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Spring 2014 Issue 3 Department of Department of Mathematics Fine Hall, Washington Rd. Princeton, NJ 08544

Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and , Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- . 1st at the Knesset. ning NSF postdoctoral fellowships. Andy The upcoming International Congress of Other Princeton current and past faculty- Manion and Owen Biesel won departmen- in Seoul, Korea will be who received the prize are: tal graduate student teaching awards, and well represented by Princeton faculty. (1989), (1995), Jon Fickenscher and Luc Nguyen won the , János Kollár and Fernan- (1996), and Elias Stein (1999). inaugural junior faculty teaching awards for do Coda Marques will be plenary speak- their excellent work as instructors. Gradu- ers, and Mihalis Dafermos, Sasha Sodin For the full citation, go to: www.wolffund.org.il ate student Tom Beck won a teaching award and Mark Braverman (Computer Science) from the Graduate School. will be invited sectional speakers. Mihalis Adam Levine and Benoît Pausader joined is one of very few invited to speak in two The happy participants in the new course, , introduced in the fall of 2013, and taught by Michael Barany and . us as assistant professors this year, with sections (PDEs and ). Benoît winning a Sloan Foundation fel- Sasha and Mark will be respectively speak- lowship. Tasho Kaletha also became a new ing in mathematical physics and theoretical assistant professor, being promoted from computer science. The Abel Math and music: our annual recital Veblen Research Instructor. We initiated the Minerva Distinguished and Florian Sprung joined us as Veblen In- Visitor program, welcoming back Andre Prize for structors. Javier Gómez Serrano and Steve Okounkov from Columbia, who gave a se- Yakov Thanks to the efforts of our Graduate This year’s performers were: Sivek joined us as instructors, and Jonathan Administrator, Jill LeClair, the members ries of 10 lectures. We thank the Fernholz Sinai Tim Brown (piano) Kommemi as an NSF postdoctoral research Foundation for making this possible. of our department and their friends and fellow. Assistant Professor Sucharit Sarkar Laurent Côté ’14 (violin) The Abel Prize, established in 2001 by the families had the opportunity to enjoy was awarded an NSF Career Grant. I’d like to thank Bob and Luisa Fernholz, Norwegian government and named after another delightful afternoon of music. Matthew de Courcy-Ireland, graduate the Class of 1971, Wei-Tong Shu, and the The Department has had excellent rela- Norwegian Niels Henrik The recital took place on May 8 in Taplin student (piano) Arnold and Lukens families for their very Abel (1802-1829) is presented annually by tions with the Institute for Advanced Study. generous support. Auditorium and was followed, as usual, by Mark McConnell, lecturer, (baritone) Its faculty frequently give courses and the King of Norway to one or more out- a well attended reception in the Common Being surrounded by exceptional col- Isabelle Nogues ’15 (violin) advise our graduate students. To formalize standing mathematicians.The six million Room. this connection, , Helmut leagues totally committed to their re- Norwegian krones prize will be awarded to Florian Sprung, Veblen instructor (ban- Many thanks also to our musicians, who Hofer, Robert MacPherson and Richard search, mentoring and teaching missions, Sinai at a special ceremony in Oslo on May doneón) Jill LeClair took time to prepare and play for us Taylor were named Visiting Lecturers with immensely talented graduate students 20th, in recognition of his status as one of despite the demands of thesis writing and Ryan Peckner, graduate student (piano) Rank of Professor. playfully pushing themselves mathemati- the most influential mathematicians of the cally, and very gifted undergraduates trying 20th century and for his “fundamental con- approaching exams. Feng Zhu ’14 (piano) Essential to the functioning of the Depart- to figure out how they will change the tributions to dynamical systems, ergodic and ment is having excellent staff members. world is both an awesome and humbling theory, and mathematical physics.” Following careful searches we welcomed experience. Join us next year in the Minh-Tam Trinh ’14 (piano) For the full citation, go to: www.abelprize.no Ben Rose (from Computer Science) as our David Gabai *77, *80, Chair audience or on stage! new systems manager, Michelle Matel as [email protected] Faculty appointments Recent Ph .D.s

Our most recent Ph.Ds theirthesesandwheretheytheir advisors, went Princeton after Assistant Professors Instructors Boris Alexeev Sung-Jin Oh J. Conway S. Klainerman An assortment of results in Finite energy global well-posedness of the Adam Levine Antonio Ache Steven Sivek and compressed sensing. (3+1)-dimensional Yang-Mills equations Topology (specifically: the study of proper- Conformal , Differential Low-dimensional Topology (with a special Voleon Capital Management, CA, using a novel Yang-Mills heat flow gauge. ties and applications of Heegaard Floer Geometry, Partial Differential Equations. focus on contact and symplectic geometry, Senior Research Scientist. UC Berkeley-Miller Institute, Postdoc. homology). Ph.D., University of Wisconsin, Madison Floer homology theories, and knot theory.) Ali Altug Nicolas Reichert Ph.D. (2010); M.Phil. (2008); M.A. (2012); B.S., Universidad Simón Bolívar, Ph.D., Massachusetts Institute of Technol- P. Sarnak A. Chang Caracas, Venezuela (2005). ogy (2011); S.B. in Computer Science and Analysis experiments with the trace Some results on a full nonlinear equation (2006), Columbia University; A.B. magna National Science Foundation Postdoctoral Engineering, MIT (2006). National Science formula. Columbia University, Postdoc. in Conformal Geometry. University of cum laude, (2005). Research Fellow, 2012-2014; Postdoctoral Foundation Postdoctoral Research Fellow, Washington, Acting Assistant Professor. National Science Foundation Postdoctoral Owen Biesel Research Fellow/NSF Postdoctoral Fellow, 2012-2015; Postdoctoral Fellow, Harvard M. Bhargava Rodolfo Rios Zertuche Research Fellow, 2010-2013. Princeton University (2012-2013). University (2011-2013). Galois closures for rings. Leiden A. Okounkov Lecturer/NSF Postdoctoral Fellow, University, Postdoc. Near-involutions, the Pillowcase Brandeis University (2012-2013). Distribution, and Quadratic Differentials. Yaim Cooper Princeton University, Lecturer; Fall ’13: R. Pandharipande Brown University-ICERM; 2014: Max The geometry of stable quotients in genus Planck Institute for Mathematics, Postdoc. one. Harvard University, NSF Postdoc. Samuel Ruth Gabriele DiCerbo M. Bhargava J. Kollár A bound on the average rank of Effectiveness boundedness results in j-Invariant zero elliptic curves. Princeton algebraic and analytic geometry. Columbia University, Lecturer; Bloomberg, NY, University, Postdoc. Software Engineer. Mohammad Farajzadeh Tehrani Giulia Saccà G. Tian G. Tian On moduli spaces of real curves in Fibrations in Abelian varieties associated symplectic manifolds. , to Enriques surfaces. SUNY/Stony Brook, Visiting Assistant Professor. Postdoc. Kevin Hughes Arul Shankar E. Stein M. Bhargava Arithmetic analogues in harmonic analysis: Geometry of numbers methods for global Results related to Waring’s problem. fields. IAS, Member (1 year); Harvard Benoit Pausader Javier Gómez Serrano administrative positions 2013-2014 University of Edinburgh, Postdoc. University, Postdoc. Philip Isett Analysis (partial differential equations Analysis. Hydrodynamics of Incompressible Daniel Shenfeld S, Klainerman and their interactions with physics and Fluids. A. Okounkov Chair: David Gabai Hölder continuous Euler flows with Abelianization of stable envelopes in geometry). Ph.D., Universidad Autónoma de Madrid Associate Chair: János Kollár compact support in time. MIT, C.L.E. symplectic resolutions. GNS Healthcare, Chargé de recherche, CNRS, U. Paris 13 (2013); M.S., Universidad Autónoma de Directors of Graduate Study: Moore Instructor. , MA, Director of Machine Madrid (2010). Dual degrees in mathemat- Alex Ionescu and Nicolas Templier Learning (2012); Visiting Researcher, Princeton Uni- Junehyuk Jung ics and engineering from the Universidad Department Representative: János Kollár versity (2011); Courant Instructor, New P. Sarnak Politécnica de Cataluña, Spain. Associate Department Representative: Kevin Wilson York University (2011); Assistant Profes- Jennifer Johnson On the zeros of automorphic forms. Re- M. Bhargava sor, Brown University (2008); Senior Advisor: John Mather quired South Korea Military Service. Three perspectives on n points P^{n-2}. Knewton, NY, Data Scientist. Assistant moniteur normalien, Junior Advisor: Tasho Kaletha Michael McBreen Cergy-Pontoise University (2006). Placement Officer: Vlad Vicol A. Okounkov Guangbo Xu Department Manager: Kathleen Applegate Quantum cohomology of hypertoric G. Tian Graduate Administrator: Jill LeClair varieties and geometric representations of Symplectic vortex equation and adiabatic Undergraduate Administrator: LeeAnn Coleman Yangians. MIT, Instructor, Postdoc. limits.UC Irvine, Postdoc.

YoungHan Park Shiwu Yang, I. Rodnianski Image by Rob Scharein using the P. Sarnak software KnotPlot (knotplot.com) Nonlinear wave equations on time Hyperbolic hypergeometric dependent inhomogeneous backgrounds. monodromy groups and geometric , Postdoc. finiteness. WorldQuant, VP of Research. page 2 page 15 From our alumni Faculty appointments

Untangling laws and knots a letter from Kenneth Perko ‘64 Veblen Research Instructors The Veblen Research Instructorships are joint 3-year appointments between our department and the School of Mathematics at the A mathematics major receiving Honorable supervising, inter alia, the tricky busi- ematical Society 45 Institute for Advanced Study. Typically, a Veblen Research Instructor will spend the first and third years of his/her appointment Mention for the Class of 1861 Prize, I trod ness of their political contributions. After (1974) and is now well teaching and conducting research in our department; the middle year is spent at the Institute without teaching duties. A Veblen a carefully planned career path from Har- Stanley Friedman (Koch’s deputy mayor in known to topologists as “The Perko Pair.” Research Instructor maintains offices in both institutions and is encouraged to participate in the mathematical life at each. vard Law School to a Wall Street law firm charge of everything, including the selec- I expect it’s the only thing about me that to a cushy corporate job and a comfortable tion of judges) went to jail, I could brag to will be remembered 50 years from now. Florian Sprung early retirement. My legal experience in- my boss that we hadn’t wasted a penny. Difficult as it may be for conspiracy theo- cluded off-the-record examination at State , elliptic curves, automorphic forms and My wife of 45 years is a Vassar-pedigreed, rists to believe, I am not the Kenneth Perko representations (exploring how families of special values of Department headquarters of secret cables Columbia-trained architect who worked that worked secretly for the Air Force on L-functions relate to families of algebraic objects.) from an ambassador discussing corporate for a world-class prima donna, job cap- stealth bombers, drones and the “star wars” bribery of a friendly foreign govern- Ph.D., Brown University (2013); M.Sc., The University of taining a small museum on Washington project, whose talk at Princeton was miss- Tokyo (2009); B.A., Columbia University (2006). ment—this notwithstanding my previous Square. We have two children, one of each attributed to me in our Class Notes on private tour of East Germany, arranged by traditional sex, and a grandson. When we page 33 of the February 9, 1994 PAW. its then foreign minister. My experience at give up our Scarsdale mini-estate it will be Princeton as Chairman of the largest stu- subdivided into three residential lots and dent social organization on campus (some a public cull-de-sac, to be named “Perko might say, anti-social) prepared me well for Court.” le

