Spring 2016 Issue 5 Department of

Letter From the Chair Celebrating the Lives of John and Alicia Nash We cannot look back on the past Returning from one of the crowning year without first commenting on achievements of a long and storied the tragic loss of John and Alicia career, John Forbes Nash, Jr. and Nash, who died in a car accident on his wife Alicia were killed in a car their way home from the airport last accident on May 23, 2015, shock- May. They were returning from ing the department, the University, Norway, where John Nash was and making headlines around the awarded the 2015 from world. the Norwegian Academy of Sci- ence and Letters. As a 1994 Nobel Nash came to Princeton as a gradu- Prize winner and a senior research ate student in 1948. His Ph.D. thesis, in our department “Non-cooperative games” (Annals for many years, Nash maintained a of Mathematics, Vol 54, No. 2, 286- steady presence in Fine Hall, and he 95) became a seminal work in the and Alicia are greatly missed. Their then-fledgling field of game theory, life and work was celebrated during and laid the path for his 1994 Nobel a special event in October. Memorial Prize in Economics. After finishing his Ph.D. in 1950, Nash This has been a very busy and pro- held positions at the Massachusetts ductive year for our department, and Institute of Technology and the In- we have happily hosted conferences stitute for Advanced Study, where 1950s Nash began to suffer from and workshops that have attracted the breadth of his work increased. paranoid schizophrenia, which per- (and Princeton He was always known for apply- sisted for the next three decades. As alumni) from around the world. ing novel approaches to the hardest the subject of Sylvia Nasar’s biog- problems, and throughout the early raphy, A Beautiful Mind, and the Since the fall, we have honored Pro- 1950s his research extended to the 2001 film of the same name, Nash fessors John Conway, Yasha Sinai, fields of partial differential - equa became far more than an influential and on the occa- tions and geometric analysis. For mathematician; he became a symbol sion of their birthdays and to mark these contributions, Nash shared of hope and an inspiration for those their great contributions to their the 2015 Abel Prize with Louis Ni- suffering from schizophrenia and respective fields. We also hosted renberg. for their loved ones. Nash’s story the 31st Annual goes from the peaks of academic in April and have the annual visit “I think he prided himself that achievement to the valley of despair, of the “Women and Mathematics he had his way of thinking about yet he managed to overcome his Program” (co-sponsored with the things,” recounts Professor David condition. After receiving the Nobel Institute for Advanced Study) and Gabai *80. “He was such an ex- Prize, he returned to Princeton in a workshop in traordinary exemplar of the things 1995 as a senior research mathema- taking place this May. Significant that this department strives for. Be- tician, where he remained a regular mathematics are discussed and cel- yond great originality, he demon- fixture in Fine Hall until his death. ebrated at these events, which also strated tremendous tenacity, cour- provide us with the opportunity age and fearlessness.” Professor Sergiu Klainerman: “We to see the familiar faces of former all miss him. It was not just the leg- graduate students and junior facul- Were Nash’s story solely that of end behind him. He was a very, very ty who are now well-established in his mathematical achievements, nice person to have around. He was their various fields. it would be amazing enough. Un- very kind, very thoughtful, very fortunately, beginning in the mid- Continued on next page... Continued on next page... Page 1 Nash ...continued from previous page From the Chair ...continued from previous page considerate and humble. All that contributed to his legacy We take pride in the awards bestowed upon our col- in the department. The fact that he was always present in leagues, alumni, and students. Professor Emeritus the department, I think that by itself was very moving. was recently awarded the 2016 Abel It’s an example that stim- Prize by the Norwegian government, a prize that was ulated people, especially awarded to Professor in 2014 and John students. He was an in- Nash in 2015. Professor Christopher Skinner was a spiring figure to have recipient of a highly-prestigious Simons Investigator around, just being there award. Professor Fernando Codá Marques (together and showing his dedica- with our former Assistant Professor André Neves) tion to mathematics.” received the Oswald Veblen Prize in Geometry from the American Mathematical Society. Stefanos Are- To honor and celebrate takis, an assistant professor in our department, was the lives of John and awarded one of 20 Alfred P. Sloan Research Fellow- Alicia Nash, the depart- ships for 2016, as was graduate alumni Elena Fuchs ment hosted an all-day *10, who is now an assistant professor of mathemat- event on October 24, ics at the University of Illinois, Urbana-Champaign. 2015. There were lec- tures on Nash’s work and In October we recognized some of our outstanding its legacy by Nobel Prize teachers by awarding departmental teaching awards winning economist Eric to assistant professors Adam Levine and Javier Gó- shares remebrances at Maskin (Harvard), Pro- mez Serrano, and graduate student Gregory Gauth- the University Chapel fessor Sergiu Klainer- ier. man (Princeton), Abel Prize recipient Mikhail Gromov (IHES), and Professor This is the end of my term as an Acting Chair of the János Kollár (Princeton); a talk by Nasar on the lives Department. Our chair, Professor , has of John and Alicia Nash; and a memorial service at the been on a very well-deserved hiatus at the Institute University Chapel. for Advanced Study, enjoying once again his life as a full-time professional mathematician. David will be Over 600 people attended the service at the Chapel where returning for his second term as Chair next year. It family, friends and colleagues of the Nashes shared their has been my privilege to work with my colleagues, remembrances. Remarks were given on behalf of Presi- the University’s Administration and our amazing dent Eisgruber by Robert Durkee, Vice President and staff on continuing the tradition of excellence in our Secretary of the University, followed by Kirsti Strøm department. Bull, President of the Norwegian Academy of Science and Letters; Louis Nirenburg, who shared the 2015 Abel It is my pleasure to thank Bob and Louisa Fernholz, Prize with Nash; David Smith, President of the MIT Wei-Tong Shu, and the Class of 1971 Fund for their Club of Princeton (where Alicia was an active member); very generous and ongoing support of the activities James Manganaro, friend of John and Alicia; and John of our department. I also want to thank Otto Al- David Stier, John Nash’s son. brecht for his generous donation of the Gomboc, a Sylvia Nasar gave a talk on the lives of John and Alicia Nash small sculpture of a convex body that will be placed in our Common Room for everyone to enjoy.

