Spring 2012, Issue 1 Department of

On behalf of our depart- An ment, welcome to the inaugural issue of the “Fine outstanding Newsletter!” student We constantly feel the John Vincent Pardon ’11 need to reach out to each other and share informa- Mathematics Major and tion on “what is happening Class Valedictorian received at Fine Hall.” Over the the 2012 AMS-MAA-SIAM years, we also felt the urge Frank and Brennie to share the information with our alumni for Outstanding Research in and friends. We like to think we share a Mathematics by an Undergradu- common bond as residents of Fine Hall ate Student for work done Photos by: left, Frank Wojciechowski, right, Denise Applewhite and through our love of mathematics and while he was at Princeton. at , was honored “for devotion to the profession. We hope the The Morgan Prize is presented annually solving a problem on distortion of knots newsletter will serve to connect us. by the American Mathematical Society, posed in 1983 by Mikhail Gromov.” The Many things have happened at Fine Hall dur- the Mathematical Association of America, prize citation referred to the”brilliant geo- ing the last year. Our department has three and the Society for Industrial and Applied metric understanding” that Pardon brought new senior faculty members: Professors Mathematics. The prize was awarded on to bear on this problem and went on to say: Peter Constantin (jointly appointed with Friday, January 5, 2012, at the Joint Math- “John’s elegant proof was a beautiful mix the Program in Applied and Computational ematics Meetings in Boston. of and combined with Peter Ozsvath Shou- Mathematics), , and Pardon, now a first-year graduate student some analytic arguments.” continued on page 5 Wu Zhang, 10 new junior faculty hired for the present 2011-12 academic year, 9 new junior faculty for the 2012-13 academic Notes from the conference in honor of Eli Stein May, 2011 on page 8 year; 6 new staff members have joined us Major overhaul of the mathematics curriculum on page 12 over the past two years. We have the good Panorama of Topology: A conference in honor of William Browder news that Mihalis Dafermos from Cam- took place on May 8-11, 2012. Details on our website; a story will be published in our next issue. bridge and Sophie Morel from Harvard have accepted our offers and will join our faculty during the next academic year. We are strengthening our undergraduate The Minerva The Distinguished program by re-organizing and updating Distinguished Visiting Professorship the curriculum for each of our course Lecture Series in Mathematics offerings. We are also adding new “bridge courses” for our math majors and begin- will allow for a distinguished mathemati- will provide funding for a distinguished ning graduate students. cian to visit our department and deliver to visit our department for three accessible lectures on a topic of cur- a semester and give an accessible lecture This year, due to the generous support of rent interest over a period of one to two course, to meet once a week, on a topic of the Fernholz Foundation, we will begin weeks. current interest. the Minerva Distinguished Lecturer series and a Distinguished Visiting Professor program, We are happy to announce that Jean- The purpose of these positions is to enrich which will bring distinguished visitors to Pierre Serre accepted to open the lecture our mathematical environment and increase our department to give series of lectures in series. He will be followed by interaction and discussion both within our advanced topics on a yearly basis. and Ian Agol. department and across universities. I hope you will enjoy reading the newslet- ter and provide us with feedback and that ALUMNI, FACULTY, STUDENTS, FRIENDS: this will be a starting point for us to share our common experiences and concerns Send us your comments. Share your stories. Ask your favorite professors questions. with each other! Suggest activities you would be likely to attend. Write to us at: With warm regards, chairAlice of the department Chang [email protected]

Administrative positions Professors for 2012-13 academic year Peter Constantin is the William R. Kenan, Jr. Professor of Mathemat- Chair: ics and Applied and Computational Mathematics, jointly appointed David Gabai with the Program in Applied and Computational Mathematics, where Associate Chair: he also selves as director. Peter Constantin comes to us from the Christopher Skinner where he was chairman of the mathematics department for the last five years. Constantin’s research focuses on Directors of Graduate Study: turbulent convection, the of exploding stars and other topics Alex Ionescu related to fluid dynamics. Nicolas Templier

Undergraduate Representative: Peter Ozsvath, who comes to Princeton from MIT, received the Christopher Skinner AMS’s Oswald Veblen Prize in Geometry with Zoltán Szabó in 2007, Associate Undergraduate “for their contributions to 3- and 4-dimensional topology through Representative: their Heegaard theory”. Ozsvath obtained his Ph.D. Jennifer Johnson from Princeton in 1994. His current research is directed mainly in low-dimensional topology gauge theory. Senior Advisor: John Mather

Junior Advisor: Shou-Wu Zhang’s main contributions are in number theory and ar- Placement Officer: ithmetical where he developed the theory of posi- Micah Warren tive line bundles in Arakelov theory as well as the theory of arithmetic dynamics. Before Princeton, Zhang was a professor at where he received his Ph.D. in 1991.

General Relativity at Princeton (GRAP) GRAP, partly funded by an FRG grant, is a new center, dedicated to mathematical GR and its applications, established in the fall of 2011 within our department. Its principal investigators are Alex Ionescu, and Igor Rodnianski in mathematics and Frans Pretorius and Paul Steinhardt in physics. External consultants are Spyros Alexakis, University of Toronto, Mihalis Dafermos, Cambridge University (at Princeton from Spring 2013) and Jeremy Szeftel, Ecole Normale Superieure, Paris.

CURRENTLY IN THE PRINCETON The mission of the group is to: MATHEMATICS DEPARTMENT consolidate the strength of the mathematics department in Analysis, Geometry and PDEs related to mathematical GR; 65 regular faculty members reach out across the usual departmental barriers to train a new generation of gradu- 12 visitors and research staff members ate students and postdocs with interdisciplinary skills, strongly rooted in the physical, 4 emeritus faculty in residence mathematical and computational aspects of gravity and cosmology; 66 graduate students 73 undergraduate majors. take advantage of and contribute to the revival of scientific interest in GR within both the mathematics and physics communities as well as to foster closer collabora- tion, consultation and synergy between them; consolidate and expand the strength of the two departments in theoretical and nu- merical relativity, as well as cosmology, by developing our young talent and attracting new ones. page 2

