Algebraic varieties defined over number fields, called arithmetic varieties, can be studied from several points of view: algebraic geometry, algebraic number theory, complex geometry and analysis, non-Archimedean geometry, etc. Historically, these disciplines have been combined for the treatment of Diophantine problems. The usual strategy consists in encoding the different facets of arithmetic varieties in their global invariants, that are objects that systematically measure and constrain the possible integral solutions. They can refer both to the size and to the arithmetic complexity e.g. in the theory of heights, as well as the obstruction for realising certain geometric constructions e.g. in the various cohomological theories. This approach has evolved and has given rise to new topics and questions that are actively being developed today: Arakelov geometry and arithmetic intersections, motives, periods, regulators, etc.

In this conference we propose to gather researchers who approach the global invariants of arithmetic varieties from several angles. We aim to foster the interaction between those interested in fundamental geometric aspects of complex, non-Archimedean and cohomological nature on the one hand, and concrete aspects such as Diophantine problems on the other hand. We hope that the participants will have the opportunity to discover the questions that their peers are facing, and that this will motivate interdisciplinary collaborations.