27/11/2019, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alex Bullivant, University of Leeds
$3+1D$ 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.