活动地点：CMS 201

活动类型：学术报告

主讲人：​陈庆陶博士

活动时间：2016-06-28 16:00:00--2016-06-28 17:00:00

活动内容：

陈庆陶博士专题学术报告

 

 

报告题目：Congruence relations, Cyclotomic Expansions and Volume Conjectures

报告人：陈庆陶 博士（瑞士联邦理工 ETH）

 

时间：2016年6月28日（周二）下午4:00

 

地点：数学中心201教室

Abstract：

    In this talk, I will illustrate a new point of view that yields subtle relations for various quantum invariants of knots. I will first discuss congruence relations for colored Jones polynomials and their relationship with the cyclotomic expansion obtained by Habiro. A key observation is that the root of unity used in the Volume Conjecture of Kashaev-Murakami-Murakami naturally occurs in this context as the gap in the cyclotomic expansion of the colored Jones polynomials.

   I will then apply the same ideas idea to colored SU(n) invariants of knots. In joint works with K. Liu, P. Peng and S. Zhu, we have discovered strong congruence relations for these invariants, which suggest the existence of certain cyclotomic expansions generalizing Habiro's as well as versions of the Volume Conjecture for these colored SU(n) invariants.

   If time permits, I will also discuss applying this viewpoint to the superpolynomial associated to reduced triply-graded HOMFLY-PT homology.