As many of you know, Princeton Reunions will take place from May 26th through 29th. We invite you to join us for our annual open house on Friday, May 27th, at 2 p.m. in the Fine Hall Common Room.

Igor Rodnianski, Acting Chair

Page 2 Faculty Awards Stefanos Aretakis Fernando Codá Marques made international headline news. was among 5 shared the 2016 Oswald Veblen In 1994 he cracked Fermat’s Last Princeton fac- Prize in Geom- Theorem, which at the time was the most famous, and long-running, un- ulty members etry with André solved problem in the subject’s his- selected as Sloan Neves (Imperial tory.” Research Fellows College London this year by the and Princeton Shou-wu Zhang Alfred P. Sloan faculty mem- was named a 2016 Simons Fellow Foundation. ber from 2005- in Mathematics 2009) by the . The *01 Fellows Pro- received honorary doctorate degrees Christopher Skinner *97 grams provide from the Indi- was named one of the 2015 Simons funds to faculty an Institute of Investigators. for up to a se- Technology, Ma- The citation for mester-long re- dras and Bates Professor Skin- search leave from classroom teach- College. Profes- ner remarks on ing and admin- sor Bhargava's his work “in istrative obligations with the goal of other honors this increasing creativity and providing year include: the and arithmetic intellectual stimulation.

Credit: Denise Applewhite Indo-Canadi- geometry. One an Chamber of of his striking Fellows of the Ameican Commerce’s Male Professional of recent results is Mathematical Society the Year Award, India Abroad Pub- a proof, in joint work with collabo- Professors Alice Chang, Mihalis lisher’s Award for Excellence, the rators, that a positive proportion of Dafermos *01, Australian Mathematical Society’s elliptic curves defined over the - ra and Shou-wu Blue Hat Award, Children’s Hope tional numbers satisfy the Birch– Zhang have been India’s Making a Difference Award, Swinnerton-Dyer conjecture.” named fellows of and the Asian American Engineer the American of the Year Distinguished Science Sir Andrew J. Wiles, Mathematical and Teaching Award. Professor of Mathematics, Emeri- Society for 2016. tus at Princeton and a Royal So- János Kollár Chang was cited ciety Research was awarded the 2016 Frederic Es- for her “contri- Professor at ser Nemmers butions to geo- Mathematics the University metric analysis, Prize for “his of Oxford, has nonlinear partial fundamental been awarded contributions the 2016 Abel differential equa- to algebraic ge- Prize “for his tions, and har- ometry, includ- Credit: Denise Applewhite stunning proof monic analysis;” ing the minimal of Fermat’s Last Dafermos for his model program Theorem by way of the modular- work in general and its applica- ity conjecture for semistable elliptic relativity and tions, the theory of rational con- curves, opening a new era in num- PDEs; and Zhang for his “contribu- nectedness and the study of real al- ber theory.” The citation continues, tions to Arakelov geometry, arithme- “Andrew J. Wiles is one of very gebraic varieties.” Professor Kollár tic dynamics, and for extensions of few mathematicians—if not the only was also named Fellow of the Amer- the Gross-Zagier formula”. ican Academy of Arts and Sciences. one—whose proof of a theorem has page 8 Page 3 Faculty Appointments New Assistant Professor Hansheng Diao Adam Marcus Algebraic Number Theory Algorithms, , and Optimization Ph.D. in Mathematics, , 2014. B.S. in Math- Adam Marcus comes to Princeton ematics, Massachusetts Institute from where he was of Technology, 2009. the Gibbs Assistant Professor in Previous position: Applied Mathematics. Member, Institute for Advanced Study, 2014-15. Marcus graduated from the Uni- versity of Washington, St. Louis in Tarek Elgindi 2003 with a B.A. in Applied Mathematics and an M.A. Nonlinear Partial Differential Equations arising in Mathematics before completing his Ph.D. in 2008 at in Fluid Dynamics the Georgia Institute of Technology. Marcus’ doctoral (50% Instructor, 50% NSF Post- work was in Algorithms, Combinatorics, and Optimiza- doc) tion under the supervision of Prasad Tetali, with a minor in Information Theory. Ph.D. in Mathematics, , Courant Institute of New Instructors Mathematical Sciences, 2014. B.S. in Mathematics (with Hon- Nicolas Boumal ors), University of Wisconsin— Optimization and Algorithms Madison, 2009. Previous position: Ph.D. in Applied Mathematics, Postdoctoral Research Fellow/NSF Postdoctoral Université Catholique de Lou- Fellow, Princeton University Mathematics De- vain, 2014; M.A. in Engineering partment, 2014-15. in Applied Mathematics, Univer- sité Catholique de Louvain, 2010; B.A. in Engineering summa cum Ori Parzanchevksi laude (with a major in Applied Groups and representation theory, Words and dis- Mathematics and minor in Electri- tributions in groups, Spectral theory of discrete cal Engineering, 2008. and continuous structures, p-adic analysis, Struc- Previous position: tural combinatorics and algebraic Postdoctoral Research at INRIA and École Normale Su- , Random processes. périeure in Paris, France, 2014-2015. Ph.D. in Mathematics, the He- Rafael Montezuma brew University of Jerusalem, Differential Geometry & Geometric 2013. M.Sc. in Mathematics, Analysis summa cum laude, the Hebrew University of Jerusalem, 2008. Ph.D. in Mathematics, IMPA (In- B.Sc. in Mathematics and Amir- stituto de Matemática Pura e Apli- im program, summa cum laude, cada), 2015; M.S. in Mathematics, the Hebrew University of Jerusa- IMPA, 2011; B.S. in Mathemat- lem, 2006. ics, UFC-Ceará Federal University, Previous position: 2009. Member, Institute for Advanced Study, 2013- 2015.

