Academics

YMSC Topology Seminar | Computing the TVBW 3-manifold invariants from Tambara-Yamagami categories

Time:Mon., 17:00-18:00, Apr. 1, 2024

Venue:Zoom meeting ID: 405 416 0815 Password: 111111

Organizer:陈伟彦、高鸿灏、黄意、林剑锋

Speaker:Eric SAMPERTON (Purdue)

Abstract:

I'll give a quick intro to spherical fusion categories and the Turaev-Viro-Barrett-Westbury construction, which associates an invariant of oriented 3-dimensional manifolds to each such category. Some of the simplest spherical fusion categories are the so-called Tambara-Yamagami categories, which depend on the data of a finite abelian group A, a choice of isomorphism between A and its dual, and a sign +1 or -1. Despite their fairly simple definition, these categories are known to give rise to TVBW invariants that are NP-hard to compute. I'll explain what this means, and then describe my recent work with Colleen Delaney and Clement Maria establishing an efficient algorithm for computing these invariants on 3-manifolds with bounded first Betti number. I will also try to say a few things about why such complexity/algorithm results are interesting in the context of 3-manifold topology and quantum computation.

DATEMarch 31, 2024
SHARE
Related News
    • 0

      YMSC Topology Seminar | Invariants of real vector bundles

      Abstract:I will describe a complete set of numerical invariants for deciding whether a real vector bundle is stably trivial. These invariants are integers and rational angles which will be a priori given in contrast to the usual theory of secondary characteristic classes. The definition of these invariants features a duality between the reals and quaternions, moreover a quaternionic version of...

    • 1

      YMSC Topology Seminar | Generic 3-manifolds are hyperbolic

      Abstract:In this talk, we first introduce various models to study what a generic 3-manifold looks like. We then focus on the Heegaard splitting model of 3-manifolds, equipped with geometric complexity using Teichmuller metric. The main result is that the Hempel distance of a generic Heegaard splitting goes linearly to the infinity. In particular, generic 3-manifolds are hyperbolic in this mode...