Pardon Receives Waterman Award Letter from the Chair

Home , Charles Fefferman, John Pardon, Maryna Viazovska, Morgan Prize

Spring 2017 Issue 6 Department of Mathematics Princeton University

Letter From the Chair Congratula- others went to Assistant Profes- tions to our 28 sors Nicholas Sheridan and Han Pardon Receives undergraduate Liu (ORFE). math majors Waterman Award Some highlights among faculty of the class of Professor John 2016 and to recognitions include Charlie Fef- ferman *69 winning the Wolf Pardon '11 has the 8 graduate received a Na- students who Prize in Mathematics, the fourth current faculty member and the tional Science are now *16. Foundation About half of sixth Princeton alum to do so. John Pardon ’11 won the NSF’s Alan T. Water- the undergrads man Award, went off to grad Alan T. Waterman Award. Also, Professor Allan Sly was awarded which is the na- school, others found positions in tion's highest finance and industry and a few the Doeblin Prize and Assistant honor for early- followed other paths including Professors Adam Marcus and career scientists the Korean army. We look for- Vlad Vicol were awarded NSF and engineers. ward to hearing both from and CAREER grants. See page 4 The prize car- about you in the future. for a more complete list of major ries a five-year, $1 million grant. recognitions. We are thrilled that John Pardon ’11 Pardon was recognized for "rev- and Allan Sly joined the De- Our beloved Scott Kenney retired following 30+ years of ser- olutionary, groundbreaking re- partment as professors, Tatyana sults in geometry and topology" Shcherbyna as an assistant pro- vice, including 25 years as De- that "have extended the power fessor, and Otis Chodosh, Ziyang partment Manager followed by of tools of geometric analysis to Gao, Ilya Khayutin, Francesco 5 years as Special Projects Man- solve deep problems in real and Lin, Evita Nestoridi, and Kon- ager. In all his roles he was uni- complex geometry, topology, and stantin Tikhomirov as instruc- formly welcoming, approachable dynamical systems," according to tors and that Emmanuel Abbe and totally devoted to the De- the prize citation. He was select- (PACM, EE) and Ramon van partment. To many of us Scott ed along with Baratunde Cola, an Handel (ORFE) became Associ- was the face of the Math Depart- associate professor of mechanical ated Faculty. They have all made ment. He will be sorely missed. engineering at Georgia Tech. a difference to the Department. Continued on next page... Continued on page 14... Congratulations to our 2nd place Putnam team; Eric Schneider, Alex Song, and Xiaoyu Xu and to Eric Schneider and Murilo Zanarella who both earned N1 distinction. All our finishing grad students did very well, though some chose new directions. Four of this year’s twenty Sloan Foun- dation Fellowship winners in mathematics went to our former grad students Wei Ho *09, Chi Li *12, Jonathan Luk *12, and Aaron Pixton ’08 *13, and two

Provost David Lee, President Christopher Eisgruber, and Dean of the Faculty Debra Prentice congratulated Pardon at a special tea in his honor. Faculty Appointments Professor John Pardon From the Chair John Pardon ’11 returned to Princeton as a profes- Continued from previous page... sor this year, having completed his Ph.D. at Stanford I must report the loss of three long- University in 2015, where he was then appointed as time faculty: Professor Emeritus an assistant professor. John C. Moore, Professor Emeri- tus Gerard Washnitzer *50, and As an undergraduate math major at Princeton, Professor John Mather *67. John Pardon’s groundbreaking solution to Gromov’s knot- Mather’s untimely passing cut distortion problem was published in the Annals of short a very active research career. Mathematics and earned him the 2012 Morgan Prize. Please read the brief biographies on the following pages. Pardon continues to work on long-standing prob- The primary research goal of lems. His proof of the 3-dimensional Hilbert-Smith conjecture in 2013 Fine Hall is to address the most was the first general result on that venerable problem since the 2-di- interesting, fundamental and mensional solution more than 60 years earlier. challenging mathematical problems, find beauty and structure His groundbreaking achievements were recognized this April when he where it was not known to ex- received the National Science Foundation’s Alan T. Waterman Award, ist and to find new mathemati- the nation’s highest honor for early-career scientists. cal directions. Whether we are undergrads writing senior the- "My main personal motivation to work on problems in mathematics is ses, graduate students, postdocs, aesthetic," Pardon has said. "The most satisfying part of doing math- instructors, assistant profes- ematics is to find a beautiful proof or a beautiful theorem. I can only sors or long time senior faculty, hope that I have succeeded in a small way in this respect." we all share this common goal. Through our teaching and advis- Pardon is also an accomplished cellist and has joined the department’s ing, our faculty strives to trans- growing musical ensemble. mit their excitement, curiosity and understanding to our stu- Professor Allan Sly dents and they in turn enliven Fine Hall with their energy and Allan Sly joined the department this fall as a pro- enthusiasm. We particularly val- fessor, coming to us from the Department of Statis- ue independence, so while we are tics at the University of California, Berkeley. extremely gratified when they become prominent researchers Sly is an expert in discrete probability theory and and outstanding teachers we are its applications, focusing on the analysis of the mix- very happy when they passion- ing times of Markov chains—particularly the Glau- ately follow their own direction, ber dynamics and the role phase transitions play in even when it takes them outside the computational complexity—and in probabilis- of academic mathematics. tic models more generally. We greatly value and encourage Sly has reeived numerous recognitions for his excellent teaching. The Depart- work, including the Wolfgang Doeblin Prize (2016), a Faculty Early ment bestowed graduate stu- Career Development (CAREER) grant from the National Science dent teaching awards to Anibal Foundation (2014–2019), the Rollo Davidson Prize (2013), and a Velozo and Charles Stibitz, and Sloan Fellowship in mathematical sciences (2012). junior faculty teaching awards to Assistant Professors Nicholas Before joining the faculty at Princeton, he was an assistant profes- Sheridan and Vlad Vicol. Our sor (2011–2015) and associate professor (2015–2016) at Berkeley, teaching was also recognized where he also received his Ph.D. in 2009 under the supervision of outside of Fine Hall. We are Elchanan Mossel. He did his postdoctoral work in the theory group very proud that faculty Christine at Microsoft Research in Redmond, Washington. Taylor and Hansheng Diao were Continued on page 12... Page 2 Faculty Appointments Otis Chodosh Ziyang Gao Veblen Research Instructor Instructor Geometrical Analysis and PDEs Arithmetic Geometry

