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Spring 2015 Issue 4 Department of

Abel Prize for John Nash *50 From the Chair John Nash *50 received the 2015 Abel Prize This has been quite a year for from the Norwegian Academy of Science and the Mathematics Department; Letters for his work on partial differential however, space allows for mentioning but equations. Nash shares the $800,000 prize a few of the highlights. To start with, we with , a professor emeritus are overjoyed to have Maria Chudnovsky, at NYU's Courant Institute of Mathemati- Fernando Marques and Assaf Naor as new cal Sciences. The prize recognized Nash and members of the senior faculty. Their pres- Nirenberg for “striking and seminal contri- ence has already made a major impact on butions to the theory of nonlinear partial the Department. differential equations and its applications to *01 won the .” Nash’s name is attached at last summer’s International Congress of to a range of influential work in mathematics, in Seoul, Korea. Manjul is including the Nash-Moser inverse function not only an extraordinary theorem, the Nash-De Giorgi theorem (which stemmed from a problem Nash undertook but also an unusually gifted teacher and at the suggestion of Nirenberg), and the Nash embedding theorems, which the academy tabla player. described as “among the most original results in geometric analysis of the twentieth century.” According to David Gabai, the Nash embedding/immersion theorems, which John Nash *50 and Louis Nirenberg from required unusual insight as well as tremendous technical expertise, played an important NYU are this year’s Able Prize winners. role in the development of young mathematicians who came in contact with Nash at While John is famous for winning the 1994 Princeton in the 1970s. in Economics for his Ph. D. the- sis work on non-cooperative games, this is the first major recognition for his extraor- dinary work on isometric embeddings and partial differential equations which most mathematicians consider incomparably deeper work. With Yasha Sinai winning the Abel prize in 2014, this marks the first time Fields Medal for the Abel prize has gone to mathematicians Manjul Bhargava *01 at the same institution in consecutive years. Manjul Bhargava is awarded a Fields Last summer saw the passing of two long Medal for developing powerful new time professors, Harold Kuhn 50* and Ed methods in the of numbers, Nelson. Harold and Ed were original and which he applied to count rings of small influential mathematicians who respectively rank and to bound the average rank of changed the face of mathematical econom- elliptic curves. ics and constructive . A special day was held on April 22, 2015 to from the award citation commemorate Ed’s work. Our finishing graduate students wrote mar- Manjul Bhargava *01, the Brandon Fradd, sity). The prize comes with a monetary velous theses and obtained excellent first Class of 1983, Professor of Mathematics, award of Canadian $15,000 as well. positions. Of the twenty Sloan Foundation was awarded the 2014 Fields Medal on Bhargava’s Ph.D. thesis (written under fellowships in mathematics awarded this August 13, at the opening ceremony of the the direction of , the James year, eight went to former Princeton grad- 2014 International Congress of Mathemati- S. McDonnell Distinguished University uate students; Richard Bamler, Boris Bukh, cians in Seoul, Republic of Korea by South Professor of Mathematics, Emeritus), Vivek Shende, Andrew Snowden, Jacob Korean President Park Geun-hye. provided a reformulation of Gauss’s law for Tsimerman, Melanie Wood, and Hau-tieng For 2014, there were four Fields Medalists the composition of two binary quadratic Wu from Math and Lin Lin from PACM. In ( of the CNRS in , Martin forms. He showed that the orbits of the addition, assistant professors Vlad Vicol and Hairer of the University of Warwick in group SL(2,Z)3 on the tensor product Tasho Kaletha were also winners. the UK, and former Princeton professor of three copies of the standard integral We have many excellent teachers among of Stanford Univer- continued on next page continued on next page ....continued

