Principal Investigators | Affiliated Scientists

Principal Investigators

  • Jennifer Balakrishnan

    Jennifer S. Balakrishnan, Boston University

    Jennifer S. Balakrishnan is a number theorist working on explicit methods for curves. 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. She is currently the Clare Boothe Luce Assistant Professor of Mathematics at Boston University. Previously, she was a Titchmarsh Research Fellow at the Mathematical Institute of the University of Oxford, a Junior Research Fellow of Balliol College, Oxford, and an NSF Postdoctoral Fellow at Harvard. Balakrishnan received an AB and AM from Harvard University and a PhD in Mathematics from MIT.

  • Noam D. Elkies

    Noam D. Elkies, Harvard University

    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.

  • Brendan Hassett

    Brendan Hassett, Brown University

    Brendan Hassett is 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.

  • Bjorn Poonen

    Bjorn Poonen, MIT

    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.

  • Andrew Sutherland

    Andrew Sutherland, MIT

    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. He currently serves on the boards of Mathematics of Computation, the L-functions and Modular Forms Database, and the Number Theory Foundation. He is a managing editor of Research in Number Theory and current record-holder for the largest cloud-based research computation (580,000 cores).

  • John Voight

    John Voight, Dartmouth College

    John Voight is associate professor of mathematics at Dartmouth College. 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 (under review) 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).

Affiliated Scientists

  • Vishal Arul

    Vishal Arul, MIT

    Vishal Arul is a fifth-year graduate student in the Department of Mathematics at MIT. He is studying number theory and algebraic geometry under the guidance of Bjorn Poonen.

  • Eran Assaf

    Eran Assaf, Dartmouth College

    Eran Assaf obtained his doctorate from the Hebrew University of Jerusalem in 2017. He joined the team in September 2019 as a postdoc at Dartmouth College. His main research interests are the p-adic local Langlands correspondence, Shimura varieties, p-adic representations of p-adic groups and computation of fundamental domains for arithmetic modular groups.

  • Alex Best

    Alex Best, Boston University

    Alex Best is a graduate student at Boston University working with Jennifer Balakrishnan. Previously he worked on highly optimized computer arithmetic at TU Kaiserslautern. Before that, he obtained a masters from the University of Cambridge and a B.Sc. in Discrete Mathematics from the University of Warwick, where his interests in computational number theory first began.

  • Alexander Betts, Harvard University

    Betts is a postdoc at Harvard, specialising in arithmetic and anabelian geometry, relating fundamental groups of varieties to their arithmetic properties. His thesis, completed at the University of Oxford under the supervision of Minhyong Kim, showed that classical Néron-Tate height functions on abelian varieties admit very natural descriptions in terms of fundamental groups of torsors on abelian varieties.

  • Raymond van Bommel, MIT

    Raymond van Bommel is currently a research scientist at MIT. Previously, he was a research associate at Johannes Gutenberg-Universität Mainz, Germany. Before he obtained his PhD at Universiteit Leiden, The Netherlands, under the supervision of David Holmes and Fabien Pazuki. During this time, he worked on the algorithmic computation of the different numerical invariants surrounding the Birch and Swinnerton-Dyer conjecture, first for hyperelliptic curves and later for non-hyperelliptic curves. He joined the MIT team in 2019.

  • Andrew Booker, University of Bristol

    Andrew Booker is Professor of Pure Mathematics at the University of Bristol. He received his PhD from Princeton University in 2003 under the supervision of Peter Sarnak. His interests lie in automorphic forms and analytic number theory, including computational aspects, and he is noted for the development of algorithms for the rigorous computation of L-functions and associated data. Between 2013 and 2019, he was co-PI of the EPSRC-funded grant “LMF: L-functions and modular forms” which helped to support the LMFDB.

  • Ben Breen, Clemson University

    Ben Breen received his Ph.D. at Dartmouth College in June 2020. He is currently an RTG postdoctoral scholar at Clemson University. His research interests lie in computational number theory and arithmetic geometry. His current research focuses on explicit methods for Hilbert modular forms and Cohen-Lenstra style heuristics.

