La semaine de l’IMB

On lance un dé et la personne choisie improvise un exposé en 15 minutes.

Suivi d'un repas d'équipe à la passerelle.

If $A/k$ is an abelian variety, there are no non trivial maps (linear, bilinear, quadratic) from $A$ (or $A \times B$) to $G_m$. However, seeing these objects as fppf sheafs of anima (i.e., $\infty$-groupoids) rather than fppf sheafs of sets, the space/anima of linear maps, bilinear and quadratic maps is highly non trivial. Using the Dold-Kan correspondance, we can interpret their $\pi_1$ as, respectively:

- linear maps $A \to BG_m$, i.e. as elements of the dual abelian variety $\widehat{A}=Hom(A, BG_m)$

- biextensions of $A \times B$ by $G_m$

- cubical structures on $G_m$-torsors on $A$

This talk will be divided in three part.

In the first elementary part, we will sketch the many analogies between bilinear and quadratic maps on one hand, and polarisations and line bundles on an abelian variety on the other hand.

In the second part, we will give a sketch of the animation procedure and why it explains the above analogies.

Finally, in the third part, we will give algorithmic applications. In particular, cubical arithmetic serves as a swiss-knife toolbox for abelian varieties, since it can be used to recover the biextension arithmetic and theta group arithmetic, and allows to compute pairings, isogenies, radical isogenies, isogeny preimages, change of level... If time permits, we'll also give an example on how it sheds new lights on the DLP, notably via the monodromy leak attack.

La mécanique quantique a 100 ans cette année. Elle a, pendant toutes ces années, alimenté de multiples sources de belles mathématiques. Une telle source est la question toujours d’actualité : ``Mais en quoi donc est-elle si différente de la mécanique classique ?’’ Dans cet exposé nous illustrerons un aspect de cette interrogation : l’utilisation de quasi-probabilités (Wigner, Kirkwood-Dirac, ...) pour (tenter de) capter la frontière classique-quantique. 

L'ordre du jour sera le suivant :

1. Approbation du compte rendu de la réunion du conseil scientifique du 18/11.

2. Examen et classement des demandes de contrats doctoraux fléchés de l'EDMI

3. Discussion autour de la politique scientifique de l'IMB, en particulier concernant les aspects numériques (dans le contexte d'une demande émanant du VP numérique et transmise par le département SIN à tous les labos le constituant).

4. Informations de la direction.

5. Questions diverses.

Pensez à donner votre procuration.

The Ewens-Pitman model is a distribution on random partitions of {1, . . . , n} indexed by two parameters $\alpha\in$ [0,1) and $\theta$ > - $\alpha$. We establish, for large sample size n, a law of large numbers, a central limit theorem for the number of blocks and a joint central limit theorem for the numbers of blocks of given size in the Ewens-Pitman random partition under the ''large $\theta$'' regime, where the parameter $\theta$ depends linearly on n. We conclude by showing two statistical applications of our results: a posterior version of the CLT for the number of blocks is used to perform uncertainty quantification for the Bayesian  nonparametrics approach to species sampling problems, while the joint CLT is used to develop a novel estimator for the parameters of the model. 

This talk is based on (partly ongoing) joint work with B. Bercu, E. Dolera and S. Favaro.

In this talk, we are interested in the group Aut(X,0) of automorphisms of the germ (X,0) of a complex analytic space. We show that Aut(X,0) contains a contracting automorphism if and only if the singularity (X,0) is quasi-homogeneous. This extends previous results by Favre and Ruggiero for the normal surface case, as well as the recent results by Ornea and Verbitsky for the isolated singularity case. Our proof relies on embeddings and normal forms techniques.