| Hörsaal D2
Vortrag: Theta series in geometry and arithmetic
Abstract: In how many ways can a given integer be written as a sum of four squares? We explain how theta series can be used to study such representation numbers of positive definite quadratic forms. For indefinite quadratic forms, Kudla and Millson showed that there are analogous theta series relating the geometry of special cycles on locally symmetric spaces to modular forms, generalizing celebrated work of Hirzebruch and Zagier. Conjectures of Kudla predict similar results for arithmetic special cycles in Arakelov Chow groups of orthogonal Shimura varieties. Finally, we will report on some recent results in this context.