L. Berger (ENS de Lyon)
Titre : (phi,Gamma)-modules and locally analytic vectors
Résumé : This talk is about the attempt to construct overconvergent (phi,Gamma)-modules when Gamma is a p-adic Lie group. I will explain why the theory of locally analytic vectors seems to play a role, as a replacement for Tate's normalized trace maps.

B. Bhatt (IAS)
Titre : Integral structures on de Rham cohomology
Résumé : I will describe joint work in progress with Andrew Snowden on the construction of canonical integral structures on the de Rham cohomology of smooth projective varieties over number fields. Our construction relies on integral p-adic Hodge theory.

O. Brinon (Université de Bordeaux)
Titre : The overconvergent Hodge-Tate map
Résumé : In the Siegel case, using the point of view of overconvergent Igusa towers, I will explain why the Hodge-Tate map is overconvergent as well. This is a joint work with F. Mokrane and J. Tilouine.

G. Dospinescu (ENS de Lyon)
Titre : Injectivity of Colmez's Montreal functor
Résumé : This is joint work with P. Colmez and V. Paškūnas, whose goal is the complete classification of absolutely irreducible unitary admissible Banach space representations of GL_2(Q_p) (and their reduction modulo p) for all primes p (completing previous work of Paskunas). In this talk we will explain how the injectivity of the Montreal functor is related to this problem (and several other results) and sketch the proof of this injectivity.

J. Hauseux (École Polytechnique)
Titre : Extensions entre séries principales p-adiques et modulo p de G(F)
Résumé : Soit G un groupe réductif connexe déployé sur une extension finie F de Q_p. On détermine les extensions entre séries principales continues unitaires p-adiques et lisses modulo p de G(F) dans le cas générique. Pour cela, on calcule le delta-foncteur HOrd_P d'Emerton sur certaines induites en utilisant une filtration de Bruhat. Ces extensions interviennent dans le programme de Langlands p-adique et modulo p.

V. Paškūnas (Université d'Essen)
Titre : Reduction modulo p of irreducible p-adic Banach space representations of GL_2(Q_p)
Résumé : This is a joint work with Colmez and Dospinescu. We show that the reduction modulo p of an absolutely irreducible p-adic Banach space representation of GL_2(Q_p) has the shape predicted by the mod p Langlands correspondence. The result had been known for p>3 previously, the new proof works for all primes p.

T. Schmidt (Université de Münster)
Titre : Arithmetic D-modules and locally analytic representations
Résumé : We describe some new results connecting Berthelot's arithmetic D-modules on homogeneous spaces to locally analytic representations of p-adic reductive groups. This is work in progress with D. Patel and M. Strauch.

P. Schneider (Université de Münster)
Titre : Rigid character groups, Lubin-Tate theory, and (phi,Gamma)-modules
Résumé : The talk will describe work in progress with B. Xie in which we build, for a finite extension L of Q_p, a new theory of (phi,Gamma)-modules whose coefficient ring is the ring of holomorphic functions on the rigid character variety of the additive group o_L, resp. a "Robba" version of it.

T. Tsuji (Université de Tokyo)
Titre : The p-adic Simpson correspondence and Higgs isocrystals
Résumé : The p-adic Simpson correspondence of Faltings between small Higgs bundles and small generalized representations, and another approach for it by A. Abbes and M. Gros both depend on the choice of a certain smooth lifting of the relevant variety. I will give a way to eliminate this dependence by working with a kind of (iso)crystals, which I call Higgs (iso)crystals, instead of bundles. I will also discuss cohomology of Higgs isocrystals and comparison of cohomologies.

J. Weinstein (Université de Boston)
Titre : Moduli of p-divisible groups
Résumé : I will explain why moduli spaces of p-divisible groups become perfectoid spaces at infinite level. This is joint work with Peter Scholze.

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