LOGIC SEMINAR
Spring 2011
Campus map
Wednesday, May 4, 2011
3:45–5:00 p.m.
Speaker: Alexei Kolesnikov,
Towson University
http://pages.towson.edu/akolesni/
Place: Monroe Hall (2115 G Street), Room 267
Title: Generalized
Amalgamation and Homology in Model Theory
Abstract: The first part of this
talk will be a non-technical survey of generalized amalgamation properties in
model theory, with focus on ShelahÕs and ZilberÕs work on excellent classes. The recent research of the
speaker with John Goodrick and Byunghan
Kim on the construction of homology groups is motivated, in part, by the desire
to better understand generalized amalgamation. The second part of the talk will
focus on the construction of homology groups for certain families of functors whose properties are motivated by model theory.
Thursday, April 28, 2011
5:15–6:15 p.m.
Speaker: Wesley Calvert, Southern
Illinois University
http://www.math.siu.edu/calvert/index2.html
Place: Monroe Hall (2115 G Street), Room 267
Title: Degrees
Coded in Geometry
Abstract: It has
been known since the Ph.D. thesis work of Linda Richter in the 1980s that
algebraic structures --- groups, for instance --- can encode Turing degrees in
an intrinsic (isomorphism-invariant) way. From more recent work, we know
that structures arising from algebraic geometry, including schemes, have a
similar capacity. Since much of the difficulty around understanding these
results comes from the definitions in algebraic geometry, a significant part of
the present talk will focus on introducing the structures to be constructed.
Wednesday, April 20, 2011
5:15–6:15 p.m.
Speaker: Byunghan
Kim, Yonsei
University, South Korea
http://web.yonsei.ac.kr/bkim/
Place: Monroe Hall (2115 G Street), Room 267
Title: Tree
Property 1
Abstract: I will talk
about recent joint work (with Hyeung-Joon Kim)
on the notions related to the tree property 1 (TP1)
introduced by Shelah, or equivalently 2-strong
order property. We give a type-counting criterion for TP1 and show
the equivalence of TP1 and k-TP1. Then we
introduce the notions of weak k-TP1 for k>1, and also give type-counting
criteria for them. We do not know whether weak k-TP1 implies TP1, but at
least we prove that each weak k-TP1 implies 1-strong
order property. Our generalization of tree-indiscernibility
results of Dzamonja and Shelah is
crucially used throughout the paper.
Wednesday, April 20, 2011
3:45–5:00 p.m.
Speaker: John Goodrick, University of Andes, Bogot‡, Colombia
http://matematicas.uniandes.edu.co/~goodrick/
Place: Monroe Hall (2115 G Street), Room 267
Title: Homology
Groups for Types in Model Theory
Abstract: We present definitions of
homology groups Hn(p) for a complete
type p in a stable (or simple, or
rosy) theory. We show how these groups relate to certain previously studied
amalgamation properties. We can compute H2(p) ÒexplicitlyÓ for strong types in
stable theories and show that the groups that can occur as H2(p) are precisely the profinite
abelian groups.
Wednesday, April 13, 2011
5:15–6:15 p.m.
Speaker: Joe
Mourad,
Georgetown University
Place: Monroe Hall (2115 G Street), Room 267
Title: Tree Representations,
Arithmetic Hierarchy, and Reverse Mathematics
Abstract: This talk
will be self-contained, but continue with the theme of looking at the
arithmetic hierarchy from the perspective of higher recursion
theory/descriptive set theory. Tree representations of arithmetic sets as well
as basis theorems will be discussed. This will provide a context to give a
brief introduction to reverse mathematics. Model theoretic methods as well as
recursion theoretic methods will be discussed.
Special Joint Logic-Quantum Computing-Topology
Seminar
Thursday, March 31, 2011
6:15–7:15 p.m.
Speaker: Zbigniew Oziewicz, Universidad Nacional Autonoma de Mexico
Place: Monroe Hall (2115 G Street), Room 267
Title: Applied Category Theory:
Graph-Operad Logic (Unified
Approach to Frobenius Algebras: Associative and
Non-Associative)
Abstract:
We
are looking for
necessary and sufficient conditions on low-dimensional algebras to be Frobenius algebras. We introduce the concept of a solvable Frobenius algebra. We formulate Frobenius
algebra within the abelian monoidal
category of operad of graphs.
