Functions on the Commuting Stack via Langlands Duality - ICBS 2024

Explore complex mathematical concepts in this 1-hour 4-minute lecture by Penghui Li at BIMSA. Delve into the construction of a semi-orthogonal decomposition of the cocenter of the universal variant of the affine Hecke category for a complex reductive group. Learn how this construction is used to calculate endomorphisms of a Whittaker object in the cocenter through a diagram organizing parabolic induction of character sheaves. Examine the implications of assuming a universal variant of Bezrukavnikov's spectral description of the affine Hecke category, leading to a formula for the dg algebra of global functions on commuting stacks of complex reductive groups. Discover how this formula demonstrates that the ring of invariant functions on the commuting scheme is reduced. Gain insights into this collaborative work with David Nadler and Zhiwei Yun, exploring the intersection of complex mathematical theories and their applications in the context of Langlands duality.