Number Theory Seminar: Joakim Færgeman
Speaker: Joakim Færgeman (Princeton)
Titel: Motivic realization of rigid local systems on curves via geometric Langlands.
Abstract: A natural problem in the study of local systems on complex varieties is to characterize those that arise in the cohomology of a family of varieties. We refer to such local systems as motivic. In 1992, Simpson conjectured that for a reductive group G, rigid G-local systems with suitable conditions at infinity are motivic. This was proven for curves when G = GL_n by Katz who classified such rigid local systems. In this talk, we sketch a proof of Simpson's conjecture for curves for an arbitrary reductive group G. Our proof goes through the geometric Langlands program in characteristic zero.