Title: The Chevalley Map in Positive Characteristic

Abstract: We will study the pushforward of smooth measures with respect to the Chevalley map for GLn(Fq((t))). We will prove that, under the condition of the existence of resolution of singularities, this pushforward has an almost bounded density function. This result plays a key role in the proof of local integrability of characters of cuspidal representations of GLn(Fq((t))).

The talk is based on joint work with Dmitry Gourevitch, David Kazhdan, and Eitan Sayag.