Otis Chodosh joins the department Ziyang Gao completed his Ph.D. after a year as a Research Fellow at in 2014 at Université Paris-Sud Cambridge University. He completed Orsay and Leiden University, his graduate and undergraduate stud- Netherlands. He received the ies at Stanford, receiving his Ph.D. 2015 Stieltjes Prize from the in 2015. Otis was an NSF Graduate Dutch Research School in Math- Research Fellow at Stanford, and received that institution's ematics, awarded anually for the best Ph.D. thesis. Walter J. Gores Award for excellence in teaching. After completing his doctorate, Ziyang spent time at CNRS in Paris and at the Institute for Advanced Ilya Khayutin Study in Princeton before coming to Princeton. Veblen Research Instructor Ergodic Theory, Number Theory Francesco Lin Veblen Research Instructor Ilya Khayutin completed his un- Gauge Theory, Topology dergraduate and graduate degrees at Hebrew University in 2006 and Francesco Lin received his 2016, respectively. In 2015 Ilya re- Ph.D. from MIT in 2016 af- ceived the Springer Prize for Doc- ter his undergraduate studies toral Students, in 2014 the Zocho- at Università di Pisa in 2012. vitzky Prize for Excellence in Research, and in 2008 Francesco received the Johnson the Wolf Scholarship for an Excellent Master's Thesis. Prize at MIT for best published research by a graduate student, the MIT Praecis Presidential Fellowship, and the St. John's College Evita Nestoridi (Oxford) exchange scholarship. Instructor Combinatorics, Probability Tatyana Shcherbyna Evita Nestoridi received her Assistant Professor Ph.D. from Stanford in 2016 Analysis, Mathematical Physics and her bachelor's degree from the National and Kapodistrian Tatyana Shcherbyna works University of Athens, Greece in in random matrix theory and 2011. At Stanford she received statistical mechanics. Before the Centennial Teaching Award and the Colleen and coming to Princeton she was a Robert D. Haas Graduate Fellowship. member at the Institute for Ad- vanced Study from 2015–2016 Konstantin Tikhomirov and 2012–2013, and a postdoc- Instructor toral fellow at St. Petersburg State University. Discrete Mathematics Tatyana received her Ph.D. in 2012 from the In- After his undergraduate work at stitute for Low Temperature Physics, Kharkiv, Samara State University in Rus- Ukraine and her bachelor's degree in 2007 sia, Konstantin moved to the Uni- from V.N. Karazin Kharkiv National University, versity of Alberta, where he com- Ukraine. pleted his Ph.D. in 2016. There he received numerous prizes and fel- She received the President of Ukraine award for lowships, including the Faculty of Science Dissertation young scientists (2011–2012), the JSC "Gazprom Award, and the Dean's Excellence Award. In 2010 he Neft" award for postdoctoral fellows (2014), and also received the Young Scientists Award from the Rus- the Ahiezer's fond prize (2009). sian Government. Page 3 Honors and Awards Michael Aizenman Peter Sarnak NSF CAREER Grants has been elected received an hon- Assistant Professors Adam Mar- a foreign mem- ary degree from cus and Vlad Vicol were award- ber of Academia the University ed NSF CAREER grants. The Europa and was of St. Andrews Faculty Early Career Develop- named a fellow ment (CAREER) Program is a of the Ameri- at its June 2016 Foundation-wide activity that of- can Academy graduate cer- fers the National Science Founda- of Arts and Sci- emony. tion's most prestigious awards in ences. support of early-career faculty. Manjul Bhargava Amit Singer Sloan Fellowships was elected an has been Assistant Professors Nicholas honorary fellow named a Na- by the Indian Sheridan and Han Liu (ORFE) tional Finalist were named Sloan fellows this Academy of Sci- for the Blavat- ences and was year. The 2017 class of Sloan nik Awards for fellows in mathematics also in- named a fellow Young Scien- of the Ameri- cludes Wei Ho *09, Assistant tists. The Bla- Professor at the University of can Academy vatnik Fam- of Arts and Sci- Michigan; Chi Li *12, Assistant ily Foundation, Professor at Purdue University; Credit: Denise Applewhite ences. with the guid- Jonathan Luk *12, Assistant ance of the New York Academy Professor at Stanford Univer- Charles Fefferman of Sciences, founded the Blavat- sity; and Aaron Pixton '08 *13, nik Awards for Young Scientists Assistant Professor at the MIT. shared the 2017 in 2007 to celebrate the innova- Wolf Prize in tive achievements of young post- Mathematics doctoral and faculty scientists for his work in who work in New York, New a number of ar- Jersey, or Connecticut. eas, including complex multi- Department Administration variate analysis, Allan Sly Chair: partial differen- David Gabai tial equations, was awarded the Associate Chair: and sub-elliptical problems. He Doeblin Prize János Kollár shares this prize with Richard from the Ber- Acting Associate Chair: Schoen of the University of Cali- noulli Society Christopher Skinner fornia at Irvine. for Mathemati- Directors of Graduate Study: cal Statistics and Peter Ozsváth Peter Oszváth Probability. The and Javier Gómez Serrano Department Representative: has been elected Doeblin Prize János Kollár a foreign mem- "is awarded to a Acting Dept. Representative: ber of the Hun- single individu- Christopher Skinner garian Academy al for outstanding research in the Assoc. Department Representative: field of probability, and who is at Jennifer Johnson of Sciences for Acting Assoc. Dept. Rep. his work in the the beginning of his or her mathematical career. " Christine Taylor topology of 3- Senior Advisor: and 4-dimen- Zeev Dvir sional manifolds and his proof of Junior Advisor: Mark McConnell the Thom conjecture with Profes- Placement Officer: sor Zoltán Szabó. Vlad Vicol Page 4 Honors and Awards