Page 4 Teaching Awards Junior Faculty Teaching Awards Each year the Mathematics Department recognizes ju- nior faculty and graduate students for exceptional un- dergraduate teaching. A major component of the selec- tion criteria is based on teaching evaluations from their students.

This year’s Junior Faculty Teaching Awards were giv- en to Javier Gómez Serrano and Adam Levine. Gómez Serrano’s students touted his ability to teach “fast-paced and well-planned” lectures while also making compli- cated ideas seem simple. As one of them put it: “Profes- sor Serrano is the man. Period.”

Levine’s students showed an equal level of admiration, noting that his lectures were entertaining as well as enlightening, and that students were inspired to work hard for a teacher who really cared about helping them understand and appreciate mathematical thinking.

Graduate Teaching Award Adam Levine (left) and Javier Gómez Serrano receive their awards. Gregory Gauthier is this year’s Graduate Student Teaching Award From the Math Club Your-Professor lunches. Math Club winner. His also hosted social events such as students were The Mathematics Club had an- biweekly board game nights in the inspired by other successful, busy year. In the Fine Common Room (pictured), a his enthusiasm regular colloquium series, profes- Pi Day celebration, and the annual and dedica- sors and researchers in the Math- end-of-the-year banquet for stu- tion to learn ematics, Computer Science, ORFE, dents and faculty. as much as and Physics departments gave talks possible in his accessible to undergraduates on In November, the annual Princeton linear algebra various mathematical subjects. Un- University Mathematics Competi- class, and were dergraduates of various years and tion (PUMaC) attracted over 100 impressed not graduate students met up in groups Princeton undergraduate volun- only by the for the family-style mentoring pro- teers and over 500 high school com- clarity of this explanations but also gram Mentoring Möbius, and chat- petitors from across the country and by the quality of his jokes. Classes ted with their professors at Meet- around the world. were engaging, helpful, lively, and fun, and the students were grate- ful to know how much Greg cared about helping them succeed in a class they found to be quite challeng- ing and abstract. The Department is also grateful for Greg’s work as a mentor for the Putnam team, where he showed the same dedication and enthusiasm.

The Teaching Award certificates were presented at a special tea on Monday, October 12th, and are ac- companied by a cash award. Page 5 Finite Simple Groups: Thirty Years of the Atlas and Beyond A Conference Celebrating the Atlases and Honoring John Conway on the Occasion of his 80th birthday.

The classification of finite simple The first day of the conference was groups was announced to be com- dedicated to John Conway (Pro- pleted in 1983 and has been con- fessor of Mathematics, Emeritus, Speakers: sidered a major accomplishment Princeton University) in celebra- Caltech of modern mathematics. Since tion of his many fundamental con- then, it has opened up a new and tributions to the area. Michel Broué Paris 7 powerful strategy to approach and Jon Carlson University of Georgia resolve many problems that were Poster sessions were set up in the considered inaccessible in lobby outside of the auditorium, John Conway Princeton theory, number theory, combina- providing opportunities for math- Rob Curtis Birmingham torics, coding theory, algebraic ge- ematicians to discuss their research ometry, and other areas of math- for an hour each day during the Meinolf Geck Stuttgart ematics. Beginning with Conway, conference. A reception (provid- Sasha Ivanov Imperial College Curtis, Norton, Parker and Wil- ed by Labyrinth Books) was held son's book, the Atlas of Finite on the first day of the conference Radha Kessar City University, London Simple Groups (Oxford University to mark the publication of a biog- Martin Liebeck Imperial College Press, 1985), character tables and raphy of John Conway: Genius At other information on these groups Play, The Curious Mind of John Gunter Malle TU Kaiserslautern has been compiled in what are Horton Conway, written by Siob- Gabriel Navarro Valencia now known collectively as the At- han Roberts and published by lases. Blooomsbury USA. Gabriele Nebe RWTH Aachen

