TQFT and Knot seminar

报告人 Speaker:Satoshi Nawata (Fudan University)
组织者 Organizer:Hao Wang, Xiaoyue Sun,Yuanyuan Fang
时间 Time:Fri.,13:30-15:00pm,Nov.25,2022
地点 Venue:Online Zoom ID: 9383671691 Password: 123456

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
https://us02web.zoom.us/j/9383671691?pwd=cUdMak5La1Q4d214TVZUQXhLaU5yQT09

 

Abstract:

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.