Affine actions, and tilings of the plane

Michael Wemyss (University of Glasgow)

Monday 26th September, 2016 16:00-17:00 Maths 522


There is an expectation, now proved in many cases, is that various surgeries in algebraic geometry induce an “affine pure braid group” acting on the derived category.  I will explain why we care about this (from a geometric perspective), and I will also explain some of the Coxeter combinatorics background, which is completely independent of the geometric motivation.  The remarkable thing is that the geometry predicts unseen phenomenon, like an affine version of the symmetries of a pentagon, which does not exist algebraically.  Towards the end I will explain how this can all be packaged into a very easy-to-state combinatorial problem: given two nodes of a Dynkin diagram, produce a tiling of the plane.  Rather surprisingly, these tilings are new, and exhibit some very beautiful behaviour.

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