dealing with the sort of folks who run New fi York City, where I served as an officer of My second family is a collection of two- faced knots (with thin Khovanov homol- scores of subsidiaries of the corporate and Ana Caraiani partnership owners of Rockefeller Center ogy) the first of which is illustrated at page (Radio City Music Hall was the most fun), 263 of Proceedings of the American Math- , Representation Theory and Algebraic Geometry. Ph.D., Harvard University (2012); B.A. Summa cum Laude, Princeton University (2007). The famous Perko Knots National Science Foundation Postdoctoral Research Fellow, 2012-2015; L.E. Dickson Instructor, , 2012-2013. Knot tables Ana Caraiani (’07) works in algebraic num- gold medals in the International Math as a senior (2007), and the Miller Prize for Mathematicians started tabulating knots ber theory and specifically on the Lang- Olympiad). the best senior thesis (2007). After gradu- in the late 19th century and by the 1885 Junior faculty pro lands program. The As an undergraduate at Princeton she ating summa cum laude from Princeton Tait table listed all possible knots with is a vast network of meant to explored the different fields of mathemat- in 2007, she entered Harvard University build bridges between most areas of pure ics (such as analysis and topology) and es- where she studied under Richard Taylor up to 10 crossings. Contemporary tables mathematics, such as representation theory, *88. She was awarded a three-year NSF reach 16 crossings. pecially enjoyed the math reading courses algebraic geometry, and number theory. that allowed her to delve deeper into a research fellowship upon receiving her A knot table begins with the “unknot”, She is particularly interested in study- particular topic. Her first serious encoun- Ph.D. in 2012 and spent the first year of a simple circle, and continues with the ing geometric realizations of Langlands ter with number theory occurred through her fellowship as an L.E. Dickson Instruc- trefoil, the knot with three crossings and correspondences, in questions concerning her senior thesis under the guidance of tor at the University of Chicago. so on, with various numbers of knots of local-global compatibility and in p-adic Andrew Wiles, a great experience that Since returning to Princeton in September aspects of the Langlands program. She various crossings. convinced her to continue with number 2013, Caraiani has been partially support- recently worked on a project relating mod- theory in graduate school. What attracted ed by her NSF fellowship. This year, she A major difficulty for knot theorists ularity lifting theorems (i.e., the kinds of her most to number theory was that tools taught MAT 214: Numbers, Equations, and consists in establishing knot equivalence, theorems that led to the proof of Fermat’s from other fields have to be used—some- Proofs, an introduction to mathematical that is, to precisely determine when two last theorem) to local questions about the times unexpectedly—to solve problems. reasoning and proofs through elementary knots can be considered the same. The existence of certain p-adic Banach spaces. The Langlands program is precisely about number theory. She also taught MAT 419: accepted definition is that two knots are Caraiani was born in Romania. Her par- building connections between different Topics in Number Theory: Algebraic Num- equivalent if one can be transformed into ents are engineers who used to give her areas of mathematics. ber Theory, a course she designed to serve the other through ambient isotropy, a brainteasers as a child, which she always In addition to the prizes Caraiani received as an introduction to modular forms. type of deformation of R3 upon itself. enjoyed. When she was about 12 years old, before college, she also received numerous Caraiani will be spending the upcoming fall untangle all the knots, errors have contin- 10161 and 10162. These two knots be- she read a book about the recent proof departmental prizes including the Class of term at the Mathematical Science Research Two knots can be considered the same ued to hide in the tables and to be missed Perko Knots came the famous when our of Fermat’s last theorem and decided to 1861 Prize (2005), the Andrew H. Brown Institute (MSRI) in Berkeley, CA, and the if they can be deformed to result in by even the most experienced topologists. alumnus, Kenneth Perko, a lawyer at the become a mathematician. As a result, she Prize for outstanding work as a junior 2015-16 academic year at the Institute for identical knots. But, as even for experi- A famous case is that of the knots known in time, discovered in 1974 that they are in began training for and participating in a (2006), the Covington Prize for excellence Advanced Study. enced topologists it has not been easy to the Rolfsen’s table as knots numbers fact identical. number of math Olympiads (winning two page 14 page 3 Awards and recognition Events

Sun-Yung Alice Chang John Mather Sucharit Sarkar Advisory Council meeting Doctor Honoris Causa of Université 2014 Brouwer Prize CAREER Grant by the NSF Pierre et Marie Curie The award was presented at the Dutch Assistant Professor Sarkar was awarded the The Math Department’s Advisory Council faculty, senior faculty, staff members, as providing recommendations and giving This degree is a mark of honorary distinc- Mathematical Conference held on April grant March 2014. met April 17-18, 2014 for the first time well as the Chair of Physics, the Dean of their view of the state of the Department. tion given to a scientist; it honors not 16–17, 2014 at Delft University of Tech- The Faculty Early Career Development in seven years. The Council, chaired by the Graduate School and the Dean of the We are grateful to the Council for taking only the scientific excellence of men and nology. (CAREER) Program is a Foundation-wide Dr. Luisa Fernholz, consists of eight major Faculty. A dinner for the Advisory Council time from their extremely busy sched- women, all of whom are involved in the ad- activity that offers the National Science figures in and around Mathematics, includ- and faculty members was held on Thursday ules to focus on the improvement of the vancement of science, but also their com- Professor Mather was awarded this prize for work in the field of Dynamic Systems. Foundation’s most prestigious awards in ing four alumni (one of whom couldn’t evening, April 17th. Department. mitment to humanism and their contribu- support of junior faculty who exemplify make the meeting). They took a very close tion to the evolution of society as a whole. The award citation highlights his pio- The Council wrote a report for the De- neering work on the weak Kolmogorov- the role of teacher-scholars through out- look at the Department, meeting with partment and University Administration The award was presented at a ceremony Arnold-Moser theory and the theory of standing research, excellent education and undergraduates, graduate students, junior on November 13, 2013 at La Sorbonne in Arnold diffusion. the integration of education and research Paris. within the context of the mission of their organizations. Such activities should build a firm foundation for a lifetime of leader- David Gabai Sophie Morel ship in integrating education and research. Elected to the American Academy of Arts Microsoft Research Prize in Algebra and and Sciences Number Theory Professor David Gabai, Chair and Hughes This inaugural prize, awarded by the Asso- Peter Sarnak Rogers Professor of Mathematics, has been ciation for Women in Mathematics (AWM) Honorary degree Shandong University elected to the American Academy of Arts was presented at the Joint Mathematics A special Number Theory Conference to and Sciences. Meetings held in Baltimore, Maryland in honor Peter Sarnak was organized by the One of the nation’s most prestigious hon- January 2014. Shandong University during his visit to ac- orary societies, the Academy is also a lead- Established in 2012, this prize recognizes cept an honorary doctoral degree. ing center for independent policy research. exceptional research in algebra and num- The award ceremony, on January 7 2014, Members contribute to Academy publica- ber theory by a woman early in her career. was followed by three days of lectures tions and studies of science and technology The award is made possible by a generous focusing on research areas influenced by policy, energy and global security, social contribution from Microsoft Research. Its Sarnak’s work. Participating speakers policy and American institutions, and the biennial presentation serves to highlight came from the China, Canada, Hungary, humanities, arts, and education. outstanding contributions by women in the Israel and the USA. field of algebra and to advance the careers of the prize recipients.

From left to right, front row: Luisa Fernholz, Henry Laufer; back row: David Eisenbud, Elwyn Berlekamp, John Fry, Robert Fefferman, Elliott Lieb Benoît Pausader David Gabai (Chair of the Department), Flavio Bartmann. Foreign Member of the Royal Society Sloan Fellow Professor Elliott Lieb, professor of math- The Sloan Research Fellowships seek to ematics and Higgins professor of physics stimulate fundamental research by early-ca- at Princeton University, was elected to reer scientists and scholars of outstanding Yasha Sinai, right, celebrating the We are very grateful to our recent major donors: the Fellowship of the Royal Society as a Abel Prize with staff members, promise. They are awarded in recognition Scott Kenney, Special Projects Foreign Member on May 2, 2013. of distinguished performance and a unique Manager, and Carrie Heyer, The Fernholz Foundation for its gen- Bradford H. Arnold Jane H. Lukens W30 Assistant Business and Grants A bequest from the A bequest from Foreign Members are elected for life potential to make substantial contributions Manager. erous funding of the Minerva Lectures *42 and Mary Ellen Arnold Fellow- to establish the Jaywood Lukens ’30 through a peer review process on the basis to their field. and the Minerva Distinguished Visiting ship Fund to provide financial assistance Scholarship Fund for undergraduate of excellence in science. Each year 8 new Professor program and its support of our to selected graduate students studying in scholarships in memory of her husband, Foreign Members are elected by existing graduate program. the mathematics department. Jaywood Lukens, “for whom mathematics Fellows. There are currently about 140 was fundamental in his profession as an Foreign Members. actuary and for whom mathematics ‘was The Class of 1971 Endowed Fund The Wei-Tong Shu *90 Fellowship always fun.’” for Mathematics for discretionary Fund to provide financial assistance to support to strengthen the mission of the Math Department graduate students. Department of Mathematics.