Fields Medal for Manjul Bhargava (continued) Department Chair’s letter (continued) representation correspond to quadratic Persi Diaconis, whose research incorpo- our faculty and students. won rings (i.e., rings of rank 2 over Z) together rates decks of cards and coin-flipping with the University’s Phi Beta Kappa teaching with three ideal classes whose product is other random problems. Bhargava thought award and grad student Thomas Beck won trivial. This recovers Gauss’s composition they would be a good way to introduce stu- a teaching award from the Graduate School. law in an original and computationally ef- dents to a field considered dry and daunt- Departmental teaching awards went to in- fective manner. He then studied orbits in ing to many. “The Mathematics of Magic structors Jeffrey Case and Mihai Fulger more complicated integral representations, Tricks and Games” was designed to show and graduate students Nathan Dowlin and which correspond to cubic, quartic, and the artistic and creative side of mathemat- Thomas Beck. quintic rings, and counted the number of ics, which Bhargava asserted is how math- Departmental staff play the crucial behind rings with bounded discriminant. ematicians approach their research. He the scenes role that enables us to focus on Bhargava next turned to the study of repre- wanted to offer this seminar to freshmen our research, teaching and studies. Eszter sentations with a polynomial ring of invari- to capture their enthusiasm early in their Rudy joined the Department as Grants and ants. The simplest such representation is college careers while introducing them Business Manager, replacing Alberta Molnar given by the action of PGL(2,Z) on the to the ‘correct’ and ‘fun’ side of math- who got promoted to a managerial position space of binary quartic forms. This has two ematics. For this initiative, Bhargava was in the Sponsored Research office, and is off independent invariants, which are related awarded several grants from the University, to a great start. to the moduli of elliptic curves. Together including the 250th Anniversary Fund for Innovation in Undergraduate Education Our Department Manager Kathy Apple- with his graduate student, Arul Shankar, gate received the Presidential Achievement Bhargava used delicate estimates on the and a grant from the University’s Council on Science and Technology. Award. Kathy has done tremendous work number of integral orbits of bounded for the Department and so we are delighted height to bound the average rank of elliptic Students appreciated his enthusiasm and that she has been recognized at the highest curves. Generalizing these methods to outstanding commitment to his classes. university level. curves of higher genus, he recently showed His availability to the students and dedica- that most hyperelliptic curves of genus at tion to providing interesting topics and Coming full circle, Scott Kenney has an- least two have no rational points. visiting lecturers was unsurpassed in the nounced his pending retirement. To many Department. of us Scott was the embodiment of the Math Bhargava’s work is based both on a deep Department. During his 25 years as De- understanding of the representations of Sharing his love of mathematics extends be- partment Manager, chairs came and went, arithmetic groups and a unique blend of yond the university. He recently returned but from day visitors to long-time faculty he algebraic and analytic expertise. from a tour of India where he traveled to was there as a constant, welcoming and ap- Bhargava joined the Mathematics Depart- a large number of high schools to discuss proachable soul always ready to tackle prob- ment as a full professor in 2003. In addi- the beauty of mathematics with students. lems from the complex to the mundane. He is also head of a committee devoted to tion to the Fields Medal, he has received While members of our faculty, students and numerous other awards including the 2012 bringing scientists from all over the world to visit schools throughout India. staff have received high profile recognitions , the 2011 (pre- for their research, teaching and service, sented by the Toulouse Mathematics Insti- Bhargava was born in Ontario, but their awards reflect but a small fraction of tute in France) and the Packard Foundation raised in New York on Long Island with the tremendous productivity, energy, and Fellowship in Science and Engineering in frequent trips to Jaipur, India, to visit fam- enthusiasm that permeates Fine Hall. 2004. He was elected to the U.S. National ily. His interests include Sanskrit poetry Academy of Sciences in 2013. and Tabla drumming. Considered a tabla Finally, it is my pleasure to thank Bob and expert, he has given numerous free tabla Luisa Fernholz, Wei-Tong Shu and the Class Bhargava is an outstanding teacher on both of 1971 Fund for their very generous and the graduate and undergraduate levels. In performances at student cultural programs, international fairs, and charity benefits on ongoing support of the activities of our De- recent years, he developed a very popular partment. freshman seminar called “The Mathemat- both the Harvard and Princeton campuses. ics of Magic Tricks and Games,” which had Thank you for reading this newsletter and the maximal enrollment of 15 students reconnecting with the Department. I’d love in Spring 2013 and Spring 2015. He also to hear your thoughts and views. taught “The Magic of Numbers” in the Amazing. Everyone was engaged and it was always so much fun. I don’t know how this course could be improved. It was Spring 2007 and Spring 2010, an under- the best experience ever, and even swayed me to consider David Gabai *77, *80, Chair graduate course he developed that included being a math major! I don’t really know how Professor guest lecturers, card games, and drumming Bhargava does it, but he’s able to explain with incredible [email protected] to capture the attention of the class whose clarity very complicated ideas and make them extremely enrollment neared 160 students. interesting. He seriously deserves a medal or some honorary award for the work he’s done with the class. As an undergraduate at Harvard, Bhargava Excerpt from a student evaluation was exposed to magic from his adviser, of a class taught by Manjul Bhargava page2 Faculty news: we’ll miss them Edward Nelson Professor Emeritus Born in Decatur, Georgia, Nelson lived in ability theory to attack the hard analytic Edward Nelson, 82 Italy as a child, under the dictatorship of questions of constructive quantum field died of complica- Benito Mussolini. He moved to New York theory,” as stated on the award citation. The tions from lympho- City before the start of World War II but latter paper “fired one of the first shots in ma on September later returned to Italy to attend high school. what became known as the Euclidean revo- 10, 2014 in Prince- As a graduate student at the University of lution,” according to the AMS. Among his ton, where he lived Chicago, he studied under Irving Segal and other honors, Nelson was elected to the with his wife, Sarah received his M.S. in mathematics in 1953. American Academy of Arts and Sciences in Jones Nelson. He came to Princeton after an appointment 1975, the National Academy of Sciences in Nelson received as an NSF Postdoctoral Fellow from 1956- 1997, and the American Association for the his Ph.D. from the 1959 at the Institute for Advanced Study. Advancement of Science in 2003. University of Chi- Although accomplished in many areas of Nelson enjoyed teaching and taught very cago in 1955. He was appointed Assistant mathematics, Nelson was perhaps especially successfully on both the graduate and un- Professor at Princeton University in 1959 well known for his successful application of dergraduate levels. (He had looked forward and was promoted to the rank of associ- probability to quantum field theory. He re- to teaching a junior seminar called, “Radi- ate professor in 1962 and full professor in ceived the Steel Prize for Seminal Contribu- cally Elementary Mathematics,” in the Fall 1964. He became Professor Emeritus in tion to Research in 1995 from the American semester, 2014.) 2013 upon his retirement. Nelson’s re- Mathematical Society (AMS) in recognition In addition to his wife, Nelson is survived search inspired further research and ad- of this work. The AMS also recognized two by a son and daughter, three grandchildren, vancement in the fields of analysis, prob- of Nelson’s papers (respectively published and two great-grandchildren. He was pre- ability, and mathematical . in 1966 and 1973) that “showed for the first deceased by his first wife, Nancy Wong time how to use the powerful tools of prob- Nelson.

Harold W. Kuhn *50 Professor Emeritus of Mathematical Eco- Division of Mathematics for the National forever. He is par- nomics Harold W. Kuhn *50 died peacefully Research Council from 1957-60, Mem- ticularly renowned in his sleep on July 2, 2014 in New York ber of the National Research Council from for the “Kuhn- City where he lived since 2005. He would 1961-64, and Senior Consultant and Board Tucker Theorem,” have been 89 years old on July 29, 2014. Member for MATHEMATICA, Inc., from (in collaboration Kuhn was appointed at Princeton jointly in 1961-83. He also served as a co-Director with Albert W. the Mathematics Department and the Eco- of the NATO International Summer School Tucker), which is nomics Department as an Associate Profes- in Varenna, Italy for 1967 and 1970 and as considered a ma- sor of Mathematical Economics in 1959 and co-Director of the NATO Advanced Study jor contribution to was promoted to the rank of Professor in Institute in Capri, Italy, for 1987. the development 1963. He became a Professor of Mathemati- Among his many honors were a Guggen- of nonlinear pro- cal Economics upon his retirement in 1995. heim Fellowship for 1982-83 and Honorary gramming. He also Kuhn was considered a world-leader in the Membership in the Hungarian Operations made many impor- fields of linear and nonlinear programming, Research Society (1992). He was a Fellow tant contributions to general equilibrium game theory, combinatorial problems, and of the Econometric Society (1961) and Fel- theory and the treatment of information in the application of mathematical techniques. low of the American Academy of Arts and extensive form games. Kuhn was born in Santa Monica, CA in Sciences (1992). He shared the John von Kuhn was a gifted teacher on both the un- 1925. He served in the Army Neumann Theory Prize with David Gale dergraduate and graduate levels. During his from 1944 to 1946. He received his B.S. and A.W. Tucker in 1980. tenure at Princeton, he also served diligent- from CalTech in 1947, and his M.A. (1948) He edited the first two volumes of “Contri- ly on a number of University committees and Ph.D. (1950) from Princeton. He butions to the Theory of Games” with the that had a profound impact on the Univer- joined the faculty at Bryn Mawr between late Professor Albert W. Tucker of the Math- sity community. 1952 and 1959. ematics Department. He was a member of Kuhn is survived by his wife, Estelle (nee Kuhn served as President for the Society for a prominent group of economists who in- Henken), whom he married while a gradu- Industrial and Applied Mathematics (SIAM) troduced sophisticated mathematical tools ate student at Princeton in 1949, three sons, for 1953-54, Executive Secretary of the into economic analysis and changed the field six grandsons, and a granddaughter. page 3 Faculty appointments- professors

