Groupes de travail : Groupe de travail Topologie Algébrique et TQFT

Equipe(s) Responsable(s)SalleAdresse
Topologie et Géométrie Algébrique
Christian Blanchet

Séances à suivre

Orateur(s)Titre Date DébutSalleAdresse
+ Séances antérieures

Séances antérieures

Orateur(s)Titre Date DébutSalleAdresse
+ Léo Benard Algèbres de Hopf enrubannées, l’exemple de sl(2) quantique 18/10/2016 09:30 Batiment Sophie Germain, salle 1016 (à confirmer)
On commencera par définir, exemples à l’appui, les algèbres de Hopf enrubannées, puis on montrera qu’une certaine déformation de l’algèbre enveloppante de sl(2) en est une. L’exposé sera voué à être introductif, aucune connaissance particulière du sujet ne sera présupposée.
+ Daniel Lopez Link invariants from ribbon Hopf algebras 04/10/2016 11:00 Batiment Sophie Germain, salle 1016
In this talk, we will define ribbon Hopf algebras, which are Hopf algebras endowed with an extra element giving solutions to the Yang-Baxter equation. Following ideas of R. Lawrence and T. Ohtsuki, we use these Hopf algebras to construct link invariants.
+ Martin Palmer Blob complex I: the particular case of Hochschild Homology 19/01/2016 09:30 Salle SG-1016
1er exposé du groupe de travail "Blob complex"
d'après l'article de Scott Morrison et Kevin Walker,
[[arxiv.org/abs/1009.5025->http://arxiv.org/abs/1009.5025]]
+ Christian Blanchet Non-semisimple TQFTs: the graded functor 12/01/2016 11:00 Salle SG-1016
We will define the graded TQFT functor, prove monoidality and describe the vector spaces in admissible case.
[[Page du GDT->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm]]
+ Ramanujan Santharoubane Finite dimensionality of BCGP TQFTs via skein calculus 08/12/2015 09:30 Salle SG-2018
[Page du GDT->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm]
+ Marco de Renzi Universal construction and surgery axioms 24/11/2015 09:30 Salle SG-2018
I will start the construction of the BCGP TQFTs. The first step will be the definition of the decorated cobordism category which will be used to carry out the Universal Construction. I will also introduce the modified surgery axioms which are satisfied by CGP invariants and which will be used in the following in order to figure out the properties of TQFT vector spaces. Every step will be compared to the classical case of simisimple WRT TQFTs.

[Page du GDT->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm]
+ Ramanujan Santharoubane Torsion de Reidemeister, polynôme d'Alexander et TQFT non semi-simple en r=2 03/11/2015 09:30 [Batiment Sophie germain - salle 2018->https://www.math.univ-paris-diderot.fr/ufr/acces]
Abstract: Nous verrons comment la spécialisation en r=2 des invariants de Costantino, Geer et Patureau donne :
1) Le polynôme d'Alexander-Conway pour des entrelacs.
2) La torsion de Reidemeister-Turaev pour les 3-variétés closes.
Cet exposé sera basé sur l'article de C. Blanchet, F.Costantino, N. Geer et B. Patureau intitulé "NON SEMI-SIMPLE TQFTS, REIDEMEISTER TORSION AND KASHAEV'S INVARIANTS".
[Page web du gdt->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm]
+ Marco de Renzi CGP invariants of closed 3-manifolds 20/10/2015 09:30 Salle SG-2018
Abstract: I will present some of the results contained in the paper Quantum Invariants of 3-Manifolds via Link Surgery Presentations and Non-Semi-Simple Categories by Costantino, Geer and Patureau. We will construct two families of invariants of closed 3-manifolds indexed by a natural parameter r>1. These invariants are built out of the non-semisimple category of representations of the unrolled quantum group U_q^H(sl_2) at a 2r-th root of unity we saw in the first talk. The secondary invariants conjecturally extend the original Reshetikhin-Turaev invariants for the small quantum group \barU_q(sl_2). The use of richer categories pays off as these non-semisimple invariants are strictly finer than the original semisimple ones: indeed they can be used to recover the classification of lens spaces, which Reshetikhin-Turaev invariants could not always distinguish.
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[Page du GDT->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm]
+ Cristina Anghel The modified link invariants for representations of unrolled quantum sl(2) 06/10/2015 09:30 Salle SG-2018
[Page du GDT->http://webusers.imj-prg.fr/~marco.de-renzi/gdt.htm]
+ Nathan Geer Unrolled quantum sl(2) 22/09/2015 14:00 Salle 1020, batiment Sophie Germain
In this talk I will discuss a particular quantization of the Lie algebra sl(2). I will start by giving the definition of the algebra. We will see that the finite dimensional modules over this algebra from a ribbon category, where the simple modules are indexed by the complex numbers. This category is not semi-simple. However, I will prove that generically the tensor product of two simple modules is semi-simple.
+ Marco De Renzi Invariants quantiques non semisimples 14/10/2014 14:00 Batiment Sophie Germain, salle 7060
D'après Costantino-Geer-Patureau
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