In this talk we will discuss generating finite and infinite
symmetric groups. No specialist knowledge is required.

(Coffee and cookies at 3:30 Room 334)

An important class of problems in dynamical systems has to do with
classifying systems up to isomorphism.  In this talk, I will discuss
homomorphisms (also known as factor maps) and isomorphisms of measurable
dynamical systems and what is known about their existence, culminating
Sinai's Factor Theorem and Ornstein's Isomorphism Theorem.  I will also
talk about new work studying the existence of factor maps with a special
monotonicity property. 

(Coffee and cookies at 2:30 Room 334)

In 1940 S. M. Ulam posed a question concerning the stability of
homomorphisms. After that D. H. Hyers gave an affirmative answer to this
question. M. Das, T. Riedel and P. K. Sahoo dealt with Hyers-Ulam stability
of Flett's points i.e. points which satisfy Flett's mean value theorem.
The Hyers-Ulam stability of n-th Flett's points for which a generalized
Flett's mean value is satisfied and of Lagrange's points will be discussed
during the talk. 

(Coffee and cookies at 3:30 Room 334)

Ultra-high-frequency (UHF) data is naturally modeled as a marked point
process (MPP). Even though econometricians model UHF data as a MPP,
they view UHF data as an irregularly-spaced time series. In this talk,
we take the angle of probabilists and view UHF data as an observed
sample path of a MPP. Then, we propose a general filtering model for UHF
data where the signals are latent processes with time-varying and the
observations are in a generic mark space with other observable factors.
The statistical foundations of the proposed model, likelihoods, posterior,
likelihood ratios and Bayes factors, are studied. They all are of continuous
time, of infinite dimension and are characterized by stochastic differential
equations such as filtering equations. These equations are derived.
Mathematical foundations for consistent, efficient algorithms will be
established. Two general approaches for constructing algorithms will be
discussed. One approach is Kushner's Markov chain approximation method, and
the other is " Sequential Monte Carlo" method or " particle filtering"
method. Simulation and real data examples will be provided.

(Coffee and cookies at 3:30 Room 334)

Dr. Howie is Regius Professor Emeritus at St. Andrews. He has an
international reputation as a researcher, author and doctoral advisor. His
ten doctoral students are all active in research. In addition to more than
seventy research papers he has written the following books:
 
* An introduction to semigroup theory, Academic Press, 1976.
* Automata and languages, Oxford University Press, 1991.
* Fundamentals of semigroup theory, Oxford University Press, 1995.
* Real analysis, 2001.
* Complex analysis, Springer, 2003.
 
His talk will be accessible to graduate students, and will include some
recent results in the algebraic theory of semigroups.

(Coffee and cookies at 3:30 Room 334)

A class of stochastic processes with linear conditional
expectations and quadratic conditional variances is studied. They have a
structure of second order harnesses, processes which are somewhat related to
martingales. Originally, (first order) harnesses were introduced in sixties
by Hammersly. They are intensively studied nowadays, mostly, due to the
Paris school led by Marc Yor.
It appears that such processes are Markov and their transition
probabilities are conveniently defined in terms of systems of orthogonal
polynomials. Special cases of these processes are known to arise from the
non-commutative generalizations of the Levy processes.
This is a joint work with Wlodek Bryc (Univ. of Cincinnati).

(Coffee and cookies at 3:30 Room 334)

William T. Tutte's first mathematical research was completed while he
was an undergraduate chemistry major at Cambridge. He and his colleagues,
Brooks, Smith, and Stone, gave the first theory-driven solution to the
problem of covering a square of integer side length with non-overlapping
squares of all-different integer side lengths. Tutte spent the war years
at Bletchley Park, where he almost single-handedly broke the German Army
High Command code (not the Enigma code).
 
Tutte's 417 page thesis, written at Cambridge during the 3 years
immediately following the war, solved the then most important problem in
matroid theory - characterizing those matroids that can be derived from
graphs - using exclusion of minors introduced by Wagner for graphs. In
his thesis, he also introduced the polynomial now named after him. The
Tutte polynomial subsumes the chromatic polynomial, the tree counting
polynomial, and the flow polynomial, and it has applications in knot
theory and elsewhere.
 
Tutte continued his career with further extraordinary results. He did
foundational work in several branches of graph theory, including
characterizing graphs with 1-factors, enumerating graphs, advancing the
theory of chromatic polynomials, and characterizing classes of graphs with
Hamiltonian cycles. Tutte was made a Fellow of the Royal Society of
Canada in 1958, a Fellow of the Royal Society in 1987, and an Officer of
the Order of Canada in 2001.
 
In the March, 2004, issue of the AMS Notices, James Oxley (Louisiana
State University) and the speaker, Arthur Hobbs (Texas A&M University),
published an article on the life and work of William T. Tutte. In the
present talk, Prof. Hobbs will give a more extended review of some of the
more interesting aspects of Tutte's work and life.
 
___________________________
 
Arthur M. Hobbs is a professor at Texas A&M University. He was Tutte's
student from 1968 to 1971 and has over 40 published papers. His recent
research work has been on uniform density in graphs and matroids, a
subject initiated by Tutte, and on Hamiltonian cycles in graphs, a subject
in which Tutte made major contributions.