Department Colloquium, Fall
2007
| Colloquium |
Seminars |
Clec Lectures |
Public Lectures |
Distinguished Lectures |
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Date
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Speaker
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Title
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| Monday, August 27, 5-6pm, MP3314 |
Patrick Iglesias
(CNRS and Hebrew University of Jerusalem) |
Every Symplectic Manifold is a Coadjoint Orbit
|
| Monday, September 3, 5-6pm, MP3314 |
Labor Day |
| Monday, September 10, 5-6pm, MP3314 |
Xiangdong Xie (Georgia Southern University) |
Group theory and Geometry |
| Monday, September 17, 5-6pm, MP3314 |
Goran Lesaja (Georgia Southern University) |
Complexity of Algorithms for Linear Programming Problem
|
| Monday, September 24, 5-6pm, MP3314 |
Francis Jordan (Georgia Southern University) |
Dualities between covering properties of a space and
local properties of its space of real-valued
functions |
| Monday, October 1st, 5-6pm, MP3314 |
Xiezhang Li (Georgia Southern U.) |
The Optimal Parameter of SOR-k Method for p-Cyclic Matrices
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| Monday, October 8, 5-6pm, MP3314 |
Victor Maymeskul (Georgia Southern University) |
Minimal Discrete Energy Problems on Compact Sets in
Euclidean Spaces |
| Friday, October 12, 3-4pm, MP3314 |
Iwo Labuda (University of Mississippi) |
Unity of compactness |
| Monday, October 15, 5-6pm MP3314 |
Andrew Sills (Georgia Southern University) |
Polynomial Generalizations of q-Series Identities |
| Monday, October 22, 5-6pm, MP3314 |
Alina Iacob (Georgia Southern University) |
DG-injective complexes |
| Monday, October 29, 5-6pm, MP3314 |
Robert McLean (University of Tennessee) |
Using Matlab to Study Speech Perception |
| Monday, November 5, 5-6pm, MP3314 |
Broderick Oluyede |
Length-Biased and Current Duration
Sampling |
| Monday, November 12, 5-6pm, MP3314 |
Yangbo Ye (University of Iowa) |
Recent progress in computed tomography |
| Monday, November 19, 5-6pm, MP3314 |
Liancheng Wang (Kennesaw State U.) |
 |
| Monday, November 26, 5-6pm, MP3314 |
Billur Kaymakcalan (Georgia Southern U.) |
On Fredholm Integral Equations on Time Scales |
| Monday, December 3, 5-6pm, MP3314 |
Brauch Fugate (University of Kentucky) |
Uniquely Arcwise Connected Continua and the Fixed Point Property |
Details of Fall 2007 lectures
1. Monday, August 27, 5pm-6pm, MP 3314
Speaker: Patrick Iglesias, CNRS.
Title: Every Symplectic Manifold is a Coadjoint Orbit
Abstract:
Agreeing to work in the category {Diffeology}, we shall see
how the moment
map identifies every symplectic manifold (M,w) with some
coadjoint orbit of
its group of automorphisms Diff(M,w). Thus,
coadjoints orbits are the unique
models of symplectic manifolds.
2. Monday, September 10,
5pm-6pm, MP3314
Speaker : Xiangdong Xie, Georgia Southern University
Title : Group theory and Geometry
Abstract :
I shall explain some basic ideas of geometric group theory, and at the end
I will mention some of my own results.
The talk will be accessible to
graduate students.
3. Monday, September 17,
5pm-6pm, MP3314
Speaker : Goran Lesaja, Georgia Southern
University
Title : Complexity of Algorithms for
Linear Programming Problem
Abstract :
A great many practical problems from wide areas of industry, business,
and science can be modeled as Linear Programming (LP) problem. Therefore, design
and analysis of efficient algorithms for LP problem are of great importance. In
this talk we will review iteration complexity of several main LP
algorithms.
First, it will be shown that LP problem is not NP-complete which indicates
a possibility that the polynomial algorithm may exists. Next, the complexity of
much celebrated Simplex Algorithm will be discussed. It will be shown that
unfortunately Simplex Algorithm has exponential worst-case complexity. However,
the average-case complexity is much better; it is polynomial, which
theoretically explains the success and good behavior of the algorithm that is
usually observed in practical applications.
In the sequel, the complexity of the Ellipsoidal Algorithm will be
discussed. Its importance comes from the fact that it was the first algorithm
for LP with polynomial worst-case complexity. However, the importance was mainly
theoretical because it was soon shown that it does not perform well in practice.
