The unbounded denominators conjecture

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Yunqing Tang, Princeton University
IAS - Simonyi Hall Seminar Room SH-101

In-Person and Online Talk

Passcode: The three digit integer that is the cube of the sum of its digits

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.