Matemale Spring School 2022
Witten's finiteness conjecture for skein modules
May 16-20
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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)
2.5 Proof of the Conjecture for lens spaces and the complement of the trivial 2-components link (Jozef Przytycki)
3. Proof for the 3-torus and dehn-fillings of two bridge knots (Giulio Belletti)
3.5. Gilmer-Masbaum’s evaluation map (Gregor Masbaum)
4. Skein category of a surface (Laura Marino)
5. The skein category TFT (Iordanis Romaidis)
11. Introduction to Deformation Quantization modules (Renaud Detcherry)
6. Internal skein algebras and modules (Patrick Kinnear)
7. Stated skein algebras and modules
8. Skein algebras as deformation quantization (Emmanuel Graff)
9.5. Quantum moment map (Jennifer Brown)
9. Internal skein algebras as deformation quantization (Eilind Karlsson)
10. Gluing of internal skein modules (Benjamin Haïoun)
12. Finite dimensionality for holonomic DQ modules (Julien Korinman)
13. 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 registered by the end of March.
List of participants:
Rhea Palak Bakshi (ETH Zurich)
Giulio Belletti (Heidelberg University)
Noufel Bouchareb (Université d'Aix-Marseille)
Jennifer Brown (University of California Davis)
Paolo Cavicchioli (Università di Modena)
Yenni Cherik (Université d'Aix-Marseille)
Renaud Detcherry (Université de Bourgogne)
Paolo Farina (Université de Toulouse)
Thomas Fiedler (Université de Toulouse)
Jonte Gödicke (University of Hamburg)
Emmanuel Graff (Université de Caen)
Baptiste Gros (ENS Lyon)
Benjamin Haïoun (Université de Toulouse)
David Jordan (University of Edinburgh)
Eilind Karlsson (Technische Universität München)
Corina Keller (Université de Montpellier)
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)
Gregor Masbaum (Sorbonne Université)
Gabriel Montoya-Vega (Georges Washington University)
Delphine Moussard (Université d'Aix-Marseille)
Vincentas Mulevicius (MPIM Bonn)
Stepan Orevkov (Université de Toulouse)
Jozef Przytycki (George Washington University)
Iordanis Romaidis (University of Hamburg)
Anthony Saint-Criq (Université de Toulouse)
Vladimir Vershinin (Université de Montpellier)
Thomas Voss (University of Hamburg)
Jeffrey Weenink (University of Groningen / Nanyang University of Singapore)
Haiping Yang (Imperial College London)
Butian Zhang (Université de Toulouse)
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