Assistant Professors Instructors

Zeev Dvir Costante Bellettini Zsolt Patakfalvi Joint appointment with Veblen Research Algebraic Geometry, Computer Science Instructor. Geometric Complex Geometry. Department.Theoreti- Analysis, Geometric Ph.D. University of cal Computer Science. Measure theory, Cali- Washington, Seattle. Ph.D. and Ms.C. brated , El- Masters (summa cum Computer Science, liptic Partial Differential laude), Eotvos Lorand Weizmann Institute of Equations. Ph.D. ETH, Univ. in Budapest, Science. Bs.C. in Math- Zurich, , Hungary. Masters in ematics and Computer Science, Tel Aviv Masters, Scuola Normale Superiore of Pisa Computer Science, Technical University University. Previously in the Computer (Italy) and University of Pisa. of Budapest, Hungary. Science Department, Princeton Univer- sity and the Institute for Advanced Study, School of Mathematics. Jeffrey Case Claudiu Raicu Instructor & NSF Algebraic geometry, Postdoctoral Fellow. commutative Global Reimannian and and their computa- Stefan van Zwam Lorentzian Geometry, tional aspects, tensors, . Ph.D. Conformal Geometry, representation theory, and M.Sc. from Geometric Analysis, toric varieties, resolu- Technische Univer- General Relativ- tions. Ph.D. U.C. siteit Eindhoven, The ity. Ph.D. and M.A. Berkeley; B.S. Univer- Netherlands. Previous U.C. Santa Barbara, B.S. in Mathematics sity of Bucharest, Romania. position: Postdoctoral and Computer Science, Minnesota State Researcher, Centrum University. Previous position: Postdoctoral Wiskunke en Infor- Research Fellow/NSF Postoctoral Fellow, Kevin Tucker matica, Amsterdam, The Netherlands. Mathematics Department, Princeton Univ. Algebraic geometry. Ph.D. Univ. of Michi- gan, B.Sc. Univ. of Chi- Xinyi Yuan Jonathan Fickenscher cago. Previous position: Number Theory, Interval Exchange Postdoctoral Research Arakelov Geometry, Transformations and Fellow, Univ. of Utah. Automorphic Forms, Rauzy Diagrams, Af- Shimura Varieties and fine Interval Exchange Algebraic Dynamics. Transformations, Linear Ph.D. in Mathematics, Involutions and Gen- Columbia University eralized Permutations. and B.S. in Mathemat- Ph.D. Rice University; ics, Peking University, Beijing. Previous B.S. in Computer Science & Mathematics, Simons Research Fellow/ positions: Clay Research Fellow, Clay University of Texas at Dallas. Postdoctoral Research Mathematics Institute, Cambridge, MA. Associate Penka Georgieva Fabio Pusateri Symplectic Topol- Analysis, PDE’s, ogy, Moduli Spaces, , Gromov-Witten Hamilltonian Dynam- Theory. Ph.D. Stanford ics. Ph.D., Courant University; M.Sc. and Institute, NYU; M.A. B.Sc. Sofia Univiver- and B.S., University of sity, Bulgaria. Roma Tre, Italy.

Claudiu Raicu was awarded The Princeton University Engineering Council “Excellence in Teaching” Award for enhancing the quality of education at Princeton University through dedication and commitment to student learning that surpassed the norm. page 3

Honored Retired Simon (Si) Bernard Kochen David Gabai the Hughes-Rogers Professor of Math- Si is a major figure in mathematics whose contributions in areas of ematics, was elected to the National mathematical logic, , number theory, and quantum Academy of Sciences on May 3, 2011. mechanics are well known to and of interest to many who are not professional mathematicians. Si was born in Antwerp, . Fleeing from the Nazis, his family was saved due to the selfless bravery of a Norwegian ship captain, who took them from Calais to England where he grew up. He later emigrated to Canada and earned his bachelor’s and master’s degrees at McGill University. He obtained his Ph.D. from Princeton in 1959 for a thesis in mathematical logic directed by Alonzo Church. He joined the faculty at , rising to professor by 1965, but returned to Princeton in 1967. He served as chair of the mathematics department from 1990 to 1993; after that and until his retirement this year, he continued to serve the department as Amit SInger departmental representative and associate chair with general responsibility for the under- (jointly appointed Associate Professor graduate academic program in mathematics. in the Mathematics Department and the Si is widely known for three very important and striking results in mathematics, applying Program in Applied and Computational techniques of mathematical logic to problems in a variety of fields with results to which he Mathematics) was awarded the Presidential has left his name as a lasting memorial. Early Career Award for Scientists and Engi- 1. Ax-Kochen Theorem, for which he and James Ax in 1967 shared the Frank Nelson Cole neers. This is the highest honor bestowed Prize in Number Theory. This result was developed in a distinguished series of papers by the government on sci- applying p-adic techniques and model theory to problems of Diophantine number theory. ence and engineering professionals in the Si’s subsequent work in that area led to what are now known as the Kochen ring and the early stages of their independent research Kochen operator in number theory. careers. 2. Kochen-Specker Theorem in , a result that imposes constraints on the permissible types of hidden variable theories that attempt to explain some of the pe- culiarities and indeterminacy of quantum mechanics through deterministic models involv- ing hidden states. This theorem demonstrates a contradiction between basic assumptions Manjul Bhargava of hidden variable theories and the predictions of quantum theory. The prediction of the Thomas D. Jones Professor of Math- quantum mechanics on which the Kochen-Specker Theorem was based has been con- ematical Physics and the Brandon Fladd, firmed by a recent experiment. Class of 1983, Professor of Mathematics, and Igor Rodnianski (on leave at MIT) 3. A strengthening of the Kochen-Specker Theorem is the more recent work by Si and were awarded the 2011 Fermat Prize estab- John Conway on the Free Will Theorem. That theorem asserts that if human experiment- lished in 1989 by the Toulouse Mathemat- ers have a certain amount of free will then so do elementary particles. ics Institute in France. The biennial prize is offered to researchers whose work is accessible to the greatest number of math- Congratulations to our ematicians in fields shaped by Renaissance former faculty members French mathematician Pierre de Fermat. Bhargava was recognized for his work on various generalizations of the Davenport- Ingrid Daubechies for becoming the Heilbronn estimates and for his recent president of the International Mathematical startling results (with Arul Shankar) on Union (2011–2014) the average rank of elliptic curves. for being awarded Rodnianski was recognized for his funda- the 2010 , for work done mental contributions to the studies of the while a member of our department. equations of and to the Demetrios Christodoulou and propagation of the light on the space-time for being elected to curves (in collaboration with Mihalis Manjul Bhargava, left, and Igor Rodnianski, right, receive the National Academy of Sciences on May Dafermos, Sergiu Klainerman, and Hans the Fermat Prize at the Université Toulouse III in Toulouse, France, from Bertrand Monthubert,center, president of 3, 2012. Lindblad). the university. page 4

