Two-block Springer fibers and Springer representations in type D
Friday, 16.6.17, 10:15-11:15, Raum 404, Eckerstr. 1
We explain how to construct an explicit topological model for\nevery two-block Springer fiber of type D. These so-called topological\nSpringer fibers are homeomorphic to their corresponding algebro-geometric\nSpringer fiber. They are defined combinatorially using cup diagrams which\nappear in the context of finding closed formulas for parabolic\nKazhdan-Lusztig polynomials of type D with respect to a maximal parabolic\nof type A. As an application it is discussed how the topological Springer\nfibers can be used to reconstruct the famous Springer representation in an\nelementary and combinatorial way.
Algebraic models of the euclidean plane
Friday, 23.6.17, 10:15-11:15, Raum 404, Eckerstr. 1
A fake euclidean plane is a real algebraic surface whose complexification has the rational homology type of the plane and whose real locus is diffeomorphic to the euclidean plane, but which is not isomorphic as a real algebraic surface to the affine plane. In this talk, I will give elements of classification of such surfaces up to biregular isomorphisms of real algebraic varieties as well as up to birational diffeomorphisms, that is, algebraic birational maps whose restrictions to the real loci are diffeomorphisms. (Joint work with F. Mangolte (Angers) and J. Blanc (Basel)).
The Mumford-Tate conjecture for products of K3 surfaces
Friday, 30.6.17, 10:15-11:15, Raum 404, Eckerstr. 1
The Mumford-Tate conjecture relates the Hodge structure on the singular cohomology of an algebraic variety (over a number field) with the Galois representation on the etale cohomology of that variety. In this talk we explain a new technique that allows us to prove this conjecture for products of K3 surfaces. Along the way we also prove that the system of l-adic realisations of an abelian motive form a compatible system.\n