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CIRM – Centre International de Rencontres Mathématiques

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.

Graph theory and combinatorics are thriving fields, closely connected to many other areas of Mathematics such as probability, topology, numbertheory and geometry, as well as optimization and algorithms. Recently, computational aspects are also becoming more and more central to the core theoretical problems of the field. These include flag algebras, reinforcement learning and other AI approaches, including machine assisted proof verification and computer algebra systems. This workshop will cover a broad spectrum of topics from analytic, enumerative, extremal and probabilistic combinatorics, as well as random graphs. Talks will expose the latest trends and methods in these areas and provide a springboard for future collaboration amongst participants.

Bioinformatics and computational biology; Coding and data compression; Combinatorics on words; Data mining; Information retrieval; Natural language processing; Pattern discovery; String algorithms; String processing in databases; Symbolic computing; Text searching and indexing

The conference is supported by le conseil régional de Bourgogne-Franche-Comté, l'Université Bourgogne - Franche-Comté, Dijon Métropole, Università degli Studi di Firenze, l'université Franco Italienne, le Laboratoire d'Informatique de Bourgogne, l'Agence Nationale de la Recherche (Project ANR Pics), National Science Foundation and National Security Agency.

CIRM – Centre International de Rencontres Mathématiques