Department Junior Faculty and Hansheng Diao and Christine Graduate Teaching Awards Taylor Honored with Excellence in Teaching Awards The Department's annual teaching awards were announced at a special tea on Monday, October 10, Mathematics Department members Hansheng 2016. This year's Junior Faculty Teaching Awards Diao and Christine Taylor were awarded the Ex- went to Assistant Professors Nicholas Sheridan cellence in Teaching Award by the Undergraduate and Vlad Vicol, and the Graduate Student Teach- and Graduate Engineering Student Councils on ing Awards went to Charles Stibitz and Anibal Ve- March 2, 2017. lozo. The awards are given by the senior faculty and are based largely on student evaluations. This student-nominat- ed award is for a pro- Professor Sheridan's students have noted his clear, fessor or TA who "was engaging lectures and have called him "an amaz- especially dedicated, ing professor" who "breaks the mold" and even taught the material "the best teacher [they] have ever had." Professor clearly, and simply de- Vicol's students shared similar praise, noting that serves to be recognized while fast-paced, his lectures were informative, for the hard work he challenging, and stimulating, and that he "wel- or she put into the comes questions" and is "always willing to help." course." These awards As one of them put it: "The absolute best." are entirely student- run, and any professor or AI instructing an engineering, mathematics, or physics course is eligible. Diao (left) and Taylor at the annual Excellence in Teaching Awards Anibal Velozo Receives Graduate School Teaching Award Anibal Velozo, a fourth year graduate student, was one of ten recipients of the 2017 Graduate School Teaching Award.

Every year the Graduate School presents gradu- From left: Stibitz, Vicol, and Velozo ate students who have demonstrated excellence in teaching at the undergraduate level with the prestigious Teaching Award. By providing exceptional Though less experienced teachers, the graduate service as an assistant-in-instruction, these indi- student recipients received no less appreciation viduals have emerged within their programs and from their students. Stibitz's students found him departments as outstanding classroom leaders and a funny and personable instructor with an engag- scholars. This year's award recipients were selected ing and authentic style; one wrote: "we all love by a committee chaired by the dean of the Graduate Charlie. Math is math, but he makes it good." School and comprised of the academic affairs deans Velozo's students were inspired by his obvious and staff from the McGraw Center for Teaching and passion for mathematics, finding his lectures well Learning from a pool of nominees put forth by de- prepared and interesting. They were grateful to partments and programs. We recognize their distin- know that he really cared about helping them suc- guished achievement and thank them for their hard ceed and appreciated the work he put in to ex- work and dedication. plaining complicated material. Page 5 Faculty Memorials Professor John Mather *67, 1942–2017 By Morgan Kelly, Office of “He was a great mathematician. If 2001. “Once he started talking, Communications you were not well enough informed it was very interesting because in math to know how much he had he was extremely knowledgeable. done, there was no clue from his He also would be willing to listen, Professor of behavior that he was a great man. which to me is a great quality.” Mathematics He was modest and self-effacing,” John Mather, he said. “Because of his introverted “His death is a big loss for our remembered as personality, one had to work hard community worldwide because a “great math- to talk about John’s work with he was one of the leaders in this ematician” with him. It was an effort amply repaid, field,” Kaloshin said. “He leaves a a reserved and but you had to put in the effort. I’m big void.” pleasant demean- very happy to have put in the ef- or, died Jan. fort.” 28 of complica- Mather received numerous awards for his work, including the Birk- Photo by Mariana tions from pros- Vadim Kaloshin, a professor of Cook, “Mathemati- tate cancer at his hoff Prize in Applied Mathematics cians: An Outer View mathematics at the University from the American Mathematical of an Inner World” home in Princ- of Maryland who was Mather’s eton. He was 74. Society (2003); a Guggenheim graduate student, recalled weekly Fellowship (1989); the John J. meetings with Mather at which Carty Award from the National Mather specialized in differential they would freely share ideas Academy of Sciences (1978); topology and dynamical systems. and insights. During one session, and a Sloan Fellowship (1970). After receiving his Ph.D. in math- Mather made a comment that Mather also was a member of the ematics from Princeton in 1967, became the crux of Kaloshin’s American Mathematical Society Mather, as an associate professor Ph.D. thesis wherein he solved and the National Academy of Sci- at the Institute of Advanced a 30-year-old conjecture posed ences, among other organizations. Scientific Studies in France, soon by American mathematician Ste- distinguished himself when he phen Smale. proved a conjecture by renowned Mather is survived by his wife, French mathematician René Naomi Mather, and children Mara “His questions and comments Mather (Noah Mercer) of Los An- Thom. Mather and Thom went pushed me toward the solution on to develop the Thom-Mather geles; Thomas John Mather '99 to this conjecture. He made an (Karen Madsen) of Boston; and isotopy theorem, one of many important comment that later influential theorems in topology Frank Mather and Emily Mather became a central part of my the- of Princeton. and dynamics that bear Mather's sis,” said Kaloshin, who received name. Others include the Mather- his doctorate from Princeton in Thurston theorem and the Au- bry-Mather theory. Mather (left) with his father, Norman Mather, a professor of electrical engineering. They became the University's first father-son professors since 1932. Professor Charles Fefferman knew Mather since they were both graduate students at Princ- eton in the 1960s. While they did not study the same field, Feffer- man followed Mather’s work and appreciated his exceptional tal- ent, he said.

