Institut de Physique Théorique
Direction de la Recherche Fondamentale  -  Saclay
UMR 3681 - INP
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Vendredi 22 septembre 2017

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Soutenance de thèse de doctorat
Mardi 19/09/2017, 14h30
Amphi Darboux, Institut Henri Poincaré, Paris
GEOMETRY OF INTEGRABLESYSTEMS: FROM TOPOLOGICAL LAX SYSTEMS TO CONFORMAL FIELD THEORIES
Raphaël Belliard
IPhT

This PhD thesis is about a framework in complex geometry and methods thereof for solving sets of compatible differential equations arising from integrable systems, classical or quantum, in the context of the geometry of moduli spaces of connections over complex curves, or Riemann surfaces. It is based on the idea in mathematical Physics that integrable systems possess symmetries that impose algebro-differential constraints, so-called loop equations, on the objects of interest (e.g. partition or correlation functions). In turn, we intend to solve these constraints recursively in certain topological regimes using a particular procedure called the topological recursion. Their solutions are in general generating functions of enumerative-geometric quantities. Since they are for the most part determined by the initial data of the recursive process, it realizes in the making an algebro-geometric classification of the family of integrable models under consideration.

 

(The defense will take place at: Institut Henri Poincaré, Amphithéatre Darboux, 11 rue Pierre et Marie Curie, 75005, Paris.)


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