  • Alina Bucur

    Alina Bucur, University of California at San Diego

    Alina Bucur is an Associate Professor at the University of California at San Diego. She received her Ph.D. from Brown University in 2006 under the supervision of Jeffrey Hoffstein. After that, she held a position as a Moore Instructor at Massachusetts Institute of Technology (postdoc, 2006-2009) and had visiting positions at the Institute for Advanced Studies (2006-2007 and 2009-2010) and MSRI (2011). Her research interests lie in the area of multiple Dirichlet series and arithmetic statistics. Bucur’s work combines techniques from analytic number theory, probability, and arithmetic geometry and has been supported by two Simons Collaboration Grants.

  • Atticus Christensen

    Atticus Christensen received a PhD in mathematics at MIT under the direction of Bjorn Poonen in 2020.

  • Fabien Cléry, Brown University

    Dr. Fabien Cléry received his Ph.D. in 2009 from the University of Lille 1. Since then, he has held positions at the University of Amsterdam, the University of Hannover, the University of Siegen, the Max Planck Institute for Mathematics in Bonn, and the University of Loughborough. His research interests are on two types of modular forms focusing on the theory but also on computational aspects. The two types of modular forms that he is currently studying are Siegel modular forms and Picard modular forms.

  • Edgar Costa

    Edgar Costa, MIT

    Edgar Costa received his Ph.D. in 2015 from the Courant Institute of Mathematical Sciences at New York University and was a Postdoctoral Fellow at ICERM during the semester program “Computational Aspects of the Langlands Program”. Prior to joining the collaboration, he was an Instructor in Applied and Computational Mathematics at Dartmouth College. Costa’s research interests are centered around effective methods in arithmetic geometry, arithmetic statistics, and number theory. His current research is focused on the development and application of theoretical and computational techniques to study the interconnections predicted by the Langland’s program.

  • Alex Cowan, Harvard University

    Alex Cowan received his Ph.D. from Columbia University in 2019 and is currently a research scientist at Harvard University. His research interests include elliptic curves, arithmetic statistics, and analytic number theory.

  • John Cremona

    John Cremona, University of Warwick

    John Cremona has been a Professor at the University of Warwick since 2007. After obtaining his DPhil under Birch at Oxford in 1981, he held positions at the University of Michigan and Dartmouth College in the US, and the universities of Exeter and Nottingham in the UK. Cremona is best known for developing and implementing modular symbol algorithms and using these to compile tables of elliptic curves over the rationals, and has extended this work to compile similar elliptic curve tables over imaginary quadratic fields. Between 2013 and 2019, he was PI on a major grant “LMF: L-functions and modular forms, which part-funded the computing infrastructure and workshops which underpin the LMFDB.

  • Lassina Dembélé

    Lassina Dembélé, University of Luxembourg

    Lassina Dembélé worked for the collaboration at Dartmouth College through spring 2019. His current research interests are in computational number theory, Hilbert modular forms, automorphic forms, and Galois representations. Broadly speaking, his work is in the framework of explicit methods in the p-adic and mod p Langlands programme.

  • Maarten Derickx

    Maarten Derickx, University of Groningen

    Maarten Derickx’s research interests lie primarily in computational number theory. His main focus is Galois representations of elliptic curves over number fields and the corresponding rational points on modular curves, as well as how a good understanding of these can be used in the modular approach to Diophantine equations and the modularity of elliptic curves. Derickx obtained his Ph.D. under the supervision of Bas Edixhoven at Universiteit Leiden in 2016 and was a postdoctoral researcher under Michael Stoll at Universität Bayreuth after this. He worked for the collaboration as a research scientist at MIT through 2019.

  • Netan Dogra

    Netan Dogra, King's College London

    Netan Dogra’s research is on the solution of Diophantine equations using p-adic analytic and etale topological methods. He is a Royal Society University Research Fellow at King’s College London. Before that he held post-doctoral positions at the University of Oxford, Imperial College London, and Radboud University. He received his PhD in 2015 from the University of Oxford.

  • Francesc Fité, MIT

    Francesc Fité was a member at the IAS for the 2018-19 academic year. He obtained his Ph.D. in 2011 at Universitat Politècnica de Catalunya. He has been a postdoc in Bielefeld, Essen, and Barcelona. His main research interests are number theory and arithmetic geometry, with special emphasis on the arithmetic and modularity of low dimensional abelian varieties. Fité joined the collaboration as a research scientist at MIT in 2019.

