MS Seminar (Mathematics - String Theory)

Speaker: Omar Kidwai (University of Toronto)
Title: Higher length-twist coordinates for character varieties
Date: Thu, Apr 18, 2019, 13:15 - 14:45
Place: Seminar Room B
Abstract: We describe joint work with L. Hollands on a construction of special holomorphic Darboux coordinates on certain SL_N (particularly N=2,3) character varieties. We consider degenerate examples of "spectral networks" of Gaiotto-Moore-Neitzke (certain graphical objects on a Riemann surface), generalizing the so-called "Fenchel-Nielsen" networks of Hollands-Neitzke. We compute the associated "spectral coordinates" using the "abelianization map", taking connections on the Riemann surface to abelian holonomy data on a spectral cover, generalizing the "complexified Fenchel-Nielsen" coordinates of Kourouniotis-Tan for SL(2)-connections to higher rank. Time permitting, I will discuss some physical applications to computing superpotentials coming from 4d N=2 supersymmetric QFTs.
Remarks: Blackboard talk