page 4 page 13 Events Awards and recognition

The International Mathematical Union Executive Committee meeting NSF Mathematical Yakov Sinai Senior facultypro Sciences The International Mathematical Union responsible for organizing the International also awards a number of scientific prizes, Yakov Grigorevich Sinai was born in Moscow, Russia. His grandfather, Veniamin Kagan, (IMU) is an international scientific organi- Congress of Mathematicians, held every including the Fields Medals. The Executive Postdoctoral Research was a geometer, and his parents were prominent researchers in the medical and biologi- zation whose purpose is promoting inter- four years; the next ICM will be held in Committee of the IMU met in Fine Hall Fellowships cal sciences. He received his Ph.D. degree from . Prior to his national cooperation in mathematics. It is Seoul, South Korea in August 2014. IMU March 7–8, 2014. Princeton appointment, he held combined positions at Moscow State University and the Landau Institute of Theoretical Physics of the Russian Academy of Sciences. Sinai was Allison Miller Aaron Pollack elected as a foreign associate of the National Academy of Sciences and as a foreign mem- ber of the Academy of Arts and Sciences in the United States. He is a full member of the Russian Academy of Sciences, the Brazilian Academy of Science, the Hungarian Academy of Science, the Polish Academy of Science, and Academia Europea as well as being recently elected as a foreign member of the Royal Society in London. In addition to these honors, fi Sinai was awarded the Boltzmann Medal (1986), the Dannie Heineman Prize (1990), the le Dirac Prize (1992), the Wolf Prize in Mathematics (1997), the Nemmer Prize (2002), and the Henri Poincáre Prize (2009). In addition to the recent Abel Prize, Sinai’s great contributions to mathematical physics were rewarded with the Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society at the Joint Mathematics Meetings in San Diego, California in 2013. The prize was awarded to Sinai for “his pivotal role in shaping the theory of dynamical Shrenik Shah Bohua Zhan systems and for his groundbreaking contributions to , , statistical mechanics, and mathematical physics.” The overwhelming influence of Sinai’s work over the past fifty years was also noted in the citation, with reference to his more than 250 research papers, several books, and his supervision of more than 50 doctoral students, many of whom have become leaders in the field in their own right. Sinai joined the Princeton faculty as a full professor in 1993 and has taught classes in Prob- ability Theory and Random Processes. He served on the editorial board for the for ten years and currently serves on the editorial boards for the Journal in Statistical Physics and the Journal in Probability Theory and its Applications. Sinai’s current research is on mathematical fluid dynamics and ergodic theory. He and From left to right: John Toland, Sylwia Markwardt, Vasudevan Srinivas, Manuel de Léon, Cheryl Praeger, , Marcelo Viana, Yiming Long, Dong Li *06 recently constructed a new theory showing the appearance of new vortices Christiane Rousseau, Laszló Lovász, Alexander Mielke, Ingrid Daubechies, Martin Grötschel. Not pictured: Peter Olver, Hyungju Park The purpose of the Mathematical Sci- as well as the merging and splitting of the vortices. They also developed a version of the ences Postdoctoral Research Fellowships Renormalization Group Method. This indicates a possibility of constructing new types of (MSPRF) is to support future leaders in solutions to equations of fluid dynamics. Sinai’s work with Francesco Cellarosi *11 con- mathematics and statistics by facilitating tains new results about the ergodic properties of the Moebius function and the methods Robert F. Coleman *79, died of a Since 1994, with the support of the NSF, the Institute for Advanced Study, together with their participation in postdoctoral research they’ve developed have direct implications to several classical problems of number theory. heart attack on March 24, 2014. He was Princeton University, has hosted an intensive eleven-day mentoring program for under- environments that will have maximal im- Sinai currently teaches a popular graduate seminar in Ergodic Theory and Statistical 59 years old. graduate, graduate, and postdoctoral women in mathematics. pact on their future scientific development. Mechanics using the textbook he co-authored with Leonid Korvalov (“Probability Theory, Coleman was a mathematics professor The program brings Awards will support research in areas of Random Processes and Random Fields,” published by Springer-Verlag in 2007). at the University of California, Berkeley together research math- mathematics and statistics, including appli- since 1983. His research dealt primar- ematicians with students cations to other disciplines. ily with number theory, p-adic analysis, and postdocs on the and . He received a MacArthur Fellowship in 1987. campus of the Institute and is designed to ad- Princeton Graduate School Coleman had been diagnosed with Mul- dress issues of gender Teaching Award tiple Schlerosis almost thirty years ago imbalance in mathemat- and was well-known for his good humor, Thomas Beck has been selected as one of 5 ics. Activities include fearlessness, and his ability to overcome Teaching Award recipients for 2014. The lectures and seminars difficult circumstances. He leaves behind awards were presented at the annual Trib- on a focused mathemati- his wife, Tessa Drake-Coleman, sister ute to Teaching reception on April 29. Y. Sinai, the Norwegian Rosalind, and brother Mark. A memorial cal topic, mentoring, consul, Zenia Chrysos- discussions on peer rela- Each winner will receive $1,000. tomidis and students at service will take place from 2-4 p.m. on celebratory party for the Saturday, May 31, 2014 at the Bancroft tions, an introduction The annual Teaching Awards are sponsored Able Prize in Fine Hall. Hotel in Berkeley, California. to career opportunities, by the Graduate School and selected by Photo by John Jameson. and a Women-in-Science Dean of the Graduate School and the As- seminar. sociate Dean for Academic Affairs. page 12 page 5 Teaching Awards Graduate news Teaching awards recognize excellence in teaching at the undergraduate level. Selection for both awards was made by a committee of senior faculty members.

Junior Faculty Teaching Graduate Teaching This is the fi rst year of the “Department of Mathematics Junior Faculty Teaching Award.” The This is the second year of the “Department recipients are Jonathan Fickenscher and Luc Nguyen. of Mathematics Graduate Teaching Award.” Last year, it was awarded to Daniel Shenfeld. This year’s recipients are Owen Biesel and Andrew Manion. Owen received his Ph.D. in June; Andy is a current graduate student. Selection for both awards was made by a committee of senior faculty members. From the director of The Graduate Open House March 2014 graduate studies Alexandru Ionescu

From left to right: The Open House is our annual event for of outstanding applicants. The incoming It has been a privilege serving as a direc- Jonathan Fickenscher students admitted to the Ph.D program graduate students form a group with varied tor of graduate studies again this year. Our Luc Nguyen Andrew Manion to check out the Department and speak research interests and national back- graduate program continues to grow: we to faculty and graduate students in order grounds: the international cohort includes are expecting a new class of 19 students to help form their final decision on what students from Australia, China, Germany, in Fall 2014, one of the largest classes in graduate program to attend. Greece, India, Italy, Korea, Russia and recent years. The Graduate School has Jonathan Fickenscher Owen Biesel This year again, our department had the South Africa. been, again, very supportive at all stages of selection and recruitment, and I am In the course he developed and taught for difficult task of choosing from a large pool The nominations remarked that Fick- The nominations high- looking forward to collaborating with them the Freshmen Scholars Institute, which has enscher is “a versatile teacher” and “an lighted Biesel’s commitment to teach- again next year. especially insightful, judicious and gener- become the cornerstone of the Institute’s ing and dedication to his students and ous colleague” who has worked “tirelessly” effort to prepare students for the complex his”excellent pedagogical instincts” and and with “patient enthusiasm and care” for problem solving required in Princeton’s “talent for communicating love of mathe- his students (and fellow instructors!) and freshman math, chemistry, and physics matics to students who come to the subject that, as one student wrote, his “ dedica- curriculum, he has engaged students with a with very little confidence or enthusiasm.” tion to teaching is phenomenal.” He has teaching style described as “ lively,” “acces- his course evaluations for MAT 100 far inspired students to do their best to meet sible,” “helpful,” and even “amazing.” exceeded those of past instructors in a his uncompromising expectations in math similar course. Students comented that he courses at all levels made “math fun and easy to understand” and that he was “an exceptional professor” Luc Nguyen who “helped to challenge us, encouraged tor-- one of the best instructors I’ve had in participation, responded to all questions, The nominations remarked that he is “an and offered help outside of class” and “nice, my 4 years at Princeton.” Complex Analysis exceptionally skilled teacher” who “views funny, and overall interesting” his teaching as an important service, and ”Luc rocks. At first I was intimidated by takes his responsibilities to the students, the math symbols I didn’t understand and Andrew Manion the department and other instructors very I didn’t understand why things needed seriously.” Students from the courses he has proving- they seemed true and that was Manion was commended for skill and taught during his time at Princeton said the enough for me. But later I came to abso- effectiveness in teaching. He “was truly following: lutely love his teaching. Best math teacher exceptional, easily surpassing the perfor- “Luc is a fantastic teacher and is always I’ve had. Also, super funny, made class mance of dedicated teachers with much willing to do whatever is necessary to help enjoyable. And fun to hangout with and more experience” and his course evalua- his students succeed. I wish he could be my very approachable in office hours.” Complex tions were among the highest ever obtained math teacher for EVERY MATH CLASS!” Calc II Analysis by an instructor in the first-year courses taught in the Princeton Mathematics ”Professor Nguyen was able to make even ”The quality of the class was awesome. He Department. Students commented that he a topic as obscure as multivariable calculus made the class laugh and comfortable. He was “an awesome teacher,“ “honestly, the sound relevant, practical, and interesting.... told jokes and got the class involved. Even best math professor I have ever had in my l also admired his ability to throw in a joke better than that, he taught the course quite life,” and “one of my favorite professors this and get the whole class laughing when the well.” Calc II semester and just a generally cool guy.” topics were getting tricky or boring.” Calc II ”Prof Nguyen was an outstanding instruc- page 6 page 11 Undergraduate news Awards

A treasure trove: The Math Club Princeton Summer Awards presented on Class Day 2013 AlexanderAlexander IIrizariza namednamed Our department has a precious resource and listening to a talk on A Recipe on Pi by Math Research SalutatorianSalutatorian in the The Princeton Undergraduate Math Visiting Professor William Dunham. from the Guide for Math Students pub- Evgeni Simeonov Dimitrov Irene Ilias Giechaskiel Andy Zhu lished online by the Princeton Math Club and and recipients Mathematics major Alex Club, a well organized and very dynamic Yuan Lo George B. Peter A. Greenberg ’77 Prize The club also holds the Princeton Univer- recipients of the 2013 of the 2013 Iriza ‘14 was named student-run group that has managed to Covington Prize in Mathematics sity Mathematics Competition (PUMaC) The summer program at Princeton funds awarded awarded for outstanding accomplishments this year’s Salutatorian. provide a variety of activities and useful every year. Participants are high school eight weeks of on-campus mathematical for excellence in mathematics. in mathematics information to the undergraduate math Iriza will graduate with a students from around the country and also research and/or guided independent study. certificate in the Program community. around the world, including countries such Any eight weeks during the summer will Ashwath Rabindranath and Maxim Rabi- Ante Qu ’15 and Alexander Smith ’15 for Applied and Compu- Its activities include: as Bulgaria and China. do, provided you can make arrangements tational Mathematics, and to work with your adviser during that pe- novich recipients of the 2013 Middleton recipients of the 2013 Class of 1861 Prize • undergraduate colloquia (weekly) The Princeton Undergraduate Math Club Miller ’29 Prize awarded for the best inde- awarded to sophomores who received the will return to Princeton in the fall to pursue • riod; they do not even have to be contigu- a masters degree in computer science. board game nights, (biweekly) has recently compiled a comprehensive ous, so you could for instance, work for pendent work in mathematics. highest scores on the Putnam Examination. • field trips (e.g. to the Museum of Math) Guide for Math Students intended for four weeks in June, then leave for a couple He is also a recipient of the 2013 Andrew • meet-your-professor lunches undergraduates interested in mathematics. of weeks and return to finish the program H. Brown Prize awarded to an outstanding The Guide includes an extensive Course The advising program Mentoring Moebius, in mid-July. Over the past two years, the junior in mathematics as well as the Man- Guide, as well as sections on Summer described in our first newsletter, is also run program has provided $4000 stipends to Teaching in the Freshman Scholars Program fred Pyka Memorial Prize in Physics. Iriza Opportunities, Undergraduate Research, by the Club. approximately 10 math majors; rising ju- by Jon Fickenscher received the Shapiro Prize for Academic Combining Math with Other Subjects Excellence twice. In the past year, the club members collabo- niors and seniors are given preference, but (including Computer Science, Economics, rising sophomores are often accepted. For the past two summers, I have enjoyed rated with Princeton Public Library in or- Finance), Applied Math, Club Academic teaching Problem Solving in Mathematics, The Salutatorian is the second highest ganizing the Mercer County Math Circle, Events, and Club Social Events. The Princeton program differs from REUs a quantitative component of the Freshman ranked student in a class (the first being the an approximately biweekly event that in several respects. Primarily, it offers sig- Scholars Institute (FSI) program. The six- valedictorian). Traditionally, the Salutato- consists of talks for high nificant scope for choice: you can choose week course is a fast-paced experience that rian gives the first speach at a graduation, school and middle school to work on whatever kind of project exposes incoming freshmen to topics rang- a salutation. Because Princeton tradition requires that the salutation be delivered in http://blogs.princeton.edu/mathclub students in the area. interests you, provided you can find a ing from calculus to differential equations. supervisor. This means you can work on a We focus on intuition to develop concepts, Latin, the Salutatorian is most often a clas- This year, the club hosted sics major. a special Pi Day celebra- project that would simply not be offered at as intuition is a universal aid in mathemati- tion on 3/14, which in- an REU. Moreover, while this is not always cal reasoning at any level. Students who Iriza studied Latin in high school and earned volved eating a lot of pies, the case, particularly if you participate in continue to hone their intuition in future a perfect score on the National Latin Exam one of the top REUs, REUs generally focus mathematics courses at Princeton in ad- and a bronze medal at the International on areas slightly outside the mainstream dition to enjoying academic success, find Olympiad in Linguistics. At Princeton, he and problems that require relatively little their coursework more enlightening. continued his interest in the Latin language specialized knowledge. The result is that by taking classic Roman literature courses. an REU experience, particularly early The program curriculum has been refined in your undergraduate career, will likely from year to year. This coming summer, we are happy to retain last year’s format be more of an opportunity to focus on a Eugene Katsevich has been named a 2014 single, specific problem than a way to learn for the six-week course, spending roughly two weeks each on limits/continuity, Hertz Fellow. Katsevich will receive a sti- mathematics that you’re likely to use in the pend and full tuition for graduate school, future. In contrast, the Princeton program differentiation and applications to higher mathematics. Between three weekly lec- and will begin his Ph.D. studies at Stanford represents a chance to build significant in the fall. foundational knowledge in a specific area, tures and lunch “office hours” in the dining which is particularly useful if you wish to hall, FSI instructors get to spend signifi- great apprehension; they feel they are less for her guidance. I will remain apprecia- pursue research in it. cantly more time with students per week than during a regular semester. prepared than some of their classmates. tive to Scott Kenney for bringing this pro- However, by the end of FSI, background gram to my attention during my first year This program admits students with widely takes a back seat to the work accomplished at Princeton as well as his general encour- diverse backgrounds, and I enjoy hear- in the course itself. It is very rewarding agement. Furthermore, I am grateful to ing about their experiences. One student to watch students’ confidence and ability Professors Gabai and Kollár, and Dr. John- came from a high school with a graduating The official website of Princeton Univer- grow in such a short span of time. son, and Dean McKay for the opportunity class size of about twenty, and he had to sity Mathematics Competition (PUMaC) to welcome members of the class of 2018 essentially teach himself calculus. Other I am thankful to Diane McKay, the Direc- among other valuable information contains to Princeton life this coming summer. We students already attended full calculus tor of FSI and Associate Dean of the Col- the problem sets of past competitions have a dynamic and eager group of faculty courses that banned the use of calculators lege, for placing her trust in me regarding and graduate students involved, and I am (typically, the lack of calculators comes this course and to Dr. Jennifer Johnson, http://pumac.princeton.edu excited to work with them and provide as a shock to incoming students). Many the Associate Departmental Representative these students with this unique Princeton students enter the program expressing and a Senior Lecturer in our department, The PUMaC team experience. page 10 page 7 The Minerva Program Administrative staff changes

