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Relations in the tautological ring of the moduli spaces of stable curves and integrable systems.

Le : 19/12/2017 11h00
Par : Paolo Rossi (IMB, Dijon)
Lieu : I 001
Lien web :
Résumé : In this talk I will present our recent result by which the conjectural equivalence between the Dubrovin-Zhang and the Double Ramification hierarchies can be translated into an infinite family of tautological relations in the cohomology ring of the moduli space of stable curves, for all genera and number of marked points. Because of their somewhat un-geometric origin, it is hard to make a connection with other known relations, like Pixton's conjecturally complete system. I'll give a down-to-earth introduction to the geometry of the tautological ring and I'll report on the status of our project to prove the relations and the original DR/DZ conjecture and show several side results and applications. This is a joint work with Buryak, Dubrovin and Guéré.