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Home , Goro Shimura, Hillel Furstenberg, Peter Sarnak, Yakov Sinai

2020–2021 • Issue 9 Department of From the Chair Teaching During a Pandemic

I would like to extend my sin- "The first indication we had of the bining live lectures and office hours cerest congratulations to the class coming disruption was at the very with pre-recorded content. Instructor of 2021, as well as those graduate beginning of the spring 2020 semester Dr. Andrew Yarmola taught MAT201: students who will complete their when junior faculty who'd spent the “The lecture itself contained basic final public orals over the next few winter abroad were having difficulty examples, the pre-recorded problems months. While the past two years getting back into the country. were usually more detailed and al- have presented some unusual ob- "Big restrictions kicked in suddenly lowed students to focus on specific stacles, I am proud to see our stu- during midterm week. At that point topics (and review as they saw fit). dents continue to thrive academically everyone was trying to be hopeful All-in-all, my sense is that the students as they rally towards their goals. I am also happy to welcome the that life would return to normal in saw more worked-out problems in live undergraduate classes of 2019 and a few weeks, but it rapidly became Zoom precepts and pre-recorded prob- 2020, as well as those graduate clear that optimism might not be the lems vs. a usual non-virtual year.” students who have completed their best strategy." Dr. Jennifer Johnson, A variety of approaches gave us a PhDs since our last publication, as Senior Lecturer and Associate Direc- better idea of what was and was not new members of our distinguished tor of Undergraduate Studies oversees working. “We saw through student alumni. the department’s large, multi-section feedback that higher production videos Much has changed on a global calculus and linear algebra courses, did not necessarily equate to a better scale in recent times, and the Princ- and as it became clear that the spring learning experience for the students; eton University Math Department term would have to transition to an they much preferred videos that felt holds no exemption. But while we online format she began work with our more ‘real’ to them, for example videos find ourselves in a time of unique dedicated faculty to ensure the spring recorded at a chalkboard” recalls Dr. challenges, it is also proving to be semester was able to carry on and to John Fickenscher, Associate Research a time of exceptional achievements. prepare for the likelihood of a full year Scholar and Lecturer. Last spring, when the university transitioned to online teaching and of virtual teaching. While recorded course materials research in response to the COV- Going Virtual worked well as supplementary mate- ID-19 pandemic, we found ourselves The immediate move online in the rial to the courses, Dr. Johnson saw in largely unfamiliar territory. De- spring of 2020 naturally led to experi- in mid-semester feedback that stu- spite this, I am pleased to report that mentation with teaching styles, com- ...continued on page 11 the math department was able to le- verage academic, administrative, and technological resources to swiftly or- Inside this issue: chestrate the framework for this new Faculty Retirements— Page 4 way of learning, which continued to Faculty Memorials— Page 5–6 improve over the 2020-2021 academ- ic year. In addition to the facilitation Honors and Awards — Pages 6–7 of online classes, the department has Climate and Inclusion — Page 9 also kept its seminar program active Alumni News — Page 9 with an online schedule that matches that of previous years, and continues Special Events — Page 10 ...continued on next page Undergraduate Program — Page 13 Graduate Program — Page 14 From the Chair from the Chair ...continued from previous page tures. This July, will also to cultivate academic collaboration as The department also created a new retire to Emeritus status after twenty- we adapt to these unexpected changes. Climate and Inclusion Committee eight years with the department. It is inspiring to witness the unwaver- this year. Chaired by Professor Peter Among his many professional achieve- ing perseverance, enthusiasm, and ca- Sarnak, this committee of faculty, ments, Sinai's extensive work in math- maraderie of our faculty, students, and students, alumni, and staff has begun ematical physics and staff as they rise to meet the challenges the hard work of addressing important earned him the in 2014. of such an unprecedented chapter in issues to our community. In addition He has also made a significant impact our university’s history. to town hall meetings and directed as a teacher, and has advised over 50 This year, we welcomed one new mentorship programs, a new Horizons students throughout his career. Assistant Professor, four new instruc- Lectures series began this year, where Members of the department have tors, and four new researchers to the speakers are invited to give both a continued to receive accolades and department. We are also pleased to research talk and host a seminar on awards in the field of mathematics. report that seven new instructors and the societal impacts of mathematics To highlight a few of many notable assistant professors have accepted with respect to diversity, inclusion, and achievements, Aleksandr Logunov was offers to join our junior faculty over mentorship. Our inaugural Horizons named both a Packard Fellow and a the next couple of years. During this Lecturer was Trachette Jackson of the Sloan Research Fellow, and received academic year, we were honored to University of Michigan, who hosted a the New Horizons Prize; and Tristan have Chenyang Xu join our depart- compelling panel discussion. Buckmaster received a Clay Research ment as a Professor of Mathematics. Since the last publication of Fine Award (joint with Philip Isett *13 and We welcomed Jacob Rasmussen of Letters, the department lost two stellar former Assistant Professor Vlad Vi- the University of Cambridge, as our . Professor Emeritus col). Our alumni have also continued Minerva Distinguished Visitor in the Goro Shimura, internationally re- a tradition of success, with Hillel Fur- spring of 2020, and James Maynard of nowned within the fields of modern stenberg *58 receiving the Abel Prize, the University of Oxford delivered an , and *93 taking home the online series of three Minerva Lec- and automorphic forms, passed away Breakthrough Prize. in May of 2019. We also lost Professor In closing, allow me to express my Department Administration Emeritus John Conway, who passed disappointment that alumni weekend Chair last April. A prolific and imaginative events, and many end-of-year activi- Igor Rodnianski thinker, Conway’s enormous math- ties, are once again canceled as a result ematical contributions will leave a of the pandemic. The department’s Associate Chair lasting mark on current and future Alumni Reception is an important János Kollár generations of mathematicians. tradition, and I count myself among Departmental Representative At the end of the 2019-2020 aca- the many members of the department János Kollár demic year, we celebrated the retire- who look forward to reconnecting with ment of Professor Robert Gunning, alumni during this exciting time of Director of Graduate Studies Mihalis Dafermos who has been a member of the depart- year. Despite this set back, I know that Evita Nestoridi ment since 1956. Among his many many of you will continue to stay in contributions to the university, Robert touch with members of the Fine Hall Senior Advisors served as Chair of the Mathemat- family, and I look forward to welcom- John Pardon ics Department, Chief Marshall for ing you all at future events. Junior Advisor University Convocations, and Dean of Mark McConnell the Faculty. An extraordinary teacher, he also received the President’s Award Placement Officer for Distinguished Teaching in 2003. Ana Menezes He transitioned to Emeritus status last Igor Rodnianski year. Department Chair Page Faculty Appointments Professor Chenyang Xu 2019-20 2020-21 The depart- Academic Year Academic Year ment is Daniel Álvarez Gavela Allen David Boozer pleased to Instructor Instructor Topology announce the Symplectic Geometry appointment Jacob Carruth Alan Chang of Chenyang Postdoctoral Research Associate Instructor Xu as a Profes- Analysis Analysis sor of Math- Duncan Dauvergne ematics. Instructor Evra Shai Instructor A leader Probability Number Theory in Algebraic Michele Fornea Geometry with a focus on birational Postdoctoral Research Associate Tristan Leger geometry, Professor Xu completed his Number Theory Postdoctoral Research Associate Analysis PhD here at Princeton in 2008 under Yusuf Bariş Kartal the supervision of Professor János Kol- Instructor lár. Xu was a CLE Moore Instructor at Symplectic Topology Sarah Peluse Veblen Research Instructor MIT from 2008-2011, after which he Ben Krause , Number Theory took positions as an assistant profes- Postdoctoral Research Associate sor at the University of Utah beforing Analysis Hannah Schwartz Postdoctoral Research Associate joining Peking University as a research Nicholas Marshall fellow and then a professor. Most re- Postdoctoral Research Fellow Topology cently Xu was a professor at MIT. Harmonic Analysis John Sheridan Professor Xu has received nu- Joaquín Moraga Postdoctoral Research Associate merous awards, including the 2016 Instructor Algebraic Geometry Ramanujan Prize, the 2019 New Algebraic Geometry Horizons Prize in Mathematics, and Takumi Murayama Fan Wei the 2021 Frank Nelson in Postdoctoral Research Fellow Postdoctoral Research Associate Combinatorics Algebra. Xu was elected to the 2020 Algebraic Geometry class of Fellows of the American Math- Eden Prywes Ruobing Zhang ematical Society for his "contributions Postdoctoral Research Associate Assistant Professor to algebraic geometry, in particular Functional Analysis Differential Geometry the minimal model program and the Ary Shaviv K-stability of Fano varieties." Postdoctoral Research Associate Analysis Senior Faculty Sophie Spirkl Appointments Instructor Graph Theory Two new Professors of Mathematics will join the department for the 2021- Maxime van de Moortel 2022 academic year, June Huh and Instructor PDEs, Emmy Murphy. Huh was previously hte Fernholz Visiting Professor in our Jingwei Xiao Veblen Research Instructor department and a Visiting Professor at Number Theory the IAS, and Murphy was previously a Professor at Northwestern University.

