Schedule and Abstracts

Schedule

All times are in BST (UTC+1).

8:55 Conference welcome

9:00 Francesco Gallinaro

9:45 Eugenio Colla

10:30 Break

11:00 Vincent Bagayoko

11:45 Stefan Ludwig

12:30 Lunch

13:30 Soinbhe Nic Dhonncha

14:15 Shahar Oriel Kagan

15:00 Mostafa Mirabi

15:45 Break

16:00 Frank Wagner

17:00 Close

Speakers and Abstracts

Vincent Bagayoko (Université de Mons, Ecole Polytechnique): Towards a composition law on surreal numbers via hyperseries

Conway's class No of surreal numbers has proved to be a fertile playing field in which several tame first-order theories, that extend the theory of dense linear orders without endpoints, find a natural model. This includes the theories of real numbers as an ordered group, an ordered field, an exponential ordered field, and the elementary theory of transseries as an ordered valued differential field - all of which are model complete and decidable. I would like to partly extend this picture to a yet unspeficied theory of ordered differential fields of functions equipped with a law of composition. This turns out to be related to the definition of a structure of field of hyperseries on No. I will introduce the notion of hyperseries and my work towards that goal. This includes joint work with Joris van der Hoeven, Elliot Kaplan and Vincenzo Mantova.

Eugenio Colla (Università di Torino): Ramsey monoids

Recently, Solecki introduced the notion of Ramsey monoid to produce a common generalization to famous theorems in Ramsey theory such as Hindman's theorem, Carlson's theorem, and Gowers' FIN_k theorem.

In this framework, Hindman's theorem states that the monoid of one element is Ramsey, while Carlson's and Gowers' theorems say that some other particular monoids are Ramsey. In joint work with Claudio Agostini, we characterize the class of finite Ramsey monoids by simple algebraic means. This extends seminal results by Solecki.

Francesco Gallinaro (University of Leeds): Around exponential-algebraic closedness

The exponential algebraic closedness conjecture, formulated by Zilber in his study of the model theory of complex exponentiation, predicts that all systems of exponential polynomial equations which do not contradict Schanuel's conjecture have a solution in the complex numbers. Similar questions, based on analogues of Schanuel's conjecture, arise in the study of other analytic functions, such as the exponential maps of abelian varieties and the modular j-function. In this talk I'll state these conjectures stressing their model theoretic consequences and discuss some partial results, focusing on the abelian variety case.

Stefan Ludwig (University of Münster): Metric valued fields in continuous logic

By work of Ben-Yaacov complete valued fields with value groups embedded in the real numbers can be viewed as metric structures in continuous logic. For technical reasons one has to consider the projective line over such a field rather than the field itself.

In this talk we introduce the above setting and give a classification of the complete theories of metric valued fields in equicharacteristic 0 in terms of their residue field and value group. This can also be seen as an approximate version of the Ax-Kochen-Ershov principle from classical discrete model theory. As a second result we give a negative answer to a question of Ben-Yaacov on the existence of a model companion for metric valued fields enriched with an isometric automorphism.

Mostafa Mirabi (Wesleyan University): Asymptotic classes of finite trees

In this talk first, we discuss the notion of asymptotic classes which was introduced by Macpherson and Steinhorn in 2008. Then we discuss some examples. Finally, as long as time permits, I will try to explain an idea of how to characterize N-dimensional asymptotic classes of finite trees (and their expansions). This is joint work (in progress) with Cameron Hill.

Soinbhe Nic Dhonncha (University of Manchester): Modules and Categories

TBC.

Shahar Oriel Kagan (Hebrew University of Jerusalem): An omega-categorical, strictly stable small theory with a "large" Polish structure

A Polish structure is a pair (G, X) where G is a Polish group acting on a set X so that the stabilizer of any singleton is a closed subgroup of G. We say that (G, X) is small when for every n in N there are only countably many orbits on X^n. Given a countable structure M, the pair (Aut(M), S(M)) is a Polish structure.

It was conjectured in the article "Definable topological dynamics" by Krzysztof Krupiński that (Aut(M), S(M)) is small whenever M is a saturated model of a small NIP theory. We explain why Hrushovski's omega-categorical, strictly stable pseudoplane P refutes the conjecture and give an outline for the proof that (Aut(P), S(P)) is not small. This is a joint work with Isabel Muller under the supervision of Itay Kaplan.

Frank Wagner (Université Claude Bernard Lyon 1): Linearisation in finite-dimensional theories

We shall define a general notion of dimension, and study groups and rings whose interpretable sets carry such a dimension. In particular, we obtain definability results for dimensional fields and domains.

We shall apply this to prove a general linearisation result for an unbounded set of endomorphisms of a finite dimensional connected abelian group.