| Résume | 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). |
