Non-semisimple quantum invariants and topological field theories
In this course, we give an introduction to quantum invariants of 3-manifolds and topological field theories associated to non-semisimple tensor categories. The topics of the course include:
1. A brief review on finite tensor categories and Hopf algebras.
2. Lyubashenko's 3-manifold invariant associated to modular tensor categories.
4. Modified trace for tensor ideals.
5. Surgery TFT of De Renzi, Gainutdinov, Geer, Patureau-Mirand and Runkel.
6. Non-compact TFT of Costantino, Geer, Patureau-Mirand and Virelizier.
7. A new open-closed non-compact TFT from universal construction.
1. A brief review on finite tensor categories and Hopf algebras.
2. Lyubashenko's 3-manifold invariant associated to modular tensor categories.
4. Modified trace for tensor ideals.
5. Surgery TFT of De Renzi, Gainutdinov, Geer, Patureau-Mirand and Runkel.
6. Non-compact TFT of Costantino, Geer, Patureau-Mirand and Virelizier.
7. A new open-closed non-compact TFT from universal construction.
Lecturer
Date
8th April ~ 24th June, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Wednesday | 13:30 - 16:55 | A3-3-301 | ZOOM 03 | 242 742 6089 | BIMSA |
Reference
[L] Lyubashenko, V.: Invariants of 3-manifolds and projective representations of mapping class groups via quantum groups at roots of unity. Commun. Math. Phys. 172, 467–516 (1995).
[GKP] Geer, N., Kujawa, J. & Patureau-Mirand, B. M-traces in (Non-Unimodular) Pivotal Categories. Algebr Represent Theor 25, 759–776 (2022).
[DGGPR] De Renzi, M., Gainutdinov, A., Geer N., Patureau-Mirand B., Runkel, I.: 3-Dimensional TQFTs from non-semisimple modular categories. Sel. Math. New Ser. 28, 42 (2022).
Costantino F., Geer N., Patureau-Mirand B., Virelizier A.: Non compact (2+1)-TQFTs from non-semisimple spherical categories. arXiv:2302.04509v3.
[GKP] Geer, N., Kujawa, J. & Patureau-Mirand, B. M-traces in (Non-Unimodular) Pivotal Categories. Algebr Represent Theor 25, 759–776 (2022).
[DGGPR] De Renzi, M., Gainutdinov, A., Geer N., Patureau-Mirand B., Runkel, I.: 3-Dimensional TQFTs from non-semisimple modular categories. Sel. Math. New Ser. 28, 42 (2022).
Costantino F., Geer N., Patureau-Mirand B., Virelizier A.: Non compact (2+1)-TQFTs from non-semisimple spherical categories. arXiv:2302.04509v3.
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
No
Language
Chinese
Lecturer Intro
Yilong Wang graduated from The Ohio State University in 2018. After working in Louisiana State University as a postdoc researcher, he joined BIMSA as an assistant research fellow in 2021. His research interests include modular tensor categories and topological quantum field theories.