Stokes phenomenon, dynamical r-matrices and Poisson geometry

Diplôme Thèse Stokes phenomenon, dynamical r-matrices and Poisson geometry eng 2016-05-20 author Xu Xiaomeng 791115 director Alexeev Anton 134019 10.13097/archive-ouverte/unige:84496 urn:nbn:ch:unige-844965 Sc. 4930 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. Dewey 510 25 Section de mathématiques 11 false 848 Groupe de Lie et espaces de modules 4b97b833-ff4c-4638-98cb-b53824056c34 Thesis Public Thesis_XiaomengXU.pdf 958936 application/pdf openAccess Faculté des sciences / Section de mathématiques

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Xu, Xiaomeng