Maria Chudnovsky *03 Assaf Naor Fernando Codá Marques returned to Princeton as a full professor joined our department as a full professor joined our department as a full professor on jointly appointed in the Mathematics De- on September 1, 2014. Prior to coming September 1, 2014 after being a professor partment and the Program in Applied and to Princeton, he was appointed Professor at IMPA—Associacão Instituto Nacional Computational Mathematics on January 1, of Mathematics at the Courant Institute of de Matemática Pura e Aplicada in Rio de 2015. She comes from Columbia Univer- Mathematical Studies, New York Univer- Janeiro, Brazil. His field of research is in sity, where she was appointed as Liu Family sity. His field of research includes Analy- Geometric Analysis. Professor of Industrial Engineering and Op- sis, Probability, Quantitative geometry, and Marques received his Ph.D. in Mathematics erations Research and Professor of Mathe- their applications to , math- from Cornell University in 2003 studying matics. Her field of research is in Discrete ematical physics, and theoretical with Jose Escobar. He was the recipient of Mathematics and, specifically, in the areas of science. His work on the Lipschitz Exten- the 2012 Academy of Sciences for the De- graph theory and combinatorial optimiza- sion Problem is an example of his very sig- veloping World (TWAS) Prize, cited “for his tion. nificant contributions. contributions to the field of differential ge- Chudnovsky received her Ph.D. in Math- Naor received his Ph.D. in Mathematics ometry, particularly for his work on varia- ematics from Princeton University in 2003 from the Hebrew University in tional problems in conformal geometry and working with Paul Seymour as her thesis ad- in 2002, where he also received an M.Sc. in applications of the theory of Ricci flow.” He visor. She received a M.Sc. from Technion 1998. His awards include Bocher Memorial also was awarded the 2012 International Institute of Technology in 1999. Prize in 2011, the in 2008, and Centre for ’ (ICTP) Ra- Her awards include the MacArthur Foun- the European Mathematical Society prize manujan Prize for Young Mathematicians dation Fellowship in 2013, and the D.R. in 2008. He has been a prominent speaker from Developing Countries (It is supported Fulkerson Prize in 2009, which she shares at the (Zygmund- by the Norwegian Academy of Science and with collaborators Neil Robertson, Paul Calderón Lectures in 2011), International Letters through the Abel Fund, with the co- Seymour, and Robin Thomas. She was also Congress of Mathematicians in Hyderabad, operation of the International Mathematical awarded a five-year Clay Mathematics Insti- the Indian state of Andhra Pradesh (2010), Union.) Fernando gave a plenary address tute Research Fellowship in 2003. She was and was the plenary speaker at the annual at the International Congress of Mathemati- an invited speaker for the Combinatorics meeting of the Israel Mathematics Union cians in Seoul Korea, in 2014. Section of the International Congress of and the Clay Research Conference, both in Marques is one of the world’s young leaders Mathematics held in Seoul, South Korea in 2008. He also served as our Minerva Lec- in geometric analysis. He has made several 2014. She was appointed jointly at Princ- turer in October 2013 and gave a series of fundamental contributions to a broad range eton and the Institute for Advanced Study talks in our department as part of that spe- of problems in geometric analysis, includ- as a Veblen Research Instructor from 2003- cial program. ing the very recent solution to the long- 2005 and was promoted to assistant profes- standing Wilmore conjecture (with André sor for 2005-2006. Neves).

NOTICE: STAFF OFFICE CHANGES LeeAnn Coleman, our Undergraduate Administrator, has moved her office to 315, along the central third floor corridor of Fine Hall. Her office is now next to that of Graduate administrator Jill LeClair, so that students can readily receive the administrative support- they need and have a ready, friendly face during difficult times. page 4 Faculty appointments/promotions ASSISTANT PROFESSORS Mykhaylo Zsolt Patakfalvi Fabio Pusateri Shkolnikov Analysis of PDEs: Dis- , (with connections to persive and Wave Equa- its applications to Complex and Arithmetic tions. Fluid Dynamics: mathematical finance, Geometry and to Com- Euler Equations and queueing theory, and muta- tive ). Water Waves. Harmonic statistical physics. Ph.D. in Mathematics, University of Wash- Analysis and applica- Ph.D. in Mathematics, Stanford Uni- ington, Seattle, 2011; Masters in Math- tions to PDE. Hamiltonian Dynamics and versity, 2012; Diploma in Mathematics, ematics (summa cum laude) Eötvös Lorand Small Divisors. Ludwig-Maximilians Univeristy in Munich, University, Budapest, , 2006; Ph.D. in Mathematics, New York Uni- Germany, 2007; Vordiplom in Mathematics Masters in , Technical versity, 2011. Masters in Mathematics , (passed with distinction; minor in comput- University of Budapest, Budapest, Hun- University of “Roma Tre”, 2006. er science), Ludwing Maximans University gary, 2004. Previous positions: Simons Postdoctoral in Munich, Germany, 2006. Previous positions: Instructor, Princeton Fellow, Princeton University, Department Previous positions: Postdoc Department of University, Department of Mathematics. of Mathematics. Statistics, UC and MSRI, Berkeley. Patakfalvi also serves as our junior Director Co-organizer of the Analysis Seminar and Shkolnikov will be moving to ORFE next of Graduate Studies. the Analysis of Fluids and related topics academic year. We wish him well in his Seminar. new position. INSTRUCTORS Lucas Culler Chun-Hung Liu , invariants of smooth 4-mani- Graph Theory, combinatorics, and algo- folds, mirror symmetry. rithms. Ph.D. in Mathematics, MIT, 2014; B.S. in Ph.D. in Mathematics, Georgia Institute of Mathematics, University of Chicago,2009. Technology, 2014; M.S. in Mathematics, National Taiwan University, 2009; B.S. in Mathematics (with minor in Computer Michaela Ignatova Science and Information Engineering), Partial Differential Equations, Mathemati- National Taiwan, 2007. cal Fluid Dynamics, Harmonic Analysis. Ph.D. in Mathematics, University of South- Jonathan Kommemi ern California, 2011; M.Sc. in Mathematics and , Sofia Uiversity 50% Instructor 50% NSF Postdoc “St. Kliment Ohridski” in Sofia, Bulgaria, General Relativity. 2006; Maitrise de Mathématiques, Uni- Ph.D. in Applied Mathematics and Theo- versité de Nates in France, 2004; B.Sc. in retical Physics, Mathematics, Sofia University “St. Kliment 2013; M.A.St. Part III of the Mathematical Ohridski,” in Sofia, Bularia, 2004. Tripos, University of Cambridge, 2009; Previous positions: Postdoc, Stanford B.A. in Mathematics (with Highest Distinc- University; Visiting Assistant Professor, tion), University of California, San Diego, University of California, Riverside. 2008.

