Monomial Braidings
发布人: 曹思圆   发布时间: 2018-04-08   浏览次数: 43


讲座题目:Monomial Braidings
主讲人:李建荣 副教授
主持人:胡乃红 教授
开始时间:2018-4-11(周三)  13:30--15:00

报告人简介:Research Fellow of Department of Mathematics, Weizmann Institute of Science
Ziskind building, 234 Herzl St. Rehovot, 7610001, Israel, since July 2016 to July 2019. He was a postdoc researcher, from Sep 2013 to July 2014, Einstein Institute of Mathematics, the Hebrew University of Jerusalem, his mentor is the famous mathematician: Professor David Kazhdan. He got his Ph.D. in Dec. 2012 from Lanzhou University, after spending his two years' studies (from Sep 2010 to Aug 2012) as a visiting student at Indiana University - Purdue University at Indianapolis under the joint guidance of Profs. Eugene Mukhin, and Vitaly Tarasov as well as Yanfeng Luo.

Monomial Braidings
Abstract: I will talk about a new method to construct braidings. A braided vector space is a pair (V, Psi), where V is a vector space and Psi: V \otimes V \to V \otimes V is a linear map which satisfies the braid equation Psi_1 Psi_2 Psi_1 = Psi_2 Psi_1 Psi_2. Given a braided vector space (V, Psi). We constructed a family of braided vector spaces (V^{\otimes n}, Psi^{\epsilon}), where \epsilon: [n] \times [n] \to \{1, -1\} is a bitransitive map.

We generalized this construction to the case of multicolors. We introduced C-braid monoids, where C is a finite set. Given a braided vector space (V, Psi), we can use C-transitive functions to parametrize the braidings on V^{\otimes n} which come from Psi_1, ..., Psi_{n-1}. These braidings are monomials in Psi_1, ..., Psi_{n-1}. Therefore we call them monomial braidings.
Since [n] \times [n] can be viewed as a bidirected complete graph, a C-transitive function \epsilon: [n] \times [n] \to C can be view as a C-transitive function on a bidirected complete graph. We generalized the concept of C-transitive functions to C-transitive functions on any directed graphs.  We showed that the number | G(C) | of all C-transitive functions on a directed graph G is a polynomial in |C|. This is a new invariant in graph theory. It is analogue to the chromatic polynomials for undirected graphs in graph theory.

This is joint work with A.Berenstein and J.Greenstein.