The second year of a successful program Will Crow Ben Rose Michelle Matel Faculty Assistant Systems Manager Assistant to the Chair/ Assistant to the De- Naor, a professor at the Courant Institute Okounkov, a professor at Columbia Uni- Will began as a tem- Ben Rose trasferred to partment Manager of Mathematical Sciences, New York Uni- versity, joined the Princeton Mathematics porary employee in our department from versity, was this year’s Minerva Lecturer. Department for the spring semester as the our department in the a similar position in A new position was cre- His research interests are analysis, prob- The Minerva Program, started in the inaugural Minerva Distinguished Visitor, spring of 2013. He be- the Computer Science ated to further assist the ability, quantitative geometry, and appli- academic year 2012-2013, continued and delivered a series of 10 lectures on came a permanent staff Department. Chair and the Depart- cations of these to combinatorics, math- this year with lectures by two distin- “Quantum groups and quantum cohomol- member in November, ment Manager. Michelle guished mathematicians: Ben received a B.S. in Matel joined us in ematical physics and theoretical computer ogy”. 2013 and can be found Computer Science from Stevens Institute in the front reception area on the third July 2013, having worked previously in a science. Okounkov works on representation theory of Technology, where he developed a Linux floor. Will has a B.A. in Philosophy, which similar position in Boston College’s Math- Naor presented three lectures on the fol- Andrei and its applications to algebraic geometry, distribution used by faculty researchers. he obtained at Davidson College in North ematics Department. lowing topics: “An introduction to the Ribe Assaf Naor Okounkov mathematical physics, probability theory A summer internship in the networking Carolina. He spent a post-baccalaureate program,” “Dichotomies and universality and special functions. In 2006, he received department at the Institute for Advanced Michelle has a B.A. (Michigan State year studying environmental biology at in metric embeddings” and “Super-expand- the “for his contributions to Study in Princeton led to a full-time job University) and an M.A. (Stanford Univer- Columbia University. ers and nonlinear spectral calculus.” bridging probability, representation theory there. sity) in Economics. She taught economics Will’s duties in the Math Department ( and Miami University A Czech-Israeli citizen, Naor obtained his and algebraic geometry.” Ben oversees the large Fine Hall network include updating our departmental website, in Oxford, Ohio) and worked in a variety undergraduate and graduate degrees from Okounkov was a professor at Princeton (shared by the Math Department and the arranging travel reservations and reim- of positions, including in the Admissions the Hebrew University in Jerusalem. He University from 2002 to 2010, an assistant Program in Applied and Computational bursements, and assisting the faculty as Office for Lasell College and as Assistant to completed his Ph.D. thesis, titled “Linear and associate professor at the University of Mathematics, also housed in Fine Hall). needed. Will’s computer skills serve him the Chair at Boston College. and Non-Linear Geometric Problems in California, Berkeley, and an instructor at His basic responsibilities are also to ensure well and he enjoys the challenge of creat- Banach Spaces,” under the supervision of the University of Chicago. that all of the users’ IT needs are met. He Michelle’s responsibilities include assisting ing highly-technical mathematical docu- . has a particular interest in Linux and enjoys the Chair with his scheduling and cor- ments by using the programs he has taught working with colleagues on the Springdale respondence, assisting the Department Assaf Naor will become a permanent himself. Linux project, a clone recompile of Red Manager with faculty reports and appoint- member of our faculty this summer. Will was born and raised in New York City Hat Enterprise Linux. ments, as well as assisting various faculty and currently lives with his partner, Amy, in members on different projects. Videos of the lectures are now available at https://www.math.princeton.edu/media/videos Ben was born and raised in NJ and cur- Yardley, PA. rently lives in Lawrenceville, NJ, with his She was born in Michigan, and currently fiancée. lives in Hillsborough, New Jersey, with her husband and their son. The “Math Guy” at Fine Hall! Alberta Molnar Business and Grants Manager Keith Devlin, Visiting Professor of

le Alberta joined the Math Department as ciliation. She serves systems and tools beginning in July, 2014. Distinguished Teaching fi our Grants Manager in September, 2010. as the departmental Alberta has especially enjoyed working Professor Devlin is Executive Director of She was promoted to Business and Grants liaison with Univer- with new faculty and helping them to, as Stanford’s H-STAR institute, a co-founder of Manager in March, 2013. Prior to coming sity research admin- she puts it, “navigate the waters” with rules the Stanford Media Xresearch network, and to Princeton, Alberta worked at Rutgers istration and other and regulations that we are required to fol- a Senior Researcher at CSLI. He is a World University for 23 years as an accountant offices as well. Her low. She works diligently with our faculty Economic Forum Fellow, a Fellow of the Staff pro in University Accounting and then as the attention to detail members to assist them with their initial American Association for the Advancement Business Manager at the Waksman Institute and strong financial grant applications and to monitor the grant of Science, and a Fellow of the American for Molecular Biology. She graduated from background have once it is awarded. Her bookkeeping skills tion, and mathematical cognition. He has This spring Professor Devlin is teaching Mathematical Society. His current research Douglass College as a music major—first made her an outstanding steward of our fi- and attention to detail are two assets she written 32 books and over 80 published Math 198, Useful Fictions: How and why is focused on the use of different media to as a piano major and then as a harpsichord nancial resources and she works to ensure readily shares with the department and the research articles. Recipient of the Pythago- mathematics is developed and then changes teach and communicate mathematics to major—and attended graduate school in departmental compliance and to communi- Math Department appreciates the dedica- ras Prize, the Peano Prize, the Carl Sagan the world. This course will combine Pro- diverse audiences. In this connection, he is music history (again as a harpsichord ma- cate clearly with faculty about grant and de- tion she brings with her to every task she Award, and the Joint Policy Board for fessor Devlin’s online course, Introduction a co-founder and President of an educa- jor) at as well. partmental financial matters. In recogniz- accomplishes. Mathematics Communications Award, in to Mathematical Thinking, with classroom tional video games company, InnerTube As the Business and Grants Manager for ing her strong abilities, the University asked Alberta is a New Jersey native proudly de- 2003, he was recognized by the California discussion to provide a view of mathemat- Games. He also works on the design of our department, Alberta is responsible for Alberta to serve on the “Academic Prime scended from several generations of Hun- State Assembly for his “innovative work and ics as a living, growing, creative human information/reasoning systems for intel- all grant-related issues including preparing Connect Group” for Princeton Prime and garian folk musicians. She has been married longtime service in the fi eld of mathematics and endeavor that classifies as both as a science ligence analysis. Other research interests grant submissions to federal agencies and Concur, which will implement a new chart to her husband, Emil, for 30 years. In ad- its relation to logic and linguistics.” He is “the and an art. include: theory of information, models of outside foundations; grant transfers to and of accounts, enhance reporting and business dition to playing her harpsichord, she also Math Guy” on National Public Radio. reasoning, applications of mathematical from other universities; approval of grant processes throughout the Princeton cam- does needlework and is an avid gardener. techniques in the study of communica- expenses; budgeting, and account recon- pus, and upgrade all University financial Keith Devlin’s course Mathematics: Making the Invisible Visible is available on YouTube page 8 page 9 The Minerva Program Administrative staff changes

