CONFERENCE
Model theory of valued fields
Théorie des modèles des corps valués
29 May – 2 June 2023
The conference will start on Monday morning at 9:00h and will end on Friday afternoon at 15:00h
Scientific Committee
Comité scientifique
Franziska Jahnke (University of Münster)
François Loeser (Sorbonne Université)
Françoise Point (Université de Paris & Université de Mons)
Silvain Rideau-Kikuchi (CNRS, Université de Paris)
Thomas Scanlon (University of California, Berkeley)
Organizing Committee
Comité d’organisation
Zoé Chatzidakis (CNRS, Université de Paris)
Franziska Jahnke (University of Münster)
Silvain Rideau-Kikuchi (CNRS, ENS Paris)
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.
Un des résultats les plus frappants de ces dernières années est la classification faite en 2020 par Will Johnson des corps de dp-rang fini : sous des hypothèses purement combinatoires (la finitude d’une certaine dimension), les corps infinis non algébriquement clos doivent posséder une topologie définissable hensélienne. Ce résultat illustre (et explique en partie) les liens très forts entre la théorie des valuations et la théorie des modèles, liens qui existent depuis les années 1960. Les corps valués sont aussi prépondérants dans les interactions de ces dernières années entre la théorie des modèles et la théorie des nombres ou la géométrie algébrique. Cette rencontre rassemblera des spécialistes des corps valués venant de l’arithmétique et de la théorie des modèles, et leur permettra de mieux connaître et comparer leurs outils, qui sont parfois fort différents. Notre but est de permettre à un dialogue durable de s’établir entre les deux communautés et de promouvoir de nouvelles interactions. Les thèmes principaux de la rencontre seront l’arithmétique des corps valués, la classifation et la théorie des modèles géométrique des corps valués, et la geométrie non-archimédienne modérée.
SPEAKERS
Sylvy Anscombe (Université Paris Cité) Transfer of decidability for existential theories of (valued) fields
Matthias Aschenbrenner (University of Vienna) The model theory of Hardy fields and linear differential equations
Itaï Ben Yaacov (Université Claude Bernard Lyon 1) Polynomials that vanish on many sets of codimension 2
Raf Cluckers (CNRS, Université de Lille & Catholic University of Leuven) Existential uniform p-adic integration and descent for integrability and largest poles
Pablo Cubides-Kovacsics (University of The Andes) Homology groups in algebraically closed valued fields
Françoise Delon (Sorbonne Université) Group Construction in C-minimal Structures
Philip Dittmann (Technical University of Dresden) Ax-Koche-Ershov principle for finitely ramified henselian fields
Yuval Dor (Apple Inc., Israel) Contracting endomorphisms of valued fields
Antoine Ducros (Sorbonne Université) Tropical functions on skeletons
Arthur Forey (EPFL Lausanne) Motivic integration with pseudo-finite residue field and fundamental lemma
Deirdre Haskell (McMaster University) Residue field domination
Martin Hils (University of Münster) Lang-Weil type bounds in finite difference fields
Ehud Hrushovski (University of Oxford) An invitation to globally valued fields
Will Johnson (Fudan University) Around NIP Noetherian domains
Konstantinos Kartas (Sorbonne Université) Beyond the Fontaine-Wintenberger Theorem
Sebastian Krapp (University of Konstanz) Definable convex and henselian valuations on ordered fields
Vlerë Mehmeti (Sorbonne Université) A Hasse principle over Berkovich analytic curves
Samaria Montenegro (University of Costa Rica) Multi topological fields and NTP2
Adele Padgett (McMaster University) The existential closedness problem for analytic solutions of difference equations
Kobi Peterzil (University of Haifa) Interpretable, definably semisimple groups in various valued fields
Michal Szachniewicz (University of Oxford) Existential closedness of ℚ^{alg} as a globally valued field
Mariana Vicaria (University of California, Los Angeles) An Imaginary Ax-Kochen/Ershov principle: the equicharacteristic zero case
Jinhe Ye (Université of Oxford) Beautiful pairs revisited
SPONSORS
