Cordian Riener (Aalto Science Institute, Helsinki)
This talk will present results on the structure of cohomology modules of symmetric (as well as multi-symmetric) real varieties and semi-algebraic sets. More precisely, we will show bounds on the number of irreducible representations of the symmetric group occurring in the isotypic decomposition of the cohomology modules of the sets in question, which are polynomial in the number of variables, as well as polynomial bounds on the corresponding multiplicities. As an application we will give some improvements on bounds for the Betti numbers of images under projections of (not necessarily symmetric) bounded real algebraic sets.
Based on joint works with Saugata Basu (Purdue University).