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Thursday, April 6, 2017

**Abstract:** The theory of congruences between automorphic forms traces back to Ramanujan, who observed various congruence properties between coefficients of generating functions related to the partition function. Since then, the subject has evolved to become a central piece of contemporary number theory; lying at the heart of spectacular achievements such as the proof of Fermat's Last Theorem and the Sato-Tate conjecture. In my talk I will explain how the modern theory gives satisfactory explanations of some concrete congruence phenomena for modular forms (the $\mathrm{GL}_2$ case), as well as recent progress concerning automorphic forms for higher rank groups. This is joint work with D. Le, B. Levin and S. Morra.