John Pardon, continued from page 1 Ben Bakker, NYU Courant Instructor John learned about this problem on his ment within Princeton’s mathematics Bhargav Bhatt, U. of Michigan Ann Arbor, own (and in high school). According to department Asst. Professor his letters of recommendation, “with this was elected to Phi Beta Kappa problem, no one had any idea how to get Richard Bamler, Stanford University, Si- won the Barry M. Goldwater Schol- mons Postdoctoral Fellow started; the key insight that cracked this problem is due to John.” His research paper arship, a national award recognizing Francesco Cellarosi, MSRI about this work appeared in the July 2011 outstanding potential in math, natural Margaret Doig, U. of Indiana, Postdoc issue (volume 174, number 1) of the AN- sciences or engineering. , MIT Tenure-track Asst. Prof. NALS OF MATHEMATICS. won a National Science Foundation Alexandra Fradkin, Center for Communi- As an undergraduate, Pardon, in addition Graduate Research Fellowship to sup- cations Research to publishing several papers and presenting port his graduate studies at Stanford University beginning this fall. Elena Fuchs, UC Berkeley, Simons Post- talks at Princeton and other institutions, doctoral Fellow, built a collection of impressive awards: as a cellist he twice won Princeton University Sinfonia’s annual concerto Hans-Joachim Hein, Imperial College, shared the Class of 1939 Princeton London, Research Associate, Scholar Award, given annually to the un- competition. Thomas Horine, Indiana U., Instructor dergraduate who, at the end of the junior was a member of the team that won year, has achieved the highest academic the non-native-speaking section of the Arie Israel, NYU - Courant, Postdoc standing for all preceding college work International Varsity Debate, a biennial Andrei Jorza, CalTech, Postdoc at the University. Chinese language competition organized Jun Kitagawa, U. of British twice won the University’s Shapiro by China Central Television and Singa- Columbia,Postdoc Prize for Academic Excellence pore’s Media Corp, held in Singapore and broadcast across the Chinese-speak- Po-Shen Loh, Carnegie Mellon U., Tenure- received prizes for outstanding achieve- track Asst. Prof ing world. Ph.D Disertations 2010Ph.D Disertations & 2011

2010 & 2011 Ph.D recipients Ph.D recipients & 2011 2010 Garvin Luli, Yale U., Gibbs Asst. Prof. Entropy Bounds for Quantum Limits Cm,w Extension by Bounded-Depth Linear Opera- Martin Luu, Stanford U., Szego Asst. Prof Extremal Problems in Combinatorial Geometry and tors Simon Marshall, Northwestern U., Postdoc Additive Combinatorics On the Cohomology and Quantum Chaos of the Donaldson’s Theorem, Heegaard Floer Homology, General Linear Group in Two Variables Richardo A. Saenz, Universidad de Colima, and Results on Knots Marcinkiewicz Multipliers in Products of Heisenberg Mexico, Research Professor, Recovering a Variety from its Derived Category Groups Iman Setayesh, School of Mathematics, L-Invariants of Low Symmetric Powers of Modular Uniqueness Theorems for Linear Wave Equations Institute for Research in Fundamental Sci- Forms and Hida Deformations Floer Homology and Dehn Surgery ences (IPM), Tehran, Postdoc Cohomology of Z-free resolutions of p-groups On the Rigidity of Charged Black Holes Vivek Shende, MIT/C.L.E, Instructor Orbit Parametrizations of Curves Gagliardo-Nirenberg-Sobolev Inequalities and Finite Jacob Tsimerman, , Ricci Solitons and Collapsed Spaces Type Junior Fellow Discrete Analogues in Harmonic Analysis Stability of Einstein Metrics of Negative Curvature Peter Varju, Visiting Researcher, Hebrew Limit Theorems for the Theta Sums Via Renormaliza- Topics in Heegarrd Floer Homology tion and Homogeneous Dynamics University – Einstein Institute of Math- The Jacquet-Langlands Correspondence for GL(2) ematics A New Construction for the First Janko Group On the Uniqueness of Kerr- Newman Black Holes A Bounded Linear Extension Operator for L2,p R2 Yi Wang, Szego Assistant Professor (2011) Moduli Spaces for Rings and Ideals Postdoctoral Member, MSRI Two Regularity Problems in Optimal Transportation Towards a Springer Theory for Global Function Zhiren Wang, Gibbs Assistant Professor, Derformations of Local Properties of Automorphic Fields Galois Representations Yale Hodge Polynomials of Moduli Spaces of Stable Pairs on K3 Surfaces Forbidden Structures and Algorithms in Graphs and

Who they are and where they are now are now are and where they Who they Phillip Whitman, Associate Director of Digraphs Research, INTECH Investment Manage- Derived Direct Summands Relative Hilbert Scheme of Points ment, Princeton Spherical Seifert Fibered Spaces, Surgeries and Heegaard Floer Homology Hilbert Schemes of Points on Integral Plane Curves Hau-Tieng Wu, Princeton University, Towards and Unconditional Andre- Oort Conjecture PACM, Postdoc Ramsey Numbers Random Walks and Spectral Gaps in Linear Groups Zhong Tao Wu, CalTech, Simons Postdoc Arithmetic Properties of Apollonian Circle Packings On Gravitational Instantons On Some Geometric Inequalities and Applications Pin Yu, Tsinghua U., Lecturer Crystalline Representations for GL(2) Over Qua- On Higher Rank Commulative Actions by Toral PoLam Yung, Rutgers U., Hill Asst. Prof dratic Imaginary Fields Automorphisms Results in Extremal and Probabilistic Combinatorics Adaptive Analysis of Complex Datasets page 5

David Gabai: Andy Manion 2010-2011 National Defense Science and Engineering Being a Director of Graduate Study (DGS) is a great job. It is fun getting to know the Graduate (NDSEG) Fellowship students; it is awesome to watch our students progress from extremely talented first Liangming Shen years to full-fledged mathematicians, and it is a pleasure to work with my co-DGS Nicolas Chinese Scholarship Council Fellowship Templier. Having Jill LeClair as our ever-friendly, welcoming and organized graduate administrator makes being DGS nearly effortless. Ila Varma National Science Foundation Fellowship It is interesting to compare how things have changed from when I was a student. The emphasis was and is to give graduate students maximal opportunity to become indepen- dent researchers while subjecting them to a minimal amount of requirements. These days The Princeton University Graduate School Graduate Student Awards some students finish in four years and most finish in five. Most of the students in my class Honorific Fellowships, which provide funding to students displaying the highest finished in four years; however, we were considered slackers because nearly all students scholarly excellence in graduate work dur- starting a few years earlier who finished, finished in three! I don’t think that current stu- ing the year, were awarded to: dents work any less hard, rather our 5th year students are functioning more like postdocs of old. They often have several papers and have multiple projects going. Last year we Richard Bamler Harold W. Dodds Fellowship reduced the language exam requirement from two to one, though many faculty wanted to eliminate it altogether. The general exam is still typically a 2.5-3 hour exam where three Peter Varju professors grill a student on three basic topics and two advanced ones; however, now a Charlotte Elizabeth Procter Fellowship. student can request his or her committee. We try to accommodate requests, but some professors are extremely popular and get grumpy when we over work them. Most of my fellow students were from North America while now well over half are international. Then and now, they all seem very impressive!

Nicolas Templier: Serving as DGS in an interesting job. I am happy to work with David Gabai and Jill LeClair. First semester as DGS is like being a first year student; there are many new skills to learn. I like the friendly atmosphere in the department which is well-suited for research and encourages the exchange of ideas between students and faculty. It is great to see students build and pursue William Cavendish was their own research path and produce outstanding theses. I awarded the 2012 Porter enjoy the lunch seminars in the common room. The speaker explains what he feels Ogden Jacobus Fellowship, 2011-2012 is really important in the subject, not just why a specific new result is better than Princeton’s top honor for what has been done before. graduate students. The fellow- ship, awarded for work of the highest scholarly excellence, New courses introduced in Spring 2012 supports the final year of Ph.D. study. MAT 509 Prof. R. Taylor MAT 584 Prof. Z. Dvir Cavendish, who will graduate : Abelian variet- Topics in Discrete ies Geometry:Incidence theorems and their in June 2012, obtained his undergraduate applications degree in mathematics at the University of MAT 540 Prof. J. Chen Chicago and a master’s at Brown Univer- Introduction to Minimal Surface Theory MAT 590 Prof. S. Zhang Topics in Arithmetic Geometry: Congru- sity. His work at Princeton focuses on low- MAT 568 Prof. P. Ozsvath ent numbers and Heegner points dimensional topology and geometry, and, Low-Dimensional Topology and more specifically, questions about symme- Symplectic Geometry: Bordered Floer MAT 595 Prof. S. Van Zwam tries of low-dimensional objects. His thesis homology Matroid Theory advisor is David Gabai. page 6

Early A young recognition woman’s for impressive path to results success Although only in his third year of graduate Ila Varma is a second year graduate stu- study, Arul Shankar has achieved a major The rank of elliptical curves dent from Albuquerque, NM, who is work- result that made his name widely circulated in a nutshell ing in algebraic number theory. in the sphere of number theory. Arul had by Arul Shankar, graduate student Ila’s orientation toward mathematics an important role in Manjul Bhargava’s started early in her education, as her work on various generalizations of the In a paper published in July 2010 with my advisor, Manjul Bhargava, we proved the parents always emphasized the importance Davenport-Heilbronn estimates and the of mathematics and logical reasoning in remarkable results on the average rank of Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves. We everything.. But she credits the Boston elliptic curves, which earned Bhargava the University sponsored PROMYS program 2011 Fermat Prize. prove that the average rank of all rational elliptic curves is finite. The methods used for having “opened my eyes to pure math- Arul, originally from Chenai, India, be- also imply that a positive proportion of ematics as a high school student”. longs to a family of mathematics lovers: his elliptic curves (in fact, at least 10% of el- As an undergraduate at CalTech, she mother is a computer scientist, his father liptic curves) have rank 0. A rational elliptic continued her contact with PROMYS by a mathematician and his younger brother curve is defined by an equation of the form working there each summer, an activity won a silver medal at the International y^2=x^3+Ax+B, where A and B are inte- that, she claims, allowed her to find more Mathematical Olympiad. gers. The set of rational solutions to such an and more reasons to spend her life studying Working with Manjul Bhargava provided equation (along with the point at ‘infinity’) mathematics. Arul not only with a deeper understanding form a finitely generated abelian group. The Her dedication to mathematics and the of mathematics, but also with invaluable rank of an elliptic curve is defined to be the quality of her work brought her a series of guidance and human experience. rank of its associated group. awards in her senior year: the Eric Temple “The major reason for my decision to work Bell Undergraduate Mathematics Research with Manjul,” says Arul, “ was that I found Prize for the best original mathematics his work to be extremely beautiful - both PROMYS is a challenging program de- paper; an Honorable Mention in the Alice the problems and the methods he employs; signed to encourage ambitious high school T. Schafer Prize for displaying excellence his work is very simple and yet incred- students to explore the creative world of in mathematics; the HSP Huygens Scholar- ibly deep. When first reading his papers, I mathematics. Each summer, approximately ship. found some of the techniques he used to be 75 high school students from around the After graduating with honors in 2009, a striking; nothing that I had seen in number country gather on the campus of Boston Fulbright Scholarship allowed her to spend theory before was anything like it. Above University for six weeks of rigorous math- a year at Leiden University in the Nether- all else, I find working on these problems ematical activity. Through their intensive lands, where she did a master’s thesis under truly enjoyable. It was also very important efforts to solve an assortment of unusually Prof. Bas Edixhoven and obtained a M.Sc. to me that Manjul is an amazingly friendly, challenging problems in Number Theory, cum laude in Mathematics. Ila came to patient, and understanding person who is participants will practice the art of math- Princeton with a prestigious NSF Graduate very generous with his time and treats his ematical discovery. Research Fellowship. students more like friends.” The Alice T. Schafer Prize for excellence Ila worked with the Princeton Math Circle in mathematics by an undergraduate woman and continued to attract high school stu- is an annual award established by the Asso- dents interested in math. She also serves as ciation for Women in Mathematics (AWM). the Organizer for the Princeton Graduate Student Seminar. page 7

Analysis and Applications: A Conference in Honor of Elias M. Stein

On the occasion of Elias M. Stein’s 80th birthday, the department hosted a major international conference in honor of his lifetime accomplishments. The conference, The inspirational role of Elias M. Stein held on May 16-20, 2011, was organized excerpts from a longer article written by Lillian Pierce ’02 GS ’09 by Charles Fefferman (Princeton Univer- sity), Alex Ionescu (Princeton University), Duong Phong (Columbia University) and I hate to break it to the Hollywood set, but that build community, and the leadership Stephen Wainger (University of Wisconsin, mathematics can be a wonderfully social of such a person can benefit an entire Madison). There was also a Panel Discus- pursuit. Of course, sometimes we like hol- of mathematics. Last May, a conference at sion lead by Lillian Pierce (Oxford Univer- ing up in solitude while we wrestle with a the Math Department celebrated the 80th sity) and Rami Shakarchi. problem. And maybe we aren’t the classiest birthday of just such a leader: Elias M. Professor Stein’s son, Jeremy Stein, a dressers on campus. But mathematicians Stein. Mathematical lectures at the confer- Professor of Economics at Harvard Uni- don’t just float around each other like noble ence illustrated the effect Prof. Stein’s versity, nominated by President Obama to gases. We talk about problems, work togeth- mathematical work has had on the field the Federal Reserve Board of Governors, er on solutions, give seminars and lectures, of harmonic analysis (and beyond), but gave a lecture on the “Financial Crisis and write papers and books, advise students, one more unusual event featured a panel Financial Reform.” contribute to an oral tradition of anecdotes, discussion of three arenas in which he has and dream about future discoveries; all had unprecedented success: mentoring, these interactions serve to build a com- collaborating, and writing books. munity of mathematicians. Once in a while someone comes along who is prodigiously Front row from left: Lillian Pierce, Stephen Wainger, accomplished not just in mathematics but Ricardo Saenz, Eli Stein, Charlie Feffermann, Alex Ionescu, D.H. Phong. Second row, from left: Kevin also in the more intangible personal skills Hughes, Alan Greenleaf, Chris Sogge, Andrea Frazer, Dalia Dafni, Po Lam Yung. Top row: Greg Zuckerman.

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From left to right: moderators: Rami Shakarchi (GS ’09) Lillian Pierce (’02, GS ’09); panelists: Loredana Lanzani (University of Arkansas), Stephen Wainger (University of Wis- consin at Madison), Gerald Folland (University of Washington, GS ’71), Ingrid Daubechies ().

