# Berkeley-Caltech-Stanford Joint Number Theory Seminar

Monday, November 15, 2021
12:30pm to 1:30pm
Online Event
The unbounded denominators conjecture
Yunqing Tang, Department of Mathematics, Princeton University,

(Joint work with Frank Calegari and Vesselin Dimitrov.) The unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of SL_2(Z) whose Fourier coefficients have bounded denominators must be a modular form for some congruence subgroup. In this talk, we will give a sketch of the proof of this conjecture based on a new arithmetic algebraization theorem.