TQFT and Knot seminar

Speaker:Hao Wang (YMSC)
Organizer:Hao Wang, Xiaoyue Sun,Yuanyuan Fang

Title: Introduction to Knot Categorification and Khovanov homology

Speaker: Hao Wang (YMSC)

Time: Fri.,13:30-15:00pm,Jan.6,2023

Venue: Tencent Meeting ID:733-789-511



This talk I will talk about the basic idea of categofication and knot homologies. After introducing the framework, I will talk about some details about the Khovanov homology, which is the categorification of the Jones polynomial.

Title: Introduction to A-polynomial(II)

Speaker: Hao Wang (YMSC)

Time: Fri.,13:30-15:00pm, Dec.23,2022

Venue:Online Tencent:455-606-281



This talk I will focus on the quantum A-polynomial. The quantum A-polynomial can be defined via the quantization of classical A-polynomial. I will also talk about the topological recursion and its relation with quantum-A-polynomial.

Title: Introduction to A-polynomial

Speaker:Hao Wang (YMSC)

Time: Fri.,13:30-15:00pm, Dec.16,2022

Venue:Online Tencent:352-226-274


This talk will focus on the mathematical concept so-called A-polynomial, which characterize the knot complement from an algebraic viewpoint. I will discuss the classical A-polynomial and its physical interpretation. Then I will talk about the quantization of the A-polynomial. 


Title: Quantum Hall effect and topological defects in two-band structures

Speaker: Zhi-Wen Chang(常治文) (Institute of Theoretical Physics, Faculty of Sciences, Beijing University of Technology)

Time: Fri.,13:30-15:00pm, Dec.9,2022

Venue: Tencent Meeting ID: 675-844-381



The report will firstly present a brief introduction to several kinds of quantum Hall effects, and their connection with topological insulators. Then, I would focus on a simple two-band model, whose topological invariant is the first Chern number C. Two types of topological defects, monopoles and merons, are proposed by analyzing the singularities of the wave functions. Monopoles are three-dimensional singular points and take place at the Dirac points, where the band gap closes up. The system experiences a topological transition when the monopoles appear, leading to C takes an indeterminate value. Merons are two-dimensional singular points, whose topological charges produces the different evaluations of C at varying mass term.

Title: A gentle introduction to the 3d/3d correspondence

Speaker: Satoshi Nawata (Physics Departement, Fudan University)

Time: Fri.,13:30-15:00pm,Nov.25,2022

Venue:Online  Zoom ID: 9383671691 Password: 123456



In this talk, I will survey the development of the 3d/3d correspondence in the past years. The 3d/3d correspondence is the duality between complex Chern-Simons theory on a 3-manifold and 3d N=2 theory labeled by the 3-manifold. Although the full picture is yet to be uncovered, it exhibits a spectacular interplay between topology of 3-manifolds and QFT. In this talk, I introduce established examples such as modular transformations, equivariant Verlinde formulas, Z-hat, and quantum modularity in the 3d/3d correspondence. I will also mention open problems in this area. The talk is supposed to be 1.5-hour long.

Time: Nov.11 (Friday),2022;13:30-15:00pm

Venue: Jinchunyuan West Building Report Hall, 3rd floor(近春园西楼三楼报告厅)
Speaker: Hao Wang (YMSC, Tsinghua University)
Title: SL(2,C) complex Chern-Simons theory and 3d quantum gravity
Abstract:In this talk, I will introduce the complex Chern-Simons theory and discss its relation with 3d quantum gravity, paving the way to discuss the A-polynomial in the future.


Time: Nov.4 (Friday),2022;13:30-15:00pm

Venue: Jinchunyuan West Building Report Hall, 3rd floor(近春园西楼三楼报告厅)
Speaker: Hao Wang (YMSC, Tsinghua University)
Title: An introduction to Volume Conjecture II
Abstract:In this talk, I will continue the discussion about the volume conjecture furthermore, including the asymptotic behavior of colored Jones polynomial, the geometric interpretation of the limit, and to connect the volume conjecture with the context of TQFT, especially the Chern-Simons theory


Title: An Introduction to the Volume Conjecture

Speaker: Xiaoyue Sun (YMSC, Tsinghua University)

Time: Oct.21 (Friday),2022;13:30-15:00pm
Venue: Jinchunyuan West Building Report Hall, 3rd floor(近春园西楼三楼报告厅)
Abstract: We will introduce the Volume Conjecture which states that a certain limit of the colored Jones polynomial of a knot would give the volume of its complement. We would use the figure-eight knot as an example to check this conjecture. The main reference is 1002.0126.


Title: Introduction to Chern-Simons theory (II)

Speaker: Xiaoyue Sun  (YMSC, Tsinghua University)

Time: Oct.5 (Wednesday),2022;18:30-20:30pm
Venue: Jinchunyuan West Building Room 3
Abstract: We have discussed the basic knot theory and classical Chern-Simons theory last time, this time we will continue to discuss Chern-Simons theory, mainly focus on its canonical quantization.


Title: Introduction to Chern-Simons theory (I)

Speaker: Hao Wang (YMSC, Tsinghua University)

Time: September 30 (Fri),2022;10:00-12:00am
Venue: Jinchunyuan West Building Room 3
Abstract: At the first discussion, we have introduced the general framework of TQFT. This time we will discuss the properties of Chern-Simons theory in detail, which is a very important kind of Schwarz TQFT that related to many branches of physics and mathematics, e.g. knot theory, string theory, conformal field theory, quantum gravity and so on. And we will continue to discuss the some basics on knot theory and the relation between the knot invariants and Chern-Simons theory.


Organizer: Hao Wang (Tsinghua)

Time: September 23 (Fri),2022;10:00-11:00am

Venue: Jinchunyuan West Building Room 3

Speaker: Hao Wang

Title: Introduction to topological quantum field theory.

Description: The knot theory is an interesting and active research area in mathematics, which has a deep relation with the topological quantum field theories (TQFT). We will discuss topological quantum field theory from both physics and mathematical perspectives and specifically,  introduce one of the most important kinds of TQFT, the Chern-Simons theory that is deeply related to the knot invariant which was discovered by Edward Witten in the famous paper “Quantum Field Theory and Jones Polynomial” published.