Ronno Das: Hypersurfaces and inclusion-exclusion

Abstract: A generic homogeneous polynomial defines a smooth hypersurface in projective space. Generalizing results of Tommasi and others, we establish homological stability for the space of such smooth polynomials, and more generally smooth sections of line bundles on smooth projective varieties, with or without marked points on the hypersurface. On the way we develop a categorification of the principle of inclusion-exclusion, building on work of Vassiliev. Parts of the talk will be based on joint work with Sean Howe and with Alexis Aumonier.