*** NOTE: during daylight savings time, the clock for this seminar REMAINS standard, GMT ***
E.g. 16:30 GMT = 17:30 UK time.
Zoom ID: 884 0948 8227
The seminar will focus on various expansions of ominimal structures, such as those with ominimal open core, dminimal structures, Hstructures, lovely pairs, RCVFs, CODFs, distal and general NIP. We target talks on pure model theory and applications. The intention is to run the seminar once every two weeks. The exact times may slightly vary, so please check below.
Upcoming talks:
April 26, 2021 (Monday)  Time: 16:30 GMT
Kobi Peterzil  University of Haifa
Title: Interpretable fields in various valued fields
Abstract:
Difficulties in analyzing interpretable objects arise when we lack (a simple) elimination of imaginaries. It turns out that in several dpminimal settings it is possible to circumvent this difficulty by focusing on onedimensional subsets
and by reducing these to several relatively understandable sorts.
We consider an interpretable field F in either a real closed valued field K or Tconvex expansions of K. In this case one can reduce the analysis to the four sorts K, k, the value group, and K/O (for O the valuation ring), then eliminate the last two sorts, and conclude that F is either definable in the field K or in k. As a result, F is definably isomorphic to K,K(i), k or k(i).
Similar analysis can be carried out in certain Pminimal structures (in particular, in padically closed fields), and probably more.
(part of a joint work with Y. Halevi and A. Hasson)
May 10, 2021 (Monday)  Time: 16:30 GMT
Deirdre Haskell  McMaster University
Title: TBA
Abstract: TBA
Past talks:
April 12, 2021 (Monday)  Time: 16:30 GMT
Alexi Block Gorman  University of Illinois at UrbanaChampaign
Title: Fractal Dimensions and Definability from Büchi Automata
Abstract: Büchi automata are the natural extension of finite automata, also called finitestate machines, to a "machine" that accepts infinitelength inputs. We say a subset X of the reals is rregular if there is a Büchi automaton that accepts (one of) the baser expansions of every element in X, and rejects the baser expansions of each element in its complement. We can analogously define rregular subsets of higher arities of the reals, and these sets often exhibit fractallike behaviore.g., the Cantor set is 3regular. There are several knownand remarkableconnections in logic to Büchi automata, including the fact that the expansion of the real additive group by every rregular subset of [0,1] (for some fixed positive integer r) interprets the monadic secondorder theory of the natural numbers with successor. In this talk, I will focus on some of the geometric behavior of closed rregular sets in terms of fractal dimensions, and discuss how closed rregular subsets of [0,1] with and without integer Hausdorff dimension form a dichotomy in terms of first order definability in expansions of the real additive group by a predicate for a specific rregular set.
➯ RECORDING
March 29, 2021 (Monday)  Time: 16:30 GMT
Vincenzo Mantova  University of Leeds
Title: A survey on exponentialalgebraic closure
Abstract:
Zilber conjectured that complex exponentiation is quasiminimal in 1997 (if not before) and produced different quasiminimal structures. He later formulated the exponentialalgebraic closedness conjecture (EAC), which would imply quasiminimality of complex exponentiation.
I will summarise what has been proved so far around EAC, including extensions to abelian exponentials, modular functions, the special case of raising to powers, and an odd spinoff with ominimal open core.
➯ RECORDING
March 15, 2021 (Monday)  Time: 16:30 GMT
Rosario Mennuni  Universität Münster
Title: The domination monoid in ominimal theories
Abstract:
The product of invariant types and dominationequivalence are not
always compatible but, when they are, they allow to define the
"domination monoid" associated to a monster model U of a firstorder theory. In the superstable case, this object parameterises
"finitely generated saturated extensions of U" and how they can be
amalgamated independently. After recalling the basic definitions
and facts, I will talk about some results from my thesis,
concerning the study of this monoid in a different context, that of
ominimal theories. This includes a reduction of the problem to
showing generation by classes of 1types, and a proof that this
holds in RCF. I will then discuss the open problem of showing
generation by 1types in general, and some possible lines of
attack.
➯ RECORDING
March 1, 2021 (Monday)  Time: 16:30 GMT
Vahagn Aslanyan

University of East Anglia
Title: Blurrings of the jfunction
Abstract: I will define blurred variants of the jfunction and its derivatives, where blurring is given by the action of a subgroup of GL_{2}(ℂ). For a dense subgroup (in the complex topology) an Existential Closedness theorem holds which states that all systems of equations in terms of the corresponding blurred j with derivatives have complex solutions, except where there is a functional transcendence reason why they should not. The proof is based on the AxSchanuel theorem and Remmert's open mapping theorem from complex geometry. For the jfunction without derivatives we prove a stronger theorem, namely, Existential Closedness for j blurred by the action of a subgroup which is dense in GL_{2}^{+}(ℝ), but not necessarily in GL_{2}(ℂ). In this case apart from the AxSchanuel theorem and some basic complex geometry, ominimality is also used in the proof (I will present the proof in this case). If time permits, I will also discuss some model theoretic properties of the blurred jfunction such as stability and quasiminimality. This is a joint work with Jonathan Kirby.
