Gapped condensation in higher categories Speaker(s): Theo JohnsonFreyd
Abstract:
Idempotent (aka Karoubi) completion is used throughout mathematics: for instance, it is a common step when building a Fukaya category. I will explain the ncategory generalization of idempotent completion. We call it "condensation completion" because it answers the question of classifying the gapped phases of matter that can be reached from a given one by condensing some of the chemicals in the matter system. From the TFT side, condensation preserves full dualizability. In fact, if one starts with the ncategory consisting purely of ℂ in degree n, its condensation completion is equivalent both to the ncategory of ndualizable ℂlinear (n1)categories and to an ncategory of lattice condensed matter systems with commuting projector Hamiltonians. This establishes an equivalence between large families of TFTs and of gapped topological phases. Based on joint work with D. Gaiotto.
Date: 17/03/2020  12:30 pm
Series: Mathematical Physics
