22 | IHES Annual Report 2020

Bertrand EYNARD Mathematical physics, CEA research director.

In 2020, BERTRAND EYNARD worked on resurgence methods for the non-perturbative resummation of asymptotic series produced by topological recurrence.

SCIENTIFIC ACTIVITY

Ofer GABBER Mathematics, CNRS research director.

OFER GABBER continued his collaborations with Lorenzo Ramero and with Adrian Vasiu. He provided an example of Frobenius non-splitting of excellent regular rings in char p>0, which was explained in a paper by Rankeya Datta and Takumi Maruyama. He contributed an appendix to a paper by Ferrand and found a more general version of the result in which the local connectivity of schemes is preserved by flat morphisms of finite presentation. He also found counterexamples to statements...

SCIENTIFIC ACTIVITY

DISTINCTIONS

Invited Speaker ICM (2014) André Aisenstadt Chair, CRM, Montreal (2015) ERC Synergie "Recursive and Exact New Quantum Theory" (ReNewQuantum) (2018) Prix Mme Claude Berthault, Académie des sciences de Paris (2019)

DISTINCTIONS

Erdős Prize in Mathematics, Israel Mathematical Union (1981) Prix Thérèse Gautier, Académie des sciences de Paris (2011)

PUBLICATIONS

Finiteness and Duality for Étale Cohomology over Certain Generalizations of Tate Algebras Oberwolfach Report 20/2020, doi: 10.4171/OWR/2020/20.

With L. Ramero Foundations for Almost Ring Theory Release 8 Pre-publication arXiv:0409584, http://math.univ-lille1.fr/ ~ramero/hodge.pdf.

With A. Vasiu Purity for Barsotti Tate Groups in Some Mixed Characteristic Situations To appear in Algebraic Geometry.

With D. Ferrand Enveloppe étale de morphismes plats par Daniel Ferrand, et suivi d'un appendice par Ofer Gabber Submitted for publication.

CONFERENCES

Germany Arithmetic Geometry, Mathematisches Forschungsinstitute Oberwolfach (19 -25 July) Finiteness and Duality for Étale Cohomology over Certain Generalizations of Tate Algebras (lecture in a hybrid meeting)

CONFERENCES

United States Homological Mirror Symmetry and Topological Recursion, Simons Collaboration on Homological Mirror Symmetry, University of Miami (27 January 1 February) Topological Recursion: a B-model Method to Compute Gromov-Witten Invariants and Enumerative Geometry I-II-III (3 conferences)

Editor of: Random Matrices, Theory and Applications, World Scientific Annales de l'Institut Henri Poincaré (D) Combinatorics, Physics and their interactions