Page 3 Faculty Retirements Robert Gunning Robert C. Gunning was born in cal community as a whole. He served as Longmont, Colorado, in 1931. He is the chair of the mathematics department actually a sixth generation Coloradan, from 1976-79, and chief marshal for where his family lived long before University convocations for a decade be- Colorado became a state, and some of his fore becoming dean of the faculty from New England ancestors date back to the 1989-1995. He was a member of the Mayflower. He received his undergradu- editorial board for Princeton University ate degree in mathematics from the Uni- Press from 1969-73, and holds fellow- versity of Colorado-Boulder in 1952, and ships in the American Mathematical So- went on to complete his graduate work ciety and the American Association for and Ph.D. in mathematics at Princeton the Advancement of Science. Addition- in 1955 under the guidance of Salomon ally, he co-chaired the AMS Summer Bochner. Institute on Theta Functions (1987) and Robert has been affiliated with the colleagues and students who nominated the AMS Summer Institute on Several Department of Mathematics at Princ- him for the award praised his superb Complex Variables (1974). eton for nearly his entire career. After lecturing skills and profound insight into Robert has contributed greatly to the a year as an NSF postdoctoral fellow at the subject matter, as one would expect, field of function theory of one and sever- the , he joined the they also highlighted his sense of humor, al variables, and is known for authoring Princeton math department as a Higgins math jokes, and positive disposition. many books in this area. Among other Lecturer in 1956. He went on to serve One student in particular summarized accomplishments, he introduced indig- as an assistant professor, Sloan Fellow, Professor Gunning as "an inspirational enous bundles, and found a solution and associate professor, before being ap- combination of all the qualities that to the Schottky problem in the theory pointed as a professor in 1966. make up an excellent teacher." of Riemann surfaces. He transfered to His excellence in undergraduate and In addition to his faculty appoint- emeritus status last year after more than graduate teaching culminated in the con- ments and teaching accomplish-ments, six decades of tremendous contributions ferral of the President's Award for Dis- Robert has contributed extensive service to Princeton's mathematics department. tinguished Teaching in 2003. While the to the University, and to the mathemati- Yakov Sinai Yakov Sinai was born on September applaud his "numerous groundbreak- 21, 1935 in Moscow, Russia. Raised in ing results in the theory of dynamical an academic family, Sinai was strongly systems in mathematical physics and in influenced by his grandfather, Veniamin probability theory." His other accolades Kagan, who served as the head of the include the Wolf Prize in Mathematics, Department of Differential Geometry the Nemmers Prize, the Henri Poincaré at Moscow State, where Yakov would Prize, and the Leroy P. Steele Prize for complete his Ph.D. in 1960 under the Lifetime Achievement. advisement of . Professor Sinai is known for his Sinai's professional mathematical work in mathematical physics and career began in 1960 at his alma mater, probability theory, and has an exten- Moscow State, where he served as a sive list of publications in these areas, Scientific Researcher for the Laboratory including several with his wife, Elena of Probabilistic & Statistical Methods. Jones Professor during the 1997-98 B. Vul, a and physicist. In 1971, he was promoted to the role academic year. A prolific teacher and He is also known for the many math- of Professor, which he held for over advisor, Sinai is known for his engag- ematical processes and equations that twenty years. In the same year, he also ing and respectful interactions with are named after him, including Kol- accepted a position as a Senior Re- students, and has had over 50 advisees mogorov-Sinai entropy, Sinai's billiards, searcher with the Landau Institute of throughout his career. Sinai's random walk, Sinai-Ruelle-Bow- Theoretical Physics at the Academy Among his many awards, Sinai en measures and Pirogov-Sinai theory. of Sciences of Russia, a position he received the Abel Prize in 2014, which He transitioned to emeritus status this held concurrently with his teaching is considered the highest mathemati- year after 60 years of outstanding con- roles throughout his career. Yakov's cal honor. The Norwegian Academy of tributions to the mathematical commu- affiliation with Princeton University Sciences and Letters, which governs nity as a whole, and nearly thirty years began in 1993, when he joined the these awards, described Yakov as "one of service to Princeton University. department as a Professor of Math- of the most influential mathematicians ematics. He also served as the Thomas of the 20th century," and went on to Page 4 Faculty Memorials