Mentoring, collaborating, and writing books excerpts from a longer article written by Lillian Pierce ’02 GS ’09 and available in its complete form online

MENTORING. The panelists discussed laborator? Panelists described the singular BOOKS. Good books in math don’t have how to be a good mentor, and several key pleasure of collaborating with Prof. Stein, an expiration date. How does one write a ideas stood out. At its heart, mentoring who conveys such genuine appreciation of good book? First one must determine if the aims to increase the awareness of all the each collaborator’s contribution, whether book you’d like to write is actually needed. possible opportunities and goals available. large or small, that it creates a positive and Then you must hold in mind your intended In particular, mentors can be role models, trusting environment that in turn stimu- audience, and shape the book so that it tells and this aspect of mentoring can be a moti- lates new ideas. Collaboration with a more a story. There is always a balance that must vation for someone who aims to encourage senior mathematician can be an important be reached, between what one wants to young mathematicians who don’t fit the form of mentoring in itself, but how does write about, and what other people want stereotypical image of a mathematician. a younger mathematician get the courage to read; in particular, the mathematics As a role model, it may be important to to collaborate with someone much more must be presented in a way that is clearly analyze the actual image you are project- knowledgeable? Just remember that a more understandable to the intended audience ing, and perhaps adjust how you present senior mathematician probably also has (for example, with intuitive, consistent yourself professionally or personally to stu- many more responsibilities, and is prob- notation). Sometimes, there is a need for dents, depending on what type of inspira- ably very happy to have a collaborator who a book that presents recent research in an tion you think the students need. Mentors will flesh out the main ideas with detailed expository fashion, so that new ideas be- can convey informal knowledge about the computations. Of course, mathematical come accessible to a wider audience. Some practice of mathematics—not technical research is not all smooth sailing, and any books codify a broad field of research, and points per se, but more of a philosophi- collaborative project will encounter chal- reading them becomes a rite of passage for cal or aesthetic sense of how math works, lenging headwinds. young researchers. Other books are true and what makes a question interesting. textbooks, meant to introduce students The altruistic mentality of mentoring need to classical mathematics. In the case of not be dissociated from other professional For advice on how to weather the storm the Princeton Lectures in Analysis series relationships one has in the context of and create a long and fruitful collaboration, by Stein and Shakarchi (, collaborating, teaching, advising. Being a one can turn back a century to the four Complex Analysis, Real Analysis, and good mentor, a good colleague, or a good axioms outlined by J. E. Littlewood, who Functional Analysis), (***) the texts pres- teacher, all involve, in some form, nurtur- had a famously successful and amicable ent classical material but in a new, unified, ing the members of the community. collaboration with G. H. Hardy, which they fashion. Readers ranging from undergradu- carried on in an epistolary fashion (yes, by ate students to senior mathematicians point It also isn’t solely the responsibility of the paper mail). mentor to initiate and sustain the relation- to the many strengths of this series: the ship—if you are feeling in need of some (1) The writer of the letter is under no ob- variety of interesting applications of the guidance, inspiration, or encouragement, ligation to check that the letter is correct; theory (and unconventional proofs of theo- look around: someone you know already is (2) The recipient of the letter is under no rems); a large selection of good problems probably ready to help. obligation to reply to (or even read) the of many different levels; a convincing pre- sentation of the historical origins of ideas. COLLABORATING. In many courses in letter; the math department, students are encour- (3) It is preferable that both collaborators aged to collaborate on solving problem not think about the same technical point at sets. Collaboration becomes even more the same time; important and rewarding when you start (4) No matter who contributes what to doing original research rather than solving the project, both are credited as equal co- known problems. How to be a good col- authors. page 9

Mentoring Moebius by Kevin Wilson, graduate student The Noetherian Ring is an informal or- ganization for the Princeton math depart- Fine Hall can be a scary place. When you arrive as a freshman, you are surrounded by ment’s women at all levels, from freshmen some of the most famous mathematicians on earth, some of the best graduate students, to senior faculty. It offers opportunities for and--perhaps most terrifying at all--some of the sharpest undergraduates in America. female mathematicians to interact with one Moreover, there are so many classes and tracks that, even for those intrepid enough to another in many different forums, with the stick around, the experience can be daunting. goal of building networks of support. Our goal in Mentoring Moebius is to help undergraduates navigate this complex world. In the fall of each year, we, in conjunction with the university’s Major Choices program and the Undergraduate Math Club, hold several events at which freshmen and sopho- Mentoring Möbius is a comprehensive mores can meet up with upperclassmen concentrators, graduate students, and faculty. mentoring program for undergraduates During these events, we encourage people to sign up for the Mentoring Moebius pro- interested in mathematics. Founded in gram. 2006 by the Noetherian Ring, this program has since 2009 been open to men as well as For those who sign up, we pair them with graduate student mentors, who have not too women. long ago been in their mentees’ shoes. Mentors get to know their mentees over lunch and coffee as well as at several dinners we sponsor each year. Our hope is that mentors help mentees figure out their interests (in math or otherwise), help them choose classes, and advise them on summer projects. Mentoring relationships often last several years. As mentees progress through their undergraduate years, mentors often help students determine the faculty member with whom they will do their independent work. Also, they introduce them to other graduate Want advice, discussions of students interested in their chosen topics. problems, gossip, Elsevier boycott? Mentoring Moebius has had great success in bringing together graduate and undergradu- ate students, and we hope it continues to do so. GREAT RESOURCES Josko Plazonic, Systems Manager, was awarded the 2010-11 President’s ONLINE Achievement Award for his outstanding contributions to the Mathematics just google them! Department and the Program in Applied and Computational Mathematics. Plazonic joined the staff in the Department of Mathematics in 2001. Some blogs of note that point to other noteworthy blogs Terry Tao *96 Training, Research and Motion (TRAM) Tim Gowers Quomodcocumque TRAM, funded by the Global Collabora- Moscow Center for Continuous Mathe- tive Research Fund, is a network between matical Education, Independent Univer- thecostofknowledge our department and other world leading sity of Moscow(Russia) Massively collaborative mathematics centers of mathematics. It provides gradu- Einstein Institute of Mathematics, The projects - polymath1 ate students and faculty with the oppor- Hebrew University of Jerusalem a great way for non-academic alumni to tunity to attend special lecture series, School of Mathematical Sciences, Tel keep in touch and participate in current workshops, and programs at one of the research. participating institutions. It also supports Aviv University research stays at the partnering institutions The Weizmann Institute of Science MathOverflow as well as joint network activities. The cur- Connect with mathematicians from all Department of Mathematics at the Aca- rent partnering institutions are: over the world; ask questions, participate demia Sinica (Taiwan) in discussions. Hausdorff Center for Mathematics, Department of Mathematics at ETH University of Bonn (Germany) Princeton Math Graduate Students’ Zurich (Switzerland) Guide to Generals Centre for Mathematical Sciences, Uni- not only useful but lots of fun! versity of Cambridge(England) www.math.princeton.edu/generals page 10