Daniel Ketover Ana Menezes Geometric Analysis, specifically Min-Max Differential Geometry. techniques and their use in producing Ph.D. in Mathematics, Assciação Instituto embedded minimal surfaces in Riemann Nacional de Mathemática Pura e Aplicada 3-manifolds. (IMPA) 2013; M.S. in Mathematics, Uni- Ph.D. in Mathematics, MIT, 2014; A.B. in versidade Federal de Alagoas (UFAL) 2009; Mathematics (Magna Cum Laude), Harvard B.S. in Mathematics, Universidade Federal College, 2007. de Sergipe (UFS) 2008, all in Brazil.

page 5 Faculty Awards Manjul Bhargava *01 Emeritus Professor John H. Foreign Fellow of the Indian National Sci- Conway ence Academy Doctor Honoris Causa of Alexandru Ioan The election, effective from 1 January 2015, Cuza University, Iasi, cites Bhargava’s “spectacular work with his The award was presented at a ceremony discovery of composition laws of higher de- held on June 24, 2014. gree, originally discovered by CF Gauss in The awarding of this degree and attendant the nineteenth century for quadratic forms.

conference in Iasi marked the official open- Vlad Vicol Junior faculty profile His work in algebraic is pro- ing of the Grigore Moisil Institute, a joint found and extraordinarily original. It has initiative of Alexandru Ioan Cuza University Ph.D., University of Southern California revolutionized the way in which number of Iasi and the University of . fields on elliptic curves are counted.” (2010); M.A., University of Southern California (2007); B.Sc., Jacobs University Bremen, Ger- many (2005). L.E. Dickson Instructor at the The Padma Bhushan award, one of the Sergiu Klainerman University of Chicago (2010—2012); Assistant highest civilian awards in the Republic of Simons Fellow in Mathematics Professor of Mathematics, Princeton Univer- India sity, since September 2012. Manjul Bhargava was contacted by the Pres- The Division for Math- ident of India to return to India to receive ematics and the Physical Sciences offers the Vicol hails from the beautiful city of Ora- the Padma Bhushan award at Rashtrapati Simons Fellows Programs in both Math- dea, in Transylvania, Romania. Bhavan (the President’s House). The award, ematics and Theoretical Physics, providing funds to faculty for up to a semester long His research lies at the intersection of par- confered by the president, is offered for tial differential equations and probability “distinguished service of high order” and research leave from classroom teaching and administrative obligations. theory, with an emphasis on problems aris- this year’s recipients include Bill and Melin- ing in fluid dynamics. His work focuses da Gates as well as the famous Indian actor on the analysis of equations describing in- Amitabh Bachchan. Amit Singer compressible Newtonian fluids, such as the Moore Investigator in Data-Driven Dis- Navier-Stokes and Euler equations. These covery models account for interactions between a broad range of space and time scales (in a The five-year awards, offered by the Gor- highly nonlinear fashion) and the accuracy don and Betty Moore Foundation will en- needed to fully resolve the underlying phe- able the recipients to make a profound im- nomena via numerical computations is out pact on scientific research by unlocking new of reach for the foreseeable future. Two of types of knowledge and advancing new data the questions that drive Vicol’s work are: science methods across a wide spectrum of Do singularities in the fluid equations ex- disciplines. ist? If they do, what do they teach us about turbulence? Tasho Kaletha The mathematical tools he uses in his re- search come from different areas in analysis, and such as harmonic analysis, regularity theory Vlad Vicol (elliptic and parabolic), spectral theory, Sloan Fellows in Mathematics stochastic analysis, infinite dimensional dy- The Sloan Research Fellowships seek to namical systems, convex integration, and stimulate fundamental research by early- integro-differential equations, among oth- Chair: David Gabai career scientists and scholars of outstanding ers. Associate Chair János Kollár : promise. They are awarded in recognition Both his graduate-level research and his Directors of Graduate Study: Alex Ionescu and Zsolt Patakfalvi of distinguished performance and a unique graduate teaching were recognized with Dept. Representative: János Kollár potential to make substantial contributions prizes: the 2009 Dennis Ray Estes Graduate Associate Dept. Representative: Jennifer Johnson to their field. Research Prize and the 2009 Theodore Ed- ward Harris Graduate Teaching Prize, both Senior Advisor: Paul Yang from the University of Southern California. Junior Advisor: Mark McConnell He was also awarded a Center for Applied

administration Placement Officer: Vlad Vicol Mathematical Sciences’ Graduate Student Dept. Manager: Congratulations to Fields Medal winner Kathleen Applegate Prize by USC in 2010. And, recently, he Graduate Administrator: Jill LeClair Maryam Mirzakhani who was on received a Sloan Research Fellowship in our faculty from 2004 to 2008. Mathematics for 2015. page 6 Teaching Awards Junior Faculty Teaching Graduate Teaching This is the second year of the Department of This is the third year of the Department of Mathematics Junior Faculty Teaching Award. Mathematics Graduate Teaching Award.

Jeffrey Case has been described by Teaching awards recognize excellence in Nate Dowlin was nominated for this teaching at the undergraduate level. Selec- his students as helpful and caring, a superb tion for both awards was made by a commit- award because of his obvious commitment and masterful lecturer who is able to pres- tee of senior faculty members. to teaching and dedication to his students. ent complex material in a way that is easy He is an innovative teacher who brings his to understand. His students range from love of mathematics to the classroom, in- math majors to non-majors and they have troducing new ways to keep his students found his classes to be a valuable learning engaged. His students commented that he experience while being highly enjoyable at stimulated their curiosity and independent the same time. He has worked as a course thinking through daily puzzles, through ex- head as well and has proven himself to be planation that revealed hidden connections, well-organized and thoughtful, taking his and through lectures that were always both duties quite seriously and serving as a valu- illuminating and engaging. One of his stu- able mentor to his teaching colleagues and dents said, “He opened every class with a to novice instructors as well. math riddle, and I looked forward to it ev- ery MWF!”

Mihai Fulger’s students have referred Thomas Beck’s student evaluations to him as ‘a great teacher with a terrific per- were overwhelmingly positive—with 17 sonality’ and ‘the perfect preceptor.’ He has out of 19 students attending his calculus been exceptionally attuned to how his stu- class giving him the highest rating of “excel- dents think and what they find challenging, lent.” His quiet and serious teaching style always able to respond to their questions served as an inspiration to his students. In with both clarity and insight. Students have his student nominations, one student said, also described him as clear and methodical “Tom was a great teacher. His teaching was while displaying a sense of humor that al- clear and organized, and he always made ways kept his classes interesting. Teaching sure we understood what was going on be- colleagues have found him to be insight- fore moving on to the next concept. He ful, judicious, and generous as well. He has was patient with our questions, and able served well as course head, taking those to explain things in a way that made sense, duties seriously and creating supplemental which I think is very valuable for a math handouts for an introductory course in lin- teacher.” Another student wrote, “I could ear algebra, which was of great use to both not have asked for a better teaching for my students and instructors alike. first math course at Princeton.”

