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Wednesday, December 1, 2021

**Abstract:** The fourier coefficients of modular forms have been of interest in number theory for several years. They are intimately connected with elliptic curves, class numbers for quadratic fields, and integer partitions. The last one may seem surprising at first, given that these complex-analytic functions "should" have nothing to do with that fact that one can write 4 as 4=3+1=2+2=2+1+1=1+1+1+1. We will focus mainly on integer partitions for this talk. In particular, we will discuss partition congruences, and at the end, discuss new congruences for related functions.