The second year of a successful program Will Crow Ben Rose Michelle Matel Faculty Assistant Systems Manager Assistant to the Chair/ Assistant to the De- Naor, a professor at the Courant Institute Okounkov, a professor at Columbia Uni- Will began as a tem- Ben Rose trasferred to partment Manager of Mathematical Sciences, New York Uni- versity, joined the Princeton Mathematics porary employee in our department from versity, was this year’s Minerva Lecturer. Department for the spring semester as the our department in the a similar position in A new position was cre- His research interests are analysis, prob- The Minerva Program, started in the inaugural Minerva Distinguished Visitor, spring of 2013. He be- the Computer Science ated to further assist the ability, quantitative geometry, and appli- academic year 2012-2013, continued and delivered a series of 10 lectures on came a permanent staff Department. Chair and the Depart- cations of these to combinatorics, math- this year with lectures by two distin- “Quantum groups and quantum cohomol- member in November, ment Manager. Michelle guished mathematicians: Ben received a B.S. in Matel joined us in ematical physics and theoretical computer ogy”. 2013 and can be found Computer Science from Stevens Institute in the front reception area on the third July 2013, having worked previously in a science. Okounkov works on representation theory of Technology, where he developed a Linux floor. Will has a B.A. in Philosophy, which similar position in Boston College’s Math- Naor presented three lectures on the fol- Andrei and its applications to algebraic geometry, distribution used by faculty researchers. he obtained at Davidson College in North ematics Department. lowing topics: “An introduction to the Ribe Assaf Naor Okounkov mathematical physics, probability theory A summer internship in the networking Carolina. He spent a post-baccalaureate program,” “Dichotomies and universality and special functions. In 2006, he received department at the Institute for Advanced Michelle has a B.A. (Michigan State year studying environmental biology at in metric embeddings” and “Super-expand- the Fields Medal “for his contributions to Study in Princeton led to a full-time job University) and an M.A. (Stanford Univer- Columbia University. ers and nonlinear spectral calculus.” bridging probability, representation theory there. sity) in Economics. She taught economics Will’s duties in the Math Department (Stanford University and Miami University A Czech-Israeli citizen, Naor obtained his and algebraic geometry.” Ben oversees the large Fine Hall network include updating our departmental website, in Oxford, Ohio) and worked in a variety undergraduate and graduate degrees from Okounkov was a professor at Princeton (shared by the Math Department and the arranging travel reservations and reim- of positions, including in the Admissions the Hebrew University in Jerusalem. He University from 2002 to 2010, an assistant Program in Applied and Computational bursements, and assisting the faculty as Office for Lasell College and as Assistant to completed his Ph.D. thesis, titled “Linear and associate professor at the University of Mathematics, also housed in Fine Hall). needed. Will’s computer skills serve him the Chair at Boston College. and Non-Linear Geometric Problems in California, Berkeley, and an instructor at His basic responsibilities are also to ensure well and he enjoys the challenge of creat- Banach Spaces,” under the supervision of the University of Chicago. that all of the users’ IT needs are met. He Michelle’s responsibilities include assisting ing highly-technical mathematical docu- Joram Lindenstrauss. has a particular interest in Linux and enjoys the Chair with his scheduling and cor- ments by using the programs he has taught working with colleagues on the Springdale respondence, assisting the Department Assaf Naor will become a permanent himself. Linux project, a clone recompile of Red Manager with faculty reports and appoint- member of our faculty this summer. Will was born and raised in New York City Hat Enterprise Linux. ments, as well as assisting various faculty and currently lives with his partner, Amy, in members on different projects. Videos of the lectures are now available at https://www.math.princeton.edu/media/videos Ben was born and raised in NJ and cur- Yardley, PA. rently lives in Lawrenceville, NJ, with his She was born in Michigan, and currently fiancée. lives in Hillsborough, New Jersey, with her husband and their son. The “Math Guy” at Fine Hall! Alberta Molnar Business and Grants Manager Keith Devlin, Visiting Professor of

le Alberta joined the Math Department as ciliation. She serves systems and tools beginning in July, 2014. Distinguished Teaching fi our Grants Manager in September, 2010. as the departmental Alberta has especially enjoyed working Professor Devlin is Executive Director of She was promoted to Business and Grants liaison with Univer- with new faculty and helping them to, as Stanford’s H-STAR institute, a co-founder of Manager in March, 2013. Prior to coming sity research admin- she puts it, “navigate the waters” with rules the Stanford Media Xresearch network, and to Princeton, Alberta worked at Rutgers istration and other and regulations that we are required to fol- a Senior Researcher at CSLI. He is a World University for 23 years as an accountant offices as well. Her low. She works diligently with our faculty Economic Forum Fellow, a Fellow of the Staff pro in University Accounting and then as the attention to detail members to assist them with their initial American Association for the Advancement Business Manager at the Waksman Institute and strong financial grant applications and to monitor the grant of Science, and a Fellow of the American for Molecular Biology. She graduated from background have once it is awarded. Her bookkeeping skills tion, and mathematical cognition. He has This spring Professor Devlin is teaching Mathematical Society. His current research Douglass College as a music major—first made her an outstanding steward of our fi- and attention to detail are two assets she written 32 books and over 80 published Math 198, Useful Fictions: How and why is focused on the use of different media to as a piano major and then as a harpsichord nancial resources and she works to ensure readily shares with the department and the research articles. Recipient of the Pythago- mathematics is developed and then changes teach and communicate mathematics to major—and attended graduate school in departmental compliance and to communi- Math Department appreciates the dedica- ras Prize, the Peano Prize, the Carl Sagan the world. This course will combine Pro- diverse audiences. In this connection, he is music history (again as a harpsichord ma- cate clearly with faculty about grant and de- tion she brings with her to every task she Award, and the Joint Policy Board for fessor Devlin’s online course, Introduction a co-founder and President of an educa- jor) at Rutgers University as well. partmental financial matters. In recogniz- accomplishes. Mathematics Communications Award, in to Mathematical Thinking, with classroom tional video games company, InnerTube As the Business and Grants Manager for ing her strong abilities, the University asked Alberta is a New Jersey native proudly de- 2003, he was recognized by the California discussion to provide a view of mathemat- Games. He also works on the design of our department, Alberta is responsible for Alberta to serve on the “Academic Prime scended from several generations of Hun- State Assembly for his “innovative work and ics as a living, growing, creative human information/reasoning systems for intel- all grant-related issues including preparing Connect Group” for Princeton Prime and garian folk musicians. She has been married longtime service in the fi eld of mathematics and endeavor that classifies as both as a science ligence analysis. Other research interests grant submissions to federal agencies and Concur, which will implement a new chart to her husband, Emil, for 30 years. In ad- its relation to logic and linguistics.” He is “the and an art. include: theory of information, models of outside foundations; grant transfers to and of accounts, enhance reporting and business dition to playing her harpsichord, she also Math Guy” on National Public Radio. reasoning, applications of mathematical from other universities; approval of grant processes throughout the Princeton cam- does needlework and is an avid gardener. techniques in the study of communica- expenses; budgeting, and account recon- pus, and upgrade all University financial Keith Devlin’s course Mathematics: Making the Invisible Visible is available on YouTube page 8 page 9 Undergraduate news Awards

A treasure trove: The Math Club Princeton Summer Awards presented on Class Day 2013 AlexanderAlexander IIrizariza namednamed Our department has a precious resource and listening to a talk on A Recipe on Pi by Math Research SalutatorianSalutatorian in the The Princeton Undergraduate Math Visiting Professor William Dunham. from the Guide for Math Students pub- Evgeni Simeonov Dimitrov Irene Ilias Giechaskiel Andy Zhu lished online by the Princeton Math Club and and recipients Mathematics major Alex Club, a well organized and very dynamic Yuan Lo George B. Peter A. Greenberg ’77 Prize The club also holds the Princeton Univer- recipients of the 2013 of the 2013 Iriza ‘14 was named student-run group that has managed to Covington Prize in Mathematics sity Mathematics Competition (PUMaC) The summer program at Princeton funds awarded awarded for outstanding accomplishments this year’s Salutatorian. provide a variety of activities and useful every year. Participants are high school eight weeks of on-campus mathematical for excellence in mathematics. in mathematics information to the undergraduate math Iriza will graduate with a students from around the country and also research and/or guided independent study. certificate in the Program community. around the world, including countries such Any eight weeks during the summer will Ashwath Rabindranath and Maxim Rabi- Ante Qu ’15 and Alexander Smith ’15 for Applied and Compu- Its activities include: as Bulgaria and China. do, provided you can make arrangements tational Mathematics, and to work with your adviser during that pe- novich recipients of the 2013 Middleton recipients of the 2013 Class of 1861 Prize • undergraduate colloquia (weekly) The Princeton Undergraduate Math Club Miller ’29 Prize awarded for the best inde- awarded to sophomores who received the will return to Princeton in the fall to pursue • riod; they do not even have to be contigu- a masters degree in computer science. board game nights, (biweekly) has recently compiled a comprehensive ous, so you could for instance, work for pendent work in mathematics. highest scores on the Putnam Examination. • field trips (e.g. to the Museum of Math) Guide for Math Students intended for four weeks in June, then leave for a couple He is also a recipient of the 2013 Andrew • meet-your-professor lunches undergraduates interested in mathematics. of weeks and return to finish the program H. Brown Prize awarded to an outstanding The Guide includes an extensive Course The advising program Mentoring Moebius, in mid-July. Over the past two years, the junior in mathematics as well as the Man- Guide, as well as sections on Summer described in our first newsletter, is also run program has provided $4000 stipends to Teaching in the Freshman Scholars Program fred Pyka Memorial Prize in Physics. Iriza Opportunities, Undergraduate Research, by the Club. approximately 10 math majors; rising ju- by Jon Fickenscher received the Shapiro Prize for Academic Combining Math with Other Subjects Excellence twice. In the past year, the club members collabo- niors and seniors are given preference, but (including Computer Science, Economics, rising sophomores are often accepted. For the past two summers, I have enjoyed rated with Princeton Public Library in or- Finance), Applied Math, Club Academic teaching Problem Solving in Mathematics, The Salutatorian is the second highest ganizing the Mercer County Math Circle, Events, and Club Social Events. The Princeton program differs from REUs a quantitative component of the Freshman ranked student in a class (the first being the an approximately biweekly event that in several respects. Primarily, it offers sig- Scholars Institute (FSI) program. The six- valedictorian). Traditionally, the Salutato- consists of talks for high nificant scope for choice: you can choose week course is a fast-paced experience that rian gives the first speach at a graduation, school and middle school to work on whatever kind of project exposes incoming freshmen to topics rang- a salutation. Because Princeton tradition requires that the salutation be delivered in http://blogs.princeton.edu/mathclub students in the area. interests you, provided you can find a ing from calculus to differential equations. supervisor. This means you can work on a We focus on intuition to develop concepts, Latin, the Salutatorian is most often a clas- This year, the club hosted sics major. a special Pi Day celebra- project that would simply not be offered at as intuition is a universal aid in mathemati- tion on 3/14, which in- an REU. Moreover, while this is not always cal reasoning at any level. Students who Iriza studied Latin in high school and earned volved eating a lot of pies, the case, particularly if you participate in continue to hone their intuition in future a perfect score on the National Latin Exam one of the top REUs, REUs generally focus mathematics courses at Princeton in ad- and a bronze medal at the International on areas slightly outside the mainstream dition to enjoying academic success, find Olympiad in Linguistics. At Princeton, he and problems that require relatively little their coursework more enlightening. continued his interest in the Latin language specialized knowledge. The result is that by taking classic Roman literature courses. an REU experience, particularly early The program curriculum has been refined in your undergraduate career, will likely from year to year. This coming summer, we are happy to retain last year’s format be more of an opportunity to focus on a Eugene Katsevich has been named a 2014 single, specific problem than a way to learn for the six-week course, spending roughly two weeks each on limits/continuity, Hertz Fellow. Katsevich will receive a sti- mathematics that you’re likely to use in the pend and full tuition for graduate school, future. In contrast, the Princeton program differentiation and applications to higher mathematics. Between three weekly lec- and will begin his Ph.D. studies at Stanford represents a chance to build significant in the fall. foundational knowledge in a specific area, tures and lunch “office hours” in the dining which is particularly useful if you wish to hall, FSI instructors get to spend signifi- great apprehension; they feel they are less for her guidance. I will remain apprecia- pursue research in it. cantly more time with students per week than during a regular semester. prepared than some of their classmates. tive to Scott Kenney for bringing this pro- However, by the end of FSI, background gram to my attention during my first year This program admits students with widely takes a back seat to the work accomplished at Princeton as well as his general encour- diverse backgrounds, and I enjoy hear- in the course itself. It is very rewarding agement. Furthermore, I am grateful to ing about their experiences. One student to watch students’ confidence and ability Professors Gabai and Kollár, and Dr. John- came from a high school with a graduating The official website of Princeton Univer- grow in such a short span of time. son, and Dean McKay for the opportunity class size of about twenty, and he had to sity Mathematics Competition (PUMaC) to welcome members of the class of 2018 essentially teach himself calculus. Other I am thankful to Diane McKay, the Direc- among other valuable information contains to Princeton life this coming summer. We students already attended full calculus tor of FSI and Associate Dean of the Col- the problem sets of past competitions have a dynamic and eager group of faculty courses that banned the use of calculators lege, for placing her trust in me regarding and graduate students involved, and I am (typically, the lack of calculators comes this course and to Dr. Jennifer Johnson, http://pumac.princeton.edu excited to work with them and provide as a shock to incoming students). Many the Associate Departmental Representative these students with this unique Princeton students enter the program expressing and a Senior Lecturer in our department, The PUMaC team experience. page 10 page 7 Teaching Awards Graduate news Teaching awards recognize excellence in teaching at the undergraduate level. Selection for both awards was made by a committee of senior faculty members.

