Algebraic Geometry with “Fancy” Coefficients

Description

Modern algebraic geometry has grown at a very fast pace in the last decades. In particular, the theory of schemes allows to define geometric objects with coefficients other than the real or the complex numbers, giving rise to new branches of geometry, devoted to the exploration of the links between the “classical" world and these new “fancy" settings.

The aim of the conference is to bring together young researchers and experts of various arithmetic techniques, in such a way to produce fertile exchanges and discussion about analogies and differences in their approach. The focus will be on five topics, selected among those that have produced the most striking applications over the last few years:

- Positive characteristic algebraic geometry
- Diophantine geometry and Arakelov theory
- Nonarchimedean geometry
- Cohomological methods
- Covers of curves and fundamental groups

Some of the talks will have a special format, with a 45 minutes introduction aiming to introduce young mathematicians to the tools that will be used in the main part of the talk. This will allow all participants to engage with topics that are not directly related to their research.