Beijing Institute of Mathematical Sciences and Applications

Ansi Bai , Hank Chun-Hao Chen , Liang Kong , Yi Long Wang , Zhi Hao Zhang , Hao Zheng

Hao Xu

Tuesday, April 1, 2025 4:00 PM - 6:00 PM

A3-1-301

Zoom 468 248 1222 (BIMSA)

Given a finite symmetry group $G$ with anomaly $\pi \in {\mathrm{H}}^4(G,U(1))$, the 4D Dijkgraaf–Witten model provides an exactly solvable gauge theory with applications in high-energy physics and topological phases of matter. The topological defects in these models form a braided fusion 2-category $\mathcal{Z}({\mathbf{2}\mathbf{Vect}}_G^{\pi })$, the Drinfeld center of $\pi$-twisted $G$-crossed finite semisimple linear categories.
Extending the theory of anyon condensation in 3D, my work (in collaboration with Décoppet) develops a higher-dimensional framework using étale algebras and their local modules in braided fusion 2-categories. In particular, I classify connected étale algebras in $\mathcal{Z}({\mathbf{2}\mathbf{Vect}}_G^{\pi })$, which correspond to twisted $G$-crossed braided multifusion categories.
Additionally, Décoppet has shown that the Drinfeld center of any fusion 2-category is either a 4D Dijkgraaf–Witten model or a fermionic analogue. Time permitting, I will also discuss classification results for fusion 2-categories via the study of Lagrangian algebras.