Goro Shimura 1930—2019 by Liz Fuller-Wright, Office of Communications objects have a natural way of being become leading figures in their fields. presented other than the conventional “I was his last graduate student, which mathematical expressions. This think- made our mathematical levels maximal- ing led him to solve many longstand- ly mismatched — he was at the height ing problems and raise new areas of of a monumental career in number inquiry. In 1964, he formulated an theory and I was a beginning graduate important conjecture, building on the student,” said Hanke, a 1999 graduate work of his friend Yutaka Taniyama, alumnus. “He advised me to ‘find my that suggested a surprising relation own problems’ — difficult advice to between elliptic and modular curves. follow, but clearly what led him to his That conjecture turned out to be key greatness. He was willing to explore to then-Princetonian ’ questions regardless of whether there solution of Fermat’s Last Theorem. was a pre-existing formalism there to “Shimura was a man of the high- support him.” Among many honors and awards, Photo by Orren Jack Turner, 1964 est standards for research as well as for life in general,” Gunning said. “I Shimura received a Guggenheim Goro Shimura, Princeton’s Michael remember many discussions of possible Fellowship in 1979, the Cole Prize Henry Strater University Professor of appointments to the Princeton math- for number theory in 1976, the Asahi Mathematics, Emeritus, died on Friday, ematics department in which a major Prize in 1991 and the Steele Prize for May 3, 2019 in Princeton, . question was whether the appointment lifetime achievement in 1996. He is a He was 89. was up to Shimura’s standards.” member of the American Mathematical “Goro Shimura was a major Hanke echoed those sentiments: Society and the Mathematical Society research mathematician, creative and “He was a tireless champion of the of Japan, and he was a visiting member original and inspiring,” said Robert highest standards of professional of the Institute for Advanced Study Gunning, a fellow math professor. “He conduct for research papers and five times. He wrote more than 100 was a quiet presence around the depart- mathematical communication — a scholarly papers and books, including ment and we will miss him deeply.” truly principled person of integrity his 2008 autobiography, “The Map of He was “a true giant in the fields who cared deeply about the literature, My Life,” and a coffee-table book about of modern number theory, arithmetic academia and the impact that compro- the Imari porcelain that he spent 30 geometry and automorphic forms, mising standards could have on the years collecting: “The Story of Imari: whose pioneering papers and ideas next generation of young researchers,” The Symbols and Mysteries of Antique have shaped these fields in unmistak- he said. “While I have known many Japanese Porcelain.” able and enduring ways,” said Jonathan Fields medalists (and co-authored sev- “I recall him showing me around his Hanke, a visiting lecturer in mathemat- eral papers with one), it is the highest home once,” Sarnak said. “He had two ics at Princeton who was Shimura’s privilege of my academic life to have desks there, one at which he worked last graduate student. “He established been his student and to grow under the in the morning on new research, and many deep and surprising connections tutelage of a master like Goro Shimura. a second one which was devoted to between these fields and often seeded I have never met his equal and deeply polishing and preparing for publication research directions with his own pio- treasure the time we have spent to- papers, and I think this was used in neering and foundational work.” gether — as adviser, then colleague and the afternoons. After making a break- The Shimura varieties, generalizing later as a friend.” through and completing a draft of a elliptic functions with complex multi- Born Feb. 23, 1930, in Hamamatsu, new paper, he would put it in a drawer plication, are at the center of geometric Japan, Shimura studied at the Uni- in the second desk for a period of a year theory, said , Princeton’s versity of Tokyo, obtaining his B.A. or so to let it mature, before returning Eugene Higgins Professor of Math- in 1952 and D.Sc. in 1958. He taught to it and presenting it to the math- ematics. “Fundamental mathematical at the and Osaka ematical community. Given his striking truths have long shelf lives, and this is University before coming to Princeton publication record, it is clear that this especially true for Shimura’s works,” in 1962 as a visiting professor and then technique was very effective.” Sarnak said. joining the regular faculty in 1964. He Shimura is survived by his wife, Shimura once said that his guiding transferred to emeritus status in 1999. Chikako, his daughter, Tomoko, and philosophy was that many geometric Many of Shimura’s advisees have his son, Haru. Page 5 Faculty Memorials

