Algebra and Combinatorics Seminar (Online)

  • November 3, 2021
  • 3:15 PM - 4:15 CST
  • Zoom (online)
  • Emily Peters,
  • Not open to the public.
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  • Details

    Speaker: Anup Poudel (Iowa)

    Title: Diagrammatic methods for ribbon tensor categories

    Abstract: It is known that given a tensor category, one can associate string diagrams to represent its morphism space. When the category has other nice structures (braided and spherical), one can view the morphism space as spanned by (colored) framed tangles up to regular isotopy. We will start by understanding the axiomatic setup for a braided spherical tensor category using diagrams. Then, we will define an orthogonal basis of trivalent graphs when the category is unitary and fusion. We will then discuss how to compute certain categorical structure constants (starting with a fusion rule) by solving a system of equations obtained by using the diagrammatic setup. An important tool for this computation is the rotation operator first introduced in a categorical framework by Morrison, Peters, and Snyder. This is based on joint work with S. Valera. Time permitting, I will also discuss other advantages of using the diagrammatic setup in understanding the space of quantum invariants coming from a ribbon tensor category (not necessarily unitary).