中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

Colloquia & Seminar

 

 

报告人 杨田Texas A&M University

Lecture 1

  Introduction to the colored Jones polynomials

  2021.8.2 (周一) 上午9:30-11:30

  点:腾讯会议448 803 869

  要:In this lecture, I will introduce the colored Jones polynomials. It is a family of polynomial invariants for a link in the 3-dimensional sphere, which generalizes the famous Jones polynomial. I will use the skein theoretical approach due to Wenzl and Blanchet-Hamburger-Masbaum-Vogel, which is a very beginner-friendly approach.

Lecture 2

  Introduction to the Volume Conjecture

  2021.8.5周四上午9:30-11:30

  点:腾讯会议106 345 940

  要:In this lecture, I will introduce the Volume Conjecture, due to Rinat Kashaev, which relates the values of the colored Jones polynomials at suitable roots of unity of a link in the 3-sphere to the hyperbolic volume of the complement of this link. As an example, I will present how this conjecture is proved when the link is the fifigure-8 knot.

Lecture 3

  Introduction to the Reshetikhin-Turaev invariants

  2021.8.9周一上午9:30-11:30

  点:腾讯会议159 524 880

  要:In this lecture, I will introduce the Reshetikhin-Turaev invariants. It is a family of complex valued invariants for closed oriented 3-manifolds, which mathe[1]matically realizes Witten’s invariants originally constructed using ideals from physics, the quantum Chern-Simons theory to be more precise. I will use the skein theoretical approach due to Blanchet-Hamburger-Masbaum-Vogel and independently Lickorish, which is very beginner-friendly

Lecture 4

  Introduction to the Volume Conjecture for the RT-invariants I

  2021.8.12(周四)上午9:30-11:30

  点:腾讯会议847 930 325

  要:In this lecture, I will talk about the Volume Conjecture for the Reshetikhin Turaev invariants, due to Qingtao Chen and myself, which relates the values of these invariants to the hyperbolic volume of the manifold. This conjecture has been verifified for many cases, including the work of Ohtsuki for the closed oriented 3-manifold obtained by doing an integral Dehn-surgery along the fifigure-8 knot. To prepare for the proof, I will introduce the main tools used there, including the quantum dilogarithm functions.

Lecture 5

  Introduction to the Volume Conjecture for the RT-invariants II

  2021.8.16周一上午9:30-11:30

  点:腾讯会议538 171 814

  要:In this lecture, I will talk about Ohtsuki’s proof of the Volume Conjecture for the Reshtikhin-Turaev invariants for the closed oriented 3-manifolds obtained by doing an integral Dehn-surgery along the fifigure-8 knot, and how possible this approach could be applied to the other cases.

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