Through the generosity of the Minerva Foundation, the Mathematics MINERVA PROGRAM - Year 4 Department hosted another special lecture series during the Fall term.

Barry Mazur *59 Diego Cordoba *98 This year’s Minerva Lecture series was giv- Our Minerva Distinguished Visitor was Di- en by Barry Mazur of in ego Cordoba of the Instituto de Ciencias mid-October 2014. The topics of Professor Matemàticas of Madrid. He spent the Fall Mazur’s three lectures were: Logic, Elliptic semester at Princeton working on ongoing Curves, and Diophantine stability. projects with our faculty and gave a series of talks on “interface dynamics for incom- pressible flows.” Cordoba remained in our department as a ‘visiting research scholar’ for the spring term. Videos of the lectures are now available at https://www.math.princeton.edu/media/videos

page 7 Events Summer Undergraduate Research Program: 2014. Once again, the Math Department was search topic that interests them, provided is felt that the experience of participating pleased to be able to offer an eight week they can find a faculty member who agrees in an REU as an undergraduate student will summer program for undergraduate math to serve as the supervisor over the summer. provide that student with the opportunity majors to conduct on-campus research In addition to our own on-campus summer to focus on a single mathematical research and/or guided independent study. Over research program, undergraduate majors problem while the Princeton program in- the past three years, the program has pro- may apply for financial support to partici- troduces students to the idea of indepen- vided $4,000 stipends to approximately 10 pate in an off-campus NSF-funded Research dent research while providing the student math majors each year. Although rising ju- Experience for Undergraduate Program with a strong foundation of knowledge in a niors and seniors are given preference, ris- (known as an REU) at another institution. specific area of mathematics, which would ing sophomores are also accepted. (REUs generally focus on mathematical ar- be useful for pursuing other research topics Undergraduate majors are encouraged to eas that are considered somewhat outside of in the future. apply for this summer research opportu- the mainstream with problems that require nity. Students are asked to choose the re- relatively little specialized knowledge.) It

The following students received support from the Mathematics Department and the Jaywood Lukens ’30 Scholarship Fund. Student Faculty mentor Topic of research Arka Adhikari ’16 Paul Yang General Relativity and Cosmic Censorship. Kubrat Danailov ’15 Jon Fickenscher Properties of Symbolic Dynamical Systems and the S-adic Conjecture. Billy Fang ’15 Jon Fickenscher Toward the S-adic Conjecture. Jack Jenkins ’15 Paul Yang Summer research on the S-adic Conjecture. Monica Marinescu ’15 Mihai Fulger Algebraic Geometry. At Princeton At Clayton McDonald ’15 Jeffrey Case Riemannian Geometry and Applications to . Alexander Payne ’16 Paul Yang Optimal Transportation and the Isoperimetric Inequality in the Heisenberg Group. Paul Rapoport ’15 David Gabai Knot theory and Homological Algebra

Bumsoo Kim ’16 Joseph Gallian The Cross Number of Zero-sum Free Sequences in Finite Abelian Groups Marya Sardarli ’15 Greg Musiker, Pavlo Quivers of Period 2

At the At of University Minnesota Pylavskyy, Vic Reiner, Dennis Stanton, Rising juniors and seniors were also invited to apply for funding made available by the NSF to Sucharit Sarkar, Assistant Professor of Math- ematics, for a research project in low dimensional topology. Daniel Dore ’16 and Yuval Wigderson ’16 received $4,000 stipends and were required to be on campus for the months of July and August. They studied two modern (and fairly important) invariants of knots: Khovanov homology and knot Floer homology. Both invariants could be studied combinatorially; the former via a cube of resolutions of a knot diagram and the latter via grid presentations of knots.

Geometry and Topology Conference

The conference was in honor of the 70th birthday of Martin Bendersky, professor at Hunter College, CUNY, and in memory of Sam Gitler *60 , who passed away this year. It took place at Fine Hall, and was co-sponsored by our department and the CUNY Graduate Center. It was organized by Tony Bahri from Rider who is a visiting research scholar here this term. Martin Bendersky Sam Gitler,

page 8 Events ANALYSIS, SPECTRA, AND NUMBER THEORY: A Conference in Honor of Peter Sarnak By Michael Rubinstein, co-organizer of the conference The conference was held at Princeton Uni- matrix theory, to shed light on number theory. These areas have seen a flurry of ac- versity and the Institute for Advanced Study, theory, for example in his statistical analy- tivity in recent years, including: the resolu- December 15 - 19, 2014 on the occasion of sis with Rudnick and Katz on distribution tion by Lindenstrauss of Rudnick and Sar- Peter Sarnak’s 61st birthday. of zeros of L-functions. Sarnak’s knack for nak’s quantum unique ergodicity conjecture The conference was well attended, with recognizing connections between seemingly for arithmetic surfaces; spectacular break- around 350 participants. These included disparate areas of mathematics, and for pos- throughs by Bhargava and his colleagues many of Sarnak’s students, postdocs, co- ing essential and fundamental questions that concerning the statistics of number fields authors, colleagues, and friends. The large lie at the interface between the difficult and and elliptic curves; detailed models and turnout is a testament to the far reaching the impossible, has inspired colleagues and predictions for the zero and value distribu- influence and importance of Sarnak’s work. students alike and has changed the land- tion of L-functions that were inspired via While L-functions and automorphic forms scape of mathematics. connections with random matrix theory; have played a central role in Sarnak’s re- The talks of the conference reflected Sar- construction and the analysis of highly effi- search, his broad view of mathematics has nak’s broad impact on mathematics. It fo- cient expander graphs; the development of allowed him to bring ideas from number cused on , with additive combinatorics based on the work theory to bear on other areas, such as in his emphasis on its many relationships with of Green and Tao. The conference empha- construction of Ramanujan graphs and also analysis and spectral theory. Highlighted sized these developments, with many lead- quantum gates. Reciprocally, he has brought topics included arithmetic quantum chaos, ing speakers in these areas. insights and techniques from other areas, analysis of families of L-functions, arithme- such as mathematical physics and random tic statistics, and connections with ergodic

