Singular modular forms on quaternionic $\mathrm{E}_8$

Abstract: The exceptional group $\mathrm{E}_{7,3}$ has a symmetric space with Hermitian tube structure. On it, Henry Kim wrote down low weight holomorphic modular forms that are "singular" in the sense that their Fourier expansion has many terms equal to zero. The exceptional group $\mathrm{E}_{8,4}$ does not have a Hermitian structure, but it has what might be the next best thing: a quaternionic structure and associated "modular forms". I will explain the construction of singular modular forms on $\mathrm{E}_{8,4}$, and the proof that these special modular forms have rational Fourier expansions, in a precise sense. This builds off of work of Wee Teck Gan and uses key input from Gordan Savin.

number theoryrepresentation theory

Audience: researchers in the discipline

The 2020 Paul J. Sally, Jr. Midwest Representation Theory Conference

Series comments: The 44th Midwest Representation Theory Conference will address recent progress in the theory of representations for groups over non-archimedean local fields, and connections of this theory to other areas within mathematics, notably number theory and geometry.

In order to receive information on how to participate (to be sent out closer to the conference), please register by October 14 here: forms.gle/zFAnQBnuPGRnKzMr7