The University of Arizona
Please note that this event has ended!

Singular modular forms on quaternionic E_8

Algebra and Number Theory Seminar

Singular modular forms on quaternionic E_8
Series: Algebra and Number Theory Seminar
Location: Zoom Meeting
Presenter: Aaron Pollack, UCSD

The exceptional group $E_{7,3}$ 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 symmetric space associated to the exceptional group $E_{8,4}$ 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 $E_{8,4}$, 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.