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Explore a mathematical lecture examining Kudla's Modularity Conjecture and its recent developments in the theory of special cycles on Shimura varieties. Learn about the foundational work of Kudla and Millson from the 1980s, which established that generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms. Discover how this groundbreaking research addresses Kudla's conjecture regarding extensions to toroidal compactifications, specifically focusing on divisors in O(p,2) and cycles in U(n,1) up to the middle degree in cohomology. Gain insights into collaborative research findings that provide answers to this long-standing conjecture, presented through joint work with François Greer and Philip Engel. Understand the mathematical techniques and theoretical frameworks used to tackle this complex problem in algebraic geometry and number theory.
