UNTLS is an informal, participating seminar devoted to the research
of foundations
of mathematics. The talks cover a variety of topics, ranging from introduction
to basics to presentation of recent research advances. Some of the
talks will
not be very different from graduate classes; others are in workshop
style. Click here
to see a list of old talks in this seminar. It is possible for UNT
math graduate students
to earn credits by attending the seminar. If you have any questions,
contact
jackson@unt.edu or sgao@unt.edu.
This semester (Fall 2007) the seminar meets Friday 2:00-3:30pm in GAB 438.
An announcement will be made here and through the department prior to every
meeting of the seminar. Come back to this page often for current information.
(Refresh your browser in order for the most recent changes to show.)
October 19, 2007
Speaker: Brandon Seward (UNT)
Title: A coloring property for countable groups, part 2
October 12, 2007
Speaker: Brandon Seward (UNT)
Title: A coloring property for countable groups, part 1
Abstract: We say that a countable group G has the coloring property if there is
a {0,1}-coloring c on G such that for all s in G there is a finite subset T of G so
that for all g in G there is t in T with c(gt) different from c(gst). This talk covers
joint work with Dr. Gao and Dr. Jackson in identifying groups which have the
coloring property. We will review some of our earlier results as well as present
more recent developements.
September 28, 2007
Speaker: Dan Walker (UNT)
Title: An introduction to non-standard analysis, Part II
September 21, 2007
Speaker: Dan Mauldin (UNT)
Title: Selection and separation theorems and problems for probability measures
Abstract: Let X be a Polish space and let Pr(X) be the Polish space of probability
measures defined on the Borel subsets of X in the weak* topology. The "first
support separation" theorem (proven
by myself, Priess and Weizsacker) for
probability measures states that if A1 and A2
are two analytic sets of probability
measures such that A1 and A2 are measure
convex and each measure in A1
is singular or orthogonal to each measure in A2, then there is
a Borel set B in X
such that each measure in A1 is supported on B and each measure in A2 is
supported on the complement of B. This separation theorem does not necessarily
hold if we do not assume the sets are measure convex. I will describe an example
due to Blackwell illustrating this. I will describe what sort of separation one can get
using Martin's axiom and some
applications to the existence of a "perfect statistic" for
probability transition kernels. Finally I will discuss some still unsolved
problems
concerning this circle of ideas.
September 14, 2007
Speaker: Dan Walker (UNT)
Title: An introduction to non-standard analysis
Abstract: We will develop the notion of non-standard analysis, which is a way of
formulating classical analysis on R without the use of limits. Central to this idea is
the construction of R*, the set of hyperreal numbers, which is a linearly ordered
field properly extending R. We will present the non-standard definitions for familiar
concepts such as convergent sequences, continuous functions, derivatives, and
integration, and show that they are equivalent to the standard definitions. If there is
time, we will see under what circumstances second-order sentences in the theory of
R "transfer" to R*.