SPEAKERS Nalini Anantharaman, Orsay , Chicago , Hebrew U. Manjul Bhargava, Princeton Ben Green, Oxford , Hebrew U. Alice Chang, Princeton Henryk Iwaniec, Rutgers Philippe Michel, EPFL J. , AIM Nicholas Katz, Princeton Werner Muller, Bonn Bill Duke, UCLA Jon Keating, Bristol . Oxford Matthew Emerton, Chicago Xiaoqing Li, SUNY-Buffalo Ze’ev Rudnick, Freydoon Shahidi, Purdue ORGANIZERS Percy Deift, NYU Richard Taylor,IAS Stephen D. Miller, Rutgers , Stanford Michael Rubinstein, Waterloo Shouwu Zhang, Princeton , Stanford videos of the lectures are available at: https://www.youtube.com/user/princetonmathematics Peter and his wonderful families

page 9 Our graduate students Naser Talebi Zadeh I work in analytic number theory. Specifi- Princeton is a heaven for mathematicians. cally, I am interested in the topics related Before coming to Princeton, I had heard to the limit multiplicity theorem and the great things about Professor Sarnak and applications of the Ramanujan conjecture Princeton. Professor Sarnak is a phenom- in geometry and graph theory. As an under- enal advisor and he is always inspiring and graduate at Sharif and later at Cambridge full of energy. He introduced me to impor- university, I explored different fields of tant problems and different projects from mathematics such as probability theory, dif- computer science to Iwasawa theory. Sar- ferential geometry, topology and analysis. I nak is certainly gifted in guiding students found the questions in number theory deep and making graduate school seem easier for and fascinating; one needs to apply tech- his students. niques and ideas from other branches of I am applying for postdoctoral positions mathematics to understand them. next year and I plan to pursue a carrier in I am very fortunate to have great parents academia. who always encouraged me and gave me I certainly grew up a lot by interacting with interesting books to read. I remember my the diverse and highly intellectual com- Nasser is in his fourth year of Ph. D. studies. mother gave me some brainteasers as a He grew up in Kerman, in the southeast of munity of Princeton university. I definitely Iran. He completed his undergraduate degree child. I realized that I was good at them! recommend international students to check at Sharif University, and received a Master’s Later, in high school, I began training for out the Davis international center program. of Mathematics from Cambridge University. and participating in math Olympiads, and I There is always something interesting go- won a gold medal in the IMO. ing on on campus. The best years of my life have been spent in Princeton.

Heather Macbeth

Heather is finishing her Ph.D this year. with a I fell in love with differential geometry as an thesis on “Kahler-Einstein metrics, Bergman undergraduate in New Zealand, when I en- metrics, and higher alpha-invariants” super- countered the oldest and most fundamental vised by Gang Tian. classification theorem in differential geom- Starting in September 2015 she will be a etry: the classification of constant-section- Moore Instructor at MIT. al-curvature manifolds according to their Heather is originally from New Zealand universal covers. The things that delighted where she completed her undergraduate me about that theorem are still what ap- studies obtaining a B.Sc. in Mathematics, peal to me now about my field of research: with First Class Honors, from the University the satisfaction and solidity of a good uni- of Auckland. formization/classification theorem, and the She obtained a Master’s in Mathematics intricate interplay of topology, analysis and (“Part III”), with Distinctio,n from Trinity Col- algebra. lege, University of Cambridge, UK. Heather’s international experience extends The graduate admissions open house. to many continents: she spent a semester in Peking at the Beijing International Center for Mathematical Research in 2013, and a semester at Albert-Ludwigs-Universitat Freiburg, Germany.

page 10 Undergraduate news The Math Club launches new journal Principia is the new mathematics research journal for undergraduates offered by the Princeton University Mathematics Club PRINCIPIA STAFF The Princeton Undergraduate Math- to encourage students to learn about new ematics Club’s new journal Principia is mathematical research. Principia aims Faculty Advisors a truly wonderful initiative! Our under- to provide young mathematicians and all graduates write so many amazing pa- Professor John Conway those interested with a resource to ex- pers and articles every year, but few of Professor Manjul Bhargava change mathematical knowledge and ideas. us ever get to read them. Principia, by The journal publishes articles and papers Editors-in-Chief : Bumsoo Kim ‘16 collecting, reviewing, editing, and pub- on current research at a level accessible to Andy Loo ‘16 lishing some of the most outstanding an interested undergraduate. Articles are and accessible of these papers (in addi- not limited to research -- a variety of non- Business Director: David Zhao ‘15 tion to recruiting other excellent articles research pieces pertaining to mathematics from undergraduate students, graduate are also published. Principia includes ex- Academic Director: Daniel Dore ‘16 students, and faculty,) is doing a great pository articles on interesting mathemati- service to the mathematical community Production Director: Elizabeth Yang ‘16 cal properties as well as some light-hearted in making these papers available for all articles. Secretary: Roy Zhao ‘17 of us to read and enjoy! All submitted articles will be peer-reviewed The name of the journal was also clever- before publication.Submission period for Webmaster : Angelica Chen ‘17 ly thought of by Prof. Conway, so that the blogs.princeton.edu/mathclub 2nd issue is ongoing until May 31. first syllable of the journal name and the name of our university coincide. I hope The Princeton University Mathematics Club is a stu- To get an article published or to join the Principia team, dent organization devoted to students with an interest in visit the Principia website for more information: and fully expect that the journal will be a math and math-related activities. The club provides advising great success! services, organizes academic and social events and facilitates the development of close connections between all members pumj.org/submission Manjul Bhargava of the Princeton mathematics community.

CONGRATULATIONS CONGRATULATIONS

The Middleton Miller ’29 Prize The 74th William Lowell Putnam Alexander Daniel Iriza ’14 Mathematical Competition Jane Wang ’14 $1000 Award Rank 6–19 The Andrew H. Brown Prize Bumsoo Kim Alexander Degener Smith ’15 Eric D. Schneider Isabelle Nogues, a junior math major, The Peter A. Greenberg ’77 Prize received a Mellon Mays Undergraduate Fel- Honorable Mention Alan Chang ’14 lowship which aims to increase the repre- Andre A. Arslan sentation of minority groups in academia. Eric Christopher Chen ’14 Mariya Sardarli Isabelle is the first math major to win the Kai Zong Khor ’14 fellowship at Princeton. Her fellowship mentor, Christine Taylor, guides her toward The Class of 1861 Prize activities and opportunities that strengthen Bumsoo Kim ’16 her candidacy for graduate school. Isabelle is fluent in French and Italian, and plays violin for the university orchestra. She plans to write a junior paper on number theoretic applications to cryptography with Ana Caraiani and a senior thesis on math and music with Manjul Bhargava.

page 11 Events

The 21st Women and Mathematics Program by Christine Taylor Intensive mentoring program for undergraduate, graduate, and postdoctoral women

