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SUMMARY:Toward a homological (re)construction of TQFTs that also unifies t
 hem [MPIM]
DTSTART:20260427T090000Z
DTEND:20260427T100000Z
DTSTAMP:20260425T234300Z
UID:indico-event-1251@math-events.uni-bonn.de
DESCRIPTION:Speakers: Martel Jules (Université Cergy-Pontoise)\n\nQuantum
  topology seminar\nTopological quantum field theories (TQFTs) originate fr
 om an idea of Witten that quantum field theories could be studied from the
  perspective of topological states and topological transitions.\nIt was ma
 thematically formalized by Atiyah as a nice linearization of a category of
  cobordisms. It was concretely realized by Reshetikhin and Turaev (RT)\, w
 ho developed a philosophy for constructing TQFTs based on representation t
 heory (of quantum groups with parameter q evaluated at roots of unity) and
 \, more generally\, on monoidal categories. This framework was later gener
 alized to allow input categories to be non-semisimple\; the Kerler–Lyuba
 shenko (KL) TQFT is an important example extending RT.\nIn this talk\, I w
 ill present a new way to (re)construct TQFTs from a different perspective:
  using twisted homologies of configuration spaces (it's an ongoing program
 ). I will motivate and present the constructions and it will be the occasi
 on to review some joint works with Bigelow\, De Renzi\, Detcherry\, or Fae
 s (depending on time).\nAn important feature is that\, by working with hom
 ologies with local coefficients in the Heisenberg ring of a surface\, we c
 onstruct an overlying functor “at q generic". It recovers (parts of) KL 
 TQFTs associated with quantum groups once we evaluate the ring at roots of
  unity\, and we have established this correspondence for quantum represent
 ations of mapping class groups.\nFor the case of knot invariants\, if time
  permits\, I will also review earlier joint work with S. Willetts\, where 
 we define\, from this setup\, his unifying invariant living in a generaliz
 ation of Habiro’s ring. This invariant encompasses both semisimple and n
 on-semisimple knot invariants.\n\nhttps://math-events.uni-bonn.de/event/12
 51/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1251/
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