, Carol, Sybil, Ted, and Zoe. If we at that time “because,” as he said, “all I can are allowed hints only of the form X see is the beautiful math.” is one to the right of Y, it would seem four hints are necessary. But suppose Paul was a devoted father to his daughters, we can include hints that still refer to two people, or “binary hints”, but in which X Emily and Cathy, and immensely proud can be farther away from Y. of them. He had always fervently believed in encouraging and promoting women As a warm-up, suppose we have just three hints for the six people: Ted is two seats in science and math and was delighted to the right of Carol; Sybil is two to the right of Zoe; and Bob is three to the right of when they became scientists in their own Ted. We see that we need only three hints to fix the relative locations of six people. right, Emily, a physician, and Cathy, a What is a unique (up to circular shift) arrangement of the six people in this case? neuroscientist. n Warm-Up: Solution to six people arrangement: a circular table with 6 people, where Carol to the left of Zoe, Zoe to the left of Ted, ..., Bob to the left of Carol: (Carol, Zoe, Ted, Sybil, Alice, and Bob).

However, if we now bring Jack and Jill into the picture, for a total of eight people, then we might ask how many binary hints we would need to fix the arrangement. Consider these five hints: Carol is three seats to the right of Jill; Alice is six to the Giulia DeSalvo right of Bob; Ted is four to the right of Zoe; Jill is six to the right of Zoe; and Carol has been is six to the right of Sybil. What arrangement would these hints produce? named the first recipient Getting even more ambitious, suppose we add Christophe and Marie, giving us of the Paul 10 people, and want the ordering to be like this: Christophe, Jack, Jill, Bob, Marie, Garabedian Carol, Ted, Zoe, Alice, and Sybil. Fellowship in Mathematics Can you formulate seven hints that will fix this arrangement? Can you do it with or Computer Science. As stated fewer than seven? by Giulia’s Ph.D. advisor, Mehryar

Mohri: “Giulia has introduced an In general, how many binary hints are required to fix an arrangement of n important and novel machine people around a table for n at least six? Can you achieve 3n/4? Can you do better learning model formed by cascades than this? We don’t know the answer to the last question. of predictors, Deep Cascades, in which leaf predictors or node For the solution, email: [email protected] questions may be linear predictors based on polynomial kernels of relatively high degree, neural networks, or members of other rich families.” Congratulations, Giulia!

7 WELCOME TO THE INSTITUTE’S NEWEST FACULTY

Yuri Bakhtin joined the Institute in Fall 2014 Vindya Bhat’s research interests include Ramsey as an Associate Professor of Mathematics. He Theory and extremal combinatorics. She received received his Ph.D. in mathematics from Moscow her B.A. from Rutgers University (2000), M.A. from State University (2001). Prior to coming to Columbia University (2007) and Ph.D. from Emory Courant, he taught at the Georgia Institute of University (2015). Prior to joining the Courant Technology. His primary areas of research are in Institute in Fall 2014 as a Clinical Instructor of random dynamics and probabilistic models of mathematical physics. Mathematics, Vindya gained 10 years of industry experience in various analytical roles.

Amos Bloomberg joined Courant in Fall 2013 Paul Bourgade joined the Institute in Fall 2014 as a Clinical Assistant Professor of Computer as an Associate Professor of Mathematics. Science, following 15 years in the internet He received his Ph.D. in Mathematics from and media sectors designing apps, games, Université Paris 6. His research lies in probability and toys. He holds a bachelors in Brain & theory (random matrices, stochastic analysis) Cognitive Sciences from the University of and its connections with other domains of Rochester (1997), and a masters in Interactive mathematics (partial differential equations, Telecommunications from NYU (2003). analytic ).

Joshua Clayton joined the Courant Institute Miranda Holmes-Cerfon joined the Institute as an in Fall 2013 as a Clinical Assistant Professor Assistant Professor of Mathematics in Fall 2013. of Computer Science. His work explores Her work lies broadly in two areas: self-assembly the creative potential of computational of nano- and micro-scale systems, and multiscale media, with a particular focus on the Web. processes in fluids. She has investigated these He received a master’s degree in Interactive in a range of applications, including soft-matter Telecommunications from New York physics, colloids, sphere packing, ion beam University in 2011. sputtering, internal waves, ocean mixing, tides, and lava tubes.

