The Geometry of the Affine Springer Fibers and Arthur's Weighted Orbital Integrals

par Zongbin Chen (Yau Mathematical Sciences Center, Tsinghua University)

mercredi 10 avr. 2019, 10:30 → 11:30 Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

The affine Springer fibers are geometric objects conceived for the study of orbital integrals. They have complicated geometric structures. We will explain our work on the geometry of affine Springer fibers, with emphasize on the construction of a fundamental domain, and show how the study of the affine Springer fibers can be reduced to that of its fundamental domain. As an application, we will explain how to calculate Arthur's weighted orbital integrals via counting points on the fundamental domain.