The cohomology of orthogonal locally symmetric spaces and the theta-correspondence

In this talk we survey work of Kudla-Millson and Funke-Millson to employ the dual pair O(p,q)xSp(n) and the theta correspondence to realize generating series with values in the cohomology for the orthogonal group as holomorphic Siegel modular forms. We also discuss the restriction of these cohomology classes to the Borel-Serre boundary and obtain a non-vanishing result.