FROM THE AMS SECRETARY

2021 Frank and Brennie Morgan Prize for Outstanding Research in by an Undergraduate Student

Ashwin Sah and Mehtaab Sawhney were awarded the AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstand- ing Research in Mathematics by an Undergraduate Student at the 2021 Annual Meeting of the AMS, held virtually January 6–9, 2021.

Citation published in top journals, including Inventiones Mathemati- The recipients of the 2021 AMS- cae, Advances in Mathematics, Mathematical Proceedings of the MAA-SIAM Frank and Brennie Cambridge Philosophical Society, the Journal of Combinatorial Morgan Prize for Outstand- Theory Series B, and Combinatorica. This is the first award to ing Research in Mathematics coauthors of joint work in the Morgan Prize history. The by an Undergraduate Student two were chosen from an especially strong slate of candi- are Ashwin Sah and Mehtaab dates due to the “quality and quantity [of their] collective work.” The committee considered that, while each inde- Sawhney, both of the Massa- pendently would be top contenders for the prize, as a team chusetts Institute of Technol- they have contributed significantly more to mathematical ogy. The award recognizes the scholarship, which should be lauded. Their expansive list duo’s groundbreaking results of coauthors, including many other impressive young across a broad range of top- Ashwin Sah mathematicians, is an excellent example of the enormous ics in , discrete benefit of collaboration in mathematics. , and probability. The pair were recognized with Honorable Mention last Working alongside one an- year (along with D. Stoner). Since then, they have produced other, Sah and Sawhney set- numerous additional significant results, including the “re- tled long-standing conjectures cent improvement of Sah of the best known upper bound and improved results by estab- for the diagonal Ramsey numbers,” making progress on lished mathematicians. They what is “arguably the most famous problem in extremal have “solved several significant combinatorics.” Their joint work on “local limit theorems open problems and developed for subgraph counts” extends the previous results of Gilmer, new techniques while working Kopparty, and Berkowitz and provides counterexamples to on exciting and central areas the conjectures of Fox, Kwan, and Sauermann. This is an in the field.” Combined, they “important and technically challenging problem, which have authored thirty papers was not even solved [in the simplest case] until about five Mehtaab Sawhney (eleven of these together) and years ago.”

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In a joint paper with Zhao on “Cayley Graphs without Duluth REU, who have each been instrumental in our a Bounded Eigenbasis,” they extend a result from Naor in mathematical endeavors. Professor Yufei Zhao has been spectral from abelian groups to “not neces- an exceptionally kind and generous mentor for both of us sarily abelian” groups. In the study of graph limits (with for the past three years, and it has truly been a pleasure to Tidor and Zhao), they found a counterexample to several interact with him closely over this time period. In partic- conjectures of Bollobás and Riordan aimed toward extend- ular, he has spent a great deal of time teaching us how to ing the theory of graph limits to the sparse regime. become better mathematicians and how to communicate These “appealing conjectures had stood open for more our results. Professor Gallian introduced us to an amazing than ten years, but their short, elegant counterexample had community of peers and mentors, informally known as escaped many of the leading researchers in the area.” The “Duluthians,” and the summers we each spent at the Du- research of Sah and Sawhney is both deep and broad, “tack- luth REU were incredibly enjoyable due in large part to his ling questions at the very forefront of current research, yet extending across the entire gamut of modern combinator- passion and expert guidance. ics,” with significant contributions to extremal graph the- We would further like to thank a number of joint col- ory, graph limits, additive combinatorics, Ramsey theory, laborators, including David Stoner, Vishesh Jain, and Ross algebraic combinatorics, combinatorial geometry, random Berkowitz. graphs, and random matrix theory. They have demonstrated Ashwin Sah would like to thank his older brother Varun a “significant amount of ingenuity, originality and technical for support in all his pursuits and to thank Dr. John Gor- ability,” resulting in a research record which is “extremely man for playing a key role in guiding him toward higher rare for undergraduate students.” mathematics. He also thanks Professor Ken Ono and Pro- fessor Jesse Thorner for their mentorship and support at Biographical Sketch: Ashwin Sah the 2019 Emory REU. Ashwin Sah was born and raised in Portland, Oregon. In Mehtaab Sawhney would like to thank Mr. Robert high school, he won a gold medal at the 2016 International Minott, Mrs. Barbara Gerson, and Mr. Richard Kurtz for Mathematical Olympiad as a member of the winning US helping cultivate an interest in mathematics and research team. Ashwin is currently a graduate student studying more broadly. He also thanks Dr. Per Alexandersson and mathematics at the Massachusetts Institute of Technology. Professor Jonathan Weed for their mentorship in his initial Other than combinatorics, Ashwin is also interested in steps into research, especially in their guidance regarding pursuing analytic number theory, Fourier analysis, and random matrix theory. Beyond math, Ashwin spends his how to broadly approach mathematical research. time helping organize math contests and participating in Finally, and most importantly, we would each indi- the effective altruism community. He is also interested in vidually like to thank our parents for their incredible economics, game theory, and artificial intelligence. support and encouragements along all our mathematical adventures. Biographical Sketch: Mehtaab Sawhney Mehtaab Sawhney grew up in Commack, New York. Citation for Honorable Mention: Noah Kravitz Mehtaab is currently a graduate student studying mathe- Noah Kravitz of is recognized with an matics at the Massachusetts Institute of Technology. In ad- Honorable Mention for the 2021 Frank and Brennie Mor- dition to combinatorics, Mehtaab is interested in statistics, gan Prize for Outstanding Research in Mathematics by an probability, and random matrix theory. Outside of math, Undergraduate Student. He has nine papers published, Mehtaab enjoys playing table tennis, playing Texas Hold many single authored, in top journals such as the Journal ’Em and Pot Limit Omaha, and watching classic movies. of Number Theory, Discrete Mathematics, the Journal of Fourier He is also interested in economics, theoretical machine Analysis and Applications, and Integers. He has made signifi- learning, and finance. cant progress on “very central and well-studied problems,” Response from Ashwin Sah including the Small Ball Inequality—where he improved and Mehtaab Sawhney upon the current understanding of the problem by lead- It is a tremendous honor to receive the 2021 Frank and ing experts in the field—and the Lonely Runner Conjec- Brennie Morgan Prize. We extend our deepest gratitude ture—where he “discovered an unexpected rigidity in the toward Mrs. Morgan and the AMS, MAA, and SIAM for problem.” Additionally, he has developed an asymptotic promoting and supporting undergraduate mathematical theory of difference bases and shown that the problem is research. We would also like to sincerely thank two of completely equivalent to a problem in Real Analysis using a our research mentors, Professor Yufei Zhao from the MIT “very sophisticated mixture of combinatorial, probabilistic math department and Professor Joseph Gallian from the and analytical arguments.”

