Explore advanced mathematical logic through this comprehensive conference series examining the intersection of model theory with combinatorics and valued fields. Delve into the relationship between formal logical languages and mathematical structures, analyzing how model theory provides powerful tools for understanding "tame" mathematical structures through their definable sets. Investigate three interconnected themes: model theory's applications to additive combinatorics, Szemerédi regularity lemmas, pseudofinite structures, and NIP theories; the model theory of Henselian valued fields with valuation topology, including motivic integration and Berkovich spaces; and applications in geometry, analysis, and number theory through fields with operators and the Pila-Wilkie counting theorem. Examine cutting-edge research on first-order rigidity of arithmetic groups, model-theoretic distality, hypergraph Ramsey theory, automorphism groups of sparse graphs, stable arithmetic regularity lemmas, and quantitative bounds on semi-algebraic sets. Study advanced topics in valued field theory including C-minimal valued fields, tropical motivic integration, perfectoid spaces, globally valued fields, and definable groups in geometric fields. Learn about recent developments in o-minimal structures, Ax-Schanuel theorems for Shimura varieties, non-archimedean geometry, and p-adic integration techniques, while exploring connections between model theory and diverse mathematical areas from differential equations to algebraic geometry.

Syllabus

Presentation of the T1 2018 : Model theory, combinatorics and valued fields
First order rigidity of high-rank arithmetic groups
Model-theoretic distality and incidence combinatorics
Let's talk about multiple crossings
Pseudo-finite dimensions, modularity, and generalisations of Elekes–Szabo
New Developments in Hypergraph Ramsey Theory
The Algebraic Revolution in Combinatorial and Computational Geometry: State of the Art
Absolute notions in model theory
Modeling limits
Automorphism groups and Ramsey properties of sparse graphs
Rank Bounds for Design Matrices and Applications
On finite dimensional omega-categorical structures and NIP theories
Ramsey classes and sparsity for finite models
More designs
Using nonstandard natural numbers in Ramsey Theory
A stable arithmetic regularity lemma in finite-dimensional vector spaces over fields of prime order
Stable and NIP regularity in groups
Metrizable universal minimal flows and Ramsey theory
A quantitative inverse theorem for the U⁴ norm over finite fields
Quantitative bounds on the topology of semi-algebraic and definable sets
Ramsey theorems for classes of structures with functions and relations
Dimension and automorphisms in the differential field of transseries
On the decidability of ℚªᵇ_p
Multi-valued algebraically closed fields are NTP₂
NIP Henselian fields
Motivic height zeta functions and motivic Euler products
Definability of Berkovich curves
Zero dimensional valuations on equicharacteristic noetherian local domains
Pushing back the barrier of imperfection
Topological transcendence degree
Specialization of difference equations in positive characteristic
C-minimal valued fields
A non-archimedean Ax-Lindemann theorem
Uniform p-adic wave front sets and zero loci of functions of C exp-class
An analogue of o-minimality for valued fields
Virtual rigid motives of definable sets in valued fields
Tropical motivic integration
An introduction to perfectoid spaces and the tilting correspondence
Toward an imaginary Ax-Kochen-Ershov principle
On definability of valuations of finitely generated fields
Motivic integration and p-adic reductive groups
On the axiomatisation of C_p with roots of unity
A tour of globally valued fields
Structure from density
On groups definable in geometric fields
Boundedness and absoluteness of some dynamical invariants in model theory
Strongly minimal groups in o-minimal structures
Ax-Schanuel for Shimura varieties
Disintegrated differential equations and mixing Anosov flows
Abraham Robinson’s legacy in model theory and its applications
On local interdefinability of analytic functions
Definable equivariant retractions onto skeleta in non-archimedean geometry
D-varieties and the Dixmier-Moeglin equivalence
Nonarchimedean integrals as limits of complex integrals
p-adic Integration along the Hitchin Fibration and Applications
Model Theory of Fields with Virtually Free Group Action
Towards Strong Minimality and the Fuchsian Triangle Groups
Definably simple groups in valued fields
Ampleness in strongly minimal structures
On PC-exact saturation