Where: Math 1311

Speaker: Organizational Meeting () -

Where: Math 1311

Speaker: Koushik Pal (UMCP) -

Where: Math 1311

Speaker: Chris Laskowski (UMCP) - math.umd.edu/~mcl

Abstract: For complete theories in uncountable languages, we show that very few implications exist between existence and uniqueness hypotheses for atomic, prime, and constructable models.

Where: Math 1311

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

Where: Math 1311

Speaker: Tim Mercure (UMCP) -

Where: Math 1311

Speaker: Yevgeniy Vasilyev (Memorial University of Newfoundland and Christopher Newport University) -

Abstract: We consider an expansion of a geometric theory obtained by adding a predicate distinguishing a "dense" independent subset, generalizing a construction introduced by A. Dolich, C. Miller and C. Steinhorn in the o-minimal context. We show that the expansion preserves many of the properties related to stability, simplicity, rosiness and NIP. We also study the structure induced on the predicate, and show that while having a trivial geometry, it inherits most of the "combinatorial" complexity of the original theory.

This is a joint work with A. Berenstein.

Where: Math 1311

Speaker: Richard Rast (UMCP) -

Where: Math 1311

Speaker: Chris Laskowski (UMCP) -

Where: MATH 1311

Speaker: () -

Where: Math 1311

Speaker: Vincent Guingona (Notre Dame) -

Abstract: VC-minimality is a model theoretic property that generalizes both o-minimality and strong minimality. Many interesting theories are VC-minimal, including algebraically closed valued fields. In my talk, I discuss recent developments in the study of VC-minimal theories. First, I examine the problem of computing VC-density in VC-minimal theories. Then, I consider the problem of classifying VC-minimality. For this, I define a new notion called dp-smallness and use this to help distinguish between VC-minimal and non-VC-minimal theories. I conclude with a proof that all VC-minimal ordered fields are real closed.

Where: Math 3206

Speaker: Uri Andrews (University of Wisconsin) -

Abstract: Stability theory attempts to classify the underlying structure of

mathematical objects. The goal of computable mathematics is to understand

when mathematical objects or constructions can be demonstrated computably.

I'll talk about the relationship between underlying structure and

computation of mathematical objects.

Where: Math 1311

Speaker: Chris Laskowski (UMCP) -

Where: Math 1311

Speaker: Douglas Ulrich (UMCP) -

Where: Math 1311

Speaker: Will Boney (Carnegie Mellon) -

Where: Math 1311

Speaker: Chris Laskowski (UMCP) -

Abstract: We construct a uniform family of complete sentences phi(n) in L(omega1, omega) such that

each phi(n) has a model of size aleph(n) but no larger. These sentences have unusual amalgamation spectra.

Where: Math 1311

Speaker: David Kueker (UMCP) -

Where: Math 1311

Speaker: Yevgeniy Vasilyev (Memorial University of Newfoundland and Christopher Newport University) -

Abstract: In a joint work with Alexander Berenstein, we introduce several equivalent conditions, including weak local modularity, weak one-basedness and generic linearity, which provide a common generalization of the "classical" linearity notions used in the strongly minimal, supersimple SU-rank 1 and o-minimal settings, to the general class of geometric theories. One of our main tools, the lovely pair expansion, allows us to find a connection between linearity and the presence of vector spaces over division rings.

Where: Math 1311

Speaker: Richard Rast (UMCP) -

Where: Math 1311

Speaker: Alf Dolich (CUNY -- Kingsborough Community College) -

Abstract: Given a model M, a maximal automorphism is one which fixes as few points in M as possible. We begin by outlining what the correct definition of "as few points as possible" should be and then proceed to study the notion. An interesting question arises when one considers the existence of maximal automorphisms of countable recursively saturated models. In particular an interesting dichotomy arises when one asks whether for a given theory T all countable recursively saturated models of T have a maximal automorphism. Our primary goal is to determine which classes of theories T lie on the positive side of this dichotomy. We give several examples of such classes. Attacking this problem requires a detailed understanding of recursive saturation, which we will also review in this talk.

Where: Math 1311

Speaker: Justin Brody (Goucher College) -

Abstract: Let $K$ be a class of structures and $\leq$ a notion of strong substructure on $K$.

We will discuss conditions under which the $(\K, \leq)$ admits a structure which is

injective (for $A \leq B$, strong embeddings of $A$ extend to strong embeddings of $B$) but not locally finite (there is some finite substructure which has no finite closure). We will also examine a conjecture of Larry Moss', which states that there is a such a structure for $K$ the class of finite graphs and $A \leq B$ whenever $A$ is isometric in $B$.

Where: Math 1311

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