University of Texas, Austin
When
Where
Title: Spectral Action in Betti Metaplectic Langlands
Abstract: The metaplectic geometric Langlands program can be understood in two ways: as a twisted analogue of the geometric Langlands program, and as a geometric analogue of the Langlands program for covering groups, namely the metaplectic Langlands program. One of the key structures in the geometric Langlands program is the spectral action, which roughly says that the spectral side acts on the automorphic side, allowing one to spectrally decompose the automorphic category over the moduli of ˇ𝐺-local systems. This can be viewed as a geometric incarnation of the automorphic-to-Galois direction. In this talk, I will start with the motivation for the metaplectic geometric Langlands program, and then discuss my recent work on constructing spectral action in the Betti metaplectic context. If time permits, I will discuss the role of factorization homology as a categorical mechanism for converting the metaplectic Hecke action into the spectral action.