| Equipe(s) | Responsable(s) | Salle | Adresse |
|---|---|---|---|
| Analyse Algébrique |
J. Grivaux, M. Robalo, P.Schapira, JB Teyssier |
1525-502 | Jussieu |
salle de Séminaire 502, Couloir 15-25, 5ème étage (Jussieu)
| Orateur(s) | Titre | Date | Début | Salle | Adresse | ||
|---|---|---|---|---|---|---|---|
| + | Nocera, Guglielmo | WHITNEY STRATIFICATIONS AND CONICALLY SMOOTH STRUCTURES | 21/02/2022 | 17:00 | |||
| A classical problem in differential topology and related areas is the following: can we stratify non smooth spaces (e.g. algebraic varieties, quotients of smooth manifolds by group ac- tions, ...) into smooth strata, in such a way that good “transversality conditions” are matched? The notion of Whitney stratification arises to give an answer to this question, and indeed alge- braic varieties, analytic varietis, semialgebraic sets and semianalytic sets admit a Whitney strat- ification. On the other hand, the notion of conically smooth structure was introduced by Ayala, Francis and Tanaka in 2017 and can be thought of as an analogue of a differential structure in the context of stratified spaces. We will explain that a Whitney stratified space always admits a cini- cally smooth structure, and if time permits we will provide an application of this result: namely, the affine Grassmannian associated to a reductive group, which is a fundamental object in the Geometric Langlands Program. This is joint work with Marco Volpe (University of Regensburg). |
 | ||||||
| + | Marco Volpe | Six functor formalism with non-presentable coefficients | 15/11/2021 | 16:00 | 1525_502 | ||
| The six functor formalism over locally compact Hausdorff spaces was developed by Masaki Kashiwara and Pierre Schapira in the book "Sheaves on Manifolds": this is done in the context of derived categories of sheaves of R-modules, with R a ring. In this talk I will show that one can extend the whole formalism to non-necessarily hypercomplete sheaves with values in any stable bicomplete ∞-category equipped with a closed symmetric monoidal structure. At the end I will show how being able to work at this level of generality allows one to prove that, if f is a map which induces a locally contractible geometric morphism, then the exceptional pullack along f satisfies a formula which was previously known to hold only for topological submersions. |
| ||||||
| + | Vivek Shende | Localization of Fukaya categories and quantizing the Hitchin system | 18/10/2021 | 14:00 | 15-25-502 | Jussieu | |
| For a complex curve C and reductive group G, the space of G-bundles on C has been of much interest to many mathematicians. For the purposes of the geometric Langlands correspondence, one wishes to construct certain `Hecke eigensheaves' over this space. It has long been expected (and in some cases known) that these should arise from quantization of fibers of Hitchin's integrable system, this being the map h: T*Bun(C, G) --> A which, for G = GL(n), records the spectral curve of a Higgs bundle. Historically this means that one tries to associate a D-module on Bun(C, G) to each fiber of h. More recently, the fact that Langlands dual groups give rise to dual Hitchin fibrations has led to the expectation that geometric Langlands duality should be some sort of homological mirror symmetry. In this talk we will take a step towards making this precise: recent results on the localization of wrapped Fukaya categories allow us to use Floer theory to associate a constructible sheaf on Bun(C, G) to a fiber of the Hitchin fibration. (More precisely, we may do for smooth fibers, in components of Bun(C, G) where there are no strictly semistable Higgs bundles, and should assume G connected center). We don't yet know how to check that we have eigensheaves, but can check some expected properties: our sheaves have the expected endomorphisms, rank, microstalks on certain components, and sheaves from different fibers are orthogonal. |
| ||||||
| + | Federico Bambozzi | Séminaire Analyse Algébrique | 24/04/2017 | 16:00 | |||
| Organisateurs : G. Ginot, A. Oancea, F. Paugam , M. Robalo, P.Schapira
Plus ou moins un lundi par mois ; salle de Séminaire 502, Couloir 15-25, 5ème étage (Jussieu) http://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 20/03/2017 | 16:00 | ||||
| Benjamin Hennion
Algèbres de Kac Moody et Géométrie Dérivée Détails: https://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 27/02/2017 | 15:30 | ||||
| Sarah Scherotzke (Bonn)
Détails: https://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 06/02/2017 | 16:00 | ||||
| https://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 05/12/2016 | 16:00 | ||||
| https://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 28/11/2016 | 16:00 | ||||
| https://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 21/11/2016 | 16:00 | ||||
|
| |||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 17/10/2016 | 16:00 | ||||
| https://webusers.imj-prg.fr/~gregory.ginot/analgNT |
| ||||||
| + | Séminaire AA : <a href="https://webusers.imj-prg.fr/~gregory.ginot/analgNT">Programme</a> | 13/10/2016 | 15:30 | ||||
| Séminaire AA : Programme |
| ||||||
| + | Patrice Le Calvez | Forçage d'orbites pour les homéomorphismes de surfaces, trajectoires transverses | 04/05/2015 | 16:00 | |||
|
Résumé: Si f est un homéomorphisme d'une surface isotope à l'identité, on peut définir la notion d'"isotopie maximale" et de "feuilletage transverse" à cette isotopie, dont le domaine coïncide avec les points qui ne sont pas fixés par l'isotopie. Toute trajectoire non triviale de l'isotopie se "projette" alors en un chemin transverse au feuilletage "la trajectoire transverse". Un petit lemme dit que si deux trajectoires transverses "s'intersectent transversalement", on peut alors construire deux autres trajectoires transverses en décroisant nos chemins. Nous obtenons ainsi un outil qui nous permet de forcer des orbites en dimension deux. Plusieurs résultats peuvent être démontrés, améliorés (généralement au cas des homéomorphismes) ou retrouvés grâce à cet outil (ex: un théorème de Handel qui affirme qu'un homéomorphisme transitif d'une surface hyperbolique de genre nul admet des orbites périodiques dont le nombre croît exponentiellement avec la période; une généralisation aux homéomorphismes de la classification de Franks-Handel des homéomorphismes conservatifs d'entropie nulle de la sphère, une conjecture de Boyland sur l'ensemble de rotation des homéomorphismes du tore ou de l'anneau). Il s'agit d'un travail commun avec Fabio Tal, de l'Université de Sao Paulo. |
| ||||||