Simons Collaborationon Arithmetic Geometry, Number Theory, and Computation

John Voight

John Voight was professor of mathematics at Dartmouth College during the Collaboration. He received his Ph.D. in 2005 from the University of California, Berkeley, and has held positions at the University of Sydney, the Institute for Mathematics and its Applications (IMA) at the University of Minnesota, and the University of Vermont. Voight’s research interests are in arithmetic geometry and number theory, with a focus on algorithmic aspects. His current research concerns computational problems for moduli spaces and automorphic forms. He is the author of a textbook on quaternion algebras and received an NSF CAREER award. He was the recipient of the Selfridge Prize in 2010 and currently serves on the board for the L-functions and Modular Forms DataBase (LMFDB). In August 2024, he became professor at the University of Sydney, where he leads a project supporting the development and expansion of Magma, a system for computations in algebra, number theory, algebraic geometry, and algebraic combinatorics. He is a Fellow of the American Mathematical Society, in the 2025 class.

Andrew Sutherland

Andrew Sutherland received his S.B. in mathematics from MIT in 1990. As an undergraduate, Sutherland co-founded the software company Escher Group, specializing in high-performance distributed computing, and after completing an NSF Graduate Fellowship at MIT, served as the company’s Chief Technology Officer for ten years. Sutherland returned to academia and completed his Ph.D. in mathematics at MIT in 2007, winning the George M. Sprowles Prize for his thesis. He joined the MIT mathematics department in 2009, and was promoted to Principal Research Scientist in 2012. Sutherland’s research focuses on computational number theory and arithmetic geometry, and he was awarded the Selfridge Prize in 2012, for his work in this area. Sutherland currently serves as Associate Editor of Mathematics of Computation, Editor in Chief of Research in Number Theory, Managing Editor of the L-Functions and Modular Forms Database, and President of the Number Theory Foundation. He was named a Fellow of the American Mathematical Society as a member of the 2021 Class.

Bjorn Poonen

Bjorn Poonen received an A.B. in Mathematics and Physics from Harvard in 1989, and a Ph.D. in Mathematics from U.C. Berkeley in 1994. In 2008, after positions at MSRI, Princeton, and U.C. Berkeley, he moved to MIT, where he is the Claude Shannon Distinguished Professor in Science. Poonen is known for developing and analyzing algorithms aimed at determining the set of rational points of a given variety. But his theorems also demonstrate the limitations of known methods, and even show that certain related problems are undecidable. Poonen has received the Guggenheim, Packard, Rosenbaum, Simons, and Sloan fellowships, as well as a Miller Professorship, the Chauvenet Prize, and the MIT School of Science Prize in Undergraduate Teaching. He is also a four-time Putnam Competition winner, a Simons Investigator, a fellow of the American Academy of Arts and Sciences and of the American Mathematical Society, and the founding managing editor of Algebra & Number Theory. In 2018, Poonen delivered an invited address at the International Congress of Mathematicians.

Brendan Hassett

Brendan Hassett is Jonathan Nelson University Professor of Mathematics and Director of the Institute for Computational and Experimental Research in Mathematics at Brown University. He received his BA in 1992 from Yale and his Ph.D. from Harvard in 1996 under the supervision of Joseph Harris. From 1996 to 2000 he worked as a Dickson Instructor at the University of Chicago, partly supported by a National Science Foundation Postdoctoral Research Fellowship. He was a faculty member at Rice University from 2000 to 2015 and chaired its mathematics department from 2009 to 2014. He has held visiting positions at the Mittag Leffler Institute in Stockholm, the Chinese University of Hong Kong, and the University of Paris (Orsay). Hassett’s research focus is algebraic geometry. His work has been recognized with a Sloan Research Fellowship, a National Science Foundation CAREER award, and the Charles W. Duncan Award for Outstanding Faculty at Rice. He is a Fellow of the American Mathematical Society and the American Association for the Advancement of Science.

Noam D. Elkies

Noam D. Elkies is professor of mathematics at Harvard University. He did undergraduate work at Columbia and obtained his doctorate at Harvard in 1987. He is known for exhibiting many integral solutions to the equation

A⁴ + B⁴ + C⁴ = D⁴

settling a 200-year-old question of Euler. Elkies also proved that elliptic curves over the rational numbers admit infinitely many supersingular primes. He is famous for ‘extreme examples’ in number theory: elliptic curves with large rank, K3 surfaces with large Picard group, etc. Elkies has also contributed to algorithms for elliptic curves over finite fields, characterizations of efficient sphere packings, and tilings of Aztec dimanonds by dominoes. In 2017 he was elected to the National Academy of Sciences.

Jennifer S. Balakrishnan

Jennifer Balakrishnan is Professor of Mathematics at Boston University.  Her research is motivated by various aspects of the classical and p-adic Birch and Swinnerton-Dyer conjectures, as well as the problem of algorithmically finding rational points on curves.  Balakrishnan received an AB and AM from Harvard University and a PhD in Mathematics from MIT.  She was an NSF Postdoctoral Fellow at Harvard, a Titchmarsh Research Fellow at the Mathematical Institute of the University of Oxford, and a Junior Research Fellow of Balliol College, Oxford.  She is the recipient of a Sloan Research Fellowship, an NSF CAREER award, and the AWM-Microsoft Research Prize in Algebra and Number Theory.