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Join this one-hour lecture by Mingjia Zhang exploring the intersection cohomology of Shimura varieties and its significance in number theory. Learn how intersection cohomology provides a cleaner relation to automorphic forms through L2 cohomology compared to usual or compact support cohomology, particularly for noncompact Shimura varieties. Discover recent findings on intersection cohomology in the context of the Fargues–Scholze local Langlands correspondence, based on joint work in progress with Ana Caraiani and Linus Hamann. This presentation is part of the 2025 Simons Collaboration on Perfection in Algebra, Geometry and Topology Annual Meeting.