In fact, in most instances the Ellipsoid Algorithm performs worse than the
Simplex Algorithm.
Finally, a class of recently developed Interior-Point Algorithms will be
introduced. Success of these algorithms is based on the fact that their
worst-case complexity is polynomial and, in addition, they perform well in
practical applications often outperforming the Simplex Algorithm applied to the
same problem. The average-case complexity will also be discussed. However, the
difference between the worst-case and average-case complexity of the
Interior-Point Algorithms is not as significant as for the Simplex
Algorithm.The Optimal Parameter of SOR-k Method for p-Cyclic Matrices
4. Monday, September 24,
5pm-6pm, MP3314
Speaker : Francis Jordan, Georgia Southern
University
Title : Dualities between covering properties of a space and
local properties of its space of real-valued
functions
Abstract :
We
will discuss the duality between a topological space X and the space C(X) of
continuous real valued functions on X with the topology of point-wise
convergence. In particular, statements about coverings of X by open sets become
statements about the neighborhood filters of points in C(X). We identify a
large class of properties for which these duality results can be proven. This
approach allows us to unify a number of past results and prove some new theorems
which answer open questions. We will also consider subsets of the real line
that satisfy some the global properties we will discuss.
5. Monday, October 1st,
5pm-6pm, MP3314
Speaker : Xiezhang Li, Georgia Southern
University
Title : The Optimal Parameter of SOR-k Method for p-Cyclic Matrices
Abstract :
click here.
6. Monday, October 8,
5pm-6pm, MP3314
Speaker : Victor Maymeskul, Georgia Southern
University
Title : Minimal Discrete Energy Problems on Compact Sets in
Euclidean Spaces
Abstract :
The problem of uniformly distributing points on spheres (more generally, on compact sets
in R^n) is an interesting, long standing, and difficult problem with numerous applications in
diverse areas (approximation theory, numerical integration, spherical t-designs, crystallography,
electrostatics, etc.). In this talk, we will discuss classical and recent results concerning
the asymptotics, separation radius, and mesh norm of optimal arrangements of N points on
d-dimensional compact sets A embedded in Rn, which interact through the Riesz potential
V = r^−s, s > 0. In particular, we will see that, for a large class of sets, optimal points are
“well distributed” on A and have local energies asymptotically of the same order, as N goes to infinity.
7. Friday, October 12, 3pm-4pm, MP3314
Speaker : Iwo Labuda,
University of Mississippi
Title : Unity of compactness
Abstract :
A Hausdorff space X is compact if
every open cover of X admits a finite subcover. It is paracompact if every open
cover script-P of X admits a locally finite refinement script-R covering X. Does
there a class Blackboardbold-D of covers of X exist such that the
paracompactness of X amounts to its Blackboard-D-compactness (each cover
script-D from Blackboard-D admits a finite subcover of X)? We answer the
question in a positive. Actually, working in a more general framework, we show
that many classical variations of compactness used in topology are instances of
Blackboard-D-compactness for suitably chosen class Blackboard-D of covers. Thus
the notion of Blackboard-D-compactness is the unifying notion behind the title
of my talk.
8. Monday, October 15,
5pm-6pm, MP3314
Speaker : Andrew Sills, Georgia Southern
University
Title : Polynomial Generalizations of q-Series Identities
Abstract :
The Rogers-Ramanujan identities are a pair of analytic/formal power
series identities, each of which assert the equality of a certain
infinite series with an infinite product. They were first discovered by
the English mathematician L.J. Rogers in 1894. Later, it was realized
that the series and products could be viewed as generating functions
for certain classes of integer partitions, and thus the
Rogers-Ramanujan identities are also combinatorial identities. Around
1980, Australian physicist Rodney Baxter showed that the
Rogers-Ramanujan identities were intimately linked to the solution of
the hard hexagon model in statistical mechanics. Around the same time,
Rutgers mathematicians Jim Lepowsky and Robert Wilson gave the first
Lie theoretic interpration and proof of the Rogers-Ramanujan
identities. This work eventually led to the discovery of vertex
operator algebras.
In my talk, I plan to give a brief but motivating introduction to
q-series, and then denomonstrate an elementary method by which any
q-series/infinite product identity of Rogers-Ramanujan type can be
generalized to a polynomial identity, which in turn has important
implications in statistical physics and algorithmic proof theory.