The main objective of this con- A banquet was held at Palmer House, Simon Norton Cambridge ference was to discuss the many Princeton University's guest house, Eamonn O’Brien Auckland applications of the Atlases while after the second day of the conference. exploring recent developments Cheryl Praeger Perth and future directions of research, Additional support for the confer- Raphaël Rouquier UCLA with particular focus given to the ence came from the National Sci- interaction between computation ence Foundation, the National Alex Ryba Queens College, CUNY and theory with applications to Security Agency, and Deutsche Aner Shalev Jerusalem number theory and algebraic ge- Forschungsgemeinschaft. ometry. Ron Solomon Ohio State

Page 6 Sinai & Ruelle: 80 Years New Directions in Statistical Mechanics and Dynamical Systems

A two-day conference was held at esting area of research. Princeton University on December 16 and 17, 2015 in honor of the 80th The first day concluded with a re- birthdays of Yakov Sinai (Princ- ception in the Professors’ Lounge eton) and (IHES). atop Fine Hall. Lectures took place in McDonnell Hall on the first day and in Taplin On the second day of the confer- Auditorium on the second day. ence, Ruelle and Sinai each gave a talk that was aimed at under- This conference immediately fol- graduate and graduate students. lowed the 114th Statistical Mechan- ics Conference at Rutgers Univer- The workshop was supported by sity, which also celebrated Ruelle the Princeton University Math- and Sinai. (The traditional format ematics Department and the In- of Rutgers’ meetings is 24-minute ternational Association of Math- talks that emphasize the physical ematical Physics. applications.) Yakov Sinai takes questions after his talk. The two-day conference that fol- Speakers: lowed at Princeton was to concen- trate on the more mathematical as- Hebrew University of Jerusalem pects of Ruelle and Sinai’s legacy. In particular, the high-level talks on Princeton University & the IAS the first day of the conference were in the areas where Ruelle and Sinai Princeton University made their seminal contributions. Senya Shlosman By emphasizing new directions and Centre de Physique Théorique open problems, the conference was Hugo Duminil-Copin able to demonstrate the breadth of Université de Genève their contributions and to show that David Ruelle they are still very active and inter- IHES Yakov Sinai David Ruelle at the reception. Princeton University

Page 7 Analysis, PDEs, and Geometry

Honoring the Work of Sergiu Klainerman After four days of fascinating talks, In his work, Professor Sergiu Klainerman and his many achieve- the conference concluded with a Klainerman, who joined Princeton’s ments, the Mathematics Depart- banquet honoring Klainerman in faculty in 1987, pioneered many of ment hosted a four-day conference the Frick Laboratory atrium. the modern methods in Harmonic from January 23 to 26. Over one Analysis and Partial Differential hundred participants, including Additional support was provide by Equations. His contributions in- thirteen of his students, came to the National Science Foundation. clude the vector-field method, the hear seventeen leaders in these discovery of null operators, applica- fields. tions of to semi- linear PDEs, Xs,b norms, L2 bilinear Speakers: estimates, bilinear restriction theo- Carlos Kenig rems, and many others. Institute for Advanced Study Joachim Krieger Sergiu Klainerman has also had Stanford University École Polytechnique Fédérale de Lausanne Jean-Yves Chemin an enormous impact in the fields of Université Pierre et Marie Curie University of California, Santa Barbara Geometric Analysis and General Peter Constantin Igor Rodnianski Relativity through his work on the Princeton University Princeton University Mihalis Dafermos stability of the Minkowski space- Princeton University Massachussets Institute of Technology time, uniqueness of black holes, Charles Fefferman Jérémie Szeftel formation of trapped surfaces, and Princeton University Université Pierre et Marie Curie Gustav Holzegel low-regularity solutions of the Ein- Imperial College London University of California, Los Angeles stein vacuum equations. Gerhard Huisken Daniel Tataru Oberwolfach University of California, Berkley To honor and celebrate Professor Alex Ionescu Princeton University Gigliola Stafflani, Sergiu Klainerman laughing with Elly Stein and Min Tang, and Terenece Tao.

