IHES Annual Report 2021 | 3938 | IHES Annual Report 2021
With A. Kislinsky Cluster Construction of the Second Motivic Chern Class Prepublication arXiv:2105.06426.
With M. Kontsevich Spectral Description of Non commutative Local Systems on Surfaces and Non commutative Cluster Varieties Prepublication arXiv:2108.04168.
Alexander GONCHAROV Mathematics, Philip Schuyler Beebe Professor, Yale University.
ALEXANDER GONCHAROV collaborated with Maxim Kontsevich, and established the non-commutative cluster Poisson structure of the moduli space of local systems of vector spaces over a noncommutative field on a decorated surface , equivariant under the action of the modular group of . He constructed a equivariant cluster structure on the dual moduli space of decorated non-commutative local systems on , described by non-commutative cluster coordinates expressed via Gelfand-Retakh's quasi-determinants. He collaborated with Alexei Kislinsky and, for any split semi-simple simply-connected algebraic group , constructed explicitly the
second motivic Chern class of the universal bundle on the classifying space of . He showed that this is essentially equivalent to the construction of the cluster structure on moduli spaces of local systems on decorated surfaces, established jointly with Linhui Shen in 2019. Applications include an explicit construction of the generator of the Picard group of Bun , and a local combinatorial formula for the second Chern class of a bundle, generalizing Gabrielov-Gelfand-Losik's formula for the first Pontryagin class.
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Gold Medal, 18th International Mathematical Olympiad (1976) European Mathematical Society Prize (1992)
Editor of: Selecta Mathematica (New Series) Journal of Noncommutative Geometry
China (P.R.) Cluster Algebras and Related Topics, School of Mathematical Sciences, Shanghai Jiao-Tong University (August 2-6) Cluster Structures on Moduli Spaces of Non-commutative Local Systems on Decorated Surfaces (video conference)
Gretchen and Barry Mazur Chair
Joseph AYOUB Mathematics, Professor, Universität Zürich.
JOSEPH AYOUB continued his research on motives and the cohomology of algebraic varieties. In particular, he completed his work on a motivic version of Pop's theorem, also known as the Ihara-Matsumoto-Oda conjecture. This work gives an anabelian description of the motivic Galois group.
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 Journal of the Institute of Mathematics of Jussieu
France Séminaire d'Arithmétique et de Géométrie Algébrique (SAGA), Laboratoire de mathématiques d Orsay (February 9) Un analogue motivique d'un théorème de Pop (seminar)
Sweden Motives and Hodge Theory, Institut Mittag-Leffler, Stockholm (October 20) Anabelian Representation of the Motivic Galois Group (conference)
Video conference Motivic Geometry Seminar Series (June 2) Anabelian Representation of the Motivic Galois Group (video conference)
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