# Topological Quantum Field Theory Seminar

### $3+1D$ Dijkgraaf-Witten theory and the Categorified Quantum Double

The quantum double is a quasi-triangular Hopf algebra whose category of representations can be interpreted physically as describing the processes of fusion and braiding of anyons in the $2+1D$ Dijkgraaf-Witten TQFT. Motivated by the possibilities of topological quantum computing in $3+1D$, in this talk I will give an informal overview of my ongoing research towards understanding the categorified quantum double and its bicategory of $2$-representations. In particular, I will focus on the relation between such constructions and the Hamiltonian formulation of $3+1D$ Dijkgraaf-Witten TQFT in order to describe the braiding and fusion of extended excitations such as loops.

Please note that there is also a TQFT Club talk in the morning on the same day starting at 11h15.

Projecto FCT UID/MAT/04459/2019.

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Current organizers: Roger Picken, John Huerta, Marko Stošić.

Mathseminars

FCT Projects PTDC/MAT-GEO/3319/2014, Quantization and Kähler Geometry, PTDC/MAT-PUR/31089/2017, Higher Structures and Applications.