Page 8 Events Geometry Festival IAS), Fengbo Hang (Courant Insti- been possible without the efforts of st The 31 Geometry Festival was held tute, NYU), Nancy Hingston (The Scott Kenney, Gale Sandor, Will at Princeton University the weekend College of New Jersey), Jen Hom Crow and Carol DiSanto. of April 8 to 10. This was the first (Georgia Tech and the IAS), Claude time that Princeton hosted the an- LeBrun (SUNY, Stony Brook), Fer- Congratulations to Our nual event. nando Marques (Princeton), Davi Putnam Team for their 3rd Maximo (Stanford) and Jake Solo- Place Finish! This year’s conference was focused mon (Hebrew University). on major recent results in geometry Princeton’s Team: Rodrigo Angelo, Andre Arslan, and Eric Schnider and related fields, including -top After the last talk on Saturday af- ics in conformal geometry, minimal ternoon, most participants joined surfaces, Kähler geometry, topology, Individual recognitions: the speakers for a very nice banquet Top 6: Bumsoo Kim Lagrangian submanifolds and sym- dinner at the Professors’ Lounge in plectic four-manifolds. Top 16: Xiaoyu Xu Fine Hall. Besides the great view Top 26: Andre Arslan and of Princeton, the atmosphere of the Zhuo Qun Song Over 70 registered participants, banquet was warm and friendly. plus members from the local math- Honorable Mention: ematics community, among whom Arka Adhikari, The next Geometry Festival will be Rodrigo Angelo, many were graduate students and held in Duke University. postdocs, attended the talks given Eric Neyman, by (UC Berkeley and the Tim Ratigan, This conference would not have Eric Schneider, and Mel Shu The Minerva Program It was another successful year for Lewis Bowen, Associate Professor nerva Lectures. His talks, “Spar- the Minerva Program, bringing at the University of Texas at Aus- cification of Graphs and Matrices,” three mathematicians, each from a tin, was the Minerva Distinguished “The Solution of the Kadison-Singer different field, to Princeton. Visitor during the fall term. Bowen’s Problem,” and “Ramanujan Graphs residency allowed time to collabo- and Free Probability,” all attrracted In November, , rate with students and faculty here; broad audiences, including members Professor at Stanford University he delivered a five-part lecture series of the Mathematics Department, the and a recipient of the 2014 Fields on “Benjamini-Schramm Conver- Program in Applied and Computa- Medal, delivered three talks: “Ge- gence in Groups and Dynamics.” tional Mathematics, and the Com- ometry and dynamics on hyperbol- puter Science Department. ic surfaces,” “Dynamics on moduli Finally, in the spring, Daniel Spiel- spaces of hyperbolic surfaces,” and man, the Henry Ford II Professor The Department is grateful for the “Counting mapping class group of Computer Science and Applied continued support of the Fernholz orbits on hyperbolic surfaces.” Mathematics at Yale University, de- Foundation that make this wonder- livered another series of three Mi- ful program possible.

Maryam Mirzakhani Lewis Bowen Daniel Spielman Credit: Maryam Mirzakhani Maryam Credit: Credit: MacArthur Foundation MacArthur Credit:

Page 9 Program for Women and Mathematics The Program for Women and Math- Research, Margarent Holen *95 and about her mathematical work and ematics is an annual two-week resi- Inna Okounkova on finance, Claudia her personal outlook on mathemati- dential program that focuses on a Perlich on display advertising, Tal cal culture. Lunch, tea and dinner particular mathematical theme. It Rabin of IBM Research, and Sandra are other highlights of the day where is generously sponsored by the NSF, Peterson of Johnson and Johnson. participants enjoy meeting Princ- IAS, and the Princeton eton graduate students, Mathematics Depart- postdocs, and faculty ment. The program as well as the spectacu- aims to recruit more lar view from the top of women in mathemat- Fine Hall. ics and to counter the higher attrition rate of Over two weeks, women female mathematicians mathematicians from all compared to their male levels learn, work, and counterparts at key tran- socialize together in sition points. a supportive environ- ment. Mathematical About 40-60 under- bonds are often created graduate, graduate and Princeton Instructor Ana Caraiani with particpants. between senior math- postdoctoral women ematicians and graduate students/ studying mathematics from insti- In the middle of the two-week pro- postdocs. Past participants over- tutions all over the U.S. gather on gram, participants spend a day in whelmingly report that they feel the campus of the Institute for Ad- Fine Hall. Last May, Professor Já- inspired and encouraged by the vanced Study in Princeton each May. nos Kollár, Veblen Fellow June Huh, women they meet during the pro- Research mathematicians such as and alumna Yaim Cooper *13 gave gram, and that the program is a vi- Professor Maria Chudnovsky *03 excellent and accessible talks on their tal opportunity to reinvigorate their and Wei Ho *09 are recruited to give work; in addition, Isabelle Nogues studies and research. Many student lecture series and colloquia which ‘15 gave a violin concert. participants return to the program in focus on a particular mathematical subsequent years as topic each year. Some topics in re- This May, our alum teaching assistants, cent years are “Combinatorics and Carlee Joe-Wong ‘11 lecturers, or collo- Graph Theory (2013),’’ “Random will talk about how quium speakers. Matrix Theory (2014),’’ “Aspects she turned her under- of Algebraic Geometry (2015),’’ and graduate thesis into a Since 1994, over “Curves, Loops, and Words in Ge- startup company, and 1,000 women math- ometry (2016).’’ Lillian Pierce ‘02 *09 ematicians have vis- will share her experi- ited Princeton as In addition to lectures and seminars, ences building support part of the Women evening Women in Science seminars networks for women and Mathemat- explore topics of interest to women mathematicians at Isabelle Nogues ‘15 gave a ics program; about mathematicians. Some popular top- Princeton and Oxford. violin concert. 70% have remained ics include “Work-Life Balance in a In addition, graduate in academia. This Mathematical Career,’’ “Surviving in student Sophie Spirkl and Profes- is an incredibly large and diverse Graduate School,’’ “Career Paths for sor Zoltán Szabó will give talks on group of women mathematicians. Women in Mathematics,’’ “Becom- their work. We also look forward The program alumnae who have ing an Academic Mathematician,’’ to brining Piper Harron back to benefitted from their experience at and “Using Language for Success Princeton. Piper’s 2016 Ph.D. the- the Women and Mathematics Pro- which Offsets Stereotypical Behav- sis, which touches on accessibility gram will help us to continue to ior.’’ Visits from female leaders in versus esotericism in mathematics, strengthen the program for future industry in recent years are very achieved viral status. She will visit women mathematicians. popular with participants; visitors the Women and Mathematics pro- include Jennifer Chayes of Microsoft gram during the first week and talk

