Institut de recherche mathématique avancée

Résumé : Lisa Traynor and I recently introduced new invariants -- generating family spectra -- of Legendrians equipped with generating families. These invariants are stable homotopy lifts of classical invariants, and are conjectured to model stable homotopy lifts of morphisms in infinitesimally wrapped Fukaya categories. As an application, we prove that one can detect infinitely many new connected components in the space of Thom's "excellent Morse functions" on Euclidean spaces. In this talk, I will introduce these topics and give a rough explanation of the proofs.

Résumé : Pour une variété algébrique lisse complexe S, j'expliquerai comment construire des sous-anneaux finiment engendrés de son anneau de Chow à l'aide de la théorie de Hodge.

Résumé : In his Esquisse d’un programme, Grothendieck called for the development of a “tame” topology, free from the pathologies of general topology. Such a framework was developed in the 1980s and 1990s by logicians under the name o-minimal geometry, based on the simple principle that, in dimension one, the only sets considered are finite unions of intervals. Remarkably, this setting has recently led to striking applications in complex algebraic geometry, particularly in Hodge theory, as well as in number theory, notably in Diophantine geometry. This talk will offer an elementary introduction to these ideas.