John Horton Conway 1937—2020 by Catherine Zandonella, Office of the Dean for Research John Horton Conway, a legendary was a “magical genius,” defined as a mathematician who stood out for his person who is not merely smarter than love of games and for bringing math- most people but whose mind works ematics to the masses, died on Satur- in highly advanced and unfathomable day, April 11, 2020 in New Brunswick, ways. The term was coined by the late New Jersey, from complications related mathematician Mark Kac to describe to COVID-19. He was 82. the physicist Richard Feynman. Known for his unbounded curiosity One of Conway’s most well-known and enthusiasm for subjects far beyond accomplishments was the Game of mathematics, Conway was a beloved Life, which he conceived in the 1970s figure in the hallways of Princeton’s to describe how life can evolve from mathematics building and at the Small an initial state. The concept builds on World coffee shop on Nassau Street, ideas that trace back to John von Neu- where he engaged with students, fac- mann, a pioneer of early computing, ulty and mathematical hobbyists with in the 1940s. Conway’s game involves himself was most proud, according to equal interest. a two-dimensional grid in which each Kochen, was his invention of a new sys- Conway, who joined the faculty in square cell interacts with its neighbors tem of numbers, the surreal numbers. 1987, was the John von Neumann Pro- according to a set of rules. Over time, This continuum of numbers includes fessor in Applied and Computational these simple interactions give rise to not only real numbers such as integers, Mathematics and a professor of math- . fractions and irrational numbers such as ematics until 2013 when he transferred , who was advised pi, but also the infinitesimal and infinite to emeritus status. by Conway during his first year as a numbers. “John Conway was an amazing graduate student at Princeton and who Later, with Kochen, Conway mathematician, game wizard, polymath is now Princeton’s Brandon Fradd, developed and proved the Free Will and storyteller who left an indelible Class of 1983, Professor of Mathemat- Theorem in 2004 to explain principles mark on everyone he encountered — ics, said that Conway’s love for games of quantum mechanics, the branch of colleagues, students and beyond — and magic tricks as a way to teach physics that dictates the behaviors of inspiring the popular imagination just mathematical concepts inspired Bhar- atoms and other elementary particles. It as he unraveled some of the deepest gava’s own approach. states that if an experimenter can freely mathematical mysteries,” said Igor “I learned very quickly that playing choose what to measure in a particular Rodnianski, professor of mathematics games and working on mathematics experiment, then elementary particles and chair of the Department of Math- were closely intertwined activities for can also freely choose their spins in or- ematics. “His childlike curiosity was him, if not actually the same activity,” der to make the measurements consis- perfectly complemented by his scientific Bhargava said. “His attitude resonated tent with physical law. originality and the depth of his think- with and affirmed my own thoughts The Free Will Theorem gained ing. It is a great loss for us and for the about math as play, though he took this attention for its implication that if entire mathematical world.” attitude far beyond what I ever ex- humans have free will, then elementary Over his long career, Conway made pected from a Princeton math professor, particles — like atoms and electrons — significant contributions to mathemat- and I loved it.” also possess free will. ics in the fields of group theory, number Conway’s genius led to many discov- Conway’s numerous honors include theory, algebra, geometric topology, eries and accomplishments far deeper the London Mathematical Society’s theoretical physics, combinatorial game and more fundamental than the Game Berwick Prize and Pólya Prize, North- theory and geometry. of Life, according to Peter Doyle, a western University’s Nemmers Prize “He was like a butterfly going from longtime friend and collaborator, and a in Mathematics, and the American one thing to another, always with magi- professor of mathematics at Dartmouth Mathematical Society’s Leroy P. Steele cal qualities to the results,” said Simon College. “People invariably describe Prize for Mathematical Exposition. Kochen, professor of mathematics, Conway as the inventor of the Game of emeritus, a former chair of the depart- Life,” Doyle said. “That’s like describ- Conway is a fellow of the Royal Society ment, and a close collaborator and ing Bob Dylan as the author of ‘Blowin’ of London and the American Academy friend. in the Wind. of Arts and Sciences. Kochen went on to say that Conway The achievement for which Conway Continued on page 12... Page 6 Faculty Awards

Noga Alon Duncan Dauvergne Peter Sarnak Alon and his was named the received Royal co-author received 2020 Doctoral Society’s Sylves- the 2021 Steele Prize Recipient ter Medal for his Prize for Math- by the Canadian “transformational ematical Exposi- Mathematical contributions across tion. Alon also shared the 2019 Socity. number theory, com- Nerode Prize, given binatorics, analysis annually for a Shai Evra and geometry.” leading paper in the field of parameter- received the 2020 ized complexity, and the ACM Paris SASTRA Ramanu- Paul Seymour Kanellakis Theory and Practice Award. jan Prize for out- received the Com- standing contribu- memorative Medal Daniel Álvarez-Gavela tions by individuals from Comenius was awarded the not exceeding the University in Vicent Castelles Prize age of 32. Bratislava at a ceremony October 3rd, 2019 by Aleksandr Logunov the BBVA Founda- received the 2021 tion and the Royal New Horizons Yakov Shlapentokh-Rothman Spanish Mathemati- Prize, was named was named a cal Society. a 2020 Sloan Sloan Research Tristan Buckmaster Research Fellow, Fellow for 2021. with Philip Is- a 2019 Packard ett *13 (now at Fellow, and re- Caltech) and former ceived the Young Assistant Professor Researcher Prize from the European Vlad Vicol (now at Mathematical Society. NYU) received a Allan Sly received the 2019 joint Clay Research Fernando Codá Marques Award. was named one of Line and Michel four 2020 Simons Loève Internation- Sun-Yung Alice Chang Investigators in al Prize in Prob- was elected as Mathematics ability. Awarded Foreign Member every two years, of Royal Swedish it is intended to Academy of Sci- recognize out- ences at its general standing contributions by researchers meeting, February in probability who are under 45 years 12, 2020 Assaf Naor received the 2019 old. Peter Constantin Ostrowski Prize Chenyang Xu was elected to the in Higher Math- will receive the National Acad- ematics. 2021 Frank Nel- emy of Sciences in son Cole Prize in 2021. Algebra.

