December 17December 18December 19December 20December 21
08:30-09:30BreakfastBreakfastBreakfastBreakfastBreakfast
10:00-11:00WagnerJahnke (Zoom)Newelski KaplanTsankov
11:00-11:30Coffe BreakCoffe BreakCoffe BreakCoffe BreakCoffe Break
11:30-12:30KaiserGismatullin HrushovskiIvanov Berenstein
12:30-14:00Lunch Break (lunch at 13:00)Lunch Break (lunch at 13:00)Lunch Break (lunch at 13:00)Lunch Break (lunch at 13:00)Lunch Break (lunch at 13:00)
14:00-15:00MoosaFree
Afternoon
and
World Cup Final
at 16:00		 Chernikov (Zoom)RzepeckiMoconja
15:00-16:00BaysPillayRamseyMacpherson
16:00-16:30Coffee BreakCoffee BreakCoffee BreakCoffee Break
16:30-17:30Tent (Zoom)Poster
session		 Terry (Zoom)
17:30-19:00Welcome Reception
19:00DinnerDinnerConference BanquetDinnerDinner

Martin Bays (Universität Münster)
Elekes-Szabó for collinearity on cubic surfaces video
Motivated by the problem of understanding higher dimensional Elekes-Szabó phenomena, we consider the spatial orchard problem on a cubic surface S, which asks for arbitrarily large finite subsets of S with, asymptotically, quadratically many collinear triples. With a smoothness assumption on S, we find that such configurations have to be essentially planar. I will aim to give at least a flavour of the proof, which involves pseudofinite dimension calculus, approximate subgroups, divisor classes, arithmetic genus, and incidence bounds.
Joint work with Jan Dobrowolski and Tingxiang Zou.

Alexander Berenstein (Universidad de los Andes)
Expansions of vector spaces with a generic submodule (joint work with C. D'Elbee and E. Vassiliev) slides and video
We study expansions of a vector space V over a field F, possibly with extra structure, with a generic submodule over a subring R of F. We show that these expansions preserve tame model theoretic properties such as stability, NIP, NTP1, NTP2 and NSOP1.

Artem Chernikov (University of California, Los Angeles)
Convolution semigroups of measures in NIP groups slides
Generalizing Newelski's work in the case of types, we investigate convolution semigroups of invariant/finitely satisfiable Keisler measures on a definable group. Under the NIP assumption we demonstrate that their Ellis group is always trivial, and describe minimal left ideals and idempotent measures under some additional assumptions.
Joint work with Kyle Gannon.

Jakub Gismatullin (Uniwersytet Wrocławski)
On pseudofinite fields and Gromov-Hausdorff distance in metric groups slides
I will report recent elementary results on two topics around pseudofinite fields and metric groups:
Both results are join with students Katarzyna Tarasek and Karol Kuczmarz.

Ehud Hrushovski (University of Oxford)
A stable analogue of Szemeredi's regularity lemma. slides
A NIP version of Szemeredi's regularity lemma, in higher dimensions, has been proved by Chernikov and Starchenko; a pseudo-finite version is due to Tao and Chevalier-Levi. In the spirit of the 'Étale site' analogy between coverings and subsets, I will formulate a (much simpler) statement that makes sense for stable theories; and hope to be able to give a complete proof. Elementary algebraic topology appears in an unexpected way.

Aleksander Ivanov (Politechnika Śląska)
Generalized continuous model theory and stability slides and video
For a countable language L all structures on ℕ form a Polish S∞-space under certain topology. H. Becker has noticed that some basic model theoretic concepts and theorems can be formulated in topological terms as statements about Polish G-spaces. Generalized model theory is an approach which studies G-spaces from this point of view. In 2017 we together with Barbara Majcher-Iwanow extended the concept of nice topologies of Becker to the general case of Polish G-spaces (removing Becker's assumption that G ≤ S∞). As a result typical notions naturally arising for logic actions can be applied in the general case of a Polish G-space. Our approach is based on continuous logic. In my talk I am going to show how these ideas are applied towards analysis of Borel complexity of model theoretic concepts. The case of stable theories is especially interesting from this point of view.

