Hyperplane arrangements, monodromy via deformation theory, and stability conditions – Michael Wemyss (University of Glasgow)

Venue

Department of Mathematics, Aula Magna.

Abstract

The infinite hyperplane arrangements associated to affine Dynkin diagrams (and their associated braid groups) are fundamental throughout mathematics. I will explain a variation on this, which allows us to produce many more arrangements. Whilst these new arrangements need not be Coxeter, they are still “labelled” by Coxeter data. The motivation comes from algebraic geometry. In that setting, monodromy around these hyperplanes corresponds to certain symmetries, which are realised using (noncommutative) deformation theory of curves. The hyperplanes turn out to control the Bridgeland stability manifold, and this in turn relates to open questions around the $K(\pi,1)$-conjecture. This is summary of joint work with Donovan, Iyama, and Hirano.

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