Where: Math 1311

Where: Math 1311

Speaker: Koushik Pal (UMD) - http://www2.math.umd.edu/~koushik/

Abstract: Kikyo and Shelah showed that if T is a first-order theory in some language L with the strict-order property, then the theory T_\sigma, which is the old theory T together with an L-automorphism \sigma, does not have a model companion in L_\sigma, which is the old language L together with a new unary predicate symbol \sigma. However, it turns out that if we add more restrictions on the automorphism, then T_\sigma can have a model companion in L_\sigma. I will show some examples of this phenomenon in two different context - the linear orders and the ordered abelian groups. In the context of the linear orders, we even have a complete characterization of all model complete theories extending T_\sigma in L_\sigma. This is a joint work with Chris.

Where: MTH 1311

Speaker: Chris Laskowski (UMD) - http://www2.math.umd.edu/~laskow/

Where: MTH 1311

Speaker: Alexei Kolesnikov (Towson University) - http://pages.towson.edu/akolesni/

Abstract: A polyadic group (or n-group) is a set with an n-ary operation that satisfies certain natural properties. In this talk, I will introduce the polyadic groups and related objects and will survey some of the results that describe the nature of such groups.

Where: MTH 1311

Speaker: Alexei Kolesnikov (Towson University) - http://pages.towson.edu/akolesni/

Abstract: A polyadic group (or n-group) is a set with an n-ary operation that satisfies certain natural properties. In this second talk, I will describe the results related to Hosszu -- Gluskin theorem about the n-ary groups.

Where: MTH 1311

Speaker: Ermek Nurkhaidarov (Penn State - Mont Alto) - http://www.ma.psu.edu/Academics/31215.htm

Where: MTH 1310

Speaker: Richard R. Rast (UMD) - http://terpconnect.umd.edu/~rastr/

Where: MTH 1311

Speaker: Koushik Pal (UMD) - www2.math.umd.edu/~koushik

Where: MATH 1311

Speaker: Dr. Chris Laskowski (UMCP) -

Where: MATH 1311

Speaker: Tim Mercure (UMCP) -

Where: MTH 1311

Speaker: Tim Mercure (UMD) -

Where: MTH 1311

Speaker: Justin Brody (Goucher College) -

Where: MTH 1311

Speaker: Koichiro Ikeda (Hosei University, Japan) -

Abstract: Evans-Wong proved if a generic structure is omega-categorical then the theory has NSOP_4.

In this talk, we generalize this result.

Slides: https://docs.google.com/open?id=0B-ow7NaULJE0dTNSUXA3TThGQWc

Where: MTH 1311

Speaker: () -

Where: MTH 1311

Speaker: Saugata Basu (Purdue University) - http://www.math.purdue.edu/~sbasu/

Abstract: I will explain how to extend the combinatorial parts of certain well known bounds on the topology (the Betti numbers) of semi-algebraic sets to the general o-minimal setting and mention some applications of such bounds in discrete geometry.

In the second part of the talk I will explain a result of Gabrielov and Vorobjov which reduces the problem of bounding the topology of arbitrary definable sets to that of compact ones, and show how it leads to the problem of proving the existence of triangulations compatible with monotone definable families. I will mention some partial results in this direction.

(The last part of the talk is joint work with A. Gabrielov and N. Vorobjov.)

Where: MTH 1311

Speaker: Koushik Pal (UMD) - www2.math.umd.edu/~koushik

Where: MTH 1311

Speaker: Alexei Kolesnikov (Towson University) -

Abstract: In [1], Hrushovski linked the failure of 3-uniqueness to the existence of a definable groupoid witnessing such failure. He remarked that a continuation of the result to the failure of n-uniqueness, for n greater than 3, would be of interest. This talk is an exposition of my joint work with Goodrick and Kim, in which we define the objects that witness the failure of n-uniqueness, develop their model-theoretic properties, and show that any failure of n-uniqueness must be witnessed by one of these objects.

Where: MTH 1311

Speaker: Chris Laskowski (UMD) -

Where: MTH 1311

Speaker: Alexei Kolesnikov (Towson University) -

Abstract: This talk continues an exposition of my joint work with Goodrick and Kim, in which we define the objects that witness the failure of n-uniqueness, develop their model-theoretic properties, and show that any failure of n-uniqueness must be witnessed by one of these objects. The second part will be devoted to the associativity properties and to a certain group action on the polygroupoids.

Where: MTH 1311

Speaker: Justin Brody (Goucher College) -

Abstract: In [1], Pourmahdian developed a framework for determining the simplicity of generic structures and produced an unstable example. I will present an overview of his paper. If time permits, I will discuss another example which I believe to be simple and make some comments on the obstructions to using Pourmahdian's framework to prove it.

1. Pourmahdian, Massoud. "Simple generic structures." Annals of Pure and Applied Logic 121.2 (2003): 227-260.

Where: MTH 1311

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

Abstract: In the talk we discuss the automorphism group of a countable recursively saturated model of Peano Arithmetic. We show that it recognizes gap stabilizers as well as stabilizers of elements realizing minimal type.

Where: MTH 1311

Speaker: Tim Mercure (UMD) -

Where: MTH 1311

Speaker: Alexei Kolesnikov and Tatyana Sorokina (Towson University) -

Abstract: This two-part talk will describe the main aspects of research in the area of multivariate splines and the algebraic geometry methods currently used in this field. The first part of the talk will focus on the classical methods used in studying multivariate splines; the second part will discuss the methods of algebraic geometry used to compute the dimension of certain spline spaces. The talk will conclude with the discussion of open questions.

Where: MTH 1311

Speaker: Alexei Kolesnikov and Tatyana Sorokina (Towson University) -

Abstract: The second talk in the series of two will describe some of the algebraic geometry methods currently used to answer questions in the field of approximation theory. We will focus on the methods of algebraic geometry used to compute the dimension of certain spline spaces. We will show that the spline spaces can be viewed as a certain homology module and will describe the chain complex that is used to compute the dimension of the homology module. The talk will conclude with the discussion of open questions.

Where: MTH 1311

Speaker: John Baldwin (UIC) -

Abstract: We will expound the following theorem of Shelah:

If a sentence of L_{omega_1, omega} has fewer than 2^{aleph_1} models in aleph_1, then pseudo-closure satisfies exchange (locally). (This requires understanding the notion of pseudo-closure and then a forcing argument.)

This exposition is joint with Laskowski and depends heavily on discussions with Koerwien and Larson as well as Shelah.

Where: MTH 1310

Speaker: Maxx Cho (UMD) -