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Congruences between modular forms

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Brandon Levin
Rice University/MPIM
Thu, 04/05/2023 - 15:00 - 16:00
MPIM Lecture Hall
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Contact: Christian Kaiser (kaiser @

The resolution of Serre's conjecture for modular forms by Khare-Wintenberger in the mid-2000s was a major achievement in the field of number theory. In this talk, I will begin by describing Serre's conjecture and its origins in the theory of congruences between modular forms. I will then describe how the conjecture is connected to representation theory in finite characteristic. This will naturally lead to higher dimensional analogues of the conjecture.  Finally, I will discuss results on these higher dimensional conjectures joint with Daniel Le, Bao V. Le Hung and Stefano Morra.

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