Intersections in Tits Cones, and Applications

Michael Wemyss, University of Glasgow. Part of the Leeds Algebra Seminar Series

I will begin by giving a purely combinatorial construction of a 2-sphere, with some points missing, based only on some combinatorial information about Dynkin diagrams.  This punctured sphere corresponds to the physicists' stringy Kahler moduli space for a certain 3-dimensional surgery in algebraic geometry, and it gives us various predictions for the derived symmetry group, which is why we care.  However, the talk is completely algebraic, and mostly combinatorial, and describes how to produce "affine" hyperplane arrangements for various Coxeter arrangements/groups which traditionally don't have affine versions.  Everything is encoded by choices of nodes in Dynkin diagrams. 

At the end, I will briefly explain some applications to noncommutative resolutions, to tilting theory, and to group actions.