邮箱 English

数学大讲堂

Knot invariants and algebraic structures based on knots

Abstract

A knot is a simple closed curve in the 3-space. Knots appeared as one of the first objects of study in topology. At first knot theory was rather isolated in mathematics. Lately due to newly discovered invariants and newly established connections to other branches of mathematics, knot theory has become an attractive and fertile area where many interesting, intriguing ideas collide. In this talk we discuss a new class of knot invariants coming out of the Jones polynomial and an algebra of surfaces based on knots (skein algebra) which has connections to many important objects including hyperbolic structures of surfaces and quantum groups. The talk is elementary, and no prior knowledge of knot theory or quantum groups is required.


About the Speaker

Thang T. Q. Le is a professor of School of Mathematics from Georgia Institute of Technology in the United States. He got his Honored Diploma (M.S.) in Mathematics of Moscow State University in 1988 and finished his Ph.D. in Mathematics of Moscow State University in November 1991.Thang started to work in the year of 1994, being as a Visiting Mathematician in International Center for Theoretical Physics (Trieste, Italy). From 1996 to 1997, he was a post-doctoral fellow of Mathematical Sciences Research Institute (Berkeley, CA). From 1994-1999, he was an assistant professor of  SUNY Buffalo and from 1999-2003 he became an associate professor of it. Since 2004, Thand has been working in Georgia Institute of Technology as a professor until now. His research interests are Differential topology, 3-manifolds, knot theory and quasicrystals.