Pavol Ševera (University of Oxford)
severa@maths.ox.ac.uk Kramers-Wannier duality, first used to find the critical temperature of 2d Ising model in statistical physics, can be formulated as a very simple 3d topological claim (and similar formulations work for higher-dimensional cases) - it is more or less Poincaré duality. In this way it yields a 3d topological field theory with coloured boundary. Classical models (Poisson-Lie T-duality) suggest a nonabelian generalization of this duality, with abelian groups replaced by quantum groups. Coloured 3d pictures of Hopf algebras will be presented. Their connection with standard Reshetikhin-Turaev invariants comes from the pictures of the Drinfeld double.