Department Colloquium, Fall 2006
Colloquium Seminars Clec Lectures Public Lectures Distinguished Lectures

Schedule

 
Date
Speaker
Title
Friday, September 1, 3:00 - 4:00 p.m., MP3314 Chunshan Zhao, Georgia Southern U. Asymptotic Behaviors of Positive Solutions to  a Class of elliptic Equations with Large Diffusion
Friday, September 8, 3:00 - 4:00 p.m., MP3314 Homeira Pjoohesh, Georgia Southern U.
Derivations and the structure of ordered rings
Friday, September 15, 3:00 - 4:00 p.m., MP3314 Aleksandr Pinzul, Georgia Southern U., Physics Dept. Non-commutative geometry: interplay between physics and mathematics
Friday, September 22 , 3:00 - 4:00 p.m., MP3314 Reinhard Piltner, Georgia Southern U. Complex Functions and Finite Elements for the 2-D Navier Equations
Friday, September 29, 3:00 - 4:00 p.m., MP3314 Lorrie Hoffman, Armstrong Atlantic U. Exploring Applications of Missing Data Algorithms
Friday, October 6, 3:00 - 4:00 p.m., MP3314 Ralph Kopperman, City College of New York The search for distance functions
Friday, October 13, 3:00 - 4:00 p.m., MP3314 Robert Taylor, Clemson U. Consistency and Validity of Dependent  Nonparametric Bootstrap Estimators
TBA Robert Taylor, Clemson U. Fun and Opportunities in Probability and Statistics
Friday, October 20, 3:00 - 4:00 p.m., MP3314 Paul Fabel, Mississippi State U. Some characterizations of almost periodic homeomorphisms.
Friday, October 27, 3:00 - 4:00 p.m., MP3314 Jung Ha An, IMA/Siemmans Princeton Medical Imaging with Variational Partial Differential
Equation(PDE) Methods
Thursday, November 2 CLEC LECTURE-POSTPONED Raphael Sorkin, Syracuse U. The genealogy of spacetime
Friday, November 3, 3:00 - 4:00 p.m., MP3314 Sze-Man Ngai, Georgia Southern U. Spectral dimension of Laplacians defined by self-similar measures with overlaps
Friday, November 10, 3:00 - 4:00 p.m., MP3314 Francois Ziegler, Georgia Southern U.
 Coadjoint orbits and unitary representations
Thursday, November 16, 6.30-7.30pm, IT 1005
PUBLIC LECTURE		 Xiezhang Li, Georgia Southern U. Tips for learning Algebra
Friday, November 17, 3:00 - 4:00 p.m., MP3314 Fred Hickernell, IIT Energy and Discrepancy for Spreading Points Evenly.
Friday, November 24 Thanksgiving break
Friday, December 1, 3:00- 4:00 p.m., MP3314 Norou Diawara, Old Dominion University  A Multivariate Class of Survival and Reliability Analysis


Details of Fall 2006 lectures

1.  Friday, September 1, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker:  Speaker:  Chunshan Zhao, Georgia Southern University

Title:  Asymptotic Behaviors of Positive Solutions to  a Class of elliptic Equations with Large Diffusion.

Abstract: I will continue my interview talk to talk about asymptotic behaviors of positive solutions to a class of elliptic equations modeling aggregation of amoebae as the diffusion coefficient goes to infinity. Results will be presented and explained first and then proofs will be sketched. A related question will be posed  at the end.
 

2.  Friday, September 8, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Homeira Pajoohesh, Georgia Southern University

Title: Derivations and the structure of ordered rings

Abstract: Consider the usual derivative operator ' on the ring of
differentiable functions. It is additive and (fg)'=f 'g +fg '. This
definition has been generalized: for every ring R, a derivation d on
R is an additive function such that d(ab)=d(a)b+ad(b). Positive
derivations on rings with an order are those such that whenever an
element is positive, its derivation is positive. We investigate the properties
of positive derivations on the lattice ordered rings of matrices and
characterize some of these rings by their positive derivations.

3.   Friday, September 15, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker:  Aleksandr Pinzul, Georgia Southern U., Physics Dept.

Title: Non-commutative geometry: interplay between physics and mathematics

Abstract: I give a brief introduction to the vast subject of
non-commutative geometry, stressing  how  it has been shaped
by both physists and mathematicians.  After reviewing the approximate
80 year history of non-commutative geometry, I
discuss some recent advances and applications.

4. Friday, September 22, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Reinhard Piltner, Georgia Southern University

Title: Complex Functions and Finite Elements for the 2-D Navier Equations

Abstract: The Navier equations are a set of coupled PDEs widely used in engineering to describe the mechanical behavior of two and three dimensional structures. For the two dimensional case they involve the unknown functions u(x,y) and v(x,y), which are displacement components in two orthogonal directions. The Navier equations have the meaning of equilibrium equations and are given in terms of partial derivatives of the displacement components u(x,y) and v(x,y). The solution for the displacement functions can be given in terms of complex valued functions. The advantage of using complex functions is that the governing differential equations are automatically satisfied. If we use the complex solution representation in a numerical method, the remaining task is to find the coefficients of the chosen functions such that the boundary conditions are satisfied in a chosen integral sense. In this presentation the Finite Element Method is chosen to obtain the approximate solutions. The steps for developing a finite element will be described, and some numerical results for selected boundary value problems will be shown.

