Sanjeev Arora

Ahlfors Lecture series

October 31 - November 1, 2019, Organizers: Yum-Tong Siu and Horng-Tzer Yau

Harvard University, Science Center Hall D

Speaker and Program


Peter Sarnak (Princeton University and Institute for Advanced Study) gives two talks about "Diophantine Analysis and Groups".
Talks on youtube.
October 31, 2019:

Lecture I
4:15-5:15 PM
in SC Hall D
Lecture I: "Applications of Points on Subvarieties of Tori"
Abstract: The intersection of the division group of a finitely generated subgroup of a torus with an algebraic sub-variety has been understood for some time (Lang, Laurent). After a brief review of some of the tools in the analysis and their recent extensions (André-Oort conjectures), we give some old and new applications; periodicity of Betti numbers, algebraicity of Painlevé equations, and the additive structure of the spectra of quantum graphs.
November 1, 2019:

Lecture II
4:14-5:15 PM
in SC Hall D
Lecture II: "Integer Points on Affine Cubic Surfaces"
Abstract: The level sets of a cubic polynomial in four or more variables tends to have many integer solutions, while ones in two variables a limited number of solutions. Very little is known in the case of three variables. For cubics which are character varieties (thus carrying a nonlinear group of morphisms) a Diophantine analysis has been developed and we will describe it. Passing from solutions in integers to integers in, say, a real quadratic field there is a fundamental change which is closely connected to challenging questions about one-commutators in sl2 over such rings.
A reception follows the Thursday lecture at 5:30 pm in the Math Department common room.

Lars Ahlfors
This is a lecture series in honor of Lars Ahlfors (1907-1996) who was William Caspar Graustein Professor of Mathematics at Harvard University from 1946 to 1977. Ahlfors won the fields medal in 1936 and the Wolf prize in 1981.


Ahlfors Lecture Series, 2009 Ahlfors Lecture Series, 2010 Ahlfors Lecture Series, 2011 Ahlfors Lecture Series, 2012 Ahlfors Lecture Series, 2013 Ahlfors Lecture Series, 2014 Ahlfors Lecture Series, 2015 Ahlfors Lecture Series, 2016 Ahlfors Lecture Series, 2017 Ahlfors Lecture Series, 2018