Links to Seminars and Other Lecture Series

1. Spring 2006 Department Colloquium
2. Distinguished Lecture Series
3. Public Lecture Series
4. CLEC Lectures
5. Seminars
    1)  Analysis Seminar
    2)  ApproximationTheory Seminar
    3)  Probability and Statistics Seminar
6. Past Colloquia:
Spring 2005
Fall 2004
Spring 2004
Fall 2003

Details of Fall 2005 lectures

1.  Friday, September 2, 2005, 3:00 p.m. - 4:00 p.m.  Room: MP 3314.

Speaker:  Sze-Man Ngai, Georgia Southern Univ.

Title: Fractal Laplacians on bounded open subsets of Euclidean spaces.

Abstract: Given a bounded open subset of a Euclidean space and a positive finite  continuous Borel measure with support
contained in the set, we define a Laplacian that extends the classical Laplacian. We show that the properties of the operator
depends on the multifractal structure of the measure. This operator has been studied by K. Naimark, M. Solomyak, E. Verbitsky
et al., especially for self-similar measures defined by iterated function systems satisfying the open set condition. We are particularly
interested in the case the open set condition fails. This work is joint with Jiaxin Hu and Ka-Sing Lau.

2.  Friday, September 9, 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314

Speaker:  Bruce McLean Georgia Southern Univ.

Title:  Inverse Limits

Abstract:  All spaces are metric and maps are continuous functions. It is not known if the confluent map of an arc-like curve is arc-like, but it is known that it is tree-like. Arc-like curves are the inverse limit of arcs and tree-like curves are the inverse limit of trees. In an attempt to better understand this forty year old problem, Brauch Fugate and my self read two papers by Ingram and one by Ryden. Ingram has 6 maps of triods that look basically the same. However 2 of the inverse limits are not arc-like, but the other four are. So when is the inverse limit of trees, arc-like? Ryden has some techniques that make it possible to see the difference in this case.
 

3.  Friday, September 16, 2005, 3:00 p.m. - 5:00 p.m.  Room: MP 3314.

Speaker: Xiezhang Li, Georgia Southern University.

Title: Spectral Properties of a Near-Periodic Row-Stochastic Leslie Matrix.

Abstract: Leslie matrix models are discrete models for the development of age-structured populations. It is known that the ratio of the
spectral radius and the second largest (subdominant) eigenvalue in modulus of a non-periodic Leslie matrix determines the rate of convergence
of the corresponding population distributions to a stable age distribution. In this talk, we further study the spectral properties of a row-stochastic
Leslie matrix A with a near-periodic fecundity pattern of type (k, d, s) based on Kirkland's results in 1993. Intervals containing arguments of
eigenvalues of A on the upper-half plane are given. Sufficient conditions are derived for the argument of the subdominant eigenvalue of A to be in
the interval [2\pi/d, 2\pi/(d-s)]$ in the cases of k=1. A computational scheme is suggested to approximate the subdominant eigenvalue when its argument is in
[2\pi/d, 2\pi/(d-s)].
 

4.  Friday,  September 23 , 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314

Speaker:  Jiehua Zhu, Georgia Southern Univeristy.

Title:  Computed Tomography Simulation with Superquadrics.

Abstract: Accurate and efficient simulation of an x-ray transform for representative structures plays an important role in research and development of x-ray CT, for the evaluation and improvement of CT image reconstruction algorithms, in particular.  Superquadrics are a family of three-dimensional objects, which can be used to model a variety of anatomical structures. In this paper, we propose an algorithm for the computation of x-ray transforms for superellipsoids and tori with a monochromatic x-ray. Their usefulness is demonstrated by projection and reconstruction of a superquadric-based thorax phantom. Our work indicates that superquadric modeling provides a more realistic visualization than quadratic modeling, and a faster computation than spline methods.
 

5. Friday,  September 30, 2005, 3:00 p.m. - 4:00 p.m., Room: MP 3314

Speaker:  Mavis Pararai, Georgia Southern Univeristy.