5. Friday, September 29, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Lorrie Hoffman, Armstrong Atlantic University (host: Broderick Oluyede)

Title: Exploring Applications of Missing Data Algorithms

Abstract:  The problem of handling missing data began to be extensively
 studied in the late 1970's. The mechanism of solution is inherently a
 multivariate one with at least four popular approaches: 1) Listwise
 Deletion, 2) Mean Imputation, 3) EM algorithm, 4) Direct Maximum
 Likelihood. Just a decade ago, journals targeted at quality assessment
 wrote of future innovations in multivariate applications. Thus in a
 quality engineering environment, the act of addressing "missingness" in
 data collection and analysis is a rather new endeavor. In this talk we
 will explore the application of these four approaches via an example
 dealing with SPAM filters. Also illustrated will be the importance of the
 concept of "missing at random" and its effect on proper convergence to the
 maximum likelihood estimates.

6. Friday, October 6, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker:  Ralph Kopperman, City College of New York. (Host: Homeira Pajoohesh)

Title: The search for distance functions

Abstract:
The ideas of limit and of Cauchy are first defined in terms of a distance, but later generalized, 

usually in terms of a topology and a uniformity, respectively. But in
fact, metrics can easily be generalized so that the original definitions 
always suffice.



7. Friday, October 13, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Robert Taylor, Clemson University (Host: Broderick Oluyede)

Title: Consistency and Validity of Dependent  Nonparametric Bootstrap Estimators

Abstract: The traditional bootstrap resamples with replacement from the original sample
observations to form arrays of rowwise independent and identically  distributed bootstrap
 random variables.  There are situations, for example, when sampling from finite populations,
where resampling without  replacement provides a more realistic bootstrap procedure
and produces dependent bootstrap random variables. 
The desired properties of  consistency and asymptotic validity are shown to hold for certain
nonparametric dependent bootstrap estimators.   In addition, it is shown that the smaller
 variation in dependent bootstrap estimators can be used  to increase precision in some of
 the estimates even in the traditional  i.i.d. setting.

8. Friday, October 20, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Paul Fabel, Mississippi State University (Host: Frédéric Mynard)

Title: Some characterizations of almost periodic homeomorphisms.

Abstract:  What can be said about the dyanamics of an isometry of a compact metric
space?
On the one hand, if X is a manifold, it is an open question whether
the orbit closure of a point can be homeomorphic to the Cantor set. (This is
related to the Hilbert Smith conjecture).
On the other hand there are some powerful structural theorems regarding
the function spaces generated by such maps. For example the closure of
the space of iterates must be a compact metrizable abelian group.
The latter fact motivates the notion of a so called `almost periodic'
homeomorphism. This is a generalization of an isometry of a compact
metric space, and can be applied to noncompact spaces.
We will discuss various examples and results that serve to classify such
maps.

9. Friday, October 27, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Jung Ha An, IMA/Siemens Princeton (Host: Steve Damelin)

Title:  Medical Imaging with Variational Partial Differential
Equation(PDE) Methods

Abstract: 

10. Friday, November 3, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Sze-Man Ngai, Georgia Southern University

Title: Spectral dimension of Laplacians defined by self-similar measures with overlaps

Abstract: Since Kigami provided a direct analytic construction of Laplacians on the Sierpinski gasket in 1989, analysis on fractals has become a very active research area. Lots of results have been obtained for Laplacians defined by the class of postscritically finite iterated function systems (IFSs). These are IFSs without overlaps. However, little is known if the IFS has overlaps. In this talk, I will present a method to obtain the spectral dimension of the Laplacian defined by certain IFSs with overlaps.

11. Friday, November 10, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Francois Ziegler, Georgia Southern University

Title: Coadjoint orbits and unitary representations.

Abstract: In a previous talk, I explained how the homogeneous symplectic manifolds of a Lie group are essentially the same thing as its coadjoint orbits -- a culmination of very "19th century" mathematics. An amazing 20th century insight is that these objects also classify the group's unitary representations in Hilbert spaces.
Unfortunately this correspondence (a.k.a. "quantization") arises out of a hodge-podge of techniques, rather than a transparent definition. In this talk I will sketch an ongoing attempt in this direction, and illustrate it by showing how it leads from light rays (classical) to solution spaces of Maxwell's equations (quantum).

12. Friday, November 17, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Fred Hickernell, IIT (Host: Steve Damelin)

Title: Energy and Discrepancy for Spreading Points Evenly.

13. Friday, December 1, 2006, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker: Norou Diawara, Old Dominion University  (Host: Broderick Oluyede)

Title: A Multivariate Class of Survival and Reliability Analysis

Abstract: Much has been conducted in the last half century in developing multivariate survival distributions. Marshall and Olkin (1967), and many others, presented a derivation of the multivariate exponential with a probability of simultaneous occurrence. Recent ideas were to establish a linear relationship between the variables. In this talk, a method for deriving general class of bivariate lifetime distributions is presented. A linear associated bivariate pairs is described that, when a solution exists, guarantees pre-selected marginal distributions, including exponential, Weibull and gamma. We further develop a general class of finite bivariate mixtures, examine its mathematical properties and discuss its application. Bivariate parameter estimation is developed and applied to data. The multivariate form is laid out.
Department Colloquium Archives

Please direct questions or comments regarding the colloquium to  Frederic Mynard

( Last updated: November 8th, 2006.)