# Séminaires : Séminaire d'Algèbre

 Equipe(s) : gr, Responsables : J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud. Email des responsables : Jacques Alev , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud Salle : 001 Adresse : IHP Description

 Orateur(s) Zhengfang WANG - Bonn, Titre Gerstenhaber algebra structure on the Tate-Hochschild cohomology Date 14/01/2019 Horaire 14:00 à 15:00 Résume The Tate-Hochschild cohomology of a singular space X is defined as the graded endomorphism ring of the diagonal inside the singularity category of X x X. Singularity categories were introduced by Buchweitz in representation theory and then rediscovered by Orlov in algebraic geometry and homological mirror symmetry. By Keller's very recent result, the Tate-Hochschild cohomology of an algebra is isomorphic to the Hochschild cohomology of its dg singularity category. In this talk, we construct an explicit complex to compute the Tate-Hochschild cohomology. We prove that there is a natural action of the little 2-discs operad on this complex. In particular, the Tate-Hochschild cohomology is a Gerstenhaber algebra. We also talk about a joint work with M. Rivera that the Tate-Hochschild cohomology of a simply-connected manifold M recovers the Rabinowitz-Floer homology of the unit disc cotangent bundle on M. Salle 001 Adresse IHP