Date January 21-23, 2026
Venue Kyushu University, Ito Campus (West Zone 1, C513 & C503)
Speakers
Dongmin Gang (Seoul National University) -- 3 talks
Title: Torus Knots and Minimal Models Revisited
Abstract: In 2003, Hikami and Kirillov uncovered an intriguing connection between torus knots K(P,Q) and Virasoro minimal models M(P,Q) by relating the Kashaev invariants of the knots to the characters of the corresponding minimal models. In the talk, I will recover and significantly extend this connection by combining the 3D–3D correspondence with a bulk–boundary correspondence. More concretely, we study the 3D supersymmetric gauge theories associated with torus-knot complements via the Dimofte–Gaiotto–Gukov construction and show that, in the infrared, these theories flow to topological field theories that support rational VOAs of minimal models at the boundary. This framework yields new Nahm-sum–like expressions for the characters of Virasoro minimal models and other related rational conformal field theories, providing a systematic algorithm for constructing characters of rational VOAs directly from the combinatorial data of an ideal triangulation of a non-hyperbolic knot complement.
Campbell Wheeler (IHES) -- 5 talks
Title: Quantum, invariants and modularity
Abstract: Around 2010, Zagier observed a bizarre almost modular property of the quantum invariants of the figure eight knot. Previous work, for example work of Lawrence-Zagier and Hikami, had shown that for non-hyperbolic manifolds the quantum invariants were related to mock modular forms. The figure eight knot is a hyperbolic manifold and Zagier coined the term quantum modularity to describe the fascinating properties of its quantum invariants. Recent work of Garoufalidis-Zagier, clarified and refined Zagier’s original observations. In this series of lectures, I will introduce sl_2 quantum invariants, their perturbation theory around hyperbolic connections, and their quantum modularity.
Schedule (Tentative)
January 21 (Wed) @ C513
11:00 -
January 22 (Thu) @ C513
January 23 (Fri) @ C503
- 12:30
This workshop is supported by JSPS KAKENHI (JP23K22388: Kazuhiro Hikami).