  • David Harvey

    David Harvey, University of New South Wales

    David Harvey is a Senior Lecturer and Australian Research Council Future Fellow at the University of New South Wales in Sydney, Australia. He received his Ph.D. from Harvard in 2008, and subsequently held a three-year postdoctoral position at New York University. Harvey’s research interests include algorithmic number theory, especially computing zeta functions of varieties over finite fields, and symbolic computation, especially algorithms for efficient arithmetic on large integers and polynomials.

  • Daniel Hast Photo

    Daniel Hast, Boston University

    Daniel R. Hast is a postdoctoral associate at Boston University currently working in number theory, arithmetic algebraic geometry, and Diophantine geometry, with a focus on p-adic approaches to rational points on varieties. He received a Ph.D. from University of Wisconsin–Madison in 2018 under the supervision of Jordan Ellenberg, and worked as a G. C. Evans Instructor at Rice University for one year before joining the Simons Collaboration in Fall 2019.

  • Campbell Hewett

    Campbell Hewett, MIT

    Campbell Hewett is a fifth-year math Ph.D. student. His advisor is Bjorn Poonen. He received an Sc.B. in math at Brown University in 2015. His interests are in algebraic geometry and number theory.

  • Everett Howe

    Everett Howe received his Ph.D. at U.C. Berkeley in 1993, under the supervision of Hendrik Lenstra. After a three-year postdoctoral position at the University of Michigan, he spent 23 years as a researcher at the Center for Communications Research, La Jolla. Currently, he is an independent mathematician, focusing his attention on curves and abelian varieties, and on computational questions arising from their study.

  • Sonal Jain, Harvard University

    Jain received his doctorate in 2007 at Harvard under the direction of Noam Elkies. He spent several years at the Courant Institute of Mathematical Sciences at NYU and was a postdoctoral fellow at MSRI. He worked as a postdoctoral research scientist with the collaboration in 2020.

  • Kiran Kedlaya

    Kiran Kedlaya, University of California, San Diego

    Kiran Kedlaya is the Stefan E. Warschawski Professor of Mathematics at University of California, San Diego. He received his Ph.D. from MIT in 2000. He is a recipient of the Presidential Early Career Award for Scientists and Engineers, a Sloan Research Fellowship, and a Guggenheim Fellowship. Kedlaya’s research covers a variety of topics in algebraic geometry and number theory, with some emphasis on the computational aspects of these areas. He has developed practical algorithms for computing L-functions of algebraic varieties using p-adic analysis, and for tabulating isogeny classes of abelian varieties over finite fields. He is a frequent contributor to Sage and the LMFDB.

  • Dohyeong Kim

    Dohyeong Kim, Seoul National University

    Dohyeong Kim is interested in the Iwasawa theory, Diophantine equations, and the arithmetic Chern-Simons theory. He worked as a research scientist for the collaboration at MIT and previously was a postdoctoral assistant professor at the University of Michigan. Before that, he was a research fellow at the Center for Geometry and Physics for two years. Kim spent his graduate and undergraduate years at the POSTECH.

  • Avi Kulkarni

    Avinash (Avi) Kulkarni, Dartmouth College

    Avi Kulkarni joined the collaboration in January 2020. His main research interests lie in arithmetic geometry and computational number theory. Before joining the collaboration, he was a postdoctoral researcher at the MPI MiS Leipzig and developer for the OSCAR computer algebra system at TU Kaiserslautern. Avi completed his PhD at Simon Fraser University in 2018.

  • Wanlin Li, Montreal

    Wanlin Li received her Ph.D. from the University of Wisconsin-Madison in 2019 under the supervision of Jordan Ellenberg. She joined the collaboration team at MIT in the fall of 2019. Her research interest lies in arithmetic geometry, particularly the study of curves, surfaces and abelian varieties over fields of positive characteristic. In 2021 she became a postdoc at the Centre de recherches mathématiques in Montreal.

