UC Berkeley

In this thesis we prove that a certain generating function of special cycles on GSpin Shimura varieties is modular. More specifically, we consider the Shimura variety corresponding to the reductive group $\Res_{F/\Q} G$, where $G=\GSpin(V)$ the GSpin group for $V$, a quadratic space over a totally real number field $F$, $[F:\QQ]=d$ with certain conditions at the infinite places. We construct a generating function in the sense of Kudla and Millson and show that its image in cohomology is an automorphic form.