Focus Week on Topological Matter - Week 1

Explore advanced concepts in topological matter through this comprehensive week-long conference featuring leading experts in mathematical physics and topology. Delve into symmetry protected topological phases, fractonic systems, and ultra unification theories while examining the mathematical foundations underlying these phenomena. Learn about higher gauge models, quantum doubles, and the relationship between topological order and higher category theory from both physical and mathematical perspectives. Investigate gapped lattice systems, tensor networks, and subfactors as they relate to topological phases of matter. Study PEPS (Projected Entangled Pair States) and bicategories, bulk fields in conformal field theory, and fusion 2-categories. Examine the Drinfeld center of monoidal 2-categories in the context of 3+1D Dijkgraaf-Witten Theory and explore higher Morita categories. Conclude with an algebraic approach to defining topological order, providing a rigorous mathematical framework for understanding these complex quantum systems.

Syllabus

Zheng-Cheng Gu - Construction and classification of symmetry protected topological phase
Meng Cheng - Fractonic topological phases: coupled layers and beyond
Juven Wang - Ultra Unification
Clement Delcamp - Excitations in strict 2-group higher gauge models of topological phases
Alex Bullivant - A tube algebra perspective on the higher quantum double
Xiao-Gang Wen - Topological order and higher category -- a physical point of view
Anton Kapustin - Geometry and topology of gapped lattice systems
Yasu Kawahigashi - Topological order, tensor networks and subfactors
Jürgen Fuchs - PEPS and bicategories
Christoph Schweigert - Bulk fields in conformal field theory
David Reutter - On fusion 2-categories
Yin Tian - The Drinfeld center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory
Claudia Scheimbauer - Higher Morita categories
Theo Johnson-Freyd - Algebraic definition of topological order