  • David Lowry-Duda, Brown University

    David Lowry-Duda’s research interests primarily lie in analytic number theory, and in particular on automorphic forms and L-functions. During his Ph.D., he developed a new approach to study the size and behavior of automorphic forms. He has contributed to data creation for the LMFDB, as well as day-to-day maintenance. Lowry-Duda completed his Ph.D. at Brown University in 2017, worked as a postdoctoral researcher at Warwick Mathematics Institute, and has returned to ICERM at Brown University for his Simons Collaboration appointment.

  • Céline Maistret, University of Bristol

    Céline Maistret was a postdoctoral faculty fellow at Boston University until 2020. Céline received her Ph.D. from the University of Warwick in 2017 and was a research associate at the University of Bristol before joining Boston University. Maistret’s work revolves around the arithmetic of abelian varieties, with a particular interest toward computations related to the parity conjecture and the Birch and Swinnerton-Dyer conjecture. She is currently a Royal Society Dorothy Hodgkin Fellow at the University of Bristol.

  • Benjamin Matschke Photo

    Benjamin Matschke, Boston University

    Benjamin Matschke is a mathematician working in algorithmic number theory, discrete geometry, algebraic topology, and combinatorics. His current focus lies in computational aspects of classical Diophantine equations, elliptic curves, and Nullstellensätze. Matschke received his Ph.D. from Freie Universität Berlin. After positions at Institute for Advanced Study, Institut des Hautes Etudes Scientifiques, ETH Zürich, Isaac Newton Institute, MPIM Bonn, MPI MiS Leipzig, Université de Bordeaux, Technion, and Koc University, he is now a Research Assistant Professor at Boston University.

  • Steffen Muller

    Steffen Müller, Unviersity of Groningen

    Steffen Müller is an assistant professor at the Unviersity of Groningen. He received his Ph.D. from Bayreuth in 2010 and was then a member of the mathematics department in Hamburg and in Oldenburg. He is mainly interested in explicit methods in arithmetic geometry, in particular, the use of archimedean and p-adic height functions to study rational points on curves and abelian varieties.

  • David Roe

    David Roe, MIT

    David Roe’s study of p-adic computation includes work on computing L-functions of varieties, p-adic modular forms and methods for tracking precision. He is also interested in the local Langlands correspondence and p-adic tori. He contributes frequently to Sage, and helped create the LMFDB database of isogeny classes of abelian varieties. David received an S.B. in mathematics and literature from MIT in 2006, completed his Ph.D. at Harvard in 2011, then worked as a postdoctoral fellow at the Universities of Calgary, British Columbia and Pittsburgh before returning to MIT.

  • Ciaran Schembri

    Ciaran Schembri, Dartmouth College

    Ciaran Schembri is a research scientist at Dartmouth College. He joined the collaboration in September 2019 after receiving his PhD from the University of Sheffield. His main interests are in number theory and arithmetic geometry, in particular on Shimura curves and abelian varieties with quaternionic multiplication.

  • Sam Schiavone

    Sam Schiavone, MIT

    Sam Schiavone is a research scientist at MIT. He received his Ph.D. in 2019 from Dartmouth College. His research interests include Belyi maps, Hilbert modular varieties, and algebras of low rank.

  • Joseph H. Silverman

    Joseph H. Silverman, Brown University

    Joseph H. Silverman is a Professor of Mathematics at Brown University, where he has been on the faculty since 1988. He is a recipient of a Sloan Research Fellowship, a Guggenheim Fellowship, and an AMS Steele Prize. His primary research interests are elliptic curves, arithmetic geometry, arithmetic dynamics, and cryptography, and he has also written a number of the standard textbooks in these areas.

  • Nicholas Triantafillou

    Nicholas Triantafillou, University of Georgia

    Nicholas Triantafillou is a postdoctoral fellow at the University of Georgia. His main research interest is in arithmetic geometry, and he is currently working on a project to understand how powerful classical Chabauty’s method is when combined with restriction of scalars and descent techniques.

  • Jan Vonk

    Jan Vonk, University of Leiden

    Jan Vonk is an assistant professor at the University of Leiden. He obtained his doctorate from the University of Oxford in 2015 and held postdoctoral positions at McGill University, the University of Oxford, and the Institute for Advanced Study. His work focuses on p-adic aspects of arithmetic geometry, in particular applications to explicit class field theory and Diophantine equations.