MS Seminar (Mathematics - String Theory)

Speaker: Hiroyuki Fuji (Nagoya Univ)
Title: Volume Conjecture and Topological Recursion
Date: Tue, Apr 06, 2010, 13:15 - 14:45
Place: Seminar Room A
Related File: 243.pdf
Abstract: Abstract for mini-review:

In this part, I will review some aspects of the three-dimensional hyperbolic geometry. As an example, the complement of the figure eight knot complement in a three sphere will be mainly discussed. After the hyperbolic volume computation, I shall present the claim of the volume conjecture.

Abstract for the seminar:

In this talk, I will discuss the relation between the colored Jones polynomial and the topological open string amplitude. On the colored Jones polynomial side, I shall use AJ conjecture to derive the higher order terms in WKB expansion of the colored Jones polynomial. On the topological string theory side, I shall compute Eynard-Orantin's topological recursion on the character variety of the knot, and compute the free energies up to fourth order. I will show the coincidence of these results under the change of a constant in the Bergman kernel.
Contact: Sugimoto
Remarks: Presentation file will be updated. Please see the newest files at
http://qken.phys.nagoya-u.ac.jp/~fuji/dfm/ipmu10_1.pdf
http://qken.phys.nagoya-u.ac.jp/~fuji/dfm/ipmu10_3.pdf