Page 10 Mathematics on the Silver Screen Ramanujan and Making The Man Who Knew Infinity On April 11th, a piece of Hollywood came to Princeton for a public lecture about the life and work of Ramanujan and the making of the film, The Man Who Knew Infinity. Professor Manjul Bhargava *01 worked with the film- makers as an associate producer and mathematical consultant on the film over the last 10 years, culminating in the April 29th U.S. premiere. Prior to opening night, Professor Bhargava gathered members of the cast, pro- duction, and distribution teams for a panel discussion and special screen- ing of the film.

Based on the amazing story of one From The Man Who Knew Infinity Credit: IFC Films of the greatest minds in history, The Man Who Knew Infinity charts the original theorems, which he attri- Following the lecture, over 180 stu- incredible life of Srinivasa Ramanu- butes to divine inspiration. dents, faculty, and staff attended a spe- jan (played by Slumdog Millionaire’s cial screening of the film at the Prince- Dev Patel), whose genius for math- The public lecture began with a talk ton Garden Theater, where it received ematics takes him from obscurity in by Bhargava on Ramanujan’s work rave reviews India to Trinity College, Cambridge and its lasting impact on mathemat- University in the early 20th century. ics. Bhargava then led a panel discus- This event was co-sponsored by the Spurred on by his mentor, G. H. Har- sion with Devika Bhise (actor), Matt Committee on Public Lectures and the dy (Academy Award winner Jeremy Brown (writer & director), Ed Press- Council on Science and Technology. Irons), Ramanujan overcomes racism man (producer), Betsy Rodgers ‘95 and the rigidity of academia to revo- (IFC Films), and Tristine Skyler ‘93 For more information on the film, lutionize the field with his startlingly (executive producer). visit: themanwhoknewinfinity.com

From left: Devika Bhise, Betsy Rodgers '95, Tristine Skyler '93, Ed Pressman, Matt Brown, and Manjul Bhargava *01

Credit: Dan Komoda Page 11 Undergraduate program Undergraduate Profile: Ana-Andreea Stoica ‘16

Ana-Andreea Stoica ‘16, looks for- pelled to apply quantitative reason- When Ana is not thinking about her ward to joining ing to the field of neuroscience. This mathematical pursuits, she enjoys the rest of her passion led her to take courses by table tennis, reading and playing class for com- Professor Amit Singer and Profes- the piano. Outside the math depart- mencement this sor Emmanuel Abbe (Department ment, she particularly enjoyed cours- May. Growing of Electrical Engineering and the es such as “Urban Sociology” and up in , Program in Applied and Compu- “Radical Political Thought” which Ana showed a tational Mathematics). She took a introduced her to new ways of think- strong interest particular interest in Professor Ab- ing and expressing herself. In fact, in mathematics be’s work and asked him to advise before beginning graduate studies at in middle school her senior thesis, titled “Communi- the University of Pennsylvania, she and competed in ty detection in the stochastic block hopes to work at a center dedicated the Mathemati- model — hypergraphs and beyond.” to the application of mathematical cal Olympiad during high school. As models to social issues. a mathematics major at Princeton, she found that the department’s fac- Summer Research for Undergraduates ulty and students formed a tight and engaging community. This inviting For the fourth year the Mathemat- grams can be an off-campus NSF- and flexible environment helped her ics Department sponsored summer funded Research Experience for overcome the challenges of Princ- research opportunities for rising Undergraduates Program (known eton life, from balancing rigorous juniors and seniors. A total of 11 as an REU) in the or course loads with independent inter- students participated in summer re- other special summer research pro- ests to learning how to interact with search programs, and all but two of grams being held elsewhere. The faculty as mentors beyond the typi- the participants remained in Princ- experience of being a participant cal student/instructor relationship. eton over the summer months to in one of these research programs work on a specific research topic can provide that student with the As an undergraduate, she felt com- of their choosing while having the chance to focus on a single mathe- opportunity to consult their faculty matical research problem or area of advisor. mathematics.

