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Explore the mathematical connections between cocenter structures in affine Hecke categories and their relationship to Langlands duality in this 54-minute conference talk presented by Penghui Li at BIMSA's ICBS2025. Delve into advanced topics in representation theory and algebraic geometry as the speaker examines how cocenter constructions provide insights into the geometric Langlands program. Investigate the categorical framework underlying affine Hecke algebras and discover how their cocenter properties illuminate fundamental dualities in the Langlands correspondence. Gain understanding of sophisticated mathematical structures that bridge representation theory, category theory, and the geometric aspects of the Langlands program through detailed analysis of cocenter computations and their implications for understanding automorphic forms and Galois representations.
