Kudla's modularity conjecture

Location: 11th Floor Lecture Hall Speaker Salim Tayou, Harvard University Session Chair Yongnam Lee, Institute for Basic Science-Center for Complex Geometry Abstract Kudla and Millson proved in the 80's that the generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms and a well-established conjecture of Kudla asks about extensions to toroidal compactifications. In this talk, I will survey recent work on Kudla's conjecture for divisors in O(p,2) and cycles in U(n,1). Joint work with Philip Engel, François Greer, and Ben Howard.