# Stable cohomology of compactifications of $\mathcal A_g$

 Topology of Algebraic Varieties Topic: Stable cohomology of compactifications of $\mathcal A_g$ Speaker: Klaus Hulek Affiliation: Leibniz Universität Hannover Date: Wednesday, January 14 Time/Room: 11:15am - 12:15pm/S-101 Video Link: http://video.ias.edu/tav/2015/0114-KlausHulek

A famous result of Borel says that the cohomology of $\mathcal A_g$ stabilizes. This was generalized to the Satake compactification by Charney and Lee. In this talk we will discuss whether the result can also be extended to toroidal compactifictaions. As we shall see this cannot be expected for the second Voronoi compactification, but we shall show that the cohomology of the perfect cone compactification does stabilize. We shall also discuss partial compactifications, in particular the matroidal locus. This is joint work with Sam Grushevsky and Orsola Tommasi.