Wednesday, March 9, 2011
5:15–6:15 p.m.
Speaker: Joe
Mourad,
Georgetown University
Place: Monroe Hall (2115 G Street), Room 267
Title: Foundations of Mathematics
and Constructing Real Numbers, Part III
Abstract: Although
this talk will be self-contained, we will continue to look at systems that give
canonical constructions of real numbers. In the previous talks we stressed the
importance of constructing sets of real numbers in a controlled way and of
representing such sets as single objects. We will apply this strategy to Pi^0_n
and Sigma^0_n classes by first taking the complements and expressing them as
Pi^1_1 classes and then looking at the complement again as a Sigma^1_1 class.
Connections to uniformization theorems such as the
Kondo-Addison Theorem and to questions in reverse mathematics will be made.
Wednesday, March 2, 2011
5:15–6:15 p.m.
Speaker: Dmitry Trushin,
Moscow State University, Moscow
Place: Monroe Hall (2115 G Street), Room 267
Title: Differential Nullstellensatz
Abstract: In this lecture,
I will discuss a naive version of a geometric approach to differential
equations. This approach allows us to study differential equations using
methods of algebraic geometry. Since many results in differential algebra
appeared in model theory, a relation of differential algebra with model theory
will be shown. I will discus polynomials and formulas, differential closedness and saturation, quantifier elimination and constructibility, Noetherian
condition and stability, and the relation between the space of types and the
spectrum with constructible topology.
Wednesday, February 23, 2011
5:15–6:15 p.m.
Speaker: Joe
Mourad,
Georgetown University
Place: Monroe Hall (2115 G Street), Room 267
Title: Foundations of Mathematics
and Constructing Real Numbers, Part II
Abstract: Although
this talk will be self-contained, we will continue to look at systems that give
canonical constructions of real numbers. The notions of stages and levels in
such constructions will be made precise and impredicate
systems will be presented. It will turn out that representations in terms of
trees are very important. We will explore how to canonically construct these
trees. The connection to uniformization theorems such
as the Kondo-Addison Theorem will be made.
Wednesday, February 16, 2011
5:15–6:15 p.m.
Speaker: Joe
Mourad,
Georgetown University
Place: Monroe Hall (2115 G Street), Room 267
Title: Foundations of Mathematics
and Constructing Real Numbers, Part I
Abstract: We will
look at construction of real numbers throughout history with an eye to seeing
how our conception of Mathematics grows along with the complexity of the real
numbers that are constructed. We will see how this conception has to lead to
current research programs in the Foundations of Mathematics. This talk
will be very elementary with the continuation the following week, touching on
current research questions.
Wednesday, February 9, 2011
5:15–6:15 p.m.
Speaker: Valentina
Harizanov, GWU
Place: Monroe Hall (2115 G Street), Room 267
Title: Computable Binary Trees and Their
Paths
Abstract: An effectively closed set may be
viewed as the set of all infinite paths through a computable binary tree. These sets have been extensively studied in
computability theory. We will show how some problems in algebra and computable
algebra can be translated to problems about effectively closed sets.
Wednesday, February 2, 2011
5:15–6:15 p.m.
Speaker: Patrick O'Neill, Towson State University
Place: Monroe Hall (2115 G Street), Room 267
Title: DNA Splicing Systems, Logically
and Algebraically
Abstract: DNA
computing is attractive for many reasons, both theoretical and practical.
Many different models of DNA computation have been proposed, and universality
results are, in general, easy to obtain. Not all models, however, are so
easily characterized. In particular,
finite splicing systems, though
among the earliest and most biologically relevant models of DNA computation,
have not been shown to conform to any known computational class. After
comparing the expressive power of splicing systems to alternative models, we
review what is currently known about finite splicing systems by presenting
partial characterizations of splicing languages in terms of several canonical
sub-regular classes, as well as describing algebraic and model-theoretic lenses
for viewing the problem. This talk aims to be accessible to
non-biologists as well as non-logicians.