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Higher Teichmüller-Thurston Theory: Representations of Surface Groups in PSL(n,R)

Objective

Higher Teichmüller-Thurston theory is the study of a specific component of representations of a surface group of genus g in PSL(n,R). Teichmüller theory depends on a parameter: the genus g of the surface. Higher Teichmüller-Thurston introduces a new paramater n so that classical theory corresponds to n=2. Teichmüller theory is a crossroad between dynamics, complex analysis, spectral theory, geometry and integrable systems. It has started with the study of Kleinian groups and have received strong impulses from many fields throughout last century. To quote but a few: arithmetic (through the study of automorphic forms), geometry (Thurston's theory of hyperbolic structures), dynamics (the ergodic properties of the geodesic flow) and physics (conformal field theory and representations of the Virasoro algebra). The main objective of the proposal is to develop new connections between dynamics, complex analysis, integrable systems beyond classical Teichmüller Theory in the context of higher Teichmüller-Thurston theory. Among the very concrete and challenging goals of this proposal, we have: A Riemann uniformisation theorem for the Hitchin component, the construction and quantisation of a universal algebra for all Hitchin components, computations of volumes and characteristic numbers of (Higher) Riemann moduli spaces, Higher Laminations. The resources will be essentially used for the hiring of post-doc, graduate students, pre-doc students, visiting scientists, international conferences and summer schools. It will take place at University Paris Sud XI.

Field of science

  • /natural sciences/mathematics/pure mathematics/algebra
  • /natural sciences/mathematics/pure mathematics/mathematical analysis/complex analysis

Call for proposal

ERC-2009-AdG
See other projects for this call

Funding Scheme

ERC-AG - ERC Advanced Grant

Host institution

UNIVERSITE DE NICE SOPHIA ANTIPOLIS
Address
Avenue Valrose 28 Grand Chateau
06100 Nice
France
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 110 520
Principal investigator
François Pierre Calixte Labourie (Prof.)
Administrative Contact
Isabelle De Angelis (Mrs.)

Beneficiaries (2)

UNIVERSITE DE NICE SOPHIA ANTIPOLIS
France
EU contribution
€ 110 520
Address
Avenue Valrose 28 Grand Chateau
06100 Nice
Activity type
Higher or Secondary Education Establishments
Principal investigator
François Pierre Calixte Labourie (Prof.)
Administrative Contact
Isabelle De Angelis (Mrs.)
UNIVERSITE PARIS-SUD
France
EU contribution
€ 1 438 680
Address
Rue Georges Clemenceau 15
91405 Orsay Cedex
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Nicolas Lecompte (Mr.)