abstract yamcats 11

Title Talk 1: Hopf monads
Title Talk 2: Quantum invariants
Title Talk 3: Three-dimensional TQFTs

Abstract :
Hopf monads generalize Hopf algebras to a non-braided setting, that is, to arbitrary monoidal categories. The initial motivation to introduce the notion of Hopf monad was to understand the Drinfeld-Joyal-Street categorical center in Hopf algebraic terms. Such a description is useful in quantum topology for comparing the Turaev-Viro and Reshetikhin-Turaev invariants of 3-manifolds, and more generally for comparing their associated topological quantum field theories (TQFTs). The Reshetikhin-Turaev construction, based on surgery presentations, is widely viewed as a mathematical realization of Witten's Chern-Simons TQFT. The Turaev-Viro construction, based on triangulations, is closely related to the Ponzano-Regge state-sum model for 3-dimensional quantum gravity. We will explain how these two constructions are related via the Drinfeld-Joyal-Street center of monoidal categories.

Talk 1 will be devoted to the theory of Hopf monads.
Talk 2 will consist in a gentle introduction to quantum invariants of 3-manifolds.
In Talk 3, we will use the Hopf monadic description of the Drinfeld-Joyal-Street center to compare the Reshetikhin-Turaev and Turaev-Viro TQFTs.

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