Joanna Klukowska joined the Courant Institute Eyal Lubetzky joined the Institute in Fall 2014 in Fall 2014 as a Clinical Assistant Professor as an Associate Professor of Mathematics. of Computer Science. She received her Ph.D. His main research interests are probability in 2013 from the Graduate Center of the City theory and combinatorics, with an emphasis on University of New York where her research interacting particle systems, random networks work was in biomedical imaging. More recently and stochastic processes arising from statistical she became interested in computer science physics. Previously, he was a Senior Researcher education and introducing students to open in the Theory Group of Microsoft Research, source projects. Redmond, where he spent 7 years, starting as a post-doctoral researcher. He received his Ph.D. in Mathematics from Tel-Aviv University in 2007, and received the Rollo Alex Mogilner joined NYU in Fall 2014 as a Davidson prize in 2013. Professor of Mathematics and Biology. Alex received Ph.D. in Applied Mathematics from the University of British Columbia in 1995, worked Michael Munn joined the Courant Institute in at UC Berkeley as a postdoc, and from 1996 Fall 2014 as a Clinical Assistant Professor of to 2014 was a Professor at the Departments Mathematics. He received his Ph.D. from the of Mathematics and Neurobiology and CUNY Graduate Center in 2008 and spent two Physiology at UC Davis. Alex’s fields of study years at the University of Warwick as an NSF include Mathematical Biology, Cell Biology postdoctoral fellow. His research interests are and Biophysics. He works on mathematical in geometric analysis and metric geometry, and computational modeling of cell motility and cell division, and as well as an interest in undergraduate conducting experimental research on galvanotaxis. mathematics education.

Mike O’Neil, Assistant Professor of Mutiara Sondjaja joined the Courant Institute Mathematics at Courant and the School of in Fall 2014 as a Clinical Assistant Professor of Engineering as of Fall 2014, received his Mathematics. She received her undergraduate Ph.D. from Yale in Applied Mathematics in degree in Mathematics from Harvey Mudd 2007. Previously, he served as an Associate College (2008) and her Ph.D. in Operations Research Scientist and Courant Instructor. His Research from Cornell University (2014). Her research focuses on numerical analysis and fast mathematical interests are continuous algorithms for integral equation methods in optimization and mathematical programming. electromagnetics, acoustics, and fluids.

8 — CIMS Newsletter, Spring 2015 Georg Stadler joined the Institute in Fall 2014 as an Associate Professor of Mathematics. Computer Science Students Best He received a Ph.D. from the University of Graz in Austria in 2004 and previously held All of North America in Global a Research Scientist position at the Institute of Computational Engineering and Sciences Computer Programming Contest at UT Austin. His main research interests are in parallel scientific computing, deterministic and probabilistic inverse problems and PDE- A team of computer science students from NYU’s Courant constrained optimization. Much of Stadler’s Institute bested the 20 other North American schools research is driven by application problems in the earth sciences, competing in the 2014 World Finals of the ACM Intercollegiate such as the flow in the earth’s mantle, seismic wave propagation and the dynamics of ice sheets. Programming Contest (IPC). The team — comprising Bowen Yu, Fabian Gundlach, and Danilo Neves Ribeiro — placed 13th out of 122 schools from across the globe. They were Elizabeth Stepp joined the Institute in coached by Evan Korth, Clinical Professor of Computer summer 2013 as a Clinical Assistant Professor Science, and adjunct faculty members Brett Bernstein and Sean of Mathematics. She received her B.S. in mathematics form Vanderbilt University McIntyre. The ACM IPC, sponsored by IBM, is the first global (1992) and her Ph.D. in mathematics from the programming competition conducted by and for the world’s University of Kentucky (2005). Before joining universities. n Courant, she spent six years on the faculty at the University of Texas at Austin.

Joseph Versoza joined Courant as a Clinical Assistant Professor of Computer Science in Fall 2014. His interests include developing modern web applications and integrating professional programming tools into computer Peter Lax, Mathematician: science education. Versoza holds an MPS from NYU’s Interactive Telecommunications An Illustrated Memoir Program. He has several years of experience in IT management, software engineering and technology education.

