**Missouri
University of Science and Technology**

**Department of
Mathematics and Statistics **

**Colloquia Fall 2008**

**The weekly "PinkSheet"
seminar schedule is available here.**

**The past: Spring 2008 Fall
2007 Spring
2007 Fall 2006 Spring
2006
Fall 2005
Spring 2005
Fall 2004
Spring 2004
Fall 2003
Spring 2003
Fall 2002
Spring 2002
Fall 2001
**

Our colloquium talks are held in Room G-5 Rolla
Building. We begin with coffee and refreshments at 4:00 pm, followed by the
hour-long lecture at 4:15 *unless otherwise noted*. The entire Missouri S&T
community is warmly invited to attend. We especially encourage undergraduate
students, graduate students, and faculty from other departments to attend.

Suggestions/nominations for speakers may be
made to Martin J. Bohner, Mathematics and Statistics Colloquium chair,
at __bohner@mst.edu
__

**Monday, August 25, 4:00 PM Note unusual day**

Horst Behncke, Universität Osnabrück, Osnabrück, Germany / Missouri S&T Faculty Host: Stephen Clark

*
Title: Periodical Cicadas
*

Abstract:
In the US one finds 6(3) species of cicadas which have the
longest known
life cycle - 13 resp. 17 years. By means of a "realistic" model we
describe
this periodicity, the convergence and evolution of these insects.

**Friday, September 12, 4:00 PM**

Hristo Voulov, University of Missouri - Kansas City, Kansas City, Missouri / Missouri S&T Faculty Host: Martin Bohner

*
Title: On the global asymptotic stability of planar dissipative maps
*

Abstract:
We consider area-contracting maps in the plane, which are often called
dissipative maps. If a smooth map has an asymptotically stable equilibrium
point P, the area-contracting property seems necessary at least locally around
P. Here we find sufficient conditions for global asymptotic stability of planar
dissipative maps. Then, we apply this result to a 15 year old open problem
about a second-order rational difference equation, posed by G. Ladas.

**Friday, September 26, 4:00 PM**

Johanna Michor, Courant Institute, New York / Missouri S&T Faculty Host: Stephen Clark

*
Title: Scattering theory for Jacobi operators with quasi-periodic background and applications to the Toda hierarchy
*

Abstract:
Jacobi operators, which can be viewed as the discrete analogue of Sturm-Liouville operators, play a fundamental role in the investigation of completely integrable nonlinear lattices, in particular, the Toda lattice.
We will develop scattering theory for Jacobi operators which are short range perturbations of (steplike) quasi-periodic finite-gap background operators via the Gel'fand-Levitan-Marchenko approach. Minimal scattering data which determine the perturbed operator uniquely will be presented. This will allow us to solve the associated initial value problem of the Toda hierarchy via the inverse scattering transform.
This talk is based on joint work with Iryna Egorova (Kharkov) and Gerald Teschl (Vienna).

**Friday, October 3, 4:00 PM**

Dennis Cook, University of Minnesota, Minneaoplis, Minnesota / Missouri S&T Faculty Host: Meggie Wen

*
Title:
Dimension Reduction Paradigms for Regression
*

Abstract:
Dimension reduction for regression, represented primarily by
principal components, is ubiquitous in the applied sciences. This is
an old idea that has moved to a position of prominence in recent
years because technological advances now allow scientists to
routinely formulate regressions in which the number *p* of predictors
is considerably larger than in the past. Although "large" *p*
regressions are perhaps mainly responsible for renewed interest,
dimension reduction methodology can be useful regardless of the size
of *p*.
Starting with a little history and a definition of "sufficient
reductions", we will consider a variety of models for dimension
reduction in regression. The models start from one in which maximum
likelihood estimation produces principal components, step along a
few incremental expansions, and end with forms that have the
potential to improve on some standard methodology. This development
provides remedies for two concerns that have dogged principal
components in regression: principal components are typically computed
from the predictors alone and then do not make apparent use of the
response, and they are not equivariant under full rank linear
transformation of the predictors.