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Biographical Sketch About the Prize Noah Kravitz was born and raised in Washington, DC, The Morgan Prize is awarded annually for outstanding where he attended Georgetown Day School. In 2020, he research in mathematics by an undergraduate student (or graduated from Yale University summa cum laude and ju- students having submitted joint work). Students in Canada, nior Phi Beta Kappa with Exceptional Distinction in both Mexico, or the United States or its possessions are eligible of his majors, Mathematics and Near Eastern Languages for consideration for the prize. Established in 1995, the and Civilizations. His two senior theses treated the Lonely prize was endowed by Mrs. Frank (Brennie) Morgan of Runner Problem and the development of medieval Arabic Allentown, Pennsylvania, and carries the name of her late number theory, respectively. Noah is now pursuing a PhD husband. The prize is given jointly by the AMS, the Mathe- in mathematics at . He has broad in- matical Association of America (MAA), and the Society for terests in combinatorics and adjacent fields, and recently Industrial and Applied Mathematics (SIAM) and carries a he has been particularly drawn to combinatorial problems cash award of US$1,200. with an additive or number-theoretic flavor. Recipients of the Morgan Prize are chosen by a joint Noah was interested in mathematics from a young age AMS-MAA-SIAM selection committee. For the 2021 prize, and participated in local mathematics competitions in high the members of the selection committee were: school. His first foray into mathematical research came • Giuliana P. Davidoff during his freshman year at Yale, and he learned more about • Tamas Forgacs the research process when he attended the Research Experi- • Nathan L. Gibson (Chair) ences for Undergraduates (REU) program at the University • Wei Ho of Minnesota, Duluth, in the summer after his sophomore • Nathan Kaplan year. At Yale, Noah was an organizer and the chief problem • Candice Price writer for the Math Majors of America Tournament for High A list of previous recipients of the Frank and Brennie Schools and Girls in Math at Yale annual competitions for Morgan Prize can be found at https://www.ams.org high school students. Noah is a US Presidential Scholar, a /prizes-awards/pabrowse.cgi?parent_id=39. Goldwater Scholar, a National Science Foundation Gradu- ate Research Fellow, and the winner of Yale’s Warren Prize Credits (for high scholarship in the humanities). His nonmathe- Photo of Ashwin Sah is courtesy of Ashwin Sah. matical academic interests include languages, philology, Photo of Mehtaab Sawhney is courtesy of Mehtaab Sawhney. philosophy, literary translation, and the history of science. Outside of academics, Noah plays the piano and the caril- lon and enjoys long-distance running. Response from Noah Kravitz It is a great privilege to receive an Honorable Mention for the Morgan Prize. I would like to thank a few (but neces- sarily not all) of the many people who helped me reach this point: Andy Lipps, my high-school calculus teacher, for teaching me about the possibilities of math beyond the classroom and taking the time to challenge me with a near-constant stream of interesting problems; Stefan Steinerberger, my adviser at Yale, for introducing me to mathematical research and providing sage advice, steady encouragement, and insightful ideas for research projects; Joe Gallian, for running a wonderful REU program and supporting me through my subsequent endeavors; Gil Kalai, for giving me the confidence to try my hand at hard open problems; my parents, for patiently listening to me talk about math, even at inopportune times; and my peers and research collaborators, for spending hours poring over problems and attempted solutions.

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