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SUMMARY:Journées de topologie quantique
DTSTART:20231113T100000Z
DTEND:20231113T153000Z
DTSTAMP:20260507T164000Z
UID:indico-event-10769@indico.math.cnrs.fr
DESCRIPTION:The “journées de topologie quantique” (quantum topology d
 ays) are a regular event aiming at bringing together\, in a somewhat infor
 mal setting\, people thinking about quantum topology in a broad sense. As 
 the name suggest this is a one day event\, with three talks and lots of ti
 me for discussions\, taking place either in Paris or in Dijon.Site web Pr
 ogram11h00 - Ramanujan Santharoubane: On the kernel of SO(3)-Witten-Reshet
 ikhin-Turaev quantum representationsGiven a surface S\, SO(3)-Witten-Reshe
 tikhin-Turaev TQFT's provide a sequence\, indexed by odd integers\, of com
 plex finite dimensional representations of the mapping class group of S ca
 lled quantum representations. One major and difficult problem is to find t
 he kernels of these quantum representations. For prime index\, Gilmer and 
 Masbaum proved that the representation preserves a lattice over the ring o
 f integers of a cyclotomic field. This allows to approximate each quantum 
 representation by homomorphisms from the mapping class group in to finite 
 groups. In this talk\, we will see that certain of these approximations ca
 n be completely understood and are related to the Johnson filtration of th
 e mapping class group. As a consequence we can find some non trivial 'uppe
 r bound' for the kernels of quantum representations. This is a joint work 
 with Renaud Detcherry.14h - Anna-Katharina Hirmer: Generalised Kitaev mode
 ls from Hopf monoids: topological invariance and examplesQuantum double mo
 dels were introduced by Kitaev to obtain a realistic model for a topologic
 al quantum computer. They are based on a directed ribbon graph and a finit
 e-dimensional semisimple Hopf algebra. The ground state of these models is
  a topological invariant of a surface\, i.e. only depends on the homeomorp
 hism class of the oriented surface but not the ribbon graph. Meusburger an
 d Voß generalised part of the construction from Hopf algebras to pivotal 
 Hopf monoids in symmetric monoidal categories. We explain the construction
  of the ground state for involutive Hopf monoids and show that it is topol
 ogical invariant. We explicitly describe this construction for Hopf monoid
 s in Set\, Top\, Cat and SSet.15h30 - Emmanuel Graff: The Homotopy Braid G
 roup is Torsion-FreeV. Lin\, in the 'Kourkova notebook'\, questions the ex
 istence of a non-trivial epimorphism of the braid group onto a non-abelian
  torsion-free group. The homotopy braid group studied by Goldsmith in 1974
  an known to be nilpotent\, naturally appears as a potential candidate. In
  2001\, Humphries showed that this homotopy braid group is torsion-free fo
 r less than 6 strands. In this presentation\, we will see a new approach b
 ased on the broader concept of welded braids\, as well as algebraic techni
 ques. This will allow us to demonstrate that the homotopy braid group is t
 orsion-free for any number of strands.\n\nhttps://indico.math.cnrs.fr/even
 t/10769/
LOCATION:Bâtiment Mirande Aile A Salle 318 - étage 3  (Institut de Math
 ématiques de Bourgogne)
URL:https://indico.math.cnrs.fr/event/10769/
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