Franziska Jahnke (Universität Münster)
An Ax-Kochen/Ershov principle for deeply ramified fields slides and video
Deeply ramified fields are a generalization of perfectoid fields and were introduced by Gabber and Ramero. As deeply ramified fields may admit immediate extensions, there is no hope for a classical Ax-Kochen/Ershov Theorem, and hence they have eluded model-theoretic machinery so far. In this talk, we present an AKE Theorem for certain perfect deeply ramified fields with a distiguished element t down to the pointed value group and "thickened" residue field. In particular, our Theorem applies to any perfectoid field, choosing a (pseudo)uniformizer for t. As a consequence, we obtain that the perfect hull of the henselization of Fp(t) is an elementary substructure of the perfect hull of Fp((t)). The material presented is joint work with Konstantinos Kartas.

Tobias Kaiser (Universität Passau)
Periods, Power Series, and Integrated Algebraic Numbers slides and video
Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the antiderivative of a power series which is algebraic over the polynomial ring over the rationals and evaluate it at a rational number. We follow this path and close these algebraic power series under taking iterated antiderivatives and nearby algebraic and geometric operations. We obtain a system of rings of power series whose coefficients form a countable real closed field. Using techniques from o-minimality we are able to show that every period belongs to this field. In the setting of o-minimality we define exponential integrated algebraic numbers and show that exponential periods and the Euler constant are exponential integrated algebraic number. Hence they are a good candiate for a natural number system extending the period ring and containing important mathematical constants.

Itay Kaplan (Hebrew University)
On large externally definable sets and NIP slides and video
Suppose that X is an externally definable set of large cardinality, when does it mean that X contains an infinite definable subset? I will discuss this question under NIP. This is joint work with Martin Bays, Omer Ben-Neria and Pierre Simon.

Dugald Macpherson (University of Leeds)
Primitive pseudofinite permutation groups slides and video
In joint work with Martin Liebeck and Katrin Tent, we consider primitive pseudofinite permutation groups, that is, pseudofinite group actions (G,X) such that G preserves no proper non-trivial equivalence relation on X. In a joint paper in Proc LMS in 2010, omega-saturated such groups were essentially classified. I will describe this result and its connections to smooth approximation, more recent related work by others, and also some initial observations towards removing the omega-saturation assumption.

Slavko Moconja (University of Belgrade)
Around Vaught's conjecture for weakly o-minimal theories slides
In our previous work we confirmed Vaught's conjecture for binary, weakly quasi-o-minimal theories (these include binary, weakly o-minimal theories). Our further goal was to try to eliminate the assumption of binarity (which was very significant in our analysis). In the talk we'll present several results in this direction. We'll isolate some properties which imply existence of continuum many countable models. Also we'll discuss the forking-dependence relation in this context, as it's properties play an important role in our analysis.

Rahim Moosa (University of Waterloo)
The degree of nonminimality is at most two and video
James Freitag and I introduced “degree of nomminimality” last year as a way of bounding how many parameters one has to consider to verify the minimality of a finite rank type. At the time we could show that in differentially closed fields (and other similar theories) this degree was bounded by the U-rank of the type plus one. Now, we, together with Remi Jaoui, can show that it is absolutely bounded by two. In fact, if the type is over constant parameters than the degree is at most one.

Ludomir Newelski (Uniwersytet Wrocławski)
Weak heirs, coheirs and the Ellis semigroups slides and video
Abstract: This is a joint work with Adam Malinowski, see http://arxiv.org/abs/2209.14838

How does the (definable) topological dynamics of a group G change when we extend the group elementarily? In particular, are the related Ellis (semi)groups related algebraically?

We work in the following combinatorial set-up. G ≺ H are groups and A ⊆ P(G), B ⊆ P(H) are algebras of sets closed under left group translation, satisfying some additional natural conditions.

Theorem 1. Assume there are generic points in S(B). Then the Ellis groups of S(A) are homomorphic images of some subgroups of the Ellis groups of S(B).

