**CUNY Graduate Center**

**Room 6417**

**Fridays 12:30pm-2:00pm**

**Organized by Alf Dolich**

**Spring 2020**

**March 13**

**The talk is cancelled.**

**Rebecca Coulson**
United States Military Academy

**The Bipartite Diameter 3 Metrically Homogeneous Graphs of Generic Type: Their Ages and Their Almost Sure Theories**

**Abstract**

The class of random graphs famously satisfies a zero-one law: every first-order sentence in the language of graphs is such that the proportion of finite graphs on n vertices which satisfy this sentence goes either to zero or to one as n goes to infinity. The 'almost-sure' theory of the class of finite graphs matches the generic theory of its Fraisse limit - the Rado graph. Interestingly, the almost-sure theory of the class of finite triangle-free graphs does not match the theory of the generic triangle free graph. In this talk, we will discuss another class of graphs which are Fraisse limits defined by forbidden configurations, and we examine two such graphs in particular. We show that for one of the them, its generic theory does match the corresponding almost-sure theory, and that for the other, the generic theory does not match the corresponding almost-sure theory.

**March 6**

**Dave Marker**
University of Illinois at Chicago

**Computability of the countable saturated differentially closed field**

**Abstract**

It's been known since work of Harrington in the early 1970s that computable differential fields have computable differential closures. Recently Calvert, Frolov, Harizanov, Knight, McCoy, Soskova, and Vatev showed that the countable saturated differentially closed field is computable. Their proof involves first creating an effective listing of all types and then using a result of Morley's on existence of computable saturated models. I will give a significant simplification of the enumeration result and, for completeness, sketch Morley's priority construction of a saturated model. Pillay has also given an alternative enumeration argument though ours seems more robust and generalizes to quantifier free types in ACFA.

**February 21**

**Patrick Speissegger**
McMaster University

**A new Hardy field of relevance to Hilbert's 16th problem**

**Abstract**

In our paper, we construct a Hardy field that embeds, via a map representing asymptotic expansion, into the field of transseries as described by Aschenbrenner, van den Dries and van der Hoeven in the recent seminal book. This Hardy field extends that of the o-minimal structure generated by all restricted analytic functions and the exponential function, and it contains Ilyashenko's almost regular germs. I will describe how this Hardy field arises quite naturally in the study of Hilbert's 16th problem and give an outline of its construction. (Joint work with Zeinab Galal and Tobias Kaiser.)

**January 24**

**Special time: 2:00-3:30pm**

**Jinhe Ye**
University of Notre Dame

**A model theoretic adic space**

**Abstract**

Working in the theory of algebraically closed valued fields, Hrushovski and Loeser used the space $\widehat{V}$ of generically stable types concentrating on $V$ to study the topology of Berkovich analytification $V^{an}$ of $V$. In this talk we will present an analogous construction which provides a model-theoretic counterpart $\widetilde{V}$ of the Huber's analytification of $V$. We show that, the same as for $\widehat{V}$, the space $\widetilde{V}$ is strict pro-definable. Furthermore, we will discuss canonical liftings of the deformation retraction developed by Hrushovski and Loeser. This is a joint project with Pablo Cubides Kovacsics.