Each May, about 40-60 women studying whelmingly report that they feel inspired Monday, May 18th, in Fine Hall, a full day of mathematics at institutions all over the US and encouraged by the women they meet talks by faculty and graduate students. gather on the campus of the Institute for during the program, and that the program Topic: Algebraic Geometry Advanced Study in Princeton for an inten- is a vital opportunity to reinvigorate their Sponsored by: sive residential mentoring program. The studies and research. Many student partici- Institute for Advanced Study two-week program aims to inspire talented pants return to the program in subsequent Princeton University Math Department women from undergraduate through doc- years as teaching assistants, lecturers, and NSF toral levels to achieve their educational and colloquium speakers. Lecture topics: Combinatorics and Graph Theory, 2013 career goals, as well as to address the isola- In the last 20 years or so, around 1000 tion and lack of support many women face Random Matrix Theory 2014 women mathematicians have visited Princ- Aspects of Algebraic Geometry 2015 in mathematics. eton as part of the Women and Mathemat- Past years’ evening Women in Science Research mathematicians such as Prof. Ma- ics Program and about 70% have remained seminar topics: ria Chudnovsky *03 and Wei Ho *09 are in academia. The program alumnae who Work-Life Balance in a Math Career recruited to give lecture series and collo- have benefitted from their experience at the Surviving in Graduate School’ Career Paths for Women in Maths quia that focus on a particular mathematical Women and Mathematics Program will help Becoming an Academic Mathematician topic each year. us to continue to strengthen the program Using Language for Success which Off- This year, the Women and Mathematics Pro- for future women mathematicians. sets Stereotypical Behavior gram participants came to Fine Hall for a full day of talks by faculty and graduate stu- dents on Monday, March 18th. Lunch and Math and music: our annual recital dinner in the Professors’ Lounge were high- This year’s Department Spring Recital was held on April 30 at 5:30 p.m. in Taplin Audi- lights of a busy day where participants en- toriaum. The performers were members of the Fine Hall community. Faculty members: joyed meeting Princeton graduate students, Florian Sprung (bandoneon), Mark McConnell (baritone); Graduate students: Yuchen postdocs, and faculty members. A violin Liu (classical guitar), Junho Peter Whang (piano), Nikita Lvov (piano), Ryan Peckner concert by Isabelle Nogues ’15 took place at *15 (piano), Matthew de Courcy-Ireland (piano); Undergraduate student: Billy Fang ’15 5 p.m. in the Woolworth Center on campus. (piano). Alumni: Adrian Banner (piano), Alex Kontorovich ’02 (clarinet and saxophone). Other “Princeton Day” activities have in- Friends and family were invited to a reception afterward in the Common Room. cluded visiting Princeton’s Plasma Physics Laboratory and panel discussions on a vari- Thank you, Jill, for ety of topics of interest. Over two weeks, women mathematicians organizing it! from all levels learn, work, and social- ize together in a supportive environment. Mathematical bonds are often created be- There is so much musical talent in this department, including PACM. tween senior mathematicians and graduate We hope to hear from many of you next year! If you are interested in students/postdocs. Past participants over- participating in future recitals, contact the organizer, Jill LeClair.

Women in mathematics Program. Photos by Katarzyna Mieczkowska

page 12 Administrative staff changes Scott Kenney Eszter Rudy Scott Kenney plans to retire after 27 years with the department. Business and Grants Manager Scott joined the Math Department as the Scott has worked steadily for over 40 years The Mathematics De- Assistant Department Manager in De- and is looking forward to pursuing other in- partment welcomed cember1986 and assumed the position of terests in this next phase of his life: relearn- Eszter Rudy as our new Department Manager in July of 1987. He ing the piano, working with stained glass, Business and Grants remained in that position for 25 years, be- and writing. He will always cherish his years Manager in January, coming the Special Projects Manager on a in the Princeton Math Department and re- 2015. (Her predeces- half-time basis in September 2012. Scott member all the people with whom he was sor, Alberta Molnar, accepted a position joined the University in 1984 and worked fortunate enough to come in contact during as the manager in the Sponsored Research in the Statistics Department and in the Reg- his tenure. Accounting Administration in the Office istrar’s Office before coming to the Math of the Vice-President for Finance and Trea- Department. He has a B.A. degree in Eng- surer in December, 2014.) Eszter comes lish/Professional Writing from the College to the Mathematics Department from the of New Jersey. Department of Operations Research and As our Special Projects Manager, Scott has Financial Engineering, where she had been worked on various conferences and special Grants Manager since September 2012. events. As the Department Manager for Prior to coming to Princeton, she held po- 25 years, Scott worked with a total of 10 sitions at Temple University and in various chairs and one acting chair. He estimates public health arenas. that his hand was on the appointment forms Eszter has a Master of Public Administra- of well over 200 junior and senior faculty, tion from Syracuse University and B.A.’s a high number of visitors, and many, many Kathleen in International Studies as well as in Italian visa-related issues over the years. Each Studies from Dickinson College. Applegate chair brought his or her own perspective In her role as the Business and Grants Man- to the task and each worked very closely Kathleen Applegate, our Deparment Man- ager, she will work closely with the Chair with Scott as the department manager. As ager, was awarded the 2014-15 President’s and Department Manager monitoring de- he looks back on those years, he remem- Achievement Award for her outstanding partmental finances and handling all grant- bers fondly the staff members with whom contribution to the Mathematics Depart- related activities, working closely with he worked, the faculty members who came ment and as a citizen of the University. Carrie Heyer, the Assistant Business and into the department as relatively inexpe- She joined the staff in the Department of Grants Manager. rienced postdocs and then returned years Mathematics in September 2012. later as tenured faculty, the Fields Medals, Eszter was born in Hungary and moved to Fermat’s Last Theorem, as well as all the ev- the United States at the age of 12. She lives with her husband and their two young sons eryday events of a busy, world-class math- Farewell party for Alberta Molnar who left our ematics department. department to become a manager for the Spon- in Pennsylvania. sored Research Accounting Administration. Scott served on many University commit- tees and was one of the early members of the Academic Managers Group (AMG) on campus, serving as chair and co-chair of the AMG and heading various AMG subcom- mittees. He received the 1998 AMG award for “his outstanding leadership, excellence in management, and continuing belief in the continuing education of academic manag- ers” from his peers. Scott and his wife, June, a retired Trenton school teacher, have three grown children, a daughter-in-law, and a 7-year-old grand- daughter. They plan to relocate to the beautiful Blue Ridge Mountains of North Carolina and to continue to travel as much as possible.

