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SUMMARY:Condensable TopologicalDefects in 4D Dijkgraaf-Witten models—Cla
 ssification of Fusion 2-Categorical Symmetries [MPIM]
DTSTART:20250716T083000Z
DTEND:20250716T100000Z
DTSTAMP:20260615T205500Z
UID:indico-event-555@math-events.uni-bonn.de
DESCRIPTION:Speakers: Hao Xu (Göttingen)\n\nHigher Differential Geometry 
 Seminar\nGiven a finite group $G$ a 4-cocycle $\\pi \\in \\mathrm{H}^4(G\,
 U(1))$\, the 4D Dijkgraaf–Witten model provides an exactly solvable gaug
 e theory with applications in high-energy physics and topological phases o
 f matter. The topological defects in this model form a braided fusion 2-ca
 tegory $\\mathscr{Z}(\\mathbf{2Vect}^\\pi_G)$\, the Drinfeld center of $\\
 pi$-twisted $G$-crossed finite semisimple linear categories. Extending the
  theory of anyon condensation in 3D\, my thesis develops a higher-dimensio
 nal framework using étale algebras and their local modules in braided fus
 ion 2-categories\, in collaboration with Décoppet. In particular\, I clas
 sify connected étale algebras in $\\mathscr{Z}(\\mathbf{2Vect}^\\pi_G)$\,
  in terms of homotopy data generalizing the group cohomology and Brauer-Pi
 card groups. Additionally\, Décoppet has shown that the Drinfeld center o
 f any fusion 2-category is either a 4D Dijkgraaf–Witten model or a fermi
 onic analogue. Time permitting\, I will also discuss classification result
 s for fusion 2-categories via the my classification results for Lagrangian
  algebras.\n\nhttps://math-events.uni-bonn.de/event/555/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/555/
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