Page 7 Teaching Awards

EXCELLENCE IN TEACHING AWARDS Students noted that Hanselman was “approachable, clear, and genu- inely caring,” and “simply amazing!” They felt he “absolutely stimulated the curiosity of all the students in the class,” and appreciated his discussions of more advanced topics such as the Fourier series. Students Gabriele Di Cerbo Ashvin Swaminathan Mohan Swaminathan also gave him kudos on his pre-lec- In 2020, Assistant Professor Gabri- cially dedicated, taught the material ture videos. ele Di Cerbo, and in 2021 graduate clearly, and simply deserves to be rec- Defant's students cast similar students Ashvin Swaminathan and ognized for the hard work he or she praise, saying he is “amazing at Mohan Swaminathan were awarded put into the course." These teaching explaining the tricky material” and the Undergraduate and Graduate awards are entirely student-run, and that “getting him as a preceptor is Engineering Student Councils. any professor or AI instructing an like winning the lottery!” This student-nominated award is engineering, mathematics, or physics Nam's students thought him a for a professor or TA who "was espe- course is eligible. “very dedicated, helpful, and pa- tient” instructor, who “made multi- variable calculus about as fun as it DEPARTMENT TEACHING AWARDS can be.” Graduate Student and Junior Faculty Finally, Paz's students called him “a fantastic instructor who broke Each year the department pres- student evaluations. down the material before exams in ents awards to junior faculty and The fall of 2019 awards went to a simple yet comprehensive way." graduate students to recoginize Assistant Professor Jonathan Han- They particularly noted his well- exceptional undergraduate teaching. selman and graduate students Colin organized board work and, in the The awards are given by the senior Defant, Danny Nam, and David Vil- words of his students, a “true linear faculty and are based largely on lalobos Paz. algebra king.” The Fall 2020 awards went to Assistant Professor Yakov Shlapen- tokh-Rothman and graduate student Boya Wen.

Yakov Shlapentokh-Rothman and Boya Wen received the Fall 2020 Department Teaching Awards.

Danny Nam, Colin Defant, David Villalobos Paz, and Jonathan Hanselman re- ceived the Fall 2019 Department Teaching Awards. Climate and Inclusion New Department Committee on Climate and Inclusion

After a series of department town graduate student for a semester-long mentoring students and developing hall meetings over the summer of independent project. The program is curricula that meet students' needs, 2020, a Climate and Inclusion Com- open to undergraduates of any year or discuss some efforts and challenges mittee was formed in September 2020 and majors interested in exploring a to building an equitable mathematical to communicate, coordinate, and create mathematical topic in-depth. Students community. The inaugural Horizons activities that enhance the depart- who are new to math or underrepre- Lectures were given by Professor ment's efforts to achieve its diversity sented in the mathematics community Trachette Jackson of the University and inclusivity goals. are especially encouraged to partici- of Michigan and six panelists on This past fall, the committee as- pate. It is an excellent way to receive April 29, 2021. To learn more about sisted with a climate survey sent to the personal attention and mentorship; the speakers, a recorded video of the Department of Mathematics members this spring semester consisted of 22 seminar discussion is available on to provide a confidential opportunity to mentorships. the Climate and Inclusion webpage share how things are going, what has This spring, the committee an- https://www.math.princeton.edu/ worked well, and what could be better. nounced a new seminar series: The climate-and-inclusion. This valuable information will give Horizons Lectures. It consists of two essential guidance to the department events, a research colloquium and a 2020-2021 Committee Members as to develop programming, provide seminar discussion on the societal Department Chair, Ex Officio Member support, and plan for the future. impacts of the mathematics profes- Igor Rodnianski A second initiative has included the sion. Speakers are invited to discuss Committee Chair Directed Reading Program. The DRP any topic of their choice. For example, Peter Sarnak is an opportunity for Princeton under- speakers might share their journey in graduates to work one-on-one with a academia, share their experiences in Senior Faculty Representative Maria Chudnovsky Junior Faculty Representatives Alumni News Takumi Murayama *58, Hebrew Carolina Araujo *04, a researcher Evita Nestoridi University of Jerusalem, and gradu- at the Institute for Pure and Ap- Graduate Student Representatives ate student of at plied Mathematics (IMPA) in Rio Tara Abrishami Princeton, received the 2020 Abel de Janeiro, Brazil, received the 2020 Shikhin Sethi Prize “for pioneering the use of meth- Ramanujan Prize for Young Mathema- Érico Silva ods from probability and dynamics ticians from Developing Countries. in group theory, number theory and Undergraduate Representative combinatorics.” He shares the prize Maggie Miller *20 and Georgios Caoimhe Boyle with Gregory Margulis of Yale. Moschidis *18 have been named 2021 Clay Research Fellows. Four Clay Staff Representatives Alex Eskin *93, the University of Chi- Research Fellowships were awarded Kathleen Applegate this year on the basis of exceptional cago's Arthur Holly Compton Distin- Lisa Giblin quality of the candidates' research and guished Service Professor, received the Maria Mastroianni 2020 Breakthrough Prize in Math- their promise to become mathematical Alumni Representative ematics "for revolutionary discover- leaders. ies in the dynamics and geometry of Miller will spend her four-year fellow- Linh Truong *16 moduli spaces of Abelian differentials, ship at Stanford while Moschidis will including the proof of the 'magic wand return to Princeton to spend his two- theorem' with Maryam Mirzakhani." year fellowship here. Page 9 Special Events Minerva Distinguished Visitor & Minerva Lectures While in-person tended, and are available to events are still restricted watch on the department's at Princeton, we were YouTube channel. pleased that we were able The Minerva programs host both a Minerva Dis- are made possible because tinguished Visitor and of the generous support of Minerva Lecture series the Fernholz Foundation, virtually this year. and we hope we are able to Jacob Rasmussen, continue these fantastic pro- currently a Reader in Ge- grams in person next year. ometry at the University Jacob Rasmussen James Maynard of Cambridge and mem- ber at the Institute for Maynard, Research Professor at the Advanced Study, and a former Princeton University of Oxford, was able to deliver Watch these lectures on undergraduate student (class of 1998) a series of three Minerva Lectures on and faculty member (Veblen Research his work with prime numbers, origi- Instructor, 2003-05; Assistant Professor, nally scheduled to happen last April in 2005-07), was appointed as our spring Princeton. Minerva Distinguished Visitor. Rasmus- We regret that we were not able to Minerva Lectures sen delivered a six-part Minerva mini- host either Maynard or Rasmussen on course on "aspects of the HOMFLY-PT campus this year, and we are grateful Horizon Lectures polynomial and its categorification, with to their willingness to contribute to our Conference talks an emphasis on geometry." research program virtually. All of their Faculty profiles We were also pleased that James virtual talks were extremely well at- math.princeton.edu/youtube