This new biography

Michael Walfish joined Courant as an about Peter Lax, written Associate Professor of Computer Science in by Reuben Hersh, 2014. He was previously on the faculty at UT was published by the Austin, and received his Ph.D. in Computer Science from MIT. His research interests are in American Mathematical systems, security, and networking; a particular Society in early 2015. focus over the last several years has been “Reuben Hersh, one of verifiable outsourcing of computations based on complexity-theoretic and cryptographic Peter’s many students, machinery. gives us a lively and beautifully illustrated biography,” says Gérard Robert Young joined the Courant Institute Ben Arous, Director of in Fall 2014 as an Associate Professor of Mathematics. He received his Ph.D. from the the Courant Institute of in 2007 and previously Mathematical Sciences. held a faculty position at the University The book chronicles of Toronto. His research interests include quantitative geometry in Lie groups and the Lax’s life, including his and his family’s escape to structure of surfaces in Euclidean space and the U.S. as the Nazis invaded Hungary, his work on nilpotent groups. the Project, his arrival at the Courant Institute (before it was named for Richard Courant), and his lifetime as one of the most influential and renowned mathematicians of both pure and applied mathematics. “This book brings out both the personal and professional aspects of Peter’s work in a captivating manner,” says Ben Arous. “It is a great read for people who know Peter as well as for those who do not.” n

9 FACULTY HONORS

Richard Bonneau was appointed Group Leader for Systems was selected to give the 2014 John Biology at the Simons Center for Data Analysis, where he Von Neumann Lecture at SIAM. The distinguished prize leads a group focused on developing new computational series, established in 1959, is awarded “for outstanding biology methods. and distinguished contributions to the field of applied mathematical sciences and for the effective communication Antoine Cerfon and Miranda Holmes-Cerfon were selected of these ideas to the community.” In September 2013, for Department of Energy Early Career Research Awards. Greengard was named Director of the Simons Center The Early Career program “supports the development of for Data Analysis at the , where he is individual research programs of outstanding scientists building and leading “a team of scientists committed to early in their careers.” Antoine was selected by the developing innovative mathematical methods and Office of Fusion Energy Sciences for his work on “High software for analyzing large-scale data sets drawn from Performance Equilibrium Solvers for Integrated Magnetic the biological and physical sciences.” Fusion Simulations” and Miranda by the Office of Advanced Scientific Computing Research for her work on “Kinetics of Selin Kalaycioglu won a 2014 NYU Golden Dozen Award Particles with Short-Range Interactions.” from NYU’s College of Arts and Science. The award, selected from nominations sent in by students and faculty, was named a 2013 Simons Fellow in “recognizes faculty for their outstanding contribution to Mathematics by the Simons Foundation. Simons Fellows, learning in the classroom.” selected for demonstrated research accomplishment, are given financial support to extend the duration of their Bob Kohn and received the 2014 AMS sabbatical research. He also gave the 2013 Tondeur Lectures Leroy P. Steele Prize for Seminal Contribution to Research, (U. Illinois, Urbana-Champaign) and the 2014 Bowen along with . They received the honor for their Lectures (U. C. Berkeley) on Quantitative Behavior paper, “Partial regularity of suitable weak solutions of the of Singular Sets. Navier-Stokes equations” (Communications on Pure and Applied Mathematics, 1982) which, as expressed in the Patrick and Radhia Cousot were awarded the 2014 AMS citation, “was and remains a landmark in the Harlan D. Mills Award for “the invention of ‘abstract understanding of the behavior of solutions to the Navier- interpretation,’ development of tool support, and its Stokes equations and has been a source of inspiration for practical application.” The award is given annually by the a generation of mathematicians.” IEEE Computer Society to recognize “researchers and practitioners who have demonstrated long-standing, Yann LeCun was awarded the 2014 IEEE Computational sustained, and meaningful contributions to the theory Intelligence Society Neural Networks Pioneer Award, and practice of the information sciences, focusing on recognizing “significant contributions to early concepts and contributions to the practice of software engineering sustained development in the field of neural networks.” through the application of sound theory.” was awarded the 2015 ICIAM Lagrange Prize Patrick Cousot and David McLaughlin have been named “in recognition of his ground-breaking, original, fundamental Julius Silver, Roslyn S. Silver, and Enid Silver Winslow and pioneering contributions to applied mathematics and, Professors. Funded by an endowment to the University in particular, to wave front propagation and combustion, from alumnus Julius Silver, Silver Chairs are awarded in scattering theory, fluid dynamics and atmosphere climate recognition of outstanding scholarly contributions. science.” The Lagrange Prize was established “to provide international recognition to individual mathematicians Rob Fergus won the 2013 IEEE CVPR (Computer Vision who have made an exceptional contribution to applied and Pattern Recognition) Longuet-Higgins prize for his mathematics throughout their careers.” 2003 paper “Object Class Recognition by Unsupervised Scale-Invariant Learning” with Pietro Perona and Andrew The Centre de Recherches Mathématiques, a Canadian Zisserman. The prize is awarded for “fundamental mathematical research center, has established the contributions in computer vision.” CRM Nirenberg Lectures in Geometric Analysis in honor of Courant Professor Emeritus Louis Nirenberg.

