Where: Kirwan Hall 1311

Speaker: Organizational meeting () -

Where: Kirwan Hall 1311

Speaker: Caroline Terry (UMCP) -

Abstract: The study of structure and enumeration for hereditary graph properties has been a major area of research in extremal combinatorics. Over the years such results have been extended to many combinatorial structures other than graphs. This line of research has developed an informal strategy for how to prove these results in various settings. In this talk we formalize this strategy. In particular, we generalize certain definitions, tools, and theorems which appear commonly in approximate structure and enumeration theorems in extremal combinatorics. Our results apply to classes of finite L-structures which are closed under isomorphism and model-theoretic substructure, where L is any finite relational language with maximum arity at least two.

Where: Kirwan Hall 1311

Speaker: Christian Rosendal (University of Illiniois, Chicago and UMCP) -

Abstract: We present a framework for investigating the large scale geometry or geometric group theory of automorphism groups of countable first order structures, which extends he geometric theory of countable discrete and locally compact groups. Within this framework, we show how the geometric structure of automorphism groups is reflected in model theoretical properties of the underlying first order structure.

Where: Kirwan Hall 1311

Speaker: Cameron Hill (Wesleyan University) -

Abstract: Given an amalgamation class K of finite structures, one recovers a generic model M, and if M has the finite sub-model property, one can ask about how Hrushovski-style pseudo-finite dimensions interact with the theory of M. In this talk, I will discuss how some discrete mathematical properties of K — namely, having a 0,1-law or having a Ramsey-lift — can be seen to govern this interaction. I will also discuss how these observations may suggest approaches to settling the question of the pseudo-finiteness of the Henson graph.

Where: Kirwan Hall 1311

Speaker: Alice Medvedev (City College, CUNY)

Where: Kirwan Hall 1311

Speaker: Gabriel Conant (University of Notre Dame) - https://www3.nd.edu/~gconant/

Abstract: We discuss some recent work concerning expansions of the group Z of integers, which are tame with respect to model theoretic dividing lines such as stability and dp-rank. Our focus is on the ordered group of integers (also called Presburger arithmetic), which is a well-known example of a dp-minimal expansion of Z. It was asked by Aschenbrenner et. al. whether every dp-minimal expansion of Z is a reduct of Presburger. We present a result in the opposite direction: there are no intermediate structures strictly between the group of integers and Presburger arithmetic. The proof of this result uses Cluckers' cell decomposition for Presburger sets, as well as work of Kadets on the geometry of convex polyhedra.

Where: Kirwan Hall 1311

Speaker: Vincent Guingona (Towson University) -

Abstract: I discuss the characterization of various model theoretic dividing lines via the collapse of generalized indiscernibles. For example, S. Shelah showed that a theory is stable if and only if all order indiscernibles are set indiscernible and L. Scow showed that a theory has NIP if and only if all ordered graph indiscernibles are order indiscernible. I give other similar characterizations for dp-rank and rosiness. Finally, I explore means of framing all of these results in a general context. This work is joint with C. Hill and L. Scow.

Where: Kirwan Hall 1311

Speaker: Alfred Dolich (CUNY) -

Abstract: We consider theories T expanding that of densely ordered Abelian groups with the property that for any model M of T and any definable subset X of M if X is infinite then X has non-empty interior. We call such theories visceral. Visceral theories arise naturally when considering dp-minimal theories. We show that in many ways visceral theories behave much like weakly o-minimal theories in that definable functions are piecewise continuous and definable sets admit a weak form of cell decomposition. Yet crucially, in a visceral theory there does not appear to be any form of local monotonicity for definable functions.

Where: Kirwan Hall 1311

Speaker: Ermek Nurkhaidarov (Penn State -- Mont Alto) -

Where: Kirwan Hall 1311

Speaker: Chris Laskowski (UMCP) -

Where: Kirwan Hall 1311

Speaker: Allen Gehret (University of Illinois, Urbana-Champaign) -

Abstract: $H$-fields are ordered differential fields which serve as an abstract generalization of both Hardy fields (ordered differential fields of germs of real-valued functions at $+\infty$) and transseries (ordered valued differential fields such as $\mathbb{T}$ and $\mathbb{T}_{\log}$). A \emph{Liouville closure} of an $H$-field $K$ is a minimal real-closed $H$-field extension of $K$ that is closed under integration and exponential integration. In 2002, Lou van den Dries and Matthias Aschenbrenner proved that every $H$-field $K$ has exactly one, or exactly two, Liouville closures, up to isomorphism over $K$. Recently (in arxiv.org/abs/1608.00997), I was able to determine the precise dividing line of this dichotomy. It involves a technical property of $H$-fields called $\lambda$-freeness. In this talk, I will review the 2002 result of van den Dries and Aschenbrenner and discuss my recent contribution.

Where: Kirwan Hall 1311

Speaker: Alexei Kolesnikov (Towson University) -

Where: Kirwan Hall 1311

Speaker: Organizational meeting () -

Where: Kirwan Hall 1311

Speaker: Christian Rosendal (UIC and UMCP) -

Where: Kirwan Hall 1311

Speaker: Vincent Guingona (Towson University) -

Where: Kirwan Hall 1311

Speaker: Douglas Ulrich (UMCP) -

Where: Kirwan Hall 1311

Speaker: Danul Gunatilleka (UMCP) -

Where: Kirwan Hall 1311

Speaker: David Sherman (University of Virginia) -

Abstract: Historically, model theory has not had much influence on functional analysis. One reason is that the ultrapowers appropriate for analysis do not quite have the same model theoretic significance as their classical counterparts. An elegant recent solution -- not the first -- is to switch to a logic in which truth values are drawn from the interval [0,1]. This "continuous model theory" is natural for analysts and has opened up a flurry of interaction between the two fields. I will try to explain what this approach is, where it came from, and what kinds of things happen when model theorists start playing with Banach spaces, C*-algebras, etc.

Where: Kirwan Hall 1311

Speaker: Justin Moore (Cornell University) -