IHES Annual Report 2020 | 35

Joseph AYOUB Mathematics, professor, Universität Zürich.

JOSEPH AYOUB has finalized his project, in collaboration with Martin Gallauer and Alberto Vezzani, on motives in rigid analytic geometry. This work offers a systematic study of motivic sheaves over general rigid analytic spaces and develops their six-functor formalism. It also offers a new method for reducing questions on rigid analytic motives to questions on usual algebraic motives. Moreover, Joseph Ayoub continued his work on anabelian representations of the motivic Galois group. This work establishes a motivic version of Pop's theorem that identifies the motivic Galois group with the automorphism group of the functor, which associates an algebraic

variety with its appropriately completed fundamental groupoid.

SCIENTIFIC ACTIVITY

DISTINCTIONS

Best PhD thesis in mathematics, Fondation E.A.D.S. (2006) Cours Peccot, Collège de France (2009) Invited Speaker ICM (2014) K theory Prize (2014)

Editor of: Épijournal de Géométrie Algébrique Annales Henri Lebesgue Annals of K theory

CONFERENCES

France Séminaires de géométrie arithmétique et motivique, Laboratoire Analyse, Géométrie et Applications, Institut Galilée, Université Paris 13 (24 January) Représentations anabéliennes du groupe de Galois motivique (seminar)

Autour des cycles algébriques, Institut de Mathématiques de Jussieu Paris Rive Gauche, Paris (12 February) Représentations anabéliennes du groupe de Galois motivique (seminar)

Video conference Electronic Algebraic K-Theory Seminar (15 December) Rigid Analytic Motivic Sheaves (video conference)

PUBLICATIONS

Nouvelles cohomologies de Weil en caractéristique positive Algebra Number Theory 14 (2020) No. 7, 1747-1790.

P1 localisation et une classe de Kodaira Spencer arithmétique Tunisian J. Math. vol. 3 (2021) No. 2, 259-308.

Alexzandria Figueroa and Robert Penner Chair