10 — CIMS Newsletter, Spring 2015 STUDENT HONORS

Theodore Rappaport and his students have been Henning Biermann Award awarded the 2015 IEEE Donald G. Fink Award for Jonathan Tompson the outstanding survey, review, or tutorial paper in Siddharth Krishna IEEE publications. Sandra Bleistein Prize Giuilia DeSalvo John Rinzel is the recipient of the 2015 Arthur T. Winfree ChengCheng Huang Prize from the Society for Mathematical Biology for “his elegant work on the analysis of dynamical behavior Hollis Cooley Prize in models of neural activity and the contributions that Olivia Chu work has made in the neurobiological community to the Janet Fabri Prize understanding of a host of phenomena (including simple Russell Power excitability as well as bursting) in single neurons, small Adriana Lopez-Alt populations of neurons, and other excitable cells.” Kurt O. Friedrichs Prize Dennis Shasha was named a 2014 ACM Fellow for Edgar Costa both technical and literary contributions to computing. Thomas Fai His technical contributions include ways to maximize The Paul Garabedian Fellowship concurrency in database indexes and fast algorithms for Giulia DeSalvo finding correlations and bursts in time series. His literary contributions include a wide-ranging study of database Max Goldstein Prize tuning, books on resampling statistics, DNA computing, Clare Carroll and mathematical puzzles. Harold Grad Memorial Prize Insuk Seo David Sontag and Thomas Wies have each received Noah Stephens-Davidowitz NSF CAREER awards. CAREER awards are the National Science Foundation’s “most prestigious awards in Moses A. Greenfield Research Award support of junior faculty who exemplify the role of Steven Delong teacher-scholars through outstanding research, excellent Hyungbin Park education and the integration of education and research The Martin and Sarah Leibowitz Prize for Quantitative Biology within the context of the mission of their organizations.” Rachel Hodos Sontag was selected for his project “Exact Algorithms for Learning Latent Structure” and Wies for “Abstracting Wilhelm Magnus Memorial Prize Programs for Automated Debugging.” Manas Rachh Aukosh Jagannath Daniel Stein was awarded a 2014 John Simon Ian Tobasco Guggenheim Fellowship in Natural Sciences in a group Math Masters Prize of 178 scholars, artists, and scientists. Fellowships Dmitry Storcheus are awarded “on the basis of prior achievement and exceptional promise.” Matthew Smosna Prize Yunzhe Jia Yuri Tschinkel was named an American Association Computer Science Master’s Thesis Prize for Advancement of Science Fellow for “outstanding Weihan Kong research in algebraic geometry and number theory and dedicated service as the Director of Mathematics and Master’s Innovation Prize the Physical Sciences at the Simons Foundation.” AAAS Andrei Petrut Dinu-Ionita Fellows are named for their “distinguished efforts to Xiaocong Wang advance science or its applications.” Bella Manel Prize Fang Fang

Thomas Tyler Bringley Fellowship Chen-hung Wu (2015) Jihun Han (2014)

11 Louis Nirenberg shares 2015 Abel Prize with John Nash by April Bacon

Photo by Mathieu Asselin. ©NYU Photo Bureau.

Louis Nirenberg has won the Norwegian Academy of Science and Letters’ 2015 Abel Prize along with co-recipient John Nash. The Abel Committee selected these “two mathematical giants of the twentieth century” for their “striking and seminal contributions to the theory of nonlinear partial differential equations and its applications to geometric analysis.” The prize will be formally presented by King Harald of Norway in Oslo in May 2015.

