Seules les adresses mails institutionnelles sont acceptées lors de la création d'un compte. La création de compte est modérée, merci d'attendre leur validation. Only institutional email addresses will be accepted when asking for an account. Account creation is moderated, please wait until then.
de 11 avril 2016 à 15 juillet 2016
Institut Henri Poincaré
Europe/Paris timezone


Dimitri Zvonkine, Paris 6

Cohomological relations on the moduli space of stable curves

We construct a family of relations between tautological cohomology classes on the moduli space Mbar_{g,n} of stable curves. This family contains all relations known to this day and is expected to be complete and optimal. The construction uses the Frobenius manifold of the A_2 singularity, the 3-spin Witten class and the Givental-Teleman classification of semi-simple cohomological field theories (CohFTs). The plan of the three talks will be as follows.

1. An introduction to moduli space and its tautological cohomology ring; simplest examples of tautological relations.

2. Cohomological field theories and Witten's r-spin class. Witten's r-spin class is actually a family of cohomology classes on the space of stable maps, defined using the space of tensor r-th roots of the canonical line bundle. I will explain why these classes satisfy the axioms of a cohomological field theory (CohFT).

3. The Givental-Teleman classification of semi-simple CohFTs. I will explain the classification theorem, show how it applies to Witten's class and how one can deduce tautological relations from it. In the end I will compute several cohomological relations using our method.

This is a joint work with R. Pandharipande and A. Pixton. 

Your browser is out of date!

Update your browser to view this website correctly. Update my browser now