Arithmetic and motives

[Workshop] Arithmetic and motives

The two universalities of arithmetic geometry -- the cohomological motivic theory and homotopical anabelian geometry -- have long developed in parallel,with occasional points of contact. The most classical example is given by the mixed Tate category à la Deligne-Goncharov, the corresponding periods à la Brown, and the Galois-Teichmüller perspective on Galois actions.
Recent years have witnessed substantial maturations on both sides. On the motivic side, this includes developments concerning refinements of the Morel-Voevodsky theory to capture non-A¹-invariant phenomena. On the anabelian side, advances include new insights into the geometry of quasi-tripods, into hyperbolic curves of Belyi type, and into further arithmetic and geometric structures related to periods (polylog, Deligne-Ihara). Significant progress has also been made in étale homotopy theory that serves as a bridge between the two, including developments in Friedlander's quasifibration method, and through higher-categorical formulations via the infinity-category of profinite anima.

The aim of this workshop is to bring together leading researchers and dynamic experts from these areas and to foster new interactions between anabelian and motivic approaches to arithmetic geometry, that go beyond the elementary.
The program will consist of survey lectures, research talks presenting recent advances, and Bourbaki-style expository presentations on some of the most recent developments in the fields.