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Mathematics People Mathematics People problems’ that he wrote at Princeton University in 2010 Tsimerman Awarded 2015 under the direction of Professor Peter Sarnak. The thesis SASTRA Ramanujan Prize concerns arithmetical questions around the Andre-Oort conjecture and makes substantial progress towards it. Jacob Tsimerman of “The Andre-Oort conjecture states that special subsets the University of To- of Shimura varieties that are obtained as Zariski closures ronto has been awarded of special points are finite unions of Shimura varieties. the 2015 SASTRA Ra- Shimura varieties are special algebraic varieties (such manujan Prize, awarded as moduli spaces of Abelian varieties) which arise as annually for outstand- quotients of suitable complex domains by arithmetic ing contributions by groups. Thus Shimura varieties lie at the heart of arithme- young mathematicians tic geometry and automorphic forms. Yves Andre initially to areas influenced by stated this conjecture for one-dimensional subvarieties, the work of Srinivasa and subsequently Frans Oort proposed that it should hold Ramanujan. The age more generally. The conjecture lies at the confluence of limit for the prize has Diophantine problems and the arithmetic of modular Jacob Tsimerman, winner been set at thirty-two forms. By assuming the Generalized Riemann Hypothesis of the 2015 SASTRA because Ramanujan (GRH), the conjecture was proved in 2006 by Klinger, Ramanujan Prize, was born achieved so much in Ullmo, and Yafaev, but as of 2008 only the very simplest in Russia, lived in Israel, and his brief life of thirty- cases had been proved unconditionally. One of the tech- moved to Canada when he two years. The prize niques to attack the Andre-Oort conjecture is to obtain was eight. He plays squash, was awarded in Decem- suitable bounds for certain Galois orbits of special points. judo, and guitar. ber 2015 at the Inter- A major achievement of Tsimerman in his thesis was to national Conference on establish certain unconditional bounds up to dimension Number Theory at SASTRA University in Kumbakonam 6, and this was published in the Journal of the American (Ramanujan’s hometown), where the prize has been given Mathematical Society in 2012. This went beyond the work annually. of Ullmo and Yafaev, who had unconditionally established The prize citation reads as follows: “Jacob Tsimerman such bounds up to dimension 3. is an extraordinary young mathematician who has made “Another very important result in his thesis was to deep and highly original contributions to diverse parts of answer in the affirmative a question due to Nick Katz number theory, and most notably to the famous Andre- and Oort whether there exists an Abelian variety over Oort conjecture. He is one of the few mathematicians the set of all algebraic numbers which is not isogenous to have complete mastery over two very different areas to the Jacobian of a stable algebraic curve over the alge- of mathematics—analytic number theory and algebraic braic numbers. This fundamental result appeared in the geometry. This has enabled him to achieve significant Annals of Mathematics in 2012. Previously Ching-Li Chai progress on a number of fundamental problems lying at and Frans Oort had answered the question assuming the the interface of the two subjects. Andre-Oort conjecture, but Tsimerman was able to do so “Much of Tsimerman’s research stems from the spec- unconditionally. tacular PhD thesis entitled ‘Towards an unconditional “About a decade ago, Jonathan Pila had introduced proof of the Andre-Oort conjecture and surrounding a new method to attack the Andre-Oort conjecture. In JANUARY 2016 NOTICES OF THE AMS 53 Mathematics People 2009 Tsimerman and Pila joined forces and over the The full list of awardees of the SASTRA Ramanujan next few years established several deep results, one of Prize follows. which was a functional transcendence statement known • 2005 Manjul Bhargava and Kannan Soundararajan as Ax-Lindemann for Abelian varieties of all dimensions (two full prizes) (Ax-Lindemann is one of the tools to attack the Andre- • 2006 Terence Tao Oort conjecture). This paper has just been accepted in the • 2007 Ben Green Annals of Mathematics. In another major joint paper of • 2008 Akshay Venkatesh Pila-Tsimerman that appeared in Compositio Mathematica • 2009 Kathrin Bringmann in 2013, they establish the Andre-Oort conjecture for cer- • 2010 Wei Zhang tain moduli spaces of Abelian surfaces. • 2011 Roman Holowinsky “The most recent advance by Tsimerman is his proof • 2012 Zhiwei Yun this year of the Andre-Oort conjecture for the moduli • 2013 Peter Scholze spaces of principally polarized Abelian varieties of any • 2014 James Maynard dimension g, which has been sought for a long time. What • 2015 Jacob Tsimerman was missing was a certain lower bound for Galois orbits of special points in dimensions greater than 6. Tsimerman’s —Krishnaswami Alladi University of Florida brilliant insight was to use a recently proven weighted average version of a conjecture of Colmez to establish the crucial lower bound, building on deep results of Andreatta, Bhatt