“Most mathematicians feel about math the way musicians feel about music — when we encoun- ter a masterpiece, it’s a great priv- ilege,” Fefferman said. Page 6 Faculty Memorials Professor Emeritus John C. Moore, 1923–2017 By Morgan Kelly, Office of the Eilenberg-Moore spectral Moore brought deep algebraic Communications sequence published in 1962. structure to algebraic topology, In 1965, he published his most May said. His work reflected his Professor Emeritus John C. cited paper, which pertained to profound and constant thinking Moore, described as a com- Hopf algebras, with renowned about mathematics, May said. mitted and influential math- mathematician and Stony Brook Moore would ruminate on mathematician, died Jan. University mathemat- ematical problems even if he were 1 in Rochester, New ics professor John in the middle of another task. York. He was 92. Milnor, who received May recalled that if Moore made his bachelor’s and doc- a mistake or got stuck during a Moore joined the toral degrees in mathe- class, he would stop everything Princeton faculty as matics from Princeton and silently ponder the error un- an instructor in math- in 1951 and 1954, re- til the correct answer came to ematics in 1952 be- spectively, and served him. So deep was he in thought fore being named an as a Princeton profes- that Moore never recalled these assistant professor sor of mathematics instances afterward, May said. in 1954. He became from 1960 to 1967. a full professor in Moore was born May 27, 1923, 1961 and was named Peter May, a Univer- in New York City. He was a Na- co-chair of the Department of sity of Chicago professor of tional Science Foundation Fel- Mathematics in 1962 before re- mathematics and graduate stu- low from 1953 to 1955 and chair tiring from Princeton in 1989. dent under Moore in the early of the United States Commission 1960s, said that his former men- on Mathematical Instruction Moore specialized in algebraic tor belonged to a “great genera- from 1960 to 1962. Moore is sur- topology and had many impor- tion” of mathematicians, many vived by a niece, Jennifer West, tant concepts named after him, of them algebraic topologists, and nephew, Jeff West. including the Borel-Moore ho- who were hugely influential. mology published in 1960, and Professor Emeritus Gerard Washnitzer *50, 1926–2017 By Morgan Kelly, Office of ercised his extensive knowledge Washnitzer's quick mind and Communications on topics in spirited yet friendly exuberance also came out in his debates, and by pushing his stu- role as an educator, Gunning Gerard Wash- dents intellectually. said. "His lectures were memo- nitzer, professor rably wild, with some notable di- of mathematics, "Gerry was always very much gressions when he was struck by emeritus, known interested in the history of math- a different idea or an alternative for his work in al- ematics, somewhat unusual approach to a problem," he said. gebraic geometry among real mathematicians, and and lively person- he taught the rather rare history Washnitzer was married to Lil- ality, died April of mathematics courses in the lian Noble née Berg, who es- 2 in hospice in department before he retired," caped from Belgium in 1941, Scotch Plains, said Robert Gunning, a Princ- from 1953 until her death Jan. Photo by Jack Turner New Jersey. He eton professor of mathematics. 23. Washnitzer is survived by was 91. his sons George Noble and Ber- Washnitzer received his Ph.D. nard Noble of New York City, Colleagues and family recalled in mathematics from Princeton and James Noble of Summit, Washnitzer as an avid reader in 1950 and joined the Princeton New Jersey, and by seven grand- who loved history as much as faculty as a professor of math- children. mathematics — particularly the ematics in 1963. history of mathematics. He ex-

