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) Travis SCHEDLER - MIT,
Titre Computational approaches to Poisson traces on quotient singularities
Horaire14:30 à 15:30
RésumePoisson traces are linear functionals on a Poisson algebra which annihilate Poisson brackets. They are dual to the zeroth Poisson (or Lie) homology, and the dimension of this space bounds the number of irreducible finite-dimensional representations of any quantization. I will consider the case where the Poisson algebra is the algebra of $G$-invariant polynomials in $2n$ variables with complex coefficients, where $G$ is a finite subgroup of $Sp(2n,C)$. I will prove some results which reduce the computation of Poisson traces, for fixed $n$ and $G$, to a finite one that can be done by computer, and will describe several results of this computation. I will also classify the complex reflection groups $G$ for $n = 2$ for which the dimension of the Poisson traces coincides with the (well-known) dimension of the zeroth Hochschild homology of the algebra of $G$-invariant differential operators in n variables, which a priori is only a lower bound. The results also imply this equality for Coxeter groups of rank $\leq 3$ and the Weyl groups $B_4$ and $D_4$. These results also give the Hilbert series of the space of Poisson traces, in terms of the polynomial degree (and when the aforementioned equality holds, also this series for the zeroth Hochschild homology). This is joint work with Etingof, Gong, Pacchiano, and Ren, part of which took place in the context of undergraduate research at MIT.
Salleà distance / remote