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Partitions with Modular Forms

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A very old question in combinatorics: for n>1, what can we say about p(n), the number of partitions of n? In 1919, Ramanujan proved that p(5n-1) is always divisible by 5, part of a collection of results known as Ramanujan’s congruences. In this talk, we try to explore (a bit) the realm of modular forms and how these functions allow us to obtain unexpected number theoretic and combinatorial results. We will go through the proof sketch of one of the theorems, possibly with other unexpected formulae along the way!

This talk is part of the The Archimedeans series.

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