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Seminar by Nils Carqueville (University of Vienna)

Title: Orbifold completion

2016.04.29 | Jane Jamshidi

Date Mon 23 May Wed 25 May
Time 15:15    16:15
Location 1531-119 (Aud. D2)


In quantum field theory, orbifolding is a procedure to construct new QFTs out of old ones with the help of certain group actions. I will describe an elegant and purely algebraic generalisation of this procedure called "orbifold completion" which is inspired by 2-dimensional topological QFT. In this framework one finds various new equivalences of categories appearing in geometry and representation theory. In particular, I shall describe new relations between simple singularities (e.g. between those of type E_8 and A_29), and between derived representations of Dynkin quivers and their Ginzburg algebras.  

Orbifold completion is expected to generalise to higher dimensions. In the second part of my talk I will present first results in an ongoing programme for dimension 3: the functorial definition and algebraic description of 3-dimensional defect TQFT. Such TQFTs naturally subsume and extend Reshetikhin-Turaev and Turaev-Viro theories. Among the expected applications of 3-dimensional orbifold completion are new invariants of knotted surfaces, as well as improved models of quantum computation.