Beeger Lecture

Day 1 (Tuesday 2 April) @ 16:15 – 17:15

Andrew Sutherland (Massachusetts Institute of Technology)

The fine art of point counting

Some of the most fundamental questions in number theory can be reduced to a problem of “counting points” on some arithmetic object: this includes questions involving Diophantine equations (Hilbert’s 10th problem), zeta functions (the Weil conjectures), algebraic varieties (the BSD and Sato-Tate conjectures), and L-functions (modularity and the Langlands program), as well as many problems in the burgeoning field of arithmetic statistics.  I will present some illustrative examples to support this claim, showing how the apparently simple act of counting points can play a pivotal role in proving theorems and formulating conjectures.  After giving an overview of some of the computational methods used to count points, I will discuss some of the challenges that arise when applying these methods at scale, challenges that have taken on increasing importance in our modern era of massive data sets, machine learning algorithms, and ever-expanding computational resources.

Biography

Andrew Sutherland is a Principal Research Scientist in the mathematics department at the Massachusetts Institute of Technology (MIT), where he received his Ph.D. in mathematics in 2007, earning the Sprowls Award for his thesis.  Sutherland’s research focuses on computational aspects of number theory and arithmetic geometry; he was awarded the 2012 Selfridge Prize for his work in these areas. He has played a leading role in several large scale collaborations in number theory, including the Polymath project on Bounded Gaps Between Primes, the L-functions and Modular Forms Database, and the sums of three cubes project, and is currently one of the Principal Investigators leading the Simons Collaboration on Number Theory, Arithmetic Geometry, and Computation.  Sutherland currently serves as 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 Fellow of the American Mathematical Society ins 2021 for his “contributions to number theory, both on the theoretical and computational aspects of the subject”.