Joseph Ayoub

Oliver Röndigs (left), Joseph Ayoub (right), Oberwolfach 2008

Joseph Ayoub (* 1980 ) is a French mathematician who studies algebraic geometry .

Ayoub received his doctorate in 2006 from Fabien Morel at the University of Paris VII ( Les six operations de Grothendieck et le formalisme des cycles evanescents dans le monde motivique ). As a post-doctoral student , he was at the Institute for Advanced Study in 2006/07 . He is a professor at the University of Zurich .

He deals with periods of algebraic varieties and the theory of motifs . Among other things, he proved a geometric version of the conjecture about periods by Alexander Grothendieck or the (stronger) conjecture about periods by Maxim Kontsevich and Don Zagier .

In 2014 he was invited speaker at the International Congress of Mathematicians in Seoul ( A guide to (étale) motivic sheaves ).

In 2017 he announced proof of the conservatism conjecture for Chow motifs .

Fonts (selection)

Periods and the conjectures of Grothendieck and Kontsevich-Zagier. Newsletter of the European Mathematical Society, March 2014, issue 91, online edition of the issue (pdf)
Une version relative de la conjecture des périodes de Kontsevich-Zagier. Annals of Mathematics (2), Volume 181, 2015, pp. 905-992
L'algèbre de Hopf et le groupe de Galois motiviques d'un corps de caractéristique nulle, 2 parts, Journal for pure and applied mathematics (Crelles Journal), Volume 693, 2014, pp. 1-149, 151-226
Motifs des variétés analytiques rigides. Mémoires de la SMF 140-141.2015
with Steven Zucker: Relative Artin Motives and the reductive Borel-Serre compactification of a locally symmetric variety. Inventiones Mathematicae, Volume 188, 2012, pp. 277-427, Arxiv
Les six opérations de Grothendieck et le formalisme des cycles évanescents dans le monde motivique, 2 parts, Astérisque, volume 314/315, 2008
The direct extension theorem. J. Group Theory, Vol. 9, 2006, pp. 307-316, Arxiv