Page 7 Women and Mathematics Princeton-IAS Program for Women and Mathematics By Christine Taylor program, participants spend a day in Fine Hall to hear lectures The Noetherian Ring Each May, about 40-60 under- given by Princeton faculty mem- graduate, graduate, and postdoc- bers. Lunch and dinner in the The Noetherian Ring is an infor- toral women studying mathemat- Professors’ Lounge are high- mal organization for the Princ- ics from institutions all over the lights of the day where partici- eton Mathematics Department's country gather on the campus of pants enjoy meeting Princeton women at all levels, from first the Institute for Advanced Study graduate students, postdocs, and year undergraduates to senior in Princeton for an intensive faculty as well as the spectacular faculty. It offers opportunities residential mentoring program. view from the top of Fine Hall. for female mathematicians to in- The two-week Program for teract with one another in many Women and Mathematics is gen- Last May, Princeton alum Carlee different forums, with the goal of erously sponsored by the NSF, Joe-Wong '11, current graduate building networks of support. IAS, and Princeton Mathemat- student Sophie Spirkl, and Profes- ics department. The program sor Zoltán Szabó talked about their The Mathematics Department aims to inspire talented women work in network behavior, graph and the Noetherian Ring host a from undergraduate through theory, and knot theory respective- luncheon in the fall to welcome doctoral levels to achieve their ly. Lillian Pierce '02 *09 shared first-year students in MAT203, educational and career goals, her experiences building sup- 215, and 216, and a luncheon in as well as to address the isola- port networks for women math- the spring to welcome sopho- tion and lack of support many ematicians throughout her career. mores who are likely math ma- women face in mathematics. jors. These luncheons are well This May, new instructor attended by math majors, gradu- Research mathematicians such Evita Nestoridi, Assistant ate student, postdocs, and facul- as Professor Maria Chud- Professor Adam Marcus, and ty members, who share their ex- novsky *03 and Wei Ho *09 Professor Assaf Naor will each periences and perspectives with are recruited to give lecture se- give expository talks on their one another. In addition, since ries and colloquia which focus work. In addition, there will be spring 2017, female graduate on a particular mathematical a two-hour computing workshop students, postdocs, faculty, and theme of current research each to instruct participants on the use visiting mathematicians meet year. Some topics in recent of GAP (Groups, Algorithms, regularly over a casual buffet years are "Combinatorics and and Programming) software for dinner at the IAS to bond social- Graph Theory (2013)", "Ran- computations in group theory. ly and mathematically. dom Matrix Theory (2014)", "Aspects of Algebraic Geometry Continued on next page... (2015)", "Curves, Loops, and Graduate and undergraduate students enjoy lunch in the Professors' Lounge Words in Geometry (2016)", as part of the Noetherian Ring "Geometry and Randomness in Group Theory (2017)".

In addition to lectures and seminars, evening Women in Science seminars explore topics of interest to women mathematicians. Some popular topics include "Work- Life Balance in a Mathematical Career", "Surviving in Graduate School", "Career Paths for Wom- en in Mathematics", "Becoming an Academic Mathematician".

In the middle of the two-week Page 8 The Minerva Program

The Minerva Program: Shmuel Weinberger and Maryna Viazovska

This year Shmuel Weinberger came to Princ- In the spring, Maryna Viazovska joined the de- eton as our Minvera Distinguished Lecturer partment as our Minerva Distinguished Visitor. and Maryna Viazovska joined us as our Mi- During her month at Princeton, Viazovska de- nerva Distinguished Visitor. livered a series of four talks on "Solving packing problems by linear programming." The sphere In the fall Weinberger, the Andrew MacLeish packing problem asks which biggest portion of Professor of Mathematics at the University of the euclidean d-dimensional space can be covered Chicago, delivered a series of three Minerva Lec- by non-overlapping unit balls. In most dimen- tures on "Episodes from Quantum Topology". sions d this question is believed be an extremely These talks focused on the questions of how ef- difficult combinatorial geometric problem. Vi- fective are solutions of topological problems, and azovska explained the surprisingly simple solu- in particular, how large solutions to geometric tions to this problem in dimensions 8 and 24 topological problems are with various measures based on linear programming bounds. of complexity.

Weinberger Viazovska

Program for Women and Mathematics Continued from previous page... Over two weeks, women mathematicians from have visited Princeton as part of the Women and all levels learn, work, and socialize together in Mathematics program; about 70% have remained a supportive environment. Mathematical bonds in academia. Over the 8-year period 1999-2006, are often created between senior mathemati- the average Ph.D. completion rate for WAM cians and graduate students/postdocs. Past undergraduate participant alum is 64.6%, while participants overwhelmingly report that they the average Ph.D. completion rate for WAM feel inspired and encouraged by the women graduate participant alumnae over the 10-year they meet during the program, and that the period 1999-2008 is 79.8%. For comparison, the program is a vital opportunity to reinvigorate 10-year completion rate for a mathematics Ph.D. their studies and research. Many student paris 51% for both genders. The program alumnae ticipants return to the program in subsequent who have benefitted from their experience at the years as teaching assistants, lecturers, and col- Women and Mathematics Program will help us