➯ RECORDING
February 15, 2021 (Monday)  Time: 16:30 GMT
Elliot Kaplan 
University of Illinois UrbanaChampaign
Title: Generic derivations on ominimal structures
Abstract: Let T be a model complete ominimal theory which extends the theory of real closed ordered fields (RCF). We introduce Tderivations: derivations on models of T which cooperate with Tdefinable functions. The theory of models of T expanded by a Tderivation has a model completion. If T = RCF, then this model completion is the theory of closed ordered differential fields (CODF) as introduced by Singer. We can recover many of the known facts about CODF (open core, distality) in our setting. This is joint work with Antongiulio Fornasiero.
➯ RECORDING
February 1, 2021 (Monday)  Time: 16:30 GMT
Itay Kaplan  Hebrew University of Jerusalem
Title: Compressible types in NIP theories
Abstract: I will present some work in progress joint with Martin Bays and Pierre Simon. I will discuss compressible types and relate them to uniform definability of types over finite sets (UDTFS), and to uniformity of honest definitions. All notions will be defined during the talk.
➯ RECORDING
January 18, 2021 (Monday)  Time: 16:30 GMT
Tingxiang Zou  Universität Münster
Title: Geometric random graphs
Abstract: Geometric random graphs are graphs on a countable dense set of some underlying metric space such that locally in any ball of radius one, it is a random graph. The geometric random graphs on R^n and on circles have been studied by probabilists and graph theorists. In this talk we will present some model theoretic views. In particular, we will show that under some mild assumptions, the geometric random graphs based on a fixed metric space will have the same theory. We will also talk about some geometric properties of the underlying metric space that can be recovered from the graphs. This is a work in progress joint with Omer BenNeria and Itay Kaplan.
➯ RECORDING
January 4, 2021 (Monday)  Time: 16:30 GMT
Chris Miller  Ohio State University
Title: Connectedness in structures on the real numbers
Abstract: We consider structures on the set of real numbers having the property that connected components of definable sets are definable. Our main analyticgeometric result is that any such expansion of the real additive group by boolean combinations of closed sets (of any arities) is either ominimal (with respect the usual order) or undecidable, and if the set of integers is definable, then so is integer multiplication. It is known that all ominimal structures on the real line have the property, as do all expansions of the real field that define the integers (easy modulo some basic descriptive set theory). We show that fusions of the real ordered additive group with expansions of the ring of integers are also examples. All results hold with "connected component" replaced by "path component" or "quasicomponent". (Joint with A. Dolich, A. Savatovsky and A. Thamrongthanyalak. Preprint available on MODNET and arXiv.)
➯ RECORDING
December 21, 2020 (Monday)  Time: 16:30 GMT
Christian d'Elbée  Hebrew University of Jerusalem
Title: Generic expansions by a reduct
Abstract: Consider the expansion T_{S} of a theory T by a predicate for a submodel of a reduct T_{0} of T. This generalizes the generic predicate construction and some theories of lovely pairs. We present a setup in which this expansion admits a model companion TS. We show that the nice features of the theory T transfer to TS. In particular, by studying independence relations, we find conditions for which this expansion preserves the NSOP_{1}, simplicity or stability of the starting theory T. We will also give concrete examples of new modelcompanion obtained by this process, among them new NSOP_{1} theories such as the expansion of an algebraically closed field of positive characteristic by an additive subgroup (ACFG) and the expansion of an algebraically closed field of any characteristic by a generic multiplicative subgroup. This construction also gives some very wild expansions of fields, such as the expansion of an algebraically closed valued field of positive characteristic by a generic additive subgroup, which has TP_{1} and TP_{2}.
➯ RECORDING
December 7, 2020 (Monday)  Time: 16:30 GMT
Artem Chernikov  University of California, Los Angeles
Title: Distality in valued fields and related structures
Abstract:
In this talk we discuss distality, a modeltheoretic notion of tameness generalizing ominimality, in valued fields and related structures. In particular, we characterize distality in certain ordered abelian groups, provide an AxKochenErshov style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g. the valued differential field of logarithmicexponential transseries, are distal. This relies in particular on a general quantifier elimination result for pure short exact sequences of abelian groups. Joint work with Matthias Aschenbrenner, Allen Gehret and Martin Ziegler.
➯ RECORDING
November 23, 2020 (Monday)  Time: 16:30 GMT
Alexander Berenstein  Universidad de Los Andes
Title: A review of expansions by predicates and some preservation theorems
Abstract: We say that a theory is geometric if the algebraic closure satisfies the exchange property and eliminates the quantifier exists infinitely.
Examples include dense ominimal theories, strongly minimal theories and SUrank one theories. In this talk we will introduce geometric theories, review
some of its expansions by predicates and the structural properties (stability, simplicity, NIP, NTP2) that these expansions preserve.
➯ RECORDING