Letters from the undergraduate advisors Manjul Bhargava Robert Gunning advisor to the seniors advisor to the juniors It has been very excit- The undergraduate mathematics program International Affairs. ing for the mathematics has been changing fairly steadily over the In each case, though, department lately, as the past half dozen years during which I have a second reader from number of mathematics majors has steadily been acting as an adviser to mathemat- the Mathematics Department was closely increased over the past few years, from ics majors. This is in part a reflection of involved with the senior, available to the about 12 a year just ten years ago to about changes in the undergraduate student student for advice and consultation and a 40 a year today. Judging from enrollment body, with the admission of more students member of the senior final examination in introductory courses this year, it seems interested in mathematics, especially more committee setting the grades for the senior this number will be rising even further in “foreign” undergraduates, with previous thesis and for the oral presentation of the the coming years! The sheer number of schooling in Europe or Asia. To that ex- thesis that has replaced the final senior enthusiastic students joining our depart- tent, the body of undergraduate mathemat- comprehensive examination in mathemat- ment lately has been a joy to see. ics majors has become rather more like the ics. There have been many factors contribut- body of graduate students in mathematics. The possibility of being a mathematics ing to this new popularity. Several faculty, It is also in part a reflection of a broadening major while interested to a great extent including Professors Bhargava, Chang, of the fields of interest of the mathematics in applications of mathematics to a range Gunning, Johnson, and Skinner, have been faculty, with more members of the depart- of areas has been an important facet of the thinking deeply about and constantly ment interested in areas closer to applied increasing interest students have in the adjusting our introductory courses to make mathematics and closer relations with fac- department. It is still the case that more them more welcoming and attractive for ulty members in other departments. For than half of the graduating seniors continue prospective majors. We are also offering instance 14 of the 37 graduating seniors in to graduate work in mathematics or applied more large, general-audience courses on 2011 had their senior theses directed by mathematics; others go on to a rather wide mathematics such as the interdisciplinary faculty in other departments: Chemistry, range of activities, such as medical school, “Magic of Numbers”, which has constantly Computer Science, Economics, Electrical graduate study in economics, work in finan- drawn over 100 students whenever it is of- Engineering, Operations Research and Fi- cial or research corporations, or teaching, fered. These courses have introduced large nancial Engineering, Philosophy, and even for instance. The proportion of women numbers of freshmen and sophomores to the Woodrow Wilson School of Public and among the undergraduate mathematics the beauty and ubiquity of mathematics, majors is still quite small, 6 of and have helped to increase the profile of 40 the 37 graduating seniors in and popularize the department on campus. 2011; but 5 of them graduated Other new popular introductory courses, 35 with high honors or highest in number theory, combinatorics, and honors in mathematics and 3 of 30 game theory, have also made the entry into them won departmental prizes. the mathematics major more flexible. 25 The undergraduates continue In addition, the entire range of mathemat- to work together well, with a ics courses has been reorganized and 20 nicely functioning undergradu- modernized so that students learn the ate math club that, among basics well, but also learn about the many 15 other activities, runs a success- new exciting developments in mathemat- ful mathematics competition 10 for high school students in this ics research in the last few years (much of it conducted at Princeton by our faculty part of the country. and graduate students!). There has also 2000 2002 2004 2006 2008 2010 2012 2014 been a broadening of the research inter- Increase in the number of mathematics majors at Princeton. ests of faculty members working in more applied areas of mathematics. Finally, the ence in communicating mathematics. The want to become professional mathemati- mathematics program has emphasized senior theses allow for further in-depth cians, but also a rapidly increasing number undergraduate research in a wide range of research in a broad range of topics in both of students who want to make a mark in in- areas, both at the junior and senior level. pure and applied mathematics topics while dustry and elsewhere, where the Princeton Through six junior seminars offered every working one-on-one with faculty mem- mathematics major and training gives them year, juniors get a glimpse of research-level bers. These initiatives have allowed us to a distinct advantage. mathematics as well as first-hand experi- attract not only many more students who page 11

Major changes to our curriculum Philosophy and...... Due to the increasing number of majors in the future) to appropriately adjust our A thesis in mathematics and in our department, it has become very course offerings to our students’ needs. philosophy by Jeremy Silver important for us to maintain a good spread The first digit of a course number indi- of courses offered on a regular basis. To This thesis will discuss two methods cates the level of the course (first year, ..., of proving completeness of S4 modal accomplish this, at the recommendation fourth year, graduate) - this is the univer- of the Math Department Curriculum logic with respect to transitive, reflexive sity standard. The second digit will be used relational models. The first is based on Committee (Manjul Bhargava, chair; to indicate the subject area (0: Logic and Alice Chang, David Gabai, Robert Gun- Makinson’s proof (1966), which uses the Foundations; 1: Number Theory; 2: Real concept of a maximal consistent set to con- ning, Christopher Skinner, and Nicolas Analysis, etc.) Templier), we have begun to put in place struct such models. The other approach the following changes to the mathematics The third digit at the 100-200 level will is algebraic. In 1948 Tarski and McKinsey curriculum at Princeton: indicate whether a course is intended as showed that S4 is complete with respect a service course, or primarily for math to the class of closure . Then in - Eliminating (or upgrading to graduate majors. In the 300’s and 400’s, it will 1951, Tarski and Jonsson extended the courses) those undergraduate courses that indicate whether courses are more applied Stone Representation Theorem to show consistently have extremely small enroll- (hence more appealing to other majors) or that every closure algebra is representable ment (eg: Second semester differential primarily intended for pure mathematics as an algebra of sets with an additional op- geometry, MAT 328) majors. In the 500’s, it will differentiate eration arising from a reflexive, transitive - Introducing some basic permanent cours- between bridge courses and more ad- relation. With this result, Tarski could have es consistently demanded by our students, vanced research-oriented courses. obtained the desired completeness result; however, he overlooked the connection but offered only occasionally in the past With these numberings, it is now MUCH between modal logic and algebra, so it was (with huge enrollments!). Eg: Representa- simpler to describe what our requirements not until Kripke (1963) that the final result tion theory. for the pure math major are, and it would was proved. In this thesis I will outline - Some of our more advanced under- also make it easier for other departments both the model-theoretic and algebraic graduate courses have traditionally been to express their math requirements. proofs and demonstrate that they are effec- considered graduate courses at most (a detailed description is available on our website) tively the “same” up to isomorphism. other institutions. We are beginning to transform these courses into what we - Students who do not come to Princeton term “Bridge courses”, i.e., courses with with prior knowledge of proofs were often Professor graduate course numbers that would be of having trouble with our math-major-entry John P. Burgess interest to advanced undergraduates as well course 215. A number of students left or the John N. Woodhull as beginning graduate students. considered leaving the math major because Professor in the depart- they simply could not keep up with their ment of Philosophy is also -The “bridge courses” have multiple ad- colleagues who had prior experience with an “associated faculty” in vantages: 1. they enable graduate students proofs. the Department of Math- to enroll in them; 2. our undergraduates ematics. His connection Therefore, we have proposed that (as at would be happy to take some graduate with the department dates to his under- other schools such as Harvard, Michigan, courses (making their transcripts more graduate years when, under the guidance Chicago,...) we offer more than one track competitive and on par with other schools, of Simon Kochen, he obtained an A.B. in of our current MAT 215. The first track such as Harvard); 3. they allow more mathematics (summa cum laude FBK) with would not be as fast-paced or assume any interaction between undergraduate and a thesis in Probability Logic. He returned prior knowledge of proofs. The second graduate students; 4. combining advanced to Princeton as a faculty member in 1975, track would have the same prerequisites as undergraduate/beginning graduate shortly after obtaining his Ph.D. in Logic & in the past. courses, would lead to increased enroll- Methodology from UC Berkeley. ments in them. Just a few years ago, we did not have Publications by prof. J.P. Burgess: enough students in 215 to allow such - The course numbers we have attached to Philosophical Logic (Princeton Foundations of Con- our courses in the past have been essen- a split; but we now regularly have 60+ temporary Philosophy), Princeton Univ. Press, 2009. students in 215, so it is natural to split up tially random, making it hard for faculty Mathematics, Models, and Modality: Selected Philosophical and students to ascertain what exactly the this course anyway. This proposal will be Essays, Cambridge Univ. Press implemented this Fall (2012) in order to courses offered, and making it hard for stu- Computability and Logic with George S. Boolos, and dents to comprehend which sets of courses further increase the flexibility of our math- Richard C. Jeffrey;Cambridge Univ. Press ematics major, and to ensure that we don’t might satisfy their requirements. The num- A Subject With No Object: Strategies for Nominalistic bers have now been assigned more logically lose any further promising mathematics Interpretation of Mathematics with Gideon Rosen, so that it is easier (both in the present and majors for this reason. Clarendon Press - Oxford page 12

