Matemale Spring School 2022 : Witten’s finiteness conjecture for skein modules

School
Matemale, France
https://sites.google.com/view/matemale-maths-school

Date(s) : 30/05/2022 - 03/06/2022   iCal
0 h 00 min

This year, we will study the recent proof by Gunningham, Jordan, and Safronov of Witten’s finiteness conjecture for skein modules of closed oriented 3-manifolds. The school is designed for Master students, PhD students and researchers, younger and older. Participants are encouraged to choose a (not yet attributed) talk in the list. We are grateful to Renaud Detcherry, Benjamin Haioun, Francesco Costantino and Ramanujan Santharoubane for elaborating the program.

The event is supported by the GDR Tresses, the CIMI, the Mathematics Institute of Toulouse, the ERC project NEDAG.

The conference will be about the proof of the finiteness conjecture for skein modules by Gunningham-Jordan-Safronov. This conjecture of Witten asserts that for any oriented closed 3-manifold, the Q(A)-vector spaces spanned by isotopy classes of links in M modulo the Kauffman skein relations is finite dimensional. The Kauffman skein modules were first introduced by Przytycki and Turaev as a way to generalize the Kauffman bracket polynomial of knots and links in the 3-sphere . The conjecture is quite surprising as, by a result of Bullock, the skein module of M specialized at A = −1 gives back the SL(2,C)-character variety of M, which is often infinite dimensional. Witten allegedly formulated the conjecture based on the intuition that a dim 3 + 1 TQFT whose values on 3-manifolds are the skein modules should exist.

More details and references here: program.

List of talks:

0. Overview (Renaud Detcherry)
1. Kauffman skein module (Paolo Farina)
2. Basic properties of skein modules (Rhea Palak Bakshi)
3. Proof on examples (Giulio Belletti)
4. Gilmer-Masbaum’s evaluation map (Gregor Masbaum)
5. Skein category of a surface (Laura Marino)
6. The skein category TFT
7. Internal skein algebras and modules (Patrick Kinnear)
8. Stated skein algebras and modules (Jules Martel)
9. Skein algebras as deformation quantization (Léo Bénard)
10. Internal skein algebras as deformation quantization (Eilind Karlsson)
11. Quantum moment map (Jennifer Brown)
12. Gluing of internal skein modules (Benjamin Haïoun)
13. Introduction to Deformation Quantization modules (Renaud Detcherry)
14. Finite dimensionality for holonomic DQ modules (Julien Korinman)
15. Proof of the conjecture (David Jordan)

Organizers :
Francesco Costantino (Institut de Mathématiques de Toulouse)
Thomas Fiedler (Institut de Mathématiques de Toulouse)
Delphine Moussard (Institut de Mathématiques de Marseille)

If you are willing to participate, please contact us by email.

We will be accommodated in the Centre de vacances “La Capcinoise”, more precisely in their gites ruraux (https://www.lacapcinoise.fr/). This is just for information, you don’t need to make a reservation by yourself. We will cover the stay of the participants.

List of participants:

Rhea Palak Bakshi (ETH Zurich)
Giulio Belletti (Heidelberg University)
Léo Bénard (Gottingen University)
Jennifer Brown (University of California Davis)
Yenni Cherik (Université d’Aix-Marseille)
Renaud Detcherry (Université de Bourgogne)
Paolo Farina (Université de Toulouse)
Thomas Fiedler (Université de Toulouse)
Emmanuel Graff (Université de Caen)
Baptiste Gros (ENS Lyon)
Benjamin Haïoun (Université de Toulouse)
David Jordan (University of Edinburgh)
Eilind Karlsson (Technische Universität München)
Patrick Kinnear (University of Edinburgh)
Edwin Kitaeff (Université de Montpellier)
Julien Korinman (Waseda University)
Theodoros Lagiotis (University of Edinburgh)
Manousos Manouras (Université de Pau / University of Zaragoza)
Laura Marino (Université de Paris)
Jules Martel (Université de Bourgogne)
Gregor Masbaum (Sorbonne Université)
Gabriel Montoya-Vega (Georges Washington University)
Delphine Moussard (Université d’Aix-Marseille)
Stepan Orevkov (Université de Toulouse)
Raphaël Paegelow (Université de Montpellier)
Anthony Saint-Criq (Université de Toulouse)
Alisa Sheinkman (University of Edinburgh)
Vladimir Vershinin (Université de Montpellier)
Butian Zhang (Université de Toulouse)

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