Speaker: Nicolás Andruskiewitsch, University of Córdoba (Argentina)
Time/Date: Friday, December 6, at 1pm
Room: HH-3017 (Mathematics Building)
Title: The role of Nichols algebras in the cohomology of finite-dimensional Hopfalgebra

Abstract:
I will report on work in progress, joint with Iván Angiono, Julia Pevtsova and Sarah Witherspoon. It was asked by Friedlander and Suslin whether the cohomology ring of a finite-dimensional Hopf algebra is finitely generated. I will explain our approach to answer affirmatively this question, extending work of several authors.

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Speaker: Lukas Woike, University of Hamburg (Germany)
Time/Date: Thursday, November 7, 10:30 am to 11:20 am
Room: EN 1001 (Engineering Building)
Title: The Hochschild Complex of a Finite Tensor Category

Abstract:
Modular functors, i.e. consistent systems of projective representations of mapping class groups of surfaces, have been constructed for non-semisimple modular categories already decades ago. Concepts from homological algebra have not been used in this construction although it is an obvious question how they should enter in the non-semisimple case. In the present paper, we elucidate the interplay between the structures from topological field theory and from homological algebra by constructing a homotopy coherent projective action of the mapping class group SL(2, Z) of the torus on the Hochschild complex of a modular category. This is a further step towards understanding the Hochschild complex of a modular category as a differential graded conformal block for the torus. Moreover, we describe a differential graded version of the Verlinde algebra.

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Speaker: Yang Yang, University of Hamburg (Germany)
Time/Date: Wednesday, November 6, 16:15 pm to 17:05 pm
Room: SN 1103 (Science Building)
Title: String-Net Models and Invariants for Mapping Class Groups

Abstract:
We show that string-net models provide a novel geometric method to construct invariants of mapping class group actions. Concretely, we consider string-net models for a modular tensor category C. We show that the datum of a specific commutative symmetric Frobenius algebra in the Drinfeld center Z(C) gives rise to invariant string-nets. The Frobenius algebra has the interpretation of the algebra of bulk fields of the conformal field theory in the Cardy case.