Title: Measurement errors in generalized poisson regression model.

Abstract: Count data regression models have been widely used in statistics to model response variables that are assumed to be observed without error. This assumption might be violated as some counts could potentially be under- or over-reported. A mixture of the generalized Poisson distribution and the quasi-binomial distribution II is used to develop the generalized Poisson regression model for underreported counts. The generalized Poisson regression model for underreported counts is found to perform better than the negative binomial regression model for underreported counts. The generalized Poisson-Poisson mixture regression model is also developed to model counts that are accurately-, under- and over-reported. This model is compared to the Negative Binomial-Poisson mixture regression model and the two models seem to be equivalent in their performance.

6. Friday, October 7 , 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314 (Visiting lecture)

(Postponed to January 13, 2006.)

Speaker:  Ram N. Mohapatra, University of Central Florida (Host: Don Fausett)

Title:  Some Extremal Problems in Polynomial and Rational Approximation.

Abstract: We shall discuss the extremal problems associated with the bounds of the ratio of ||f'/f|| . Then we shall discuss Bernsteins's inequalities for polynomials, rational functions and rational functions with a prescribed zero. Extension of these results for weighted polynomials with Hermite and Laguerre weights will also be discussed. Generalizations of the latter results and some open problems will be mentioned.
 

7. Friday,  October 14, 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314  (Visiting lecture)

Speaker: Samy Abbes, University of Maryland. (Host: Frederic Mynard)

Title:  Introduction to concurrency models and their probabilistic extensions.

Abstrat:  The talk presents models from Concurrency theory under their so-called "true-concurrent" semantics.
We analyze some probabilistic extensions of such models, in particular Petri nets and event structures.
The main issue is that the true-concurrent semantics induces a "partially ordered time", instead of the usual
totally ordered time. A combination of tools from Measure and Domain theories still allows the construction of a
probabilistic dynamics in this framework. The result is a generalization of finite Markov chains with "several tokens"
instead of a unique token. Concurrency introduces new possibilities unknown from Markov chains. In particular,
can concurrent events be independent in the probabilistic sense? We aim to give an introduction to these topics,
together with a recent information theoretic point of view.
 

8. Friday,  October 21, 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314  (Visiting lecture)

Speaker:  Ming-Jun Lai, Department of Mathematics, University of Georgia (Host: Scott Kersey)

Title:  Spherical Scattered Data Interpolation and Fitting.

Abstract:  Starting with several examples of spherical data sets, we introduce splines over spherical triangulations. They are piecewise trigonometric
polynomials with some smoothness. Then we use minimal energy, discrete least squares and smoothing methods to construct fitting/interpolatory
splines. We explain how to compute these splines and what the approximation properties of these splines. Numerical examples will be demonstrated.
 

9. Friday,  October 28, 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314 (Visiting lectures)

Speaker:  1. Victor Sirvent, Universidad Simon-Bolivar, Venezuela, and Georgia Institute of Technology (Host: Sze-Man Ngai)

Title: Space filling curves and geodesic laminations.

Abstract: In this talk we shall associate  space filling curves to connected fractals,obtained as the fixed point of an iterated function systems (IFS)
satisfying the common point property and other conditions. These curves are H\"older continuous and measure preserving. To these space filling curves
we associate geodesic laminations satisfying among other properties that points joined by geodesics have the same image in the fractal under the space
filling curve. The laminations help us to understand the geometry of the curves. We define an expanding dynamical system on the laminations.
 

Speaker: 2. Yang Wang, School of Mathematics, Georgia Tech. (Host: Sze-Man Ngai)

Title: Twindragon and other rep-tiles.

Abstract: A rep-tile is a tile which can be partitioned into several congruent pieces, each similar to the original tile. One of the best known
such tile is the Twindragon. We discuss properties and constructions of rep-tiles. We shall focus on a particular kind of rep-tiles called
self-affine tiles. These tiles are easy to construct and they can often be studied using Fourier techniques. Some open questions will also be
proposed.
 