Junior Faculty Teaching Graduate Teaching This is the fi rst year of the “Department of Mathematics Junior Faculty Teaching Award.” The This is the second year of the “Department recipients are Jonathan Fickenscher and Luc Nguyen. of Mathematics Graduate Teaching Award.” Last year, it was awarded to Daniel Shenfeld. This year’s recipients are Owen Biesel and Andrew Manion. Owen received his Ph.D. in June; Andy is a current graduate student. Selection for both awards was made by a committee of senior faculty members. From the director of The Graduate Open House March 2014 graduate studies Alexandru Ionescu

From left to right: The Open House is our annual event for of outstanding applicants. The incoming It has been a privilege serving as a direc- Jonathan Fickenscher students admitted to the Ph.D program graduate students form a group with varied tor of graduate studies again this year. Our Luc Nguyen Andrew Manion to check out the Department and speak research interests and national back- graduate program continues to grow: we to faculty and graduate students in order grounds: the international cohort includes are expecting a new class of 19 students to help form their final decision on what students from Australia, China, Germany, in Fall 2014, one of the largest classes in graduate program to attend. Greece, India, Italy, Korea, Russia and recent years. The Graduate School has Jonathan Fickenscher Owen Biesel This year again, our department had the South Africa. been, again, very supportive at all stages of selection and recruitment, and I am In the course he developed and taught for difficult task of choosing from a large pool The nominations remarked that Fick- The nominations high- looking forward to collaborating with them the Freshmen Scholars Institute, which has enscher is “a versatile teacher” and “an lighted Biesel’s commitment to teach- again next year. especially insightful, judicious and gener- become the cornerstone of the Institute’s ing and dedication to his students and ous colleague” who has worked “tirelessly” effort to prepare students for the complex his”excellent pedagogical instincts” and and with “patient enthusiasm and care” for problem solving required in Princeton’s “talent for communicating love of mathe- his students (and fellow instructors!) and freshman math, chemistry, and physics matics to students who come to the subject that, as one student wrote, his “ dedica- curriculum, he has engaged students with a with very little confidence or enthusiasm.” tion to teaching is phenomenal.” He has teaching style described as “ lively,” “acces- his course evaluations for MAT 100 far inspired students to do their best to meet sible,” “helpful,” and even “amazing.” exceeded those of past instructors in a his uncompromising expectations in math similar course. Students comented that he courses at all levels made “math fun and easy to understand” and that he was “an exceptional professor” Luc Nguyen who “helped to challenge us, encouraged tor-- one of the best instructors I’ve had in participation, responded to all questions, The nominations remarked that he is “an and offered help outside of class” and “nice, my 4 years at Princeton.” Complex Analysis exceptionally skilled teacher” who “views funny, and overall interesting” his teaching as an important service, and ”Luc rocks. At first I was intimidated by takes his responsibilities to the students, the math symbols I didn’t understand and Andrew Manion the department and other instructors very I didn’t understand why things needed seriously.” Students from the courses he has proving- they seemed true and that was Manion was commended for skill and taught during his time at Princeton said the enough for me. But later I came to abso- effectiveness in teaching. He “was truly following: lutely love his teaching. Best math teacher exceptional, easily surpassing the perfor- “Luc is a fantastic teacher and is always I’ve had. Also, super funny, made class mance of dedicated teachers with much willing to do whatever is necessary to help enjoyable. And fun to hangout with and more experience” and his course evalua- his students succeed. I wish he could be my very approachable in office hours.” Complex tions were among the highest ever obtained math teacher for EVERY MATH CLASS!” Calc II Analysis by an instructor in the first-year courses taught in the Princeton Mathematics ”Professor Nguyen was able to make even ”The quality of the class was awesome. He Department. Students commented that he a topic as obscure as multivariable calculus made the class laugh and comfortable. He was “an awesome teacher,“ “honestly, the sound relevant, practical, and interesting.... told jokes and got the class involved. Even best math professor I have ever had in my l also admired his ability to throw in a joke better than that, he taught the course quite life,” and “one of my favorite professors this and get the whole class laughing when the well.” Calc II semester and just a generally cool guy.” topics were getting tricky or boring.” Calc II ”Prof Nguyen was an outstanding instruc- page 6 page 11 Events Awards and recognition

The International Mathematical Union Executive Committee meeting NSF Mathematical Yakov Sinai Senior facultypro Sciences The International Mathematical Union responsible for organizing the International also awards a number of scientific prizes, Yakov Grigorevich Sinai was born in Moscow, Russia. His grandfather, Veniamin Kagan, (IMU) is an international scientific organi- Congress of Mathematicians, held every including the Fields Medals. The Executive Postdoctoral Research was a geometer, and his parents were prominent researchers in the medical and biologi- zation whose purpose is promoting inter- four years; the next ICM will be held in Committee of the IMU met in Fine Hall Fellowships cal sciences. He received his Ph.D. degree from Moscow State University. Prior to his national cooperation in mathematics. It is Seoul, South Korea in August 2014. IMU March 7–8, 2014. Princeton appointment, he held combined positions at Moscow State University and the Landau Institute of Theoretical Physics of the Russian Academy of Sciences. Sinai was Allison Miller Aaron Pollack elected as a foreign associate of the National Academy of Sciences and as a foreign mem- ber of the Academy of Arts and Sciences in the United States. He is a full member of the Russian Academy of Sciences, the Brazilian Academy of Science, the Hungarian Academy of Science, the Polish Academy of Science, and Academia Europea as well as being recently elected as a foreign member of the Royal Society in London. In addition to these honors, fi Sinai was awarded the Boltzmann Medal (1986), the Dannie Heineman Prize (1990), the le Dirac Prize (1992), the Wolf Prize in Mathematics (1997), the Nemmer Prize (2002), and the Henri Poincáre Prize (2009). In addition to the recent Abel Prize, Sinai’s great contributions to mathematical physics were rewarded with the Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society at the Joint Mathematics Meetings in San Diego, California in 2013. The prize was awarded to Sinai for “his pivotal role in shaping the theory of dynamical Shrenik Shah Bohua Zhan systems and for his groundbreaking contributions to ergodic theory, probability theory, statistical mechanics, and mathematical physics.” The overwhelming influence of Sinai’s work over the past fifty years was also noted in the citation, with reference to his more than 250 research papers, several books, and his supervision of more than 50 doctoral students, many of whom have become leaders in the field in their own right. Sinai joined the Princeton faculty as a full professor in 1993 and has taught classes in Prob- ability Theory and Random Processes. He served on the editorial board for the Annals of Mathematics for ten years and currently serves on the editorial boards for the Journal in Statistical Physics and the Journal in Probability Theory and its Applications. Sinai’s current research is on mathematical fluid dynamics and ergodic theory. He and From left to right: John Toland, Sylwia Markwardt, Vasudevan Srinivas, Manuel de Léon, Cheryl Praeger, Wendelin Werner, Marcelo Viana, Yiming Long, Dong Li *06 recently constructed a new theory showing the appearance of new vortices Christiane Rousseau, Laszló Lovász, Alexander Mielke, Ingrid Daubechies, Martin Grötschel. Not pictured: Peter Olver, Hyungju Park The purpose of the Mathematical Sci- as well as the merging and splitting of the vortices. They also developed a version of the ences Postdoctoral Research Fellowships Renormalization Group Method. This indicates a possibility of constructing new types of (MSPRF) is to support future leaders in solutions to equations of fluid dynamics. Sinai’s work with Francesco Cellarosi *11 con- mathematics and statistics by facilitating tains new results about the ergodic properties of the Moebius function and the methods Robert F. Coleman *79, died of a Since 1994, with the support of the NSF, the Institute for Advanced Study, together with their participation in postdoctoral research they’ve developed have direct implications to several classical problems of number theory. heart attack on March 24, 2014. He was Princeton University, has hosted an intensive eleven-day mentoring program for under- environments that will have maximal im- Sinai currently teaches a popular graduate seminar in Ergodic Theory and Statistical 59 years old. graduate, graduate, and postdoctoral women in mathematics. pact on their future scientific development. Mechanics using the textbook he co-authored with Leonid Korvalov (“Probability Theory, Coleman was a mathematics professor The program brings Awards will support research in areas of Random Processes and Random Fields,” published by Springer-Verlag in 2007). at the University of California, Berkeley together research math- mathematics and statistics, including appli- since 1983. His research dealt primar- ematicians with students cations to other disciplines. ily with number theory, p-adic analysis, and postdocs on the and arithmetic geometry. He received a MacArthur Fellowship in 1987. campus of the Institute and is designed to ad- Princeton Graduate School Coleman had been diagnosed with Mul- dress issues of gender Teaching Award tiple Schlerosis almost thirty years ago imbalance in mathemat- and was well-known for his good humor, Thomas Beck has been selected as one of 5 ics. Activities include fearlessness, and his ability to overcome Teaching Award recipients for 2014. The lectures and seminars difficult circumstances. He leaves behind awards were presented at the annual Trib- on a focused mathemati- his wife, Tessa Drake-Coleman, sister ute to Teaching reception on April 29. Y. Sinai, the Norwegian Rosalind, and brother Mark. A memorial cal topic, mentoring, consul, Zenia Chrysos- discussions on peer rela- Each winner will receive $1,000. tomidis and students at service will take place from 2-4 p.m. on celebratory party for the Saturday, May 31, 2014 at the Bancroft tions, an introduction The annual Teaching Awards are sponsored Able Prize in Fine Hall. Hotel in Berkeley, California. to career opportunities, by the Graduate School and selected by Photo by John Jameson. and a Women-in-Science Dean of the Graduate School and the As- seminar. sociate Dean for Academic Affairs. page 12 page 5 Awards and recognition Events

