RTG Seminar on Number Theory Seminar

Endoscopy is the study of how the Langlands correspondence behaves with respect to functoriality, and is thus critical to understanding the Langlands conjectures. A transfer factor, roughly speaking, is a function that helps one interpolate between different spaces and is a crucial ingredient for endoscopy. In order to define transfer factors for a general reductive group G over a p-adic field, Kaletha constructed a new canonically-defined cohomology set associated to G. The talk will first discuss the function-field analogue of this construction, focusing primarily on its new challenges. We then turn to the construction of a new cohomology set associated to a reductive group over a global function field, and show how it can be used to connect the aforementioned local transfer factors to an adelic transfer factor, and, time-permitting, new conjectures that this approach enables. Speaker(s): Peter Dillery (University of Michigan)