Modularity of Special Cycles I

Since the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms.

In this series of talks, I will survey known results and conjectures about this topic, as well as recent progress.