Sun-Yung Alice Chang John Mather Sucharit Sarkar Advisory Council meeting Doctor Honoris Causa of Université 2014 Brouwer Prize CAREER Grant by the NSF Pierre et Marie Curie The award was presented at the Dutch Assistant Professor Sarkar was awarded the The Math Department’s Advisory Council faculty, senior faculty, staff members, as providing recommendations and giving This degree is a mark of honorary distinc- Mathematical Conference held on April grant March 2014. met April 17-18, 2014 for the first time well as the Chair of Physics, the Dean of their view of the state of the Department. tion given to a scientist; it honors not 16–17, 2014 at Delft University of Tech- The Faculty Early Career Development in seven years. The Council, chaired by the Graduate School and the Dean of the We are grateful to the Council for taking only the scientific excellence of men and nology. (CAREER) Program is a Foundation-wide Dr. Luisa Fernholz, consists of eight major Faculty. A dinner for the Advisory Council time from their extremely busy sched- women, all of whom are involved in the ad- activity that offers the National Science figures in and around Mathematics, includ- and faculty members was held on Thursday ules to focus on the improvement of the vancement of science, but also their com- Professor Mather was awarded this prize for work in the field of Dynamic Systems. Foundation’s most prestigious awards in ing four alumni (one of whom couldn’t evening, April 17th. Department. mitment to humanism and their contribu- support of junior faculty who exemplify make the meeting). They took a very close tion to the evolution of society as a whole. The award citation highlights his pio- The Council wrote a report for the De- neering work on the weak Kolmogorov- the role of teacher-scholars through out- look at the Department, meeting with partment and University Administration The award was presented at a ceremony Arnold-Moser theory and the theory of standing research, excellent education and undergraduates, graduate students, junior on November 13, 2013 at La Sorbonne in Arnold diffusion. the integration of education and research Paris. within the context of the mission of their organizations. Such activities should build a firm foundation for a lifetime of leader- David Gabai Sophie Morel ship in integrating education and research. Elected to the American Academy of Arts Microsoft Research Prize in Algebra and and Sciences Number Theory Professor David Gabai, Chair and Hughes This inaugural prize, awarded by the Asso- Peter Sarnak Rogers Professor of Mathematics, has been ciation for Women in Mathematics (AWM) Honorary degree Shandong University elected to the American Academy of Arts was presented at the Joint Mathematics A special Number Theory Conference to and Sciences. Meetings held in Baltimore, Maryland in honor Peter Sarnak was organized by the One of the nation’s most prestigious hon- January 2014. Shandong University during his visit to ac- orary societies, the Academy is also a lead- Established in 2012, this prize recognizes cept an honorary doctoral degree. ing center for independent policy research. exceptional research in algebra and num- The award ceremony, on January 7 2014, Members contribute to Academy publica- ber theory by a woman early in her career. was followed by three days of lectures tions and studies of science and technology The award is made possible by a generous focusing on research areas influenced by policy, energy and global security, social contribution from Microsoft Research. Its Sarnak’s work. Participating speakers policy and American institutions, and the biennial presentation serves to highlight came from the China, Canada, Hungary, humanities, arts, and education. outstanding contributions by women in the Israel and the USA. field of algebra and to advance the careers of the prize recipients.

From left to right, front row: Luisa Fernholz, Henry Laufer; back row: David Eisenbud, Elwyn Berlekamp, John Fry, Robert Fefferman, Elliott Lieb Benoît Pausader David Gabai (Chair of the Department), Flavio Bartmann. Foreign Member of the Royal Society Sloan Fellow Professor Elliott Lieb, professor of math- The Sloan Research Fellowships seek to ematics and Higgins professor of physics stimulate fundamental research by early-ca- at Princeton University, was elected to reer scientists and scholars of outstanding Yasha Sinai, right, celebrating the We are very grateful to our recent major donors: the Fellowship of the Royal Society as a Abel Prize with staff members, promise. They are awarded in recognition Scott Kenney, Special Projects Foreign Member on May 2, 2013. of distinguished performance and a unique Manager, and Carrie Heyer, The Fernholz Foundation for its gen- Bradford H. Arnold Jane H. Lukens W30 Assistant Business and Grants A bequest from the A bequest from Foreign Members are elected for life potential to make substantial contributions Manager. erous funding of the Minerva Lectures *42 and Mary Ellen Arnold Fellow- to establish the Jaywood Lukens ’30 through a peer review process on the basis to their field. and the Minerva Distinguished Visiting ship Fund to provide financial assistance Scholarship Fund for undergraduate of excellence in science. Each year 8 new Professor program and its support of our to selected graduate students studying in scholarships in memory of her husband, Foreign Members are elected by existing graduate program. the mathematics department. Jaywood Lukens, “for whom mathematics Fellows. There are currently about 140 was fundamental in his profession as an Foreign Members. actuary and for whom mathematics ‘was The Class of 1971 Endowed Fund The Wei-Tong Shu *90 Fellowship always fun.’” for Mathematics for discretionary Fund to provide financial assistance to support to strengthen the mission of the Math Department graduate students. Department of Mathematics.

page 4 page 13 From our alumni Faculty appointments

Untangling laws and knots a letter from Kenneth Perko ‘64 Veblen Research Instructors The Veblen Research Instructorships are joint 3-year appointments between our department and the School of Mathematics at the A mathematics major receiving Honorable supervising, inter alia, the tricky busi- ematical Society 45 Institute for Advanced Study. Typically, a Veblen Research Instructor will spend the first and third years of his/her appointment Mention for the Class of 1861 Prize, I trod ness of their political contributions. After (1974) and is now well teaching and conducting research in our department; the middle year is spent at the Institute without teaching duties. A Veblen a carefully planned career path from Har- Stanley Friedman (Koch’s deputy mayor in known to topologists as “The Perko Pair.” Research Instructor maintains offices in both institutions and is encouraged to participate in the mathematical life at each. vard Law School to a Wall Street law firm charge of everything, including the selec- I expect it’s the only thing about me that to a cushy corporate job and a comfortable tion of judges) went to jail, I could brag to will be remembered 50 years from now. Florian Sprung early retirement. My legal experience in- my boss that we hadn’t wasted a penny. Difficult as it may be for conspiracy theo- cluded off-the-record examination at State Iwasawa theory, elliptic curves, automorphic forms and My wife of 45 years is a Vassar-pedigreed, rists to believe, I am not the Kenneth Perko representations (exploring how families of special values of Department headquarters of secret cables Columbia-trained architect who worked that worked secretly for the Air Force on L-functions relate to families of algebraic objects.) from an ambassador discussing corporate for a world-class prima donna, job cap- stealth bombers, drones and the “star wars” bribery of a friendly foreign govern- Ph.D., Brown University (2013); M.Sc., The University of taining a small museum on Washington project, whose talk at Princeton was miss- Tokyo (2009); B.A., Columbia University (2006). ment—this notwithstanding my previous Square. We have two children, one of each attributed to me in our Class Notes on private tour of East Germany, arranged by traditional sex, and a grandson. When we page 33 of the February 9, 1994 PAW. its then foreign minister. My experience at give up our Scarsdale mini-estate it will be Princeton as Chairman of the largest stu- subdivided into three residential lots and dent social organization on campus (some a public cull-de-sac, to be named “Perko might say, anti-social) prepared me well for Court.” le

dealing with the sort of folks who run New fi York City, where I served as an officer of My second family is a collection of two- faced knots (with thin Khovanov homol- scores of subsidiaries of the corporate and Ana Caraiani partnership owners of Rockefeller Center ogy) the first of which is illustrated at page (Radio City Music Hall was the most fun), 263 of Proceedings of the American Math- Algebraic Number Theory, Representation Theory and Algebraic Geometry. Ph.D., Harvard University (2012); B.A. Summa cum Laude, Princeton University (2007). The famous Perko Knots National Science Foundation Postdoctoral Research Fellow, 2012-2015; L.E. Dickson Instructor, University of Chicago, 2012-2013. Knot tables Ana Caraiani (’07) works in algebraic num- gold medals in the International Math as a senior (2007), and the Miller Prize for Mathematicians started tabulating knots ber theory and specifically on the Lang- Olympiad). the best senior thesis (2007). After gradu- in the late 19th century and by the 1885 Junior faculty pro lands program. The Langlands program As an undergraduate at Princeton she ating summa cum laude from Princeton Tait table listed all possible knots with is a vast network of conjectures meant to explored the different fields of mathemat- in 2007, she entered Harvard University build bridges between most areas of pure ics (such as analysis and topology) and es- where she studied under Richard Taylor up to 10 crossings. Contemporary tables mathematics, such as representation theory, *88. She was awarded a three-year NSF reach 16 crossings. pecially enjoyed the math reading courses algebraic geometry, and number theory. that allowed her to delve deeper into a research fellowship upon receiving her A knot table begins with the “unknot”, She is particularly interested in study- particular topic. Her first serious encoun- Ph.D. in 2012 and spent the first year of a simple circle, and continues with the ing geometric realizations of Langlands ter with number theory occurred through her fellowship as an L.E. Dickson Instruc- trefoil, the knot with three crossings and correspondences, in questions concerning her senior thesis under the guidance of tor at the University of Chicago. so on, with various numbers of knots of local-global compatibility and in p-adic Andrew Wiles, a great experience that Since returning to Princeton in September aspects of the Langlands program. She various crossings. convinced her to continue with number 2013, Caraiani has been partially support- recently worked on a project relating mod- theory in graduate school. What attracted ed by her NSF fellowship. This year, she A major difficulty for knot theorists ularity lifting theorems (i.e., the kinds of her most to number theory was that tools taught MAT 214: Numbers, Equations, and consists in establishing knot equivalence, theorems that led to the proof of Fermat’s from other fields have to be used—some- Proofs, an introduction to mathematical that is, to precisely determine when two last theorem) to local questions about the times unexpectedly—to solve problems. reasoning and proofs through elementary knots can be considered the same. The existence of certain p-adic Banach spaces. The Langlands program is precisely about number theory. She also taught MAT 419: accepted definition is that two knots are Caraiani was born in Romania. Her par- building connections between different Topics in Number Theory: Algebraic Num- equivalent if one can be transformed into ents are engineers who used to give her areas of mathematics. ber Theory, a course she designed to serve the other through ambient isotropy, a brainteasers as a child, which she always In addition to the prizes Caraiani received as an introduction to modular forms. type of deformation of R3 upon itself. enjoyed. When she was about 12 years old, before college, she also received numerous Caraiani will be spending the upcoming fall untangle all the knots, errors have contin- 10161 and 10162. These two knots be- she read a book about the recent proof departmental prizes including the Class of term at the Mathematical Science Research Two knots can be considered the same ued to hide in the tables and to be missed Perko Knots came the famous when our of Fermat’s last theorem and decided to 1861 Prize (2005), the Andrew H. Brown Institute (MSRI) in Berkeley, CA, and the if they can be deformed to result in by even the most experienced topologists. alumnus, Kenneth Perko, a lawyer at the become a mathematician. As a result, she Prize for outstanding work as a junior 2015-16 academic year at the Institute for identical knots. But, as even for experi- A famous case is that of the knots known in time, discovered in 1974 that they are in began training for and participating in a (2006), the Covington Prize for excellence Advanced Study. enced topologists it has not been easy to the Rolfsen’s table as knots numbers fact identical. number of math Olympiads (winning two page 14 page 3 Faculty appointments Recent Ph .D.s

