Algebra Seminar: Langlands duality for cuspidal local systems

Sam Gunningham, Montana State University

Title: Langlands duality for cuspidal local systems

Abstract: Cuspidal local systems on nilpotent orbits were defined and classified by Lusztig in his remarkable 1984 paper. Lusztig’s type-by-type classification appears again in the category of generically twisted D-modules on the moduli stack of G-bundles on an elliptic curve - a natural object of study in the geometric Langlands program. Langlands duality then predicts a surprising symmetry in Lusztig’s classification, which boils down to some interesting numerical identities in certain cases. This talk will be a report on ongoing work in progress with Dragos Fratila and Penghui Li.