Number/Representation Theory

Local components of important classes of automorphic representations associated to a number field can be organised into sets of representations of $p$-adic groups. These sets are our beloved local Arthur packets. ABV-packets, named after Adams, Barbasch and Vogan who originally proposed them for archimedean groups, generalize local Arthur packets using algebraic geometry. The geometric realization involves microlocal analysis on perverse sheaves on moduli spaces of Langlands parameters. In this talk, I will give an introduction to ABV-packets for groups over $p$-adic fields and report on some recent progress in the subject.