The homology-homotopy frontier in arithmetic geometry

[Conference] The homology-homotopy frontier in arithmetic geometry

This conference will report on recent progress at a newly permeable interface between the homotopy and (co)homology approaches in arithmetic geometry -- related to anabelian homotopy theory and (motivic) linear Galois representations and Tannaka formalism -- as can be seen in: (a) Meta-abelian anabelian geometry (e.g., m-step reconstructions for curves and fields, abelian-by-central approach, section conjecture); (b) Non-abelian Chabauty theory, which stands at the motivic and nearly-abelian frontier (e.g., with Selmer sections, approximation of rational points, and mixed Tate motives via iterated integrals); (c) The monodromy method in local systems and Tannaka formalism; (d) p-adic Hodge theory and mixed Hodge structures whose period maps indicate special loci of interest inside moduli spaces (and some algebraic vs analytic frontiers).

The goal of this conference is to establish an overarching perspective, where the explicit and gripping nature of the cohomology approach on the one hand and the panoptic nature of anabelian-homotopic theory on the other enrich each other.