Partitions with Modular Forms - Nicky Wong -The Archimedeans

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A very old question in combinatorics: for n greater than 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!

Prerequisites:
Complex analysis/methods

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  1. The Archimedeans
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Комментарии
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Can't stop watching because of intuitive example of how the 2 generating matrices differ. Even though I'm slow the presentation caught my eye.

jeffreyhowarth
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This is a great video. Modular forms and geodesics are great tools, I have lately been using them in my study of representation theory. Thank you for posting.

ross
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