9. Monday, October 22,
5pm-6pm, MP3314
Speaker : Alina Iacob, Georgia Southern
University
Title : DG-injective complexes
Abstract :
We consider two questions about the class of DG-injective complexes:
1. When is the class of DG-injective complexes closed under arbitrary
direct sums?
We show that with some additional hypotheses on the ring, the ring must
have finite global dimension for this to
happen (this is the case for Gorenstein rings and for commutative artinian
rings);
2. This is a question raised by Avramov and Foxby in 1991; they proved
that for a ring of finite global dimension every
complex of injective modules is a DG-injective complex.
Question: is the converse true?
We show that for a commutative noetherian ring of finite Krull
dimension their question has an affirmative answer.
10. Monday, October 29,
5pm-6pm, MP3314
Speaker : Robert McLean, University of Tennessee
Title : Using Matlab to Study Speech Perception
Abstract :
The
measurement system used to measure speech will be described. This requires the generation, broadcasting,
and recording of wav type files. The recorded
files are transformed into frequency domain data by the measuring equipment and
the analysis of these data will be carried out and displayed with the use of
Matlab. The coding for these results
will not be discussed but will be available for review.
The
frequency domain data obtained from a small microphone placed near the ear drum
will be used to illustrate ear canal and hearing aid effects. It is conjectured that this type of data will
offer opportunities for designing statistical experiments for investigating
hearing aid parameters and lead towards improved hearing and efficient tuning
of hearing aids. Existing patient data
will be used to demonstrate existing problems and the potential of this type of
applied research.
11. Monday, November 5,
5pm-6pm, MP3314
Speaker : Broderick O. Oluyede, Georgia Southern
University
Title : Length-Biased and Current Duration
Sampling
Abstract :
In the analysis of longitudinal data, two
semiparametric models that are often used are the Cox proportional hazards model
and the accelerated failure time model. In Cox proportional hazards model for
failure time, one assumes that the covariate effect is captured via a
proportional constant between hazard functions, with unspecified underlying
hazard functions. In accelerated hazards model, the hazards functions are
related via the scale–time change, which is a function of covariates and the
parameters. In a medical setting,
current duration sampling require knowledge of the duration of the disease of a
group of patients up to the present, but length-biased sampling requires time
needed to observe the full duration of the disease of the sampled patients. In
this talk, some results on current duration and length-biased sampling for the
accelerated failure time model and Cox proportional hazards model are presented.
Approximations via proportional hazards and length-biased exponential
distributions to the class of distribution functions with monotone hazard
functions are presented.
12. Monday, November 12,
5pm-6pm, MP3314
Speaker : Yangbo Ye, University of Iowa
Title : Recent progress in computed tomography
Abstract :
In this talk, we will survey some of the recent progress in
computed tomography, including filtered exact reconstruction along a
standard spiral or an arbitrary curve, lambda tomography which seeks an
outline of the object, interior reconstruction problems, and possible
new methods.
13. Monday, November 19,
5pm-6pm, MP3314
Speaker : Liancheng Wang, Kennesaw State University
Title :
Abstract :
14. Monday, November 26,
5pm-6pm, MP3314
Speaker : Billur Kaymakcalan, Georgia Southern University
Title : On Fredholm Integral Equations on Time Scales
Abstract :
Following the introduction of
basics of Time Scale calculus, Fredholm Integral equations are
discussed in view of existence and qualitative properties of their
solutions in the cases of separable and symmetric kernels. Similar
results in the continuos and discrete analog cases are presented to
emphasize the unification property of the Time Scales situation. Some
examples in various Time Scale settings are presented to illustrate the
theory obtained. This is a part of an ongoing project and thereby a
preliminary report. Ferhan Atici and Ozlem Batit are collaborators in
this work.
14. Monday, December 3,
5pm-6pm, MP3314
Speaker : Brauch Fugate, University of Kentucky
Title : Uniquely Arcwise Connected Continua and the Fixed Point Property
Abstract :
A continuum (compact
connected metric space) M has the fixed point Property (fpp) if every
selfmap f of M has a fixed point. We examime this property for continua
which are uniquely arcwise connected (every pair of distinct points may
be joined by a unique arc). Unless M or f is suitably restricted, M
will not have fpp. A theorem, developed jointly with Lee Mohler, gives
a condition on f which is sufficient to produce a fixed point.
Department Colloquium Archives
Please direct questions or comments regarding the
colloquium to Frederic
Mynard
( Last updated: October 17,
2007.)