Credit: Maryam Mirzakhani Maryam Credit: loquium speakers. to continue to strengthen the program for future women mathematicians. Since 1994, over 1,000 women mathematicians Page 9 Extracurricular Activities Scribble Naturally: Using Technology to Enhance Collaboration By John Stogin '11 *17 the same chalkboard, so collabor- we need to hear other research- ative research can take place even ers want. Besides peer-to-peer Can tablets between colleagues who aren’t collaboration, other possible ap- help us solve able to meet in person. plications include recording and mathematical posting solutions to problems, problems at the At the most basic level, our web- hosting a course question-and-an- research level? site supports real-time collabora- swer forum, giving lectures with What about tivedrawing (like Google docs, a tablet, holding remote seminars computers? I but for handwritten equations between multiple universities, and think so, and and diagrams) with embedded digitally organizing personal notes here's why. voice and video calling. It also and scratch work. We are look- supports uploading and export- Together with ing to talk to more students and ing PDF documents that can be researchers, especially at different some other annotated on-screen. For users Princeton stu- universities, to learn how this proj- dents, we have been talking to many people—mostly mathematicians and scientific researchers— to learn why they are still uncom- fortable using technology for their scratch work. The cool thing is we identified some ways to make it easier for mathematicians to transition to computers (especially tablets) for developing and communicating our mathematical ideas with one another. Using the ideas we learned, we started the Scribble Naturally project. Just to emphasize what computers have to offer, consider how computers helped the novelists. In the day of the typewriter, the Scribble Naturally allows collaborators to video chat while working on a digi- novelists had to think carefully tal canvas in real time. before writing things down on- paper. But today, anyone can in- without a tablet, it has a cam- ect can provide an ideal experience stantly type any idea that comes era scan feature that can convert for them. If you found this article to mind in a word processor, then paper drawings or printed equa- interesting, please contact me at they can cut and paste as they it- tions into digital markings with [email protected]. I erate towards a better paragraph. the background removed. Al- would love to hear from you. It’s very freeing. But when it though our website is designed comes to equations and diagrams, to be useful for mathematicians Try Scribble Naturally at: we’re still stuck with pen and pa- without a writing tablet, we are www.scribblenaturally.com per—the mathematician’s type- also working on a tablet compan- writer. ion app to help those who do have writing tablets to make the most John Stogin defended his disserta- The Scribble Naturally project use of them. As our project name tion, "Nonlinear Wave Dynamics website is currently in a beta suggests, we want to support any in Black Hole Spacetimes", ad- testing stage, but feel free to try mechanism through which peo- vised by Professor Sergiu Klainer- it out. Through this project, we ple draw naturally. man, this April. Next year, in ad- hope to replicate the experience dition to developing the Scribble There are a lot of directions we of two (or more) people standing Naturally project, he will start could go with this project, and in the same room and working on work at Radix Trading. Page 10 Alumni Profile Musings of a Mathematical Mom: Life After Princeton By Sasha Fradkin *11 After getting my of kids at the Golden Ph.D. from Princeton, Key Russian School. I worked for 5 years as I quickly became fas- a research mathemati- cinated with just how cian at the Center for much one can do with Communications Re- such small children, search in Princeton. with how creative and profound their questions can be, and how About 4 years ago, many deep concepts when my daughter they could appreciate was 4, I started doing if they were presented fun enrichment math with her. to them in an age appropriate Around the same time, I began way. And of course I continued blogging about our math adven- blogging about it all. tures on a blog I entitled Musings of a Mathematical Mom. Shortly after I started doing math with A little less than a year ago, I Sasha's blog covers fun ways to intro- Katie, she was joined by a friend, was presented with an exciting duce mathematical concepts to children, and not long after that I began and unique opportunity to de- e.g., using mirrors to create symmetrical teaching several larger groups velop an innovative elementary shapes school curriculum Sasha's upcoming book, Funville Adventures, will be and teach it to small math. 4) To show that math is a published by Natural Math later this year. groups of students. human endeavor and to teach it Since September, with historical perspective. I have worked as Also shortly after I began doing the Head of Math math with Katie, inspired by her at the Main Line love for stories, I started work- Classical Academy, ing on a children’s fantasy story teaching students in with interwoven math concepts. grades Kindergar- This project turned into a book ten, 2nd, and 3rd. called Funville Adventures, co- Some of my goals authored with fellow Princeton are 1) to show stu- undergraduate Allison Bishop, dents that math is that will be published by Natu- about exploration, ral Math later this year. The discovery, and look- book is a math-inspired fantasy ing for patterns, and adventure that introduces young not about memoriza- children to the concept of math- tion of facts and for- ematical functions; the functions mulas. 2) To teach/ are personified by magical - be encourage students ings with powers. to think, reason, no- tice and wonder. 3) To show them that Visit Sasha's blog, Musings of a math is much more Mathematical Mom, at: than just arithme- https://aofradkin.wordpress.com/ tic and to give them glimpses of many different areas of

