Model theory of valued fields

One of the most striking recent results in model theory is Johnson’s classification, in 2020, of fields of finite dp-rank : under purely combinatorial condition (the finiteness of a certain dimension) infinite non algebraically closed fields must come with a definable henselian topology. This result illustrates (and partially explains) the very strong relationship between valuation theory and model theory that has existed since the 1960’s. Valued fields are also at the center of the interaction between model theory number theory and algebraic geometry which blossomed in the past fifteen years. This conference will bring together specialists from the algebraic, arithmetic and the pure model theory communities that all study valued fields, but with very different tools. Our aim is, by ensuring a continued dialog between these communities, to further exchanges and promote new interactions. Its main focus will be on the arithmetic of valued fields, classification and geometric model theory in valued fields and non archimedean tame geometry.