Séminaire Géométrie et groupes discrets

Toledo Invariants of Quantum Representations

by Prof. Bertrand Deroin (CNRS & Université de Cergy)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Quantum representations form a family of representations of modular groups of surfaces with values in projective pseudo-unitary groups PU(p,q), sending Dehn twists to finite-order elements. Toledo invariants of these representations, and more general characteristic classes, extend to cohomology classes defined on the Deligne-Mumford compactification of moduli spaces, defining cohomological field theories (CohFT). We will give explicit formulae for the Toledo part of the latter in some cases, including Fibonacci quantum representations. This allows to construct/recover complex hyperbolic structures on some moduli spaces. Work in progress with Julien Marché.


IHES Covid-19 regulations:

- all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
- speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
- Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
- Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.


Organized by

Fanny Kassel