12 — CIMS Newsletter, Spring 2015 Though only 16 Abel prizes have been Although the pair never formally Jalal also quickly learned that, for Louis, awarded, Louis is the fourth Courant faculty collaborated on papers, they influenced each math is not just a passion: it is also about member to win the prize. The other three others’ work and, as added in the Abel prize fun and beauty, two things which are central recipients are Peter Lax (2005), S. R. Srinivasa citation, “the consequences of their fruitful to Louis as a mathematician and a person. Varadhan (2007), and Mikhail Gromov (2009). dialogue, which they initiated in the 1950s His appreciation of beauty extends into his “It really is phenomenal,” Donald E. McClure, at the Courant Institute of Mathematical admiration of artful objects like ceramics executive director of the American Math- Sciences, are felt more strongly today than and masks and his love of fine foods. And his ematical Society, told for ever before.” dedication to fun is exhibited by his love for its 2009 article “Complex Math, Simple Sum: telling jokes. “One thing I never told him,” 3 Awards in 5 Years.” “[The Abel Prize] has the Louis’ importance to mathematics in general says Jalal, “was that I translate his jokes same distinction as a Nobel Prize, and there’s and specifically to the life and prominence into Arabic and tell them to my friends and no other institution in the or in of the Courant Institute—of which he relatives in Lebanon. Some of the jokes are the world that has had such a concentration has been a member for seventy years—is lost in translation but most are a big hit.” of these awards.” foundational. He joined the Courant Institute (not yet named for Courant) in September But the most important thing Jalal quickly As the Abel committee elaborates in 1945 as a graduate student. He received his learned was the depth of Louis’ kindness: their citation, Nirenberg’s and Nash’s M.S. in 1947 and his Ph.D. in 1949 under “He is the kindest man I have ever met,” says “breakthroughs have developed into versatile James Stoker, after which Richard Courant Jalal. “His gentleness and kindness supersede and robust techniques that have become immediately hired him onto the faculty. anything I could ever have imagined.” Louis’ essential tools for the study of nonlinear enormous mathematical contributions are partial differential equations. Their impact Since then, Louis has received numerous matched only by his gentleness as a human can be felt in all branches of the theory.” awards, including the National Medal being. As noted in the biography of Louis The full citation, available at the 2015 Abel of Science, the American Mathematical posted on the Abel Prize’s website: “his Prize website, gets a bit technical. According Society’s Leroy P. Steele Prize for Lifetime generosity, gift for exposition and modest to Courant Professor Bob Kohn, “it weaves Achievement (1994) and for Seminal charm have made him an inspirational figure together Nirenberg’s and Nash’s themes in a Contribution to Research (in 2014 with Bob to his many collaborators, students and most remarkable, almost poetic way.” Kohn and Luis Caffarelli), the AMS Bôcher colleagues.” n Memorial Prize, the Jeffrey-Williams Prize “Partial differential equations lie at the of the Canadian Mathematical Society, foundation of many areas, both within and the Royal Swedish Academy of Science’s beyond mathematics,” explains Bob. “They inaugural (with Vladimir are the language we use to describe -- and Arnold), and the International Mathematical the tools we use to understand -- problems Union and Foundation’s in diverse areas including geometry, inaugural Chern Medal. He was elected to the engineering, and physics.” National Academy of Sciences in 1969.

“This is not a joint award because the Professor Jalal Shatah, who came to Courant committee couldn’t decide between as a postdoc after graduate studies at Nirenberg and Nash,” noted Bob at the Brown, recalls: “The first thing I learned Courant Institute’s March 30th celebration [about Louis] was that his mathematical for Louis. “Rather, it is joint because of contributions went far beyond the ones I had parallels between their mathematical styles learned about as a student. When I realized and impact. The most obvious connection this, my admiration of his work -- already is by area: geometric analysis and elliptic very high -- became even greater.” regularity are two subjects where both have made essential contributions. But there is also a more subtle connection: beyond solving important problems, each has introduced important methods and tools, which have become essential parts of the fabric of our field.”

13 THE GENEROSITY OF FRIENDS Donations from friends and alumni of the Courant Institute greatly assist our educational and research missions.

Your donations to the Courant Annual Fund are more important than ever. This unrestricted income supports students and postdocs, and their conference travel, enhances the activities of our student clubs, and helps fund the cSplash and WinC outreach programs. The Annual Fund provides matching funds to secure grants from other sources, enables the Institute to invite distinguished speakers for both technical and public lectures, and assists in creating improved public spaces in both Warren Weaver Hall and the Broadway buildings. Please join the Courant Director’s Circle with a donation of $1,000 and above. This entitles you to join special events at the Institute, including a Circle only event in the fall, and the exclusive Director’s Toast before the holiday party. Your donation will help support a truly extraordinary range of scientific and educational initiatives.