Jeremy Silver, a Adam Classen Hesterberg ’11 and 2010-2011 member of the ...... Mathematics Tigertones a Maria Monica Nastasescu ’11 capella group Like many bright high school graduates as well as of the shared the Middleton Miller ‘29 Prize for Cube Club, had best independent work in mathematics. who come to Princeton, Jeremy Silver, the opportunity ’12, was interested in apparently divergent to solve a Rubik fields - languages and linguistics, math cube at the White Tzvetelina Kirilova Tzeneva ’11 and House where the Undergraduate Student Awards and physics, philosophy - and had Tigertones had Qingzhen Sophie Wang ’11 shared been invited to difficulties choosing the one on which to sing. the Peter A. Greenberg ’77 Prize for concentrate. By his third year, he found outstanding accomplishments in math- not only a way to continue his love of ematics. many areas of knowledge but also a won- math logic, he started to look at languages derfully satisfying intersection of them: through a mathematical framework. mathematical logic. Now, as a math major, At Princeton he took courses in math, Erick Phillip Knight ’12 Andrew H. he is working on his senior thesis under the economics, engineering, philosophy and Brown Prize for outstanding junior in supervision of John Burgess the John N. linguistics and his choice of majors pro- mathematics. Woodhull Professor of Philosophy. gressed from comparative linguistics to Jeremy is one of those creative students physics and, finally, influenced by a course Evgeni S. Dimitriov ’13 the Class who manage to carve their academic path of logic taught by prof Nelson, he settled of 1861 Prize for the sophomore who by incorporating all the areas they love. In on mathematics. makes the best record on the Putnam high school Jeremy learned Latin, Greek Jeremy’s year saw the greatest increase in Examination. and Japanese. When he discovered the the number of math majors, to a large ex- beauty of mathematical forms from Pato, tent because of the increased flexibility and Mohit Agrawal ’11, a mathematics and Bertrand Russell led him to formalized diverse course offerings in the department. major from West Lafayette, Indiana, was named a George J. Mitchell Scholar to spend a year studying economics and politics at the National University of Ire- Juggling more than numbers land, Galway. The Mitchell Scholarships, The existence of a Princeton Cube Club ing that striving to solve the puzzle in less awarded by the Washington, D.C.-based and a Juggling Club might not come as than 20 seconds is not much of a challenge, U.S.-Ireland Alliance, recognize out- a surprise to those who know that the will be happy to know of the many options standing American students who exhibit university supports 300 undergraduate and to make the game more thrilling; one can the highest standards of academic excel- 50 graduate student organizations. More solve it: blindfolded, underwater in a single lence, leadership and community service. suprising is that, in both clubs, math is the breath, using a single hand, with one’s feet. major with most representatives. And knowing math seems to help. Sho- Shotaro (“Macky”) Makisumi, ‘12, came to taro, who was born in Japan, settled with Princeton with two passions acquired in his his parents in Pasadena when he was 11. early teens: mathematics and cubing. He He credits an algebra course taken as a can now look proudly at his achievements highschool student at CalTech with giving in both: he was admitted for doctoral him a mathematical approach to solving the studies at the University of Chicago and cube, especially when doing it blindfolded. at Stanford, and he founded the Princ- By the age of 15, Shotaro had obtained eton Cube Club where he helped start a seven world records in speed cubing. tradition of hosting an annual international Shotaro can also solve several cubes while competition recognized by the World Cube juggling them. And that just might help Above: Shotaro Makisumi at a competition. Association. improve his math abilities. A study con- Below: members of the juggling and cube clubs. The Cube refers to the most popular puz- ducted at the Oxford Centre zle game in the world (more than 3.5 mil- for Functional Magnetic Reso- lion sold so far), the Rubik Cube, invented nance Imaging of the Brain in the late 1970s by the Hungarian Erno (FMRIB) and published in the Rubik. Interest in the game waned in the journal Nature Neuroscience, 1980 but boomed again in the 21st century shows improved brain connec- due to intense activity on the internet. tivity as a result of the move- Those who hesitate joining the club think- ments involved in juggling. page 13

Alex Kontorovich, clarinet; Adrian Banner, piano. Manjul Bhargava, Photos by Alan Lankin tabla.

Math and Music Every year, thanks to the efforts of our The recital continued to take place in Graduate Administrator, Jill LeClair, the May until last year when its date was Some of Our Musicians department organizes a music recital in moved to December. Originally a small Taplin Hall. It is a a rewarding reminder performance by four people, over the prof. Bill Browder - flute of the strong connection between the years the recital induced more alumni prof. Manjul Bhargava -tabla abstract beauty of both mathematics and to return and more Fine Hall people to Adrian Banner *02 - piano music and the creativity necessary to dis- participate, leading to a play list of more play it to the world. It is also a delightful than 10 musicians. Alex Kontorovich ’02 - clarinet occasion for students, faculty, and alumni Lillian Pierce ’02 *09 - violin While some of our musicians are casual Robert Haraway- electric guitar to get together and share their love of amateurs, others are accomplished per- Kevin Wilson - piano music. formers, members of successful en- The recital has a long history of intermit- sembles who participate in international Francesco Cellarosi -saxophone tent production but its current form and music events. Lillian Pierce (violin) and Ilya Vinogradov - violin organization is due to the initiative of (cello) were soloists with the a visiting professor, Tim Gowers (cur- Princeton University Orchestra and won rently at Cambridge University) and three various competitions for their instru- Students, faculty, staff talented students: undergraduates Lillian ments. Adrian Banner and Alex Kontoro- and alumni who would Pierce, and Alex Kontorovich, and gradu- vich are members of the Klezdispensers, ate student Adrian Banner. The first music a popular group that appears frequently like to perform at the next recital was organized by Jill LeClair in at various East Coast locations as well as recital are encouraged to Taplin Auditorium on May 24, 2002. in Canada. Professor Manjul Bhargava is email Jill a student of world renowned tabla player, Zakir Hussain. LeClair.