Horizon Lectures The Horizons Lectures were founded "Turning cancer discoveries into effective this year as part of the department's treatments with the aid of mathematical Climate and Inclusion Committee. The modeling". series consists of two events, a research For the second part of her Hori- colloquium as well as a seminar dis- zons series, Professor Jackson hosted a cussion on the societal impacts of the panel discussion, "A Conversation with mathematics profession with the follow- Thought Leaders who are Transforming ing goals: Mathematics through Diversity, Equity, • To discuss issues of diversity and and Inclusion" with Ron Buckmire, Oc- inclusion in STEM fields. cidental College; Erika Camacho, Arizon • To provide career advice to graduate State University and the National Science students and junior faculty. Trachette Jakson Foundation; Edray Goins, Pomona Col- • To promote the work of mathemati- lege; Suzanna Sindi, UC Merced; Talitha an equitable mathematical community. cians from underrepresented groups. Washington, Clark Atlanta University; The department was honored to have Speakers are invited to discuss and Michael Young, Iowa State Univer- Trachette Jackson of the University of any topic of their choice. For example, sity. Michigan as our first Horizon Lecturer. speakers might share their own journey Professor Jackson's panel shared their Professor Jackson, who specializes in academia, share their experiences in individual journeys in academia, with in Computational Cancer Research or mentoring students and developing curri- insights into their experiences as minority Mathematical Oncology, delivered a cula that meet students’ needs, or discuss members in their academic communities. PACM Colloquium on April 26, titled some efforts and challenges to building Page 10 Going Virtual ...continued from front page and most effectively by a bit of give which introduced oral examinations dents found traditional live lecture and take between student and teacher." as a supplement to written exams. Dr. time — even through Zoom — to be “Office hours were critical during Fickenscher found that “oral exams the most effective, “many instructors the pandemic”, emphasized Dr. Mark were the most surprising and reward- moved away from small group ses- McConnell, Senior Lecturer and Ju- ing experience for both students and sions, replacing it with the whole class nior Advisor. “Teaching often uses the me personally. These opportunities working through problems all together Socratic method, where the student allowed us to connect with students in in Zoom with the instructor serving as asks questions, and in response the a much needed way and fostered bet- scribe/guide.” instructor asks more questions to get ter engagement through other course The Personal Connection the student thinking in the right direc- channels.” Dr. Yarmola agrees: “(1) it A major difficulty in online teach- tion. Office hours on Zoom makes the helped students prepare for the written ing was recreating the personal Socratic method work, because the portion and (2) it really helped miti- connection with students and recog- instructor and student can see each gate the lack of a face-to-face contact nizing those that were struggling. other's faces as they talk in real time. in lecture.” Professor Robert Gunning retired at An added bonus was seeing the deco- Help from our undergraduate the end of the 2020 academic year, rations and posters in the students' course assistants (UCAs) was also and that spring semester was his last rooms; this broke the ice in conver- essential, and in fall 2020 we hired a time teaching an undergraduate class: sation, and it gave a hint about the larger than usual number. The UCAs "The major problem was getting the students' personalities.” Instructor Dr. held sessions at a wide range of times students to react and ask questions Casey Kelleher found connecting one every week, including times when and make suggestions with the ease on one with students in office hours students in Europe or Asia would be that was possible while in the same “gave feeling of normalcy and hanging awake. And to help bridge the digital room. I did not try simply recording out, and allowed me to occasionally divide some UCAs volunteered to be an hour lecture and leaving that to the check in about how students are doing social chairs for informal meetings out- students to follow at their leisure; but mentally too.” side of class with other students and it is always surprising what difficulties The department also expanded its took the initiative and gave an intro- in understanding the material do arise, summer course offerings through the ductory workshop on LaTeX. many of which can be handled quickly Freshman Scholars Institute in 2020, Continued on next page...

Faculty tried many ways of online teaching. Instructor Duncan Dauvergne (left) spent spring recess 2020 recording the rest of his semester's lectures alone in a Fine Hall classroom, while instructor Andrew Yarmola used an iPad to record videos for his students to watch before live classes on Zoom. Page 11 Going Virtual ...continued from previous page the pandemic. For example, the depart- a computer screen; as Professor Gun- ment has an online exam review tool Eager to Return ning put it, the “give and take between for students, and we plan to integrate At the beginning of the spring 2020 student and teacher”. semester no one would have dreamed video content created over the last year of the drastic and rapid changes that into the site as guided would soon be necessary in the fight examples. against the pandemic, and it is a testa- The University is ment to the hard work of faculty and committed to return- students that our curriculum was able ing to in-person teach- to carry on as it did. ing in the fall of 2021, While most will agree that online and our faculty are teaching is no substitute for the person- eager to reunite with al connections developed in Fine Hall, our students and to both in the classrooms and the com- reconnect in a way we mon room, the past 18 months did spur have learned cannot Professor Gunning, who retired last year, taught his last be replicated through pedagogical innovation that will outlast undergraduate classes via Zoom.

