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Math-Physics Joint Seminar

Wednesday, April 17, 2019 - 3:00pm

Constantin Teleman

UC Berkeley


University of Pennsylvania


The 2-dimensional Ising lattice model on the group $\{\pm1\}$ admits a duality
which interchanges its high and low temperature phases and determines the
location of its conformal phase transition. This was recoginzed early on as
a sophisticated version of the Fourier transform. Using the notions of
extended TQFT and boundary conditions, we will relate that to a topological
(``electromagnetic'') duality in 3 dimensions, which allows us to extend
the KW duality to arbitrary finite groups (and finite semi-simple Hopf
algebras). A by-product is the classification of topological phases which
can appear in the thermodynamic limit by the Landau symmetry-breaking
subgroups. This is joint work with Dan Freed. 

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