Page 11 Undergraduate Program

Putnam Competition From the Math Club: Each year the department fields By Jenny Kaufmann '18 one or more teams in the Wil- Hello from your undergraduate Math Club president! This year Math liam Lowell Putnam competi- Club hosted a variety of events, including weekly colloquia for under- tion. This year, the competi- graduate audiences, the traditional biweekly Board Game Nights, Meet tion's 76th, Princeton's team of Your Professor dinners in which students can talk to professors in a so- Eric Schneider, Alex Song, and cial context, and the Mentoring Mobius peer mentorship program. We Xiaoyu Xu won 2nd place. also hosted the annual Pi Day celebration (complete with a dozen pies), as well as the end-of-year dinner in May, which provides students with Eric Schneider and Murilo the rare opportunity to socialize in the Professors' Lounge. Zanarella earned N1 distinction (6th-14th place), and sophomore The Math Club continues to assist with the Mercer County Math Circle, Simona Diaconu won the Eliza- a program open to all mathematically inclined high school students. At beth Lowell Putnam Prize as the this program, Math Club members teach lessons on interesting topics of highest ranking female contes- their choice. This past fall, many Math Club members became involved tant. with MathReach, a new Pace Center-affiliated outreach program which partners with a Trenton high school to broaden access to enrichment We also have seven honorable math to a more diverse array of students. Through MathReach, volun- mentions this year: Rodrigo An- teers visit classes and teach lessons in recreational math topics such as gelo, Andre Arslan, Simona Dia- Pascal’s Triangle or mathematical games and puzzles. conu, Eric Neyman, Mel Shu, Xiaoyu Xu, and Roy Zhao. In that spirit, here is a puzzle for your enjoyment: The Chocolate Bar. I have an n by m rectangular chocolate bar and want to break it up fully into nm mini bars. What is the minimum number of breaks needed to Department Awards accomplish this? What is the maximum? 2015-2016 Academic Year From the Chair George B. Covington Prize Arka Adhikari '16 Continued from page 2... awarded the Excellence in Teaching Awards by the Undergraduate Daniel Nelson Dore '16 and Graduate Engineering Student Councils, and that Anibal Velozo Middleton Miller '29 Prize received the Graduate School's Teaching Award. Yuval Wigderson '16 Elizabeth Yang '16 I thank Igor Rodnianski for serving as Acting Chair last year while I was on leave at the IAS. From overseeing the renewal of the faculty, Andrew H. Brown Prize to initiating the refurbishment of Fine Hall, to hosting events, he was Daniel Siyan Li '17 outstanding. Peter Park '17 Finally it is my pleasure to thank Bob and Luisa Fernholz, the Class Peter A. Greenberg '77 Prize of 1971 Fund, and Michael *91 & Victoria Bershadsky for their very Iason Kountouridis '17 generous and ongoing support of our Department. Their support of Joseph Obiajulu '17 faculty, students and department activities has made a huge difference. The Class of 1861 Prize I continue to be amazed by the faculty, students, and staff in our De- Xiaoyu Xu '18 partment. It is both inspiring and humbling to see the next generation of mathematicians develop and grow. Thank you for reading this newsletter and reconnecting with the Department. I’d love to hear your thoughts and views. David Gabai *77,*80 [email protected] Page 12 Graduate Program Graduate Profile: Medhi Yazdi Director of Graduate Studies: Peter Ozsváth

I worked on Princeton is a unique place to pursue gradu- geometric to- ate studies. The primary focus of the gradu- pology during ate program is to train leading researchers in my Ph.D. My mathematics, putting as few hurdles as possible thesis is about along the way. Of course the students work foliations where closely with their advisors, who are top math- I have con- ematicians; but what I think is special about structed coun- our department is the relationships between terexamples to the students, who often work very closely with a conjecture of one another, whether it is to prepare for their Bill Thurston, generals, follow our research-level courses, give my academic expository talks, or to actually engage in joint grandfather. Next Fall, I will research projects. The bonds that form in this program are strong go to the University of Oxford and, as I can attest after having graduated from here myself in 1994, where I will be a Glasstone Fel- span decades. low. This year was a particularly successful one for graduate student re- I grew up in Iran and finished cruiting. The entire department came together to this very impor- my undergraduate studies at tant end. Starting in December, a committee of seven professors Sharif University of Technol- went through the roughly 350 applications, consulting with their ogy in Tehran. I like painting colleagues along the way. In January, the full senior faculty met to go and also playing soccer. I guess through the top files to make the final admission decisions. Faculty that my love for topology and members then contacted students in their areas to provide informa- geometry and my passion for tion about research and mathematical life at Princeton. Jill LeClair painting and visual arts stem went through the daunting task of organizing what turned out to be from the same source. We had a very successful open house for our prospective graduate students. a soccer team in the intramu- During this event, many students and faculty presented their work, ral games named FC Fine, af- both formally and informally, to the prospective students who came ter Fine Hall. We used to play from around the world. At the end, we exceeded expectations, ad- as FC Fine for the past three mitting a class of 24 graduate students! years and FC Fine even won the tournament in the univer- The job of a Director of Graduate Studies (DGS) is a pleasant and sity once. I hope this tradition easy one: typically, I meet with many interesting students, who are continues as new students en- happily pursuing their dream of becoming a mathematician. When ter the program. Surely Princ- problems arise, students can turn to me for advice, or they can turn to eton has a lot to offer math- my fellow DGS, Javi Gómez Serrano, who is reliable and organized, ematically, but in my personal but more importantly very approachable and friendly. Jill LeClair, experience, the lovely people our graduate administrator, is an invaluable resource both for us and that I met in this town are even for the students. She goes far beyond the call of duty to make sure more valuable. I will certainly that the life of graduate students is as pleasant as possible, whether miss my friends, my advisor, it is by organizing various aspects of student life, lending an ear to Jill — the graduate adminis- students with professional or personal problems, or by organizing trator who always takes care of our spectacular Spring Recital, which gives our students and faculty us — and Wilhelmina who is a non-mathematical outlet for their talents. I write this the day after our lovely company for the af- the recital, with the sounds of the music still reverberating, looking ternoon chat over coffee. forward to greeting our new incoming class next year!