Conway professor of mathematics, emeritus, and The two discovered that they shared a ...continued from page 6 a former chair of the department. “He love of games and became friends. At Conway was born in Liverpool, knew so many things and he was inter- the time, Diana worked at the Uni- England, on December 26, 1937. He ested in all aspects of mathematics and versity bookstore and though not a received his B.A. from Cambridge science. He was an enthusiastic teacher; mathematician, enjoyed math and later University in 1959 and his Ph.D. from he liked to share his knowledge and became an accountant. They married in the same institution in 1964. He was a discuss things. He was very playful, 2001. faculty member at Cambridge until he and always ready to have a game, many “John was the most fascinating hu- came to Princeton. of which he invented himself.” man being I’ve ever met,” said Diana Peter Sarnak, Princeton’s Eugene Conway. “He was not only interested in Higgins Professor of Mathematics, re- "He moved into the math, he was interested in everything.” calls that “an extrovert by nature, John common room where he Diana Conway described John liked to be at the center of mathematical Conway’s willingness to talk to anyone discussions and he enjoyed thinking could always be found interested in mathematics, whether an- and inventing on the spot,” Sarnak said. holding court" other university professor or a hobbyist “To this end he gave up his regular with an interesting theory or discovery. office in the Princeton mathematics de- Kohn related a time when Conway “There were always strange charac- partment and moved into the big com- had committed to giving a large public ters showing up at our house, joining mon room where he could always be lecture and on the way to the lecture, us for dinner, or sitting with John found holding court on the latest (often asked his companions what topic he out in the back garden,” said Diana his!) mathematical development or in- should cover. Upon deciding on the Conway. “He would get buckets and vention. On days of little mathematical topic in the car, Conway successfully buckets of fan mail.” news he would be challenging others gave the lecture without any additional Conway is survived by Diana to mathematical games or puzzles and preparation. Conway and son Gareth. He is also now that I think of it, I can’t recall any Conway combined playfulness with survived by sons Alex and Oliver from instance where he did not win. a mastery of esoteric information, sev- his second marriage to wife Larissa; “The mathematical world has lost eral who knew him commented. and daughters Susie, Rosie, Ellie and a very special person but we are much Conway’s wife, Diana, first met Con- Annie from his first marriage to wife richer for all that he gave us.” way in 1996 in a coffee shop on With- Eileen Howe. He is also survived by “He was really without exaggeration erspoon Street in Princeton where they three grandchildren and six great- a genius, absolutely” said Joseph Kohn, were both regular morning customers. grandchildren. Page 12 Undergraduate Program

Program updates Course Placement Beginning in the 2019 academic year As Junior Advisor Dr. Mark McConnell travel, and at times provides a re- all placement into calculus and linear had to recreate this tradition online. "I search grant. The program is ad- algebra courses was consolidated into made a video summarizing what I would ministered by the Winston Churchill a new 2-day plcaement and orientation have said at the tea, and Michelle Matel, Foundation of the . workshop series, MAT INFO. our Undergraduate Administrator, cre- The AWM's Alice T. Schafer ated a very informative document on the Prize was established in 1990 and is Dr. Jennifer Johnson, Associated Direc- major including post-graduate paths for named for AWM former President tor of Undergraduate Studies describes math students. The Open House was and one of its founding members, that, "students in these workshops a live Zoom meeting for sophomores. Alice T. Schafer, who contributed a work through example problems with Michelle Matel and I shared information great deal to women in mathematics instructors so that they have a better about the department, and two older throughout her career. Lin's citation understanding of how each class works, math majors spoke." for this award notes that through her how they differ from high school classes, research, she has demonstrated “great and how their preparation compares to While this online material is no substi- potential to become a successful math- other students so that they can accu- tute for the connections we can make in ematician in the future.“ rately place themselves. This has been a person, Dr. McConnell notes that "the very successful program, and would not website has proved valuable for Princ- have been possible without the extensive eton Preview, the recruiting event for efforts of Michelle Matel, Undergradu- Isabella Khan '21 high-schoolers who have been accepted Undergradu- ate Administrator, and the dedicated to Princeton, as well." ate math instructors leading these workshops." major Isa- Exam Archive bella Khan Over the last several years the depart- has been ment has developed an online database Alice Lin '20 awarded a of exam problems, along with answers, has been se- Goldwater hints, and fully detailed solutions. This lected as one Scholarship, archive is searchable and allows students of this year's an annual to work independently to review and Churchill award for sythesize the ideas and techniques they Scholars and outstanding undergraduates interested are learning in class. The archive is fully has been se- in careers in mathematics, the natural established for single variable calculus lected as an sciences and engineering. and has been a much appreciated study Honorable tool. We are currently expanding the Mention of archive to include multivariable calcu- the 2020 One- and two-year Goldwater Schol- lus this summer and will soon work on AWM Alice T. Schafer Prize. arships cover tuition, fees, room and incorporating linear algebra material. Lin is one of 15 Churchill Schol- board up to a maximum of $7,500 per arship winners this year who will year. Khan was one of the 396 winners Adding video content to this system spend a year studying at the Uni- had been planned well before the past for 2020, selected from a field of 1,343 versity of Cambridge while living at difficult year, and we are working to in- nominees. The scholarship program Churchill College, which focuses on corporate the large video library created honoring Sen. Barry Goldwater was STEM subjects. She plans to com- for classes into this system. created as part of the Barry Goldwater plete Part III of the Mathematical Scholarship and Excellence in Educa- Sophomore Open House Tripos, which confers a Master of tion Foundation, a federally endowed In the spring the department usually Advanced Study in mathematics. The agency instituted by an act of Congress hosts a special tea to welcome sopho- Churchill Scholarship pays for a year in 1986. mores interested in the math major. of tuition and fees, living expenses, Page 13 Graduate Program