Our most recent Ph.Ds theirthesesandwheretheytheir advisors, went Princeton after Assistant Professors Instructors Boris Alexeev Sung-Jin Oh J. Conway S. Klainerman An assortment of results in Finite energy global well-posedness of the Adam Levine Antonio Ache Steven Sivek combinatorics and compressed sensing. (3+1)-dimensional Yang-Mills equations Topology (specifically: the study of proper- Conformal Geometry, Differential Low-dimensional Topology (with a special Voleon Capital Management, CA, using a novel Yang-Mills heat flow gauge. ties and applications of Heegaard Floer Geometry, Partial Differential Equations. focus on contact and symplectic geometry, Senior Research Scientist. UC Berkeley-Miller Institute, Postdoc. homology). Ph.D., University of Wisconsin, Madison Floer homology theories, and knot theory.) Ali Altug Nicolas Reichert Ph.D. (2010); M.Phil. (2008); M.A. (2012); B.S., Universidad Simón Bolívar, Ph.D., Massachusetts Institute of Technol- P. Sarnak A. Chang Caracas, Venezuela (2005). ogy (2011); S.B. in Computer Science and Analysis experiments with the trace Some results on a full nonlinear equation (2006), Columbia University; A.B. magna National Science Foundation Postdoctoral Engineering, MIT (2006). National Science formula. Columbia University, Postdoc. in Conformal Geometry. University of cum laude, Harvard University (2005). Research Fellow, 2012-2014; Postdoctoral Foundation Postdoctoral Research Fellow, Washington, Acting Assistant Professor. National Science Foundation Postdoctoral Owen Biesel Research Fellow/NSF Postdoctoral Fellow, 2012-2015; Postdoctoral Fellow, Harvard M. Bhargava Rodolfo Rios Zertuche Research Fellow, 2010-2013. Princeton University (2012-2013). University (2011-2013). Galois closures for rings. Leiden A. Okounkov Lecturer/NSF Postdoctoral Fellow, University, Postdoc. Near-involutions, the Pillowcase Brandeis University (2012-2013). Distribution, and Quadratic Differentials. Yaim Cooper Princeton University, Lecturer; Fall ’13: R. Pandharipande Brown University-ICERM; 2014: Max The geometry of stable quotients in genus Planck Institute for Mathematics, Postdoc. one. Harvard University, NSF Postdoc. Samuel Ruth Gabriele DiCerbo M. Bhargava J. Kollár A bound on the average rank of Effectiveness boundedness results in j-Invariant zero elliptic curves. Princeton algebraic and analytic geometry. Columbia University, Lecturer; Bloomberg, NY, University, Postdoc. Software Engineer. Mohammad Farajzadeh Tehrani Giulia Saccà G. Tian G. Tian On moduli spaces of real curves in Fibrations in Abelian varieties associated symplectic manifolds. Cornell University, to Enriques surfaces. SUNY/Stony Brook, Visiting Assistant Professor. Postdoc. Kevin Hughes Arul Shankar E. Stein M. Bhargava Arithmetic analogues in harmonic analysis: Geometry of numbers methods for global Results related to Waring’s problem. fields. IAS, Member (1 year); Harvard Benoit Pausader Javier Gómez Serrano administrative positions 2013-2014 University of Edinburgh, Postdoc. University, Postdoc. Philip Isett Analysis (partial differential equations Analysis. Hydrodynamics of Incompressible Daniel Shenfeld S, Klainerman and their interactions with physics and Fluids. A. Okounkov Chair: David Gabai Hölder continuous Euler flows with Abelianization of stable envelopes in geometry). Ph.D., Universidad Autónoma de Madrid Associate Chair: János Kollár compact support in time. MIT, C.L.E. symplectic resolutions. GNS Healthcare, Chargé de recherche, CNRS, U. Paris 13 (2013); M.S., Universidad Autónoma de Directors of Graduate Study: Moore Instructor. Cambridge, MA, Director of Machine Madrid (2010). Dual degrees in mathemat- Alex Ionescu and Nicolas Templier Learning (2012); Visiting Researcher, Princeton Uni- Junehyuk Jung ics and engineering from the Universidad Department Representative: János Kollár versity (2011); Courant Instructor, New P. Sarnak Politécnica de Cataluña, Spain. Associate Department Representative: Kevin Wilson York University (2011); Assistant Profes- Jennifer Johnson On the zeros of automorphic forms. Re- M. Bhargava sor, Brown University (2008); Senior Advisor: John Mather quired South Korea Military Service. Three perspectives on n points P^{n-2}. Knewton, NY, Data Scientist. Assistant moniteur normalien, Junior Advisor: Tasho Kaletha Michael McBreen Cergy-Pontoise University (2006). Placement Officer: Vlad Vicol A. Okounkov Guangbo Xu Department Manager: Kathleen Applegate Quantum cohomology of hypertoric G. Tian Graduate Administrator: Jill LeClair varieties and geometric representations of Symplectic vortex equation and adiabatic Undergraduate Administrator: LeeAnn Coleman Yangians. MIT, Instructor, Postdoc. limits.UC Irvine, Postdoc.

YoungHan Park Shiwu Yang, I. Rodnianski Image by Rob Scharein using the P. Sarnak software KnotPlot (knotplot.com) Nonlinear wave equations on time Hyperbolic hypergeometric dependent inhomogeneous backgrounds. monodromy groups and geometric University of Cambridge, Postdoc. finiteness. WorldQuant, VP of Research. page 2 page 15 Spring 2014 Issue 3 Department of Mathematics Department of Mathematics Princeton University Fine Hall, Washington Rd. Princeton, NJ 08544

Department Chair’s letter The department is continuing its period of Assistant to the Chair and to the Depart- transition and renewal. Although long- ment Manager, and Will Crow as Faculty The Wolf time faculty members John Conway and Assistant. The uniform opinion of the Ed Nelson became emeriti last July, we faculty and staff is that we made great Prize for look forward to many years of Ed being choices. Peter amongst us and for John continuing to hold Among major faculty honors Alice Chang Sarnak court in his “office” in the nook across from became a member of the Academia Sinica, Professor Peter Sarnak will be awarded this the common room. We are extremely Elliott Lieb became a Foreign Member of year’s Wolf Prize in Mathematics. delighted that Fernando Coda Marques and the Royal Society, John Mather won the The prize is awarded annually by the Wolf Assaf Naor (last Fall’s Minerva Lecturer) Brouwer Prize, Sophie Morel won the in- Foundation in the fields of agriculture, will be joining us as full professors in augural AWM-Microsoft Research prize in chemistry, mathematics, medicine, physics, Alumni , faculty, students, friends, connect with us, write to us at September. Algebra and Number Theory, Peter Sarnak and the arts. The award will be presented Our finishing graduate students did very won the Wolf Prize, and Yasha Sinai the by Israeli President Shimon Peres on June [email protected] well on the job market with four win- Abel Prize. 1st at the Knesset. ning NSF postdoctoral fellowships. Andy The upcoming International Congress of Other Princeton current and past faculty- Manion and Owen Biesel won departmen- Mathematicians in Seoul, Korea will be who received the prize are: John Milnor tal graduate student teaching awards, and well represented by Princeton faculty. (1989), Andrew Wiles (1995), Yakov Sinai Jon Fickenscher and Luc Nguyen won the Manjul Bhargava, János Kollár and Fernan- (1996), and Elias Stein (1999). inaugural junior faculty teaching awards for do Coda Marques will be plenary speak- their excellent work as instructors. Gradu- ers, and Mihalis Dafermos, Sasha Sodin For the full citation, go to: www.wolffund.org.il ate student Tom Beck won a teaching award and Mark Braverman (Computer Science) from the Graduate School. will be invited sectional speakers. Mihalis Adam Levine and Benoît Pausader joined is one of very few invited to speak in two The happy participants in the new course, History of Mathematics, introduced in the fall of 2013, and taught by Michael Barany and Christopher Skinner. us as assistant professors this year, with sections (PDEs and Mathematical Physics). Benoît winning a Sloan Foundation fel- Sasha and Mark will be respectively speak- lowship. Tasho Kaletha also became a new ing in mathematical physics and theoretical assistant professor, being promoted from computer science. The Abel Math and music: our annual recital Veblen Research Instructor. Ana Caraiani We initiated the Minerva Distinguished and Florian Sprung joined us as Veblen In- Visitor program, welcoming back Andre Prize for structors. Javier Gómez Serrano and Steve Okounkov from Columbia, who gave a se- Yakov Thanks to the efforts of our Graduate This year’s performers were: Sivek joined us as instructors, and Jonathan Administrator, Jill LeClair, the members ries of 10 lectures. We thank the Fernholz Sinai Tim Brown (piano) Kommemi as an NSF postdoctoral research Foundation for making this possible. of our department and their friends and fellow. Assistant Professor Sucharit Sarkar Laurent Côté ’14 (violin) The Abel Prize, established in 2001 by the families had the opportunity to enjoy was awarded an NSF Career Grant. I’d like to thank Bob and Luisa Fernholz, Norwegian government and named after another delightful afternoon of music. Matthew de Courcy-Ireland, graduate the Class of 1971, Wei-Tong Shu, and the The Department has had excellent rela- Norwegian mathematician Niels Henrik The recital took place on May 8 in Taplin student (piano) Arnold and Lukens families for their very Abel (1802-1829) is presented annually by tions with the Institute for Advanced Study. generous support. Auditorium and was followed, as usual, by Mark McConnell, lecturer, (baritone) Its faculty frequently give courses and the King of Norway to one or more out- a well attended reception in the Common Being surrounded by exceptional col- Isabelle Nogues ’15 (violin) advise our graduate students. To formalize standing mathematicians.The six million Room. this connection, Jean Bourgain, Helmut leagues totally committed to their re- Norwegian krones prize will be awarded to Florian Sprung, Veblen instructor (ban- Many thanks also to our musicians, who Hofer, Robert MacPherson and Richard search, mentoring and teaching missions, Sinai at a special ceremony in Oslo on May doneón) Jill LeClair took time to prepare and play for us Taylor were named Visiting Lecturers with immensely talented graduate students 20th, in recognition of his status as one of despite the demands of thesis writing and Ryan Peckner, graduate student (piano) Rank of Professor. playfully pushing themselves mathemati- the most influential mathematicians of the cally, and very gifted undergraduates trying 20th century and for his “fundamental con- approaching exams. Feng Zhu ’14 (piano) Essential to the functioning of the Depart- to figure out how they will change the tributions to dynamical systems, ergodic and ment is having excellent staff members. world is both an awesome and humbling theory, and mathematical physics.” Following careful searches we welcomed experience. Join us next year in the Minh-Tam Trinh ’14 (piano) For the full citation, go to: www.abelprize.no Ben Rose (from Computer Science) as our David Gabai *77, *80, Chair audience or on stage! new systems manager, Michelle Matel as [email protected]