10. Friday, November 4, 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314 (Visiting lecture)

Speaker:   Manav Das, University of Louisville.  (Host: Sze-Man Ngai)

Title:  Separation Properties for Iterated Function Systems.

Abstract:  I will discuss the various separation properties (open set condition, weak separation condition, finite-type) for self-similar
iterated function systems, including their usefulness, relative merits and some recent results. I will then introduce graph-directed iterated
function systems, and discuss the inter-relationships between the separation properties in this setting. This talk is based on joint work
with Professor Gerald Edgar.
 

11. Public Lecture Series, I.  Saturday, November 5, 2005, 10:00 - 12:00 noon, Room: 3001 Math/Physics Building.

Lecture 1.  Fractals and the golden ratio.

Speaker:  Manav Das, University of Louisville.

Lecture 2. Fractals and tilings.

Speaker:  Sze-Man Ngai, Georgia Southern Univ.
 

12. CLEC Lecture. Thursday, November 10, 2005, 6:00 p.m. - 7:00 p.m., Room: 1005, Information Technology Building.

Speaker: Richard S. Varga, Kent State University, Ohio. (Host: Xiezhang Li)

Title:  Gerschgorin and His Circles.

Abstract:
 

13. Friday,  November 11, 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314  (Visiting lecture)

Speaker:  Richard S. Varga, Kent State University, Ohio. (Host: Xiezhang Li)

Title:  The dynamical motion of the zeros of s_n(z) and its relationship with discrepancy theory, where s_n(z) is the n-partial sum of e^z.

Abstract:

14. Friday, November 18 , 2005,  3:00 p.m. - 4:00 p.m., Room: MP 3314 (Visiting lecture)

Speaker:  Kees Roos, Delft University of Technology, Netherlands.  (Host: Goran Lesaja)

Title:  Introduction to Conic Optimization with some recent applications.

Abstract: Linear Optimization (LO) deals with the problem of optimizing (i.e., minimizing or maximizing) a linear function over the intersection of an affine space and the nonnegative orthant.  Its rich mathematical theory has been developed in the last 50 years. Although the applications are numerous, there are many real-life phenomena that cannot be described by a linear model, and hence the need for Nonlinear Optimization is apparent.
Recently it has become clear that in many cases nonlinearity can be handled very well  by replacing the nonnegative orthant in LO by a nonlinear convex cone, which has led to a new field, namely Conic Optimization (CO). Prototype examples of suitable cones are the Lorenz (or ice-cream, or second order) cone and the semidefinite cone. The theory of CO is extremely beautiful. Since many nonlinear optimization problems can be put in the form of a CO model, and these models, like LO models, can be solved efficiently, there is rich potential for new applications.
In the lecture I will give an introduction to CO. Its usefulness will be illustrated by discussing some recent applications, namely: minimization of a polynomial, distance geometry, and new bounds for binary codes.
 

15. Wednesday,  November 30, 2005,  Time: 3:30 p.m. - 5:30 p.m.,  Room: 3314 (Visiting lectures)

A) Speaker:  Ravi Agarwal, Florida Institute of Technology (Host: Billur Kaymakcalan)

Title:  Singular and Nonsingular Boundary Value Problems on Infinite Intervals

Abstract: Till late 1960's very little was known about boundary value problems on infinite intervals; in fact most of the known results required rather technical hypotheses and only applied to narrowly defined classes of problems. In recent years a mixture of classical analysis and modern fixed point theory has been employed to study these problems. This has resulted in some widely applicable results which we shall discuss.

B) Speaker:  Kanishka Perera, Florida Institute of Technology (Host: Billur Kaymakcalan)

Title:  Positive Solutions of Multiparameter Semipositone p-Laplacian Problems

Abstract: We obtain multiple positive solutions of multiparameter
semipositone p-Laplacian problems using the sub- and supersolution method
and the mountain pass lemma.

For questions, suggestions or comments regarding the colloquium, please contact  Sze-Man Ngai: mailto:ngai@gsu.mat.georgiasouthern.edu.
 

( Last updated: November 17, 2005.)