page 13 From our alumni Adrian Banner *2002 Adrian Banner never left Princeton after Robert Fernholz, Ph.D., who founded IN- obtaining his Ph.D. in 2002, he just moved TECH Investment Management LLC in to the other side of Nassau Street; he is now 1987, is also an alumnus of our department. the chief executive officer and chief invest- He received his A.B. in Mathematics from ment officer of INTECH, an institutional Princeton University in 1962 (Ph.D. from equity management firm in 1967) and is cur- Adrian joined the firm in August 2002 and rently a member of the Board of Trustees of since then has been an integral part of the the Institute for Advanced Study. firm’s Princeton-based research team. He pioneered mathematical investing with INTECH uses a purely mathematical ap- the publication of Stochastic Portfolio Theory proach, through stochastic calculus, to and Stock Market Equilibrium in 1982. the equity investment process. Its unique INTECH takes advantage of its proxim- investment process is based on a theorem ity to Princeton University by engaging in published by Dr. Robert Fernholz ‘62 in his academic collaborations and conferences 1982 paper, Stochastic Portfolio Theory and with MathApplied Math/ORFE as well as Stock Market Equilibrium. The goal of the in- by hiring summer interns and graduates. vestment process is to achieve long-term Currently working at or with INTECH are: returns that outperform the benchmark mathematicians Phillip Whitman*10 and index, while controlling relative risk and Assistant Professor Mykhalyo Shkolnikov; trading costs. physicist Vassilios Papathanakos; and, soon, applied math alumnus Onur Ozyesil. in Adrian’s own words... In 2000, I did a summer internship at IN- to use rigorous mathematics to manage Before entering the world of finance Ban- TECH after completing my third year of money for their constituents’ retirement ner spread his love of mathematics through graduate studies. I had never been inter- funds. his teaching at Princeton. His successful ested in finance beforehand, but wanted lectures are available on video and their As a student of mathematics I learned to content collected in a book praised for to widen my horizons. During the intern- focus on solving difficult problems over a ship, I discovered that INTECH puts a being “one of the clearest mathematics long period of time. From Eli Stein (my texts” and “an indispensable volume for any heavy emphasis on theory -- especially advisor), I learned how to get to the “heart student seeking to master calculus.” probability theory and stochastic calcu- of the matter” without getting distracted by The Calculus Lifesaver: All the Tools You lus -- as well as applying the scientific less important but superficially attractive method to investing. While other financial Need to Excel at Calculus is published by aspects of the problem. the Princeton University Press. services companies often have strong ties with academia, INTECH has always had a Music is my main hobby; playing the piano combined focus on theoretical, academic is a wonderful release from stress. Also, my research with the practical application of lifetime of performing has made me very money management, which really appeals comfortable presenting in front of crowds. to me. I still play on weekends at concerts. My My training is in and, band, the Klez Dispensers (originally a as such, it is always an interesting chal- student band at Princeton) still performs a For more about this go to: lenge to work out how to bridge the gaps few times a year -- even at New York res- between theory and observations. taurants! My wife is a violin teacher and press.princeton.edu/video/banner/ player by profession, and our children are You can download the videos from: It is also very gratifying to be able to pro- showing early signs of musical aptitude too. vide an option for pension funds through- It is fun to play together as a family! vimeo.com/PrincetonUniversityPress out the US and the rest of the world page 14 Most recent Ph .D.s

Name Undergrad Advisor Field Thesis Title Original Placement

An, Xinliang Peking University Klainerman Analysis Formation of trapped sur- (1 faces in general relativity yr.) & (3 yrs.);Postdoc

Lewallen, Sam Harvard University Szabo Topology Floergåsbord Princeton University/ Department of Neurosci- ence/Postdoc

Miller, Alison Harvard University Bhargava Number Theory Counting simple knots via Harvard University/NSF arithmetic invariants Postdoc/Benjamin Pierce Fellow

Pollack, Aaron Skinner Number Theory Rankin-Selberg integrals /NSF in many complex vari- Postdoc ables and Rankin-Selberg integrals associated to non- unique models

Racz, Bela Eotvos Lorand Uni- Szabo Topology Geometry of (1,1)-knots Two Sigma Investments, versity, Hungary and knot floer homology NY/Researcher

Reichert, Nicolas University of Chang Conformal Some results on a full Acting Assistant Profes- Washington Geometry nonlinear equation in sor/ University of Wash- Conformal Geometry ington

Seed, Cotton MIT Szabo Topology Higher differentials on Postdoctoral Associate/ Khovanov homology MIT

Shah, Shrenik Harvard University Skinner Number Theory p-adic approaches to the Columbia University/NSF Postdoc

Sosoe, Philippe McGill University Aizenman Math Physics Fluctuation bounds for Harvard University/ two disordered models Postdoc

Sun, Hongbin Peking University Gabai Topology On closed hyperbolic UC Berkeley/Morrey As- 3-manifolds and pseudo- sistant Professor Anosov maps

Tsiokos, Eleftherios University of Athens Skinner Number Theory Integrals of automorphic Tel Aviv University/Post- forms and L-functions doc

Tu, Yu-Chao Peking University Kollár Algebraic Étale covering between University of Utah/Post- Geometry resolution of isolated doc singularities and Gaffney- Lazarsfeld theorem for homogeneous spaces

Zhan, Bohua MIT Szabo Topology Combinatorial methods in MIT/NSF Postdoc bordered Heegaard floer homology

Zhang, Yu Peking University Ionescu Analysis On the global solutions UCLA/Visiting Assistant of quasilinear dispersive Professor equations

Zong, Runpu University of Science Kollár Algebraic Topics in birational geom- IAS Member and Tech, China Geometry etry of algebraic varieties

page 15 Department of Mathematics Fine Hall, Washington Rd. Princeton, NJ 08542

Alumni , faculty, students, friends, connect with us, write to us at [email protected] We are very grateful to our recent major donors: The Fernholz Foundation for its gener- The Wei-Tong Shu *90 Fellowship Fund A bequest from Jane H. Lukens W30 to ous funding of the Minerva Lectures to provide financial assistance to Math establish the Jaywood Lukens ’30 Schol- and the Minerva Distinguished Visiting Department graduate students. arship Fund for undergraduate scholar- Professor program and its support of our ships in memory of her husband, Jaywood graduate program. Lukens, “for whom mathematics was fun- A bequest from the Bradford H. Arnold damental in his profession as an actuary and *42 and Mary Ellen Arnold Fellowship for whom mathematics ‘was always fun.’” The Class of 1971 Endowed Fund for Fund to provide financial assistance to Mathematics for discretionary support selected graduate students studying in the to strengthen the mission of the Depart- mathematics department. ment of Mathematics.

The Sarnak conference (on page 9)

Bio mathematics in the time of Shakespeare Mathematics was the key to the descovery weight of the blood flowing through the after various experiments came to the con- of the circultion of blood. In the early heart in one hour was more than three clusion that the blood circulated through 1600s Harvey, using a method introduced times that of the entire body. That proved the veins and arteries and was pumped by by Galileo, in the new physics, for the first wrong the theories of the time, which the heart, a theory that was not easily ac-

Fun facts Fun time used mathematics in the study of the assumed that blood was produced by the cepted during his lifetime. human body. Harvey calculated that the liver and absorbed by the body and Harvey, page 10