and Wood Awarded Goren, Howard, and Madapusi-Pera. “Tsimerman has made major contributions not just to the Andre-Oort conjecture, but to many other fundamental problems. Even as a graduate student at Princeton, Tsimer- man collaborated with Manjul Bhargava (recipient of the first SASTRA Ramanujan Prize in 2005) and Arul Shankar to determine the second term in the asymptotic formula for the number of cubic fields with a bounded discrimi- nant. This work appeared in Inventiones Mathematica in 2013. Especially relating to Ramanujan’s mathematics, we note his 2014 paper joint with Ali Altug entitled ‘Metaplective Ramanujan conjecture over function fields To help other latecom- Outside of mathematics, with applications to quadratic forms’ that appeared in the ers, I want to point out my recent hobbies in- International Mathematical Research Notices (IMRN). Most that I started out rela- clude reading Supreme recently, Tsimerman and Pila have turned their attention tively late in math: at Court briefs and opin- to multiplicative relations among singular moduli—a topic least half of my time in ions and ballroom danc- college was spent trying ing with my husband. dear to Ramanujan. to be an engineer (my I also love the theater, “Tsimerman has several more first-rate contributions BS is from the engineer- and in college I studied spanning algebraic geometry, number theory, mathemati- ing school at Columbia), drama with a particu- cal logic, and analysis. He is an exceptionally broad and and, before college, I ba- lar focus in performing creative mathematician. The breadth of his expertise sically spent all my time Shakespeare. seems unrivaled among number theorists of his age. All playing cricket. — Melanie Matchett indications are that he will continue to contribute at the — Bhargav Bhatt Wood very highest level and will be a major force in the world of mathematics for the next several decades.” Jacob Tsimerman was born in Kazan, Russia, on April 26, 1988. He received his PhD in 2011 from Princeton Uni- 2015 Packard Fellowships versity under Peter Sarnak, supported by an AMS Centen- Bhargav Bhatt of the University of Michigan and Mela- nial Fellowship. He held a postdoctoral position at Harvard nie Matchett Wood of the University of Wisconsin, Madi- University. In 2014 he was awarded a Sloan Fellowship and son, have been awarded Packard Fellowships by the David joined the faculty at the University of Toronto. and Lucile Packard Foundation, which provided eighteen The members of the 2015 SASTRA Ramanujan Prize early-career scientists in science and engineering flexible Committee were: funding and the freedom to take risks and explore new • Krishnaswami Alladi, chair, University of Florida frontiers in their fields of study in 2015. Bhatt works in • Henri Darmon, McGill University arithmetic geometry, a field that lies at the intersection of • Winnie Li, Pennsylvania State University algebraic geometry and number theory. Much of his work, • Hugh Montgomery, University of Michigan according to the prize citation, “draws inspiration from • Peter Paule, Johannes Kepler University, Linz topology (the study of shapes, up to continuous perturba- • Michael Rapoport, University of Bonn tion) to understand the behavior of certain subtle notions • Cameron Stewart, University of Waterloo in arithmetic geometry.” About Wood’s work, the prize 54 NOTICES OF THE AMS VOLUME 63, NUMBER 1 Mathematics People citation says, in part, “the structure of how numbers like William O’Brochta, Hendrix College, “Rational deci- 1, 2, 3,…factor into primes is incredibly complex. It not sion-making models of conflicts in the 1990s” only underlies the encryption that protects all of our data Madeline Hansalik, Texas A&M University, “Magnetic online, but also contains the oldest unsolved mysteries of spectral decimation on self-similar fractals” mathematics. Wood develops geometric and probabilistic Elliot Golias, Kent State University, “Geometry to tools that can unlock some of these mysteries.” The two number theory: Minkowski’s theorem” new fellows will receive grants of $875,000 each over five Sarah Hilsman, Hope College, “Real algebraic level years to pursue their research. curves and the intersection of lines of positive slope” Zack While, Youngstown State University, “The ulti- —From a Packard Foundation announcement mate mind-bender: Futurama’s mind-switching problem” Douglas Knowles, State University of New York at Geneseo, “Finite fun with numerical ranges” Cox Awarded Michell Medal Daniel Giles, Portland State University, “Convex optimization methods for the smallest intersecting ball Barry Cox of the University of Adelaide has been awarded problem” the 2015 J. H. Michell Medal of the Australian Mathemati- John Vastola, University of Central Florida, “On the cal Society for his “groundbreaking” contributions to the structure and calculation of a class of infinitely nested area of nanotechnology. His work involves the geometry of radicals” carbon nanotubes that properly incorporate the effect of Samantha Parsons, Roanoke College, “Interests in curvature.
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