Theorem 2. Assume every minimal left ideal in S(B) is a group. Then the Ellis groups of S(A) are isomorphic to some closed subgroups of the Ellis groups of S(B). The main motivation for the combinatorial set-up is the following model-theoretic set-up, which is its special case. Assume G is a group definable in a model M and M≺*N. We compare the G-flow Sext,G(M) and the G(N)-flow Sext,G(N). Theorems 1 and 2 translate to:

Theorem 1'. Assume there are generic types inSext,G(N). Then the Ellis groups of Sext,G(M) are homomorphic images of some subgroups of the Ellis groups of Sext,G(N).

Theorem 2'. Assume every minimal left ideal in Sext,G(N) is a group. Then the Ellis groups of Sext,G(M) are isomorphic to some closed subgroups of the Ellis groups of Sext,G(N).

The assumptions of Theorems 1 and 2 are dual to each other, just like their proofs. Theorem 1' was already proved in our paper in Israel J.Math. (2012).

The proofs use the dual notions of weak heirs and weak coheirs. We elaborate on them. In the stable case we provide a characterization in terms of local forking. Invoved in the proof of Theorem 1 is a variant of the Ellis structure theorem for some left-continuous semigroups that are not necessarily compact.

Anand Pillay (University of Notre Dame)
Approximate subgroups and topological dynamics (joint with K. Krupiński) video
We recover locally compact models for arbitrary approximate subgroups by topological dynamical methods, obtaining by these means some results of Hrushovski in "Beyond the Lascar group". This involves both the ``generalized Bohr compactification" of Glasner, as well as generalizing the machinery of topological dynamics from actions on compact spaces to actions on locally compact spaces.

Nick Ramsey (University of Notre Dame)
Independence and generically stable partial types
In joint work with Itay Kaplan and Pierre Simon, we introduce a notion of independence called GS-independence, defined in terms of generically stable partial types. We will describe a context, the class of treeless theories, in which this notion is particularly well-behaved and give applications, focusing in particular on the case of NIP treeless theories.

Tomasz Rzepecki (Uniwersytet Wrocławski)
Grothendieck groups and Ellis semigroups slides and video
Every semigroup admits a universal (initial) homomorphism into a group, called the Grothendieck group. If the semigroup is an Ellis semigroup, then this homomorphism is onto and factors through Ellis groups, and in particular, for Ellis groups of automorphism or definable group actions, it seems that it might be a new model-theoretic invariant, which is a quotient of the Ellis group, but is in general distinct.

I will describe the construction of the Grothendieck group, the kernel of the homomorphism from the Ellis group and discuss some related problems and observations.

This is joint work in progress with Krzysztof Krupiński.

Katrin Tent (Universität Münster)
More on simple polish groups
We discuss some general criteria to show that the automorphism group of a homogeneous structure (such as metric spaces, incidence geometries, graphs and hypergraphs) are simple groups (or have some obvious simple quotients) and extend this to some extremely amenable groups.

Caroline Terry (Ohio State)
Higher order stability and quadratic arithmetic regularity lemmas
We present recent work, joint with J. Wolf, in which we define a ternary analogue of the order property, called the functional order properly, and show that subsets of Fpn without the functional order property admit especially strong quadratic decompositions, in which the error part is constrained by linear structure.

Todor Tsankov (Université Claude Bernard Lyon 1)
Extremal models in affine logic
Affine logic is a fragment of continuous logic, introduced by Bagheri, where one allows only affine functions ℝn → ℝ as connectives instead of arbitrary continuous functions. This decreases the expressive power of the logic and provides additional structure on the type spaces: namely, the structure of compact, convex sets. An important role in convex analysis is played by the extreme points of these sets and, unsurprisingly, extremal models, in which only extreme types are realized, are crucial for developing affine model theory. In a joint work with Itaï Ben Yaacov and Tomás Ibarlucía, we develop the basic theory of extremal models. Some highlights include a general integral decomposition theorem (generalizing the ergodic decomposition theorem from ergodic theory) and affine ℵ0-categoricity: theories admitting a unique separable, extremal model.

Frank Wagner (Université Claude Bernard Lyon 1)
Dimensional groups slides and video
I shall generalize Zilber's and Poizat's theorems on field interpretation in soluble non-nilpotent groups and linearization of group actions to the dimensional context (which includes both the finite Morley/Lascar/SU/Thorn rank context and the o-minimal context). Part of the results are joint work with Adrien Deloro.


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