Doctoral thesis
Open access

Stokes phenomenon, dynamical r-matrices and Poisson geometry

ContributorsXu, Xiaomeng
Defense date2016-05-20

In this thesis, we study the Poisson geometry of moduli spaces of flat and meromorphic connections over Riemann surfaces, the latter involves the Stokes phenomenon. The aim is to understand some new achievements in this direction from the perspective of mathematical physics. The main results of this thesis are: (1) a construction of a gauge transformation between the standard classical r-matrix and the Alekseev-Meinrenken dynamical r-matrix, using the Stokes data of a certain irregular Riemann-Hilbert problem; (2) an extension to the quantum analogue of the Stokes phenomenon, and its relation with the Yang-Baxter equation; (3) a new finite dimensional description of the Atiyah-Bott symplectic form on the moduli spaces of flat connections over surfaces, using generalised dynamical r-matrices induced by gauge fixing procedures.

Citation (ISO format)
XU, Xiaomeng. Stokes phenomenon, dynamical r-matrices and Poisson geometry. 2016. doi: 10.13097/archive-ouverte/unige:84496
Main files (1)

Technical informations

Creation06/07/2016 10:45:00 AM
First validation06/07/2016 10:45:00 AM
Update time03/15/2023 12:27:35 AM
Status update03/15/2023 12:27:34 AM
Last indexation09/18/2023 8:48:45 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack