时间：2024年10月20日
地点：西湖大学云谷校区E4-233 & ZOOM
ZOOM ID: 959 7658 1791
PASSCODE: 118729
1. 9:30-10:00
Speaker：Honghuai Fang, Westlake University
Title：Introduction to the Volume Conjecture
Abstract：In this talk, we review the history of the volume conjecture, including the original Kashaev-Murakami-Murakami conjecture, the refined version, Chen-Yang conjecture, Andersen-Kashaev conjecture, the quantum modularity conjecture and some other types.
2. 10:20-11:20
Speaker：Chuwen Wang，Renmin University
Title：On the Volume Conjecture for Hyperbolic Dehn-filled 3-manifolds along the Twist Knots
Abstract：I will review recent developments on the Volume Conjecture, with a particular focus on our approaches to proving the conjecture for hyperbolic Dehn-filled 3-manifolds along twist knots. Additionally, I will present several related research topics concerning the Volume Conjecture. This is joint work with Huabin Ge, Yunpeng Meng, and Yuxuan Yang.
3. 13:00-14:00
Speaker：Fathi Ben Aribi, Sorbonne Université
Title：The Andersen-Kashaev Volume Conjecture for Twist Knots
Abstract：In 2011, Andersen and Kashaev defined an infinite-dimensional TQFT from quantum Teichmüller theory. This Teichmüller TQFT yields an invariant of triangulated 3-manifolds, in particular knot complements. The associated volume conjecture states that the Teichmüller TQFT of an hyperbolic knot complement contains the hyperbolic volume of the knot as a certain asymptotical coefficient, and Andersen–Kashaev proved this conjecture for the first two hyperbolic knots.
In this talk, I will present the construction of the Teichmüller TQFT and how we proved its volume conjecture for the infinite family of twist knots, by constructing new geometric triangulations of the knot complements. If time permits, I will also mention a recent extension of this work for more general 3-manifolds. This joint project with E. Piguet–Nakazawa, F. Guéritaud and K.-H. Wong.
4. 14:20-15:20
Speaker：Campbell Wheeler, Institut des Hautes Études Scientifiques
Title：Resurgence and the volume conjecture
Abstract：Kashaev's volume conjecture is an asymptotic statement about quantum invariants of hyperbolic knots. This can be refined to an all orders asymptotic statement. Hikami introduced state integrals that are conjectured to give rise to the asymptotic series coming from this all orders volume conjecture. Recently, using the description of theseseries given by Dimofte-Garoufalidis, we proved that these series are topological invariants of cusped hyperbolic manifold with Garoufalidis-Storzer. In this talk I will discuss recent work with Fantini where we prove that these asymptotic series are Borel re-summable for some simple hyperbolic knots.
5. 15:40-16:40
Speaker：Zhihao Wang, University of Groningen
Title：Kauffman Bracket Intertwiners and the Volume Conjecture
Abstract：Bonahon-Wong-Yang introduced a new version of the volume conjecture using the intertwiners between two isomorphic irreducible representations of the skein algebra. The intertwiners are built from surface diffeomorphisms; they formulated the volume conjecture when diffeomorphisms are pseudo-Anosov.
In this talk, we will review the basic definitions for the skein algebra and its representation theory at roots of unity. Then we review the Bonahon-Wong-Yang's volume conjecture. We will talk about our calculation for all the intertwiners for the closed torus and we prove the limit superior related to the trace of these intertwiners is zero. We will talk about the generalization for the Bonahon-Wong-Yang's volume to the periodic diffeomorphisms for surfaces. In the end, we offer some affirmative examples for the periodic case.
