Mathematics Colloquium:
Wednesday, 14 February 2023, 4:00 pm
=========================
Venue: Ramanujan hall
Host: Ravi Raghunathan
Speaker: Manish Patnaik
Affiliation: University of Alberta
Title: Eisenstein series and some variants on Loop Groups
Abstract: We will first review some aspects of the reduction theory for loop groups studied by Howard Garland in the 1970s. Following this, we explain how features of the Siegel domains in this setting essentially force certain cuspidal Eisenstein series on loop groups to be entire functions, in stark contrast to the finite-dimensional situation.
Switching to the case of function fields, we then introduce, following ideas of Braverman and Kazhdan, new “regularized” cuspidal Eisenstein series for loop groups. These series are no longer entire and their Fourier coefficients encode (finite-dimensional) automorphic L-functions that have previously remained inaccessible by the standard Langlands-Shahidi method.