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Exceptional theta functions

Aaron Pollack (UCSD)

Location:  Zoom
Date & time: Wednesday, 07 December 2022 at 12:00PM - 1:00PM

Abstract: Classical theta functions are certain holomorphic functions (of one or several complex variables) that possess an infinite group of discrete symmetries.  They are a key building block of modern number theory: they can be used to prove that the Riemann zeta function satisfies a functional equation (more generally, are very useful in understanding certain L-functions) and are the first concrete examples of modular forms (more generally, are useful for proving instances of Langlands functoriality).  One way to think about theta functions is that they are associated to the following pair of data: a lattice L in a positive definite quadratic space V, and a vector in a finite dimensional representation of SO(V).  I will discuss "exceptional" theta functions, which are associated with similar data, where the group SO(V) gets replaced by certain compact exceptional groups.  I will also discuss some applications.