Department Awards Two of these students received re- 2014-2015 Academic Year search stipends of $4,500 from Supported for Summer the Bershadsky Family Summer 2015: George B. Covington Prize Research fund that was adminis- Arka Adhikari ‘16 tered by the Office of the Dean of Max Simchowitz ‘15 the College. The other students re- Mark Aksen ‘17 Alexander Smith ‘15 ceived stipends of $4,000 that were Daniel Dore ‘16 Middleton Miller ‘29 Prize funded by our department and the Likith Govindaiah ‘17 Kubrat Danailov ‘15 Jaywood Lukens ’30 Scholarship Thomas Kelly ‘15 Fund. This summer program was Joane Joseph ‘16 designed to provide independent Andrew H. Brown Prize research opportunities for rising ju- Daniel Li ‘17 Daniel Dore ‘16 niors and seniors, but rising sopho- Miranda Moore ‘16 mores are also given consideration. Yuval Wigderson ‘16 Avaneesh Narla ‘17 Peter A. Greenberg ‘77 Prize Mathematics majors are also en- Joseph Obiajulu ‘17 Arka Adhikari ‘16 couraged to apply for financial Alec Payne ‘16 Bumsoo Kim ‘16 support to allow them to attend The Class of 1861 Prize research programs in mathematics Gloria Yin ‘18 Eric Schneider ‘17 at another institution. These pro- Alexander Yu ‘16 Page 12 Graduate program Graduate Profile — Antoine Song I am currently working tantly, I was influenced I am part of a trio as the cellist, and in Geometric Analysis, by the mathematicians, we performed the Ravel trio this year more precisely in the vari- the human drama and at the department recital. Although ational theory of minimal the history surrounding the connection between mathemat- surfaces, a topic recently this famous conjecture. ics and music has almost become reinvigorated by my ad- In other words, I realized commonplace, their deeper resem- visor Fernando Codá that mathematics was de- blance was not obvious to me at first. Marques and his col- fined by the people doing I rather considered music, a tempo- laborator André Neves. it, and not by the theo- ral arrangement of sounds, as a way A significant influence rems and proofs. to counterbalance the mainly visual on my choice of special- thinking required by geometric prob- ization was the solution After two years of prepa- lems, as suggested somewhere by to the Poincaré conjecture, which ap- ratory classes in France, I went to the . Actually, I have come peared around the time I started to École Normale Supérieure in Paris. to a better understanding of these consider becoming a mathematician The first time I came to Princeton as similarities thanks to composers such as a tangible possibility. Even though a visiting student, I was impressed by as Ravel. His music can be seen as the proof was too involved for me at the working conditions enjoyed by an allegory of mathematics: a highly that time, I found the whole idea of the graduate students, which partly structured, cerebral but colorful bal- deforming manifolds by geometric explains why I decided to continue ance between intellect and emotion. flows fascinating. But more impor- my Ph.D. here.

Director of Graduate Studies — Peter Ozsváth *94 Princeton has a unique graduate of my own graduate experiences, ad- general and specialized topics, take program. We select a few top stu- vice from my colleagues, place during the end of dents from all over the world, who and especially the wis- the winter and the end come here, united by their passion dom of my veteran co- of the Spring. In late De- for mathematics. Our students are DGS, Zsolt Patakfalvi. cember, the entire math given great latitude to follow their The graduate program faculty participates in se- interests, with very few formal re- also benefits greatly lecting the very top few quirements; they are encouraged to from the excellent staff, of the applicants from a start on research as soon as possible. and particularly the wide, international pool. Students typically study together, ever-friendly, thorough At roughly the same and the ensuing bonds are deep, and organized gradu- time, other universities sometimes spanning one’s math- ate administrator, Jill are also making postdoc- ematical career. I experienced this LeClair, who excels both toral offers to our finish- first-hand when I arrived here as a on routine aspects, such ing students. A Gradu- graduate student in 1989. Many of as disseminating program policies; ate Students Open House occurs my classmates went on to be lead- more exciting ones, such as organiz- typically in the early Spring. This ers in their subjects, and all of them ing the annual Mathematics Depart- is a fantastic one or two-day event were fascinating characters from ment Recital; but most importantly, filled with lectures from faculty, stu- varied backgrounds. Now, as Di- who takes a personal interest in and dents, and post-docs alike (and ex- rector of Graduate Studies (DGS), a dedication to improving the quality cellent tea and cookies!), aimed at I have a second opportunity to take of life of all of our students. recruiting our visiting prospective a good look at this program and to students. The next first-year class is watch the formation of the next gen- There are several milestones during formed by April 15th. Exams and fi- eration of mathematical leaders. the year. In the Fall, we welcome the nal thesis defenses typically occur in new entering class. General exams, the early summer, leaving us ready As DGS, I was guided by memories which are oral exams spanning both to go through the next cycle.

