Quantum phases have become a staple of modern physics, thanks to their appearance in fields as diverse as condensed matter physics, quantum field theory, quantum information processing, and topology. The description of quantum phases of matter requires novel mathematical tools that lie beyond the old symmetry breaking perspective on phases. Techniques from topological field theory, homotopy theory, and (higher) category theory show great potential for advancing our understanding of the characterization and classification of quantum phases. The goal of this workshop is to bring together experts from across mathematics and physics to discuss recent breakthroughs in these mathematical tools and their application to physical problems.
Scientific Organizers
Lukas Mueller
Alex Turzillo
Davide Gaiotto
Sponsored in part by the Simons Collaboration on Global Categorical Symmetries
Format results


Analogies between QFT and lattice systems
Anton Kapustin California Institute of Technology (Caltech)  Division of Physics Mathematics & Astronomy

Models of anyons with symmetry: a bulkboundary correspondence
Fiona Burnell University of Minnesota

Twisted Tools for (Untwisted) Quantum Field Theory
Justin Kulp Stony Brook University

Quantum double models and DijkgraafWitten theory with defects
Catherine Meusburger 
Topological sectors in quantum lattice models
Clement Delcamp Institut des Hautes Etudes Scientifiques (IHES)

DouglasReutter 4d TQFT as a generalised orbifold
Vincentas Mulevičius Vilnius University

Weak Hopf symmetric tensor networks
Andras Molnar University of Vienna


Zesting topological order and symmetryenriched topological order in (2+1)D
Colleen Delaney University of California, Berkeley


Categorical Aspects of Symmetry in Fermionic Systems
Kantaro Omori University of Tokyo