Page 13 Most recent Ph .D.s

Original Name Undergrad Advisor Field Thesis Title Placement Maria Avdeeva Moscow State Sinai Dynamical Limit theorems for B-free Queen's University, University Systems integers and the Moebius Ontario/Postdoctoral function Fellow

Nathan Dowlin Yale University Szabó Low- Khovanov-Rozansky Columbia University/ Dimensional complexes in the knot floer NSF Postdoctoral Topology cube of resolutions Research Fellow

Will Sawin Yale University Katz Number A Tonnakian category and Institute for Theory a horizontal equidistribution Theoretical Studies, conjecture for exponential ETH Zürich/Junior sums Fellow Naser Talebizadeh Sharif University Sarnak Number Optimal strong approximation University of Sardari of Technology Theory for quadratic forms Wisconsin, Madison/ Postdoctoral Research Fellow Linh My Truong University of Ozsváth/ Low- Applications of Heegaard floer MIT/NSF Pennsylvania Szabó Dimensional homology to knot concordance Postdoctoral Topology Research Fellow

Xuecheng Wang Peking Ionescu PDEs Global solutions for the gravity Princeton University/ University and Fluid water waves system: infinite Researcher dynamics depth setting and flat bottom setting

Xiu (Chris) Yang University of Ozsváth Low- Elliptic involution in bordered KCG Holdings/ Michigan, Ann Dimensional Heegaard floer homology Quantitative Arbor Topology Strategist

Ruobing Zhang Yantai University Chang/ Geometric Regularity, quantitative Stony Brook Yang Analysis geometry and curvature bonds University/Simons Instructor Waterman Award Continued from page 1... The Waterman Award is given to at most two re- Four of these seven were Princeton faculty at the cipients each year, and the pool of candidates spans time of their award: Charles Fefferman, Pardon, all science and engineering fields. Since its incep- Bill Thurston, and Ed Witten *76 (Physics); Gang tion in 1976 (the inaugural award went to Professor Tian joined our faculty after receiving the Waterman Charles Fefferman *69), only seven of 44 Waterman Award. Awards granted to date have gone to mathematicians. Of those seven, six have strong connections to Also of note is that of the seven mathematicians to Princeton. receive Waterman Awards, Fefferman, Pardon, Wit- ten, and Terence Tao *96 are Princeton alumni.

Page 14 Administrative staff changes Scott Kenney: 30 Years of Dedicated Service

My first day in the Math Depart- 10 chairs since 1986 (and two acting chairs). I had ment was in December 1986 and, my hands on the appointment forms of Fields Medal- while it doesn’t seem like yester- ists and world-famous mathematicians from all over day, it doesn’t seem like it was 30 the world. I prepared the appointment papers for years ago, either. In those days probably 200 junior faculty members and virtually I had thick brown hair and two all of the senior faculty members hired since 1986. young children (one a toddler). I dealt with visa issues, housing issues, childcare This year—on February 27th—I issues, and managed to make lots of friends along stood in front of the crowd of peo- the way. I handled the practical arrangements for ple assembled at the lovely Tea the countless mathematical conferences and remember Department was holding for me vividly my first: Eli Stein’s 60th birthday celebra- as a way for me to say good-bye to tion, which attracted mathematicians from all over Scott Kenney in 1989 “my” department. the world and served as such a tribute to the won- derful man who hired me. (Eli Stein was coming to It is with leaving that I think of those who came the end of his second stint as chair in 1986.) One of before me and the many people I’ve come in con- the later conferences I would work on would be to tact with over the years. I replaced the irreplaceable honor Eli Stein for his 80th birthday, too. Confer- Virginia (Santowaso Nonziato) Dzurkoc—Ginny to ences became like old home week and I enjoyed the all who knew her—after 44 years of service—and opportunity to catch up with those former students quickly realized that I had some catching up to do. who had found their way in their professional lives Twenty-five years later, I would step down as the since their days as graduate students in Fine Hall. Department Manager and semi-retire in a position that allowed me to handle the practicalities of seven It was not always an easy job nor did I appreciate all conferences in one year and serve. My replacement the challenges that came my way. At the end of the was Kathleen (Kathy) Applegate, whose energy is day—at the end of my career—it’s all about the peo- only matched by her big heart as she handles the ple. The people are what matters. The Princeton many challenges of being Department Manager. Mathematics Department has been my biggest sup- Kathy was gracious enough to put up with having porter and advocate. I can’t begin to thank them for her predecessor with her for four years and kind what they have given me and, as I gaze out the front enough to make me continue to feel valued and ap- porch of my new house overlooking the mountains preciated. and the bays of rhododendron that seem to be every- where, I will be perpetually grateful for my 30 years I tried to come up with some statistics for my years in the Math Department and for all the people: the in the Department and realized that I’d worked with faculty, students, and staff, who brought so much pleasure to my life. Scott shares stories after being named an Honorary Faculty Member at a special tea in his honor. Ankit Tak Department office support

Ankit joined the department in our new support position this February.

Ankit is originally from New York, and received his B.S. in International Business and Finance from Rider University in 2013.

In his spare time, Ankit enjoys travelling, noting that "travel is about finding those things you never knew you were looking for."

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] Annual Alumni Reception Friday, June 2, 2017 Fine Hall Common Room, third floor 2:00 pm — 3:30 pm

Join us for fun, refreshments, and maybe even some math!

This year's Department Recital was our largest yet, featuring 20 musicians from the Math Department, other Uni- versity departments, and the IAS. From left: Professor Clancy Rowley (MAE), Senior Lecturer Mark McConnell, Professor Emeritus William Browder; Yuchen Liu *17; and Evan O'Dorney (G1)