Strongly Correlated Topological Phases of Matter: June 5-9, 2017

Organized by: Lukasz Fidkowski, Dan Freed, and Anton Kapustin

Previously, phases of matter were mostly classified based on symmetry principles, or purely on the basis of topological properties. Recent developments however have highlighted the interplay of symmetry and topology as manifested by topological insulators and other symmetry protected topological (SPT) phases, and by symmetry enrichment of topological orders. On the theoretical side, these developments have been achieved by exploiting connections to seemingly unrelated areas of mathematical physics, such as Topological Quantum Field Theory and quantum information science, as well as to algebraic topology. The SPT phases are in fact more manageable than general topological orders, and one can hope to give a complete classification of these phases in all dimensions and for all symmetry groups. For free fermionic phases, such classification has been achieved in the works of Schnyder, Ryu, Furusaki, Ludwig, and Kitaev, while in the interacting case it has been proposed that SRE phases can be classified by invertible equivariant TQFTs, or equivalently by homotopy classes of maps of certain spectra (in the sense of algebraic topology).

Despite this progress, mathematically rigorous definitions of a gapped phase and related concepts remains elusive. This workshop, situated at the crossroads of physics and mathematics, will bring together researchers in condensed matter physics, algebraic topology, and quantum information theory to address these issues. It will include both pedagogical lectures by experts in respective fields and research talks on recent developments. Please note that there will also be a mini course held from May 30 – June 2. If you are interested attending the mini course please fill out the program application.