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Explore the deep connections between theta series and modular forms in this research seminar that surveys the modularity of special cycles in Shimura varieties. Learn how the classical work of Jacobi and Siegel on theta series of quadratic lattices producing modular forms has been vastly generalized through the groundbreaking research of Kudla and Millson, who proved that generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms. Discover the current state of knowledge in this active area of research, including established results, open conjectures, and recent developments that advance our understanding of these fundamental mathematical structures. Gain insight into how special cycles serve as a bridge between algebraic geometry and number theory, and understand the broader implications of modularity results in modern arithmetic geometry.