We are grateful to our donors

The Class of 1971 Endowed Fund for Mathematics for discretionary support “to strengthen the mission of the Department of Mathematics.”

The Fernholz Foundation for their funding of the Minerva Lecture Series and the Mi- nerva Distinguished Visiting Fellow, as well as other needs of the department.

A bequest from Jane H. Lukens W30 to establish the Jaywood Lukens ‘30 Scholarship Fund for scholarships in memory of her husband, Jaywood Lukens, for “whom mathemat- ics was fundamental in his profession as an actuary and for whom mathematics ‘was always fun.’” page 14 Wei Tong Shu *90

With the help of Prof. Shiing-Shen Chern At Princeton, I became interested in experience the more dynamic action of and Prof. Wu-Chung Hsiang, whom I met Partial Differential Equations and General the business world, I quickly switched to in China, I was accepted by the math PhD Relativity, and I wrote my dissertation in become a derivative trader at Bear Stearns. program at Princeton University. I arrived Yang-Mills equations under the supervision As my advisor, Prof. Klainerman would say, in Princeton on Sept. 3, 1986 with two of Prof. Sergiu Klainerman. After my PhD, I have no patience. I think trading fits me suitcases and $50 in my pocket. I felt I was I started my academic career in three top well with its quick actions and quick re- the luckiest person on Earth. Thus began institutions: IHES in France, IAS in Princ- sults. The analytic and quantitative training the journey of a young man from a village eton, and MIT. I was 25 at the time, my in Princeton has served me well through- in China in pursuit of the American Dream. academic success promoted my curiosity, out my career in business. which went beyond the math world. I left When Bear Stearns collapsed in 2008 dur- the “ivory tower” and went to work on Wall ing the financial crisis, I lost my job, and Street, first with two short stays at Morgan took some time off to ponder the future. Stanley and Goldman Sachs, and finally But, as I love working in the dynamic settling at Bear Stearns for 15 years, as the world of financial markets, I later returned Senior Managing Director for Head of the to the business, this time working for the Interest Rate Options and Exotics Trading Dutch Bank, ING, as the Managing Direc- in . tor for Head of the Interest Rate and Exot- With the math PhD from Princeton, I ics Trading in Asia. As a trader, I often say gained my entrance to the world of finance that I would rather be lucky than be smart as a quant and had the great fortune to every day. My best luck in life is being a work under the famous Fisher Black at Princetonian. Goldman Sachs. However, as I wanted to

Nathan Kaplan ’11

Here’s my life update, mathematical and otherwise, since graduating in 2007. I spent a year in Cambridge studying with other ‘07 math majors Ian Petrow, Tammy Broderick and Mi- chael Li, where I learned that in England everything is a little classier, including maths with its extra ‘s’ at the end. After serving my time as a ‘mathmo’ (please start using this term) I I moved over to Cambridge in to study at Harvard. I’m in my fourth year of the PhD program working on some problems in number theory with Professor Noam Elkies. In the math department I am surrounded by Princetonians like Ana Caraiani ‘07, Aaron Silberstein ‘07, Andrei Negut ‘08, George Boxer ‘10, and Adrian Zahariuc ‘11 (not to mention all the former Tigers down the road at MIT). Studying math at Princeton prepared me well for much of what I’ve encountered at Harvard, but unfortunately not so well for my 2009 appearance on Who Wants to be a Millionaire. It turns out I should have spent less time working late on problem sets and more time watching Gone with the Wind and learning about flowery textiles. Unfortunately I didn’t draw the question from an earlier season of the show, How many edges are there on a cube? (which of course is 8+6-2, by Euler’s formula), or the $50,000 question from two months before my appearance- Which of these snack foods are common examples of hyperbolic paraboloids, a type of mathematical shape? A. Funyuns, B. Bugles, C. Pringles, D. Combos. (This is left as an exercise for the interested reader.) No matter where the world of math ends up taking me (hopefully to Jeopardy next), Fine Hall will always have a special place in my heart. I am particularly excited to see it when I come back this year for my 5th reunion! I’ll close with a piece of advice for current students: Studying math at Princeton is a wonderful opportunity. Make the most of it! page 15 U.S. Postage Paid Permit No. 186 Department of Mathematics Princeton, NJ Fine Hall, Washington Rd. Princeton, NJ 08542

The George B. Covington Prize in Math- 2011-2012 Summer Program in Analysis & Geometry ematics for excellence in mathematics. funded by an NSF/RIG grant Xue Liu July 23 – Friday, August 10, 2012 Shotaro Makisumi A three-week intensive program for 30 advanced undergraduates and first-year gradu- The Middleton Miller ’29 Prize for the ate students consisting of two related courses in analysis and geometry, each with nine best independent work in mathematics. lectures spanning 1.5 weeks. Edgar Dobrian, Oleg Lazarev Undergraduate Awards Chuen-Ming Mike Wong

Week 1 into Week 2: July 23 - August 1 Week 2 into Week 3: August 1 - August 10 The Peter A. Greenberg ’77 Prize for Harmonic Analysis: Some basic opera- Nonlinear Evolution Equations outstanding accomplishments in math- tors and the role of curvature (A. Israel, (A. Ionescu and S. Klainerman, Princeton ematics. Courant Institute/NYU and E. Stein, University). Hyungjune Kang Evan Brooks Warner Princeton University). The course provides an introduction to The course provides an introduction to applications of Fourier analysis to the study The Andrew H. Brown Prize for outstand- , Lp spaces, and several of certain nonlinear evolution equations. ing junior in mathematics. essential operators, such as the Hardy- Topics covered: restriction theorems,(p) Matthew Carl Superdock ’13 Littlewood maximal function, fractional problems, Strichartz estimates; applica- integrals, and singular integrals.Presenta- tions to nonlinear Schroedinger equations, The Class of 1861 Prize for the sopho- tions on: the Radon and X-ray transform. geometric wave equations and classical more who makes the best record on the Putnam Examination. Spherical averaging operators and the field theory; applications to Yang–Mills and Qiuyi Zhang ’14 corresponding maximal functions; general- wave maps in the . izations of the above where “non-vanishing” Sigma Xi Book Award for Outstanding curvature plays a role; restriction theo- Research to. rems. Oleg Lazarev

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