Title of Seminar: Algebraic Geometry Preprint Seminar 2022
Title of Talk: Pro-étale uniformisation of abelian varieties.
Speaker: Arnab Roy, TIFR Mumbai
Date: November 22, 2022
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Any complex $g$-dimensional abelian variety admits a uniformisation in terms of its topological universal cover (which is $C^{g}$) and a lattice. From the work of Raynaud, Bosch, Lütkebohmert we know that for non-archimedean case there exist a 'uniformization' of abelian varieties, in rigid analytic category in terms of a semi-abelian rigid space and and a discrete lattice. While in the complex uniformization, the universal cover was isomorphic for all $g$-dimensional abelian varieties, the rigid analytic uniformization is not even locally constant (i.e. in the moduli space of abelian varieties). In the category of diamonds introduced by P.Scholze, there exists a new kind of "pro-étale uniformization" in terms of the perfectoid tilde limit and the $p$-adic Tate module of the abelian variety, which remains locally constant. The talk is based on https://arxiv.org/pdf/2105.12604.pdf by Ben Heuer, where the above result is proved. I shall try to explain the main idea and techniques of the proof.
Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Generalized Gibbs ensembles of the Calogero fluid
Speaker: Herbert Spohn, Technical University Munich
Date: November 22, 2022
Time: 23:30:00 Hours
Venue: via Zoom
Abstract: Over recent years there have been widespread activities to understand the hydrodynamic scale of integrable many-body systems. Since such systems have an extensive number of local conservation laws, the standard notion of Gibbs measures has to be extended so to include this very special feature. The Calogero fluid are classical particles in one dimension which interact through the pair potential $1/(\sinh)$ squared. I will explain how the transformation to scattering coordinates relates to the free energy of generalized Gibbs measures.
Title of Talk: Pro-étale uniformisation of abelian varieties.
Speaker: Arnab Roy, TIFR Mumbai
Date: November 22, 2022
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Any complex $g$-dimensional abelian variety admits a uniformisation in terms of its topological universal cover (which is $C^{g}$) and a lattice. From the work of Raynaud, Bosch, Lütkebohmert we know that for non-archimedean case there exist a 'uniformization' of abelian varieties, in rigid analytic category in terms of a semi-abelian rigid space and and a discrete lattice. While in the complex uniformization, the universal cover was isomorphic for all $g$-dimensional abelian varieties, the rigid analytic uniformization is not even locally constant (i.e. in the moduli space of abelian varieties). In the category of diamonds introduced by P.Scholze, there exists a new kind of "pro-étale uniformization" in terms of the perfectoid tilde limit and the $p$-adic Tate module of the abelian variety, which remains locally constant. The talk is based on https://arxiv.org/pdf/2105.12604.pdf by Ben Heuer, where the above result is proved. I shall try to explain the main idea and techniques of the proof.
Title of Seminar: Infosys Chandrasekharan Random Geometry Colloquium
Title of Talk: Generalized Gibbs ensembles of the Calogero fluid
Speaker: Herbert Spohn, Technical University Munich
Date: November 22, 2022
Time: 23:30:00 Hours
Venue: via Zoom
Abstract: Over recent years there have been widespread activities to understand the hydrodynamic scale of integrable many-body systems. Since such systems have an extensive number of local conservation laws, the standard notion of Gibbs measures has to be extended so to include this very special feature. The Calogero fluid are classical particles in one dimension which interact through the pair potential $1/(\sinh)$ squared. I will explain how the transformation to scattering coordinates relates to the free energy of generalized Gibbs measures.