일정: 강연1시간+질의응답30분

Title: Convergence of orbital integrals in positive characteristic

Abstract: Orbital integrals are fundamental objects in the harmonic analysis and representation theory of reductive groups over p-adic local fields. Over local function fields, however, their convergence is not known in full generality; suitable hypotheses on either the conjugacy class or the reductive group are needed.

After reviewing the basic definitions and known results, I will discuss joint work with Minju Park proving absolute convergence of orbital integrals on unitary groups over local fields of arbitrary positive characteristic. If time permits, I will also discuss the expected extension of the argument to classical groups in odd positive characteristic.