The unbounded denominators conjecture

SEMINARS, NUMBER THEORY

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March 30, 2022 3:00 pm - 4:00 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA
Speaker:

Yunqing Tang - Princeton University


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. This is joint work with Frank Calegari and Vesselin Dimitrov.