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SUMMARY:Lukas Jannik Woike: Quantum topology beyond semisimplicity
DTSTART;VALUE=DATE-TIME:20220613T143000Z
DTEND;VALUE=DATE-TIME:20220613T153000Z
DTSTAMP;VALUE=DATE-TIME:20220926T153800Z
UID:indico-event-8072@indico.math.cnrs.fr
DESCRIPTION:Through the Reshetikhin-Turaev construction\, a three-dimensio
nal topological field theory can be built from a semisimple modular catego
ry. Thanks to a result of Bartlett\, Douglas\, Schommer-Pries and Vicary\,
a semisimple modular category is even equivalent to a once-extended (anom
alous) three-dimensional topological field theory. Non-semisimple modular
categories are much more difficult to handle\, especially if one is intere
sted in a construction that takes their very non-trivial homological algeb
ra into account. In my talk\, I will explain how to organize the homologic
al algebra of a modular category through low-dimensional topology\, namely
by means of a differential graded modular functor. In particular\, I will
discuss the construction of differential graded conformal blocks\, certai
n chain complexes carrying homotopy coherent projective mapping class grou
p representations\, but also the differential graded Verlinde formula and
its connection to the Deligne Conjecture. This is joint work with Christop
h Schweigert.\n\nhttps://indico.math.cnrs.fr/event/8072/
URL:https://indico.math.cnrs.fr/event/8072/
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