GREAT · Deformations of fundamental Groups of REpresentATions

The aim of this project is to consider X a smooth projective algebraic curve and a representation ρ of π1(X) into a semisimple Lie group G, and study deformations of ρ when X deforms into a singular curve. This question will open a brand new direction in the theory of representations of fundamental groups and G-Higgs bundles. The main tool to approach the problem will be non- abelian Hodge theory to transform this topological question into the geometric one. Then we use recent new developments in the classification of representations together with new algebraic objects which recently appear in non-abelian Hodge theory to study this question. It will take us to the study the deformations of G-Higgs bundles together with deformations of harmonic bundles over X when X is a curve and varies.This project will allow the researcher to broaden her area of expertise as well as to develop new directions in her research lines. She will complement her knowledge in differential geometry in one of the most prestigious Universities and under the guidance of one of the worldwide leaders in this field.