THE DIRECTOR’S CIRCLE

The Director’s Circle is the Courant Steve Allen and Caroline Thompson Susan L. Korn Jeffrey S. Saltzman Institute’s giving society for those making Bernard C. Baldwin Barbara J. Krumsiek Ruth Shor a contribution of $1,000 or more in a given Ernest Battifarano Martin L. and Sarah Fryer Leibowitz* Lawrence Sirovich and Carole academic year. Members receive special Francesca Macartney Beale and Patrick P. Lin Hochman Sirovich* invitations as guests of the Director to Christopher Beale* Yue-Sheng Liu Elizabeth A. Smith events of interest throughout the year, with Stanley M. Benson and Joann Benson Cathleen S. and Herbert Morawetz* Thomas C. Spencer complimentary access extended where Joan S. Birman Joshua N. Newman* Joseph Spinden applicable. Additionally, those giving at Timothy S. Choate* Enlin Pan Xavier H. C. Tan the $5,000 level and above qualify for Glen de Vries* Ada Peluso Lu Ting membership in the various university-wide Anne C. Dinning* Susan Mary Puglia* Ann Hong Tucker giving societies. Join the 2014-2015 Director’s Douglas P. Doucette Jihai Qiu Peter Alexander Vasseur Circle with a gift of $1000 or more! Contact Carol Ann Fugosich Sashi P. Reddi Benjamin S. White* Robin Roy at [email protected] or Lynnel Marg Garabedian* Kurt S. Riedel* Brad Wilson (212) 998-6974 for details. Robert B. Gordon Charles M. Robins* Xin Xiong Jefferson Young Han* Chris Rorres Robert A. Young * NYU President’s Society Members — gifts David K.A. Mordecai and Samantha Jeffrey M. Rosenbluth* Sascia Yuan of $5,000 and above. Kappagoda* Louis K. Salkind and Deborah Mr. and Mrs. David Zweig David G. Korn J. Rennels*

The Courant Institute recognizes with gratitude the following alumni, faculty, and friends who have made gifts from September 1, 2013 to March 12, 2015: Barry Granoff John Grant Up to $499 Geoffrey C. Berresford Benoit Couet Xiaosong Feng Anthony E. Gray Avri J. Adleman Jalal Besharati Laura Beth Cruz Richard D. Feuer Frank A. Greco Spencer E. Alt Ion Bica Lisa H. Cyphers Martin Feuerman Jonathan Christopher Gruhl Stephen Amar Albert A. Blank Paul Vartan Czkwianianc Norman J. Finizio Shafali Gupta Salvatore Anastasio Susan G. Bloomberg Teymour T. Darkhosh Anthony A. Fiordaliso Milton Halem Sara Landis Angrist Craig Seth Brass Raoul-Sam Dhun Daruwala Nicholas Fiori Myra Halem Janis Elia Archer Robert C. Brigham Florin David Thomas R. Flack Zheng-Chao Han Babak Atri Robert F. Brodsky Dominick J. Del Casale Aaron L. Fogelson David Blake Harrison Jeffrey M. Augenbaum Neil B. Bromberg Thomas K. DeLillo Daniel B. Forger, Jr. Keith Harrow George E.R. Ault Ryan H. Brothers Stephane Pinhas Demri Richard Foy Madeline Trieger Harrow Robert E. Ayache Adrienne Brown Sidney P. Diamond Craig A. Friedman Dalia Navon Hartman Evan C. Ayala Paul J. Capobianco Vincent J. Digricoli Qi Fu Miriam Hausman Karim Samir Azer Joseph A. Cerniglia Gina Marie Dominique Bijoy M. George Suzanne A. Hecht Jonathan J. Baker Man-Yee V. Chan Kenneth P. Dressler Amy and Andrew W. Gideon Bernhard Hientzsch Elizabeth R. Balsam Chun- Chang Christopher P. Dundon Ofer Hirsch Gill Robert K. Hillman Evan Barba Sindhura Chava Gordon L. Ebbitt Henry V. Goldstein David C. Ho Wayne W. Barrett Chih-Chi Chen Jan S. Edler Yulei Gong Pearl R. S. Hochstadt Dr. and Ms. Joseph D. Becker Diana and Stephen Childress Michael E. Eigen Venu Gopalkrishna Brian P. Hotaling Mildred S. Berger Olivia You Chin Chaitanya J. Ekanadham Dmitry Goykhman Kai Huang Neil E. Berger Leo Chosid Thomas J. Emerson Arvin Grabel Devjani Huggins Stanislav Sheinkopf Berlyand Philip Chung Miss Constance Engle Betty J. Grad Vivek B. Hungund Edward A. Berndt Jason S. Clague Raymond Stuart Ennis Samuel M. Graff Barry E. Jacobs Michael E. Bernstein Richard J. Cole Dmitry Feldman Sister Elizabeth C. Graham

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