The partition function modulo 2 and 4

The Ramanujan congruences for the partition function have an extraordinary legacy in mathematics. Indeed, these results were testing grounds for deep theories developed later by Atkin and Hecke and Deligne and Serre. These days research abounds with new congruences for various sorts of restricted partition functions. In this talk the speaker will discuss new and old results about the partition function. In the case of the partition function modulo 2 and 4, he will offer new results and some few precise open questions. The problems are testing grounds for questions about harmonic Maass Borcherds products and p-adic properties of geometric modular forms as sections of line bundles on modular curves.

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