Graduate Student Profile: Director of Graduate Studies — Mihalis Dafermos John Anderson the event is primarily due to the initia- My interests Another tive of our own graduate students. lie in hyperbolic pandemic year partial differen- has come and This past year in fact saw a record tial equations, gone. It has number of applications to our gradu- which often been a difficult ate program. (Many thanks to those arise when mod- year for all faculty who participated in the Com- eling things that members of our mittee that read through all these ad- exhibit wave-like department, ditional applications…) The increase phenomena. Ex- but especially in applications may in part be due to amples include for our graduate students, whether the fact that, in view of the pandemic, the compressible Euler equations describ- they be first-years having to adjust ing gas dynamics, Maxwell's equations we waived the usual GRE require- to Princeton graduate-student life describing electromagnetic radiation, and ment (both subject and general). In without actually being in Princeton, the Einstein equations of general relativ- our highly selective program, the GRE post-generals students trying to get ity. During my time as a graduate student has never been the primary criterion their research off the ground without here, I have mostly studied stability prop- for admission, and there is a lot of the usual stimulating intellectual cli- erties of special solutions to hyperbolic lively discussion in the department, mate of Fine Hall, or students towards equations. I was also an undergrad here, among both faculty and graduate stu- the end of their Ph.D., who had to face and returned for grad school after two dents, about its merits, with a variety the prospect of applications in a very years in Switzerland. I first learned about of opinions having been expressed uncertain world. It is reassuring that, hyperbolic equations in a class taught by concerning its pros and cons. In the despite these difficulties, we have done my senior thesis advisor, Sergiu Klainer- end, we have decided to continue to our best to carry on. As the academic man, who went on to be my PhD advisor not require the GRE in our admissions year draws to a close, let us hope that as well. Since very early on, I have been process for this coming year–and for the recent glimpses of normality are particularly captivated by the connections a suitable period in the future–so as between hyperbolic equations and other indeed a signal of a fully in-person Fall to better understand how to make our areas of math, such as harmonic analysis 2021. graduate selection process the best and differential geometry. In this unusual year where we have possible. Faculty and students are al- I'm very lucky to have been able to had to learn to do things a little bit ways welcome to discuss with me their study here because of the vibrant com- differently, let me single out for special thoughts on this issue! munity focused on hyperbolic equations thanks our graduate student commit- In closing, on behalf of myself, our led by Mihalis Dafermos, Sergiu, and tee, in particular, for their essential as- Assistant DGS Evita Nestoridi, and Igor Rodnianski. I learned a great deal sistance in putting together the virtual our Graduate Program Administrator from being able to meet and work with open house we held in March. One of Jill LeClair, let me end with a special the people in this community. I also made the reasons that we will be welcoming congratulations to all our finishing countless other friends among the stu- such a large class of incredibly talented graduate students: We very much dents, faculty, and staff in Fine Hall, and new students next year, from a wide hope that the memories of Princeton also among the many visitors who would variety of backgrounds from all over that remain with you are not of the come through in pre-pandemic times. the world, is undoubtedly due to the All of these factors contributed to an empty Fine Hall of this past year, but effort graduate students made to en- outstanding experience at Princeton. My of the lively Fine Hall that you got to gage with the prospectives at our two- time was more productive, more enjoy- know in the first years of your gradu- day online event, which included both able, and ran much more smoothly than ate studies here. It is to that Fine Hall scientific and social interactions with I could have imagined, and I am grateful which we hope to be able to welcome students and faculty over zoom and for all of the fond memories I will leave you back often; you should always gathertown, and collaborative games Princeton with. I will without a doubt be consider it as your academic home! on the lookout for excuses to return and and other activities. Faculty pitched in visit in the future. too of course, but I think the success of Page 14 Ph .D.s Awarded 2019–2021

Levent Alpoge Dong Hoon (Danny) Nam “Points on Curves”, advised by Bhargava “Phase transition of epidemics on random graphs”, advised by Sly Columbia University/NSF Postdoctoral Research Fellow Quantitative Researcher John Anderson Zipei Nie “Stability results for nonlinear hyperbolic equations”, advised “On (1,1)-knots and L-space conjecture”, advised by Szabó by Klainerman HiSilicon (of Huawei Technologies, China)/Senior Researcher /Postdoctoral Scholar Federico Pasqualotto Eric C. Chen “Nonlinear waves in general relativity and fluid dynamics”, “Some regularity properties for two equations arising from flows”, advised by Constantin & Dafermos advised by Chang UC Berkeley/Morrey Visiting Assistant Professor UC Santa Barbara/Postdoctoral Research Assistant Congling Qiu Irving Dai “The Gross-Zagier-Zhang formula over function fields”, advised “Involutive Heegaard Floer homology and homology cobordism”, by Zhang advised by Szabó Yale University/Gibbs Assistant Professor MIT/NSF Postdoctoral Research Fellow Akash Sengupta Amitesh Datta “Geometric invariants and geometric consistency of Manin’s “On the Burau representation of the braid group B4”, advised conjecture”, advised by Kollár by Ozsváth Columbia University/Ritt Assistant Professor Princeton University/Lecturer Antoine Song Alexandros Eskenazis “In search of minimal hypersurfaces”, advised by Codá Marques “Geometric inequalities and advances in the Ribe program”, advised UC Berkeley/Clay Fellow by Naor Daniel Stern Trinity College, Cambridge/Junior Research Fellow “Variational theory and asymptotic analysis for the Ginzburg- Fabian Gundlach Landau equalitions and p-harmonic maps”, advised “Parametrizing extensions with fixed Galois group”, advised by Codá Marques by Bhargava University of Toronto/Postdoctoral Fellow Harvard University/Benjamin Peirce Fellow Jun Su Michael Jemison “Coherent cohomology of Shimura varieties and automorphic “Polyfolds of Lagrangian Floer theory in all genera”, advised forms”, advised by Taylor (IAS) by Hofer (IAS) University of Cambridge/Research Associate Center of Mathematical Research, Montreal/Canada Research Fellow Maya Thackeray Zhaorong Jin “A Birch and Swinnerton-Dyer formula for high-weight modular “On certain families of special cycles on Shimura varieties”, advised forms”, advised by Skinner by Skinner University of Pretoria, SA/Lecturer; Postdoctoral Research Fellow Citadel Securities/Quantitative Researcher Siyi Zhang Joonhyun La “Some problems in four-dimensional conformal geometry”, “On the models of the fluid-polymer systems”, advised by Constantin advised by Chang Stanford University/Szego Assistant Professor University of Notre Dame/Visiting Assistant Professor Holden Lee Fan Zheng “MCMC algorithms for sampling from multimodal and changing “Long term regularity of some periodic nonlinear dispersive distributions”, advised by Arora (COS) equations”, advised by Ionescu Duke University/Philip Griffiths Research Assistant Professor University of Madrid/Postdoctoral Research Assistant Lena Ji Ziquan Zhuang “Topics on algebraic varieties in arbitrary characteristic p”, advised “Birational superrigidity and K-stability”, advised by Kollár by Kollár MIT/CLE Moore Instructor University of Michigan/Assistant Professor and Research Fellow Maggie Miller “Extending fibrations of knot complements to ribbon disk complements”, advised by Gabai MIT/NSF Postdoctoral Research Fellow