Page 13 Most recent Ph .D.s

Name Undergrad Advisor Field Thesis Title Original Placement

Thomas Beck Cambridge University Fefferman PDEs Level set shape for ground MIT/C.L.E. Moore state Eigenfunctions on Instructor convex domains

Dan Collins Cornell University Skinner Number Theory Anticyclotomic p-adic Cornell University/Assis- L-functions and Ichino’s tant Visiting Professor formula

Yu Deng MIT Ionescu PDEs Long time behavior of NYU/Courant Institute/ some nonlinear dispersive Courant Instructor equations

Heather Macbeth University of Tian Kähler Geometry Kähler-Einstein metrics, MIT/C.L.E. Moore Auckland Bergman metrics, and Instructor higher alpha invariants

Andy Manion University of Notre Szabó Knot Theory; Constructions and com- UCLA/Adjunct Assistant Dame Khovanov putations in Khovanov Professor homology homology

Ryan Peckner UCLA Sarnak Number Theory Two dynamical perspec- Broad Institute of MIT tives on the and Harvard/Postdoctoral of the Möbius function Associate

Ben Schweinhart Swarthmore College MacPherson Topology of Statistical topology of Harvard University, (IAS) Complex Systems embedded graphs Center of Mathematical Sciences and Applications/ Postdoctoral Fellow

Liangming Shen Beijing University Tian Geometric Smoothing conic Kähler University of British Aeronautics and Analysis metrics and conical Columbia/Postdoctoral Astronautics Kähler- Fellow

Andrei Tarfulea University of Chicago Constantin PDEs A study in the asymp- University of Chicago/ totic behavior of nonlinear L.E. Dickson Instructor evolution equations with nonlocal operators

Ila Varma California Institute Bhargava/ Number Theory On local-global compat- Harvard University/NSF of Technology Taylor (IAS) ibility of cuspidal regular Postdoctoral Research algebraic automorphic Fellow representations of GLn

Shuyun Conan Wu University of Toronto Gabai Topology/3- 3-manifold topology with McKinsey & Associates, manifolds groups and randomness Shanghai/Associate

The annual Department Recital. From left: Gina Holland, Daniel Kriz (G2), Mark McConnell, Matthew de Courcy-Ireland (G3), and Lucia Mocz (G3), Mark Cerenzia (G3; ORFE) & Antoine Song (G1).

Page 14 Administrative staff changes Yvette Campbell with her partner, Ira, and has many bies include find- Faculty Assistant interesting hobbies including yoga, ing new bands and soap making, and various artistic en- places to go camp- The Depart- deavors. ing in the area. Fol- ment welcomed lowing in the foot- a new Faculty steps of our other Chad Maier computing staff, Assistant this Systems Support Specialist fall. Yvette has Chad has been a long history building his own Since arriving in August, 2015, server at home to of working in Chad has had a great impact im- higher educa- expand and enrich proving the organization of our what he is learning in Fine Hall. tion, and came equipment and has provided vital to Princeton support as Fine Hall underwent its in 2013 as the largest single-year deployment of William Crow Assistant Manager, Communications Assistant to the Chair in the Depart- new workstations. ment of Operations, Research and & Operations Financial Engineering. Prior to that, Chad moved to the Northeast from In November Will Yvette worked at Gettysburg College Austin, Texas where he lived from was promoted to and from 1995 to 2003 at the Institute 2007 to 2015, working in computer Assistant Manager, for Advanced Study in their Human support as well as music promotion. Communications Resources and Visa Services offices. Indeed, music is a passion for Chad, & Operations. In and he has toured Europe working his new role Will As our new Faculty Assistant, Yvette with the band Depeche Mode. is primarily responsible for process- spends more time working on the de- ing faculty reimbursement requests A native of Champaign, IL, Chad partment’s publi- and making travel arrangements for received his bachelor’s degree from cations and website visitors. the University of Illinois, Urbana- as well as taking on a larger role in Champagne in 1997. Today his hob- Yvette lives in southern New Jersey organizing our special events.

The annual Department Recital. Clockwise from top-left: Kevin Chien '17 & Demi Fang '17, Yuchen Liu (G3), Florian Sprung, Maggie Miller (G1), and Peter Ozsváth Department Administration: *94 & Shevi Sperber. Chair: David Gabai Acting Chair: Igor Rodnianski Associate Chair: János Kollár Directors of Graduate Study: Peter Ozsváth and Zsolt Patakfalvi Department Representative: János Kollár Assoc. Department Representative: Jennifer Johnson Senior Advisor: Paul Yang Junior Advisor: Mark McConnell Placement Officer: Vlad Vicol Department Manager: Kathleen Applegate Graduate Administrator: Jill LeClair Undergraduate Administrator: LeeAnn Coleman Page 15 Department of Mathematics Fine Hall — Washington Rd. Princeton, NJ 08544

Alumni , faculty, students, friends, connect with us, write to us at [email protected]

Join us for our Alumni Open House Friday, May 27th • 2:00 p.m. • Fine Hall Common Room Join Professor Emeritus John H. Conway and members of the Mathematics Department for fun, refreshments, and maybe even some math!

The annual Graduate Student Open House provides prospective students an opportunity to see the department's collegial atmosphere. Professor Christopher Skinner *97 talks with a prospective student (left), while current graduate students play cards with others.