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 <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : à distance / remote
Adresse :IHP

Depuis le 23 mars 2020, le séminaire se tient à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


Orateur(s) Zhengfang WANG - Bonn,
Titre Gerstenhaber algebra structure on the Tate-Hochschild cohomology
Horaire14:00 à 15:00
RésumeThe 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.
Salleà distance / remote