A fundamental motivating problem in homotopy theory is the attempt to the study of stable homotopy groups of spheres. The mathematical object that binds stable homotopy groups together is a spectrum. Spectra are the homotopy theorist abelian groups, they have a fundamental place in algebraic topology but also appear in arithmetic geometry, differential topology, mathematical physics and...

I would like to explain in this talk how questions in non-abelian p-adic Hodge theory and in the theory of locally analytic representations of p-adic groups lead to consider new geometric objects attached to rigid analytic spaces, which require to go beyond the formalism of diamonds and are naturally defined in the analytic geometry framework developed by Clausen-Scholze. Based on a joint...

We prove the modularity of a positive proportion of abelian surfaces over the rationals. This is joint work in progress with G. Boxer, F. Calegari and T. Gee.

Mot de clôture de Dustin Clausen, Professeur permanent et titulaire de la Chaire Jean-Pierre Bourguignon à l'IHES