Quantum topology, Vassiliev invariants and Skein theory
Abstract:
TBA
Thursday
November 9, 2000
3:00 PM in ILB 345
Please Notice Unusual
Time and Location
Xin-Min Zhang
University of South Alabama
Sierpinski Pedal Triangles
Abstract:
In this talk, we will construct a 2-parameter family of
Sierpinski-type triangles in terms of the pedal triangles of a given
triangle. This family includes the ordinary Sierpinski Triangle as
a special member when the initial triangle is equilateral. We shall
investigate the fractal dimensions of Sierpinski Pedal Triangles and
the related area ratio problems. Some computer generated graphs will
also be provided.
This talk is based on recent joint work by the speaker and Drs. R. Hitt
(of USA) and J. Ding (of USM).
The talk will be presented at a very elementary level. Everyone,
especially, undergraduate and graduate students are encouraged to come and
enjoy the discovery of a new fractal!
Thursday
November 16, 2000
4:00 PM in ILB 140 Physics Colloquium
Please Notice Unusual
Time and Location
Carl Brans
Loyola University, New Orleans
Scalar Fields and Gravity
Abstract:
TBA
Tuesday
November 21, 2000
11:00 AM in ILB 235
Please Notice Unusual
Time and Location
Nabendu Pal
University of Louisiana at Lafayette
Careers in Mathematics and Statistics
Abstract:
This talk focuses on the recent trends in the job market for the
graduate students in the areas of
Applied Mathematics;
Pure Mathematics, and
Statistics.
Among other things we will talk about job opportunities in -
different sectors (academics, government and industry)
various regions within the United States; and
international job market.
We will also discuss the excellent opportunities for the students offered
by the Department of Mathematics, University of Louisiana at Lafayette, to
pursue graduate degrees with concentration in pure as well as applied
mathematics, and statistics.
Wednesday
November 29, 2000
2:30 PM in ILB 405 Sponsored by MathStat Club
Please Notice Unusual
Time and Location
Janet P. Buckingham
Statistical Analysis Section
Southwest Research Institute
San Antonio, Texas
Statistics is NOT a four-letter word -
Statistical Applications in an R&D Environment
Abstract:
A discussion of how statistics plays a part in successful projects
in a research and development organization. Views from a consulting
statistician on a variety of problems faced by engineers and scientists will be
presented. This talk is non-technical and will give insight on applying
statistics to research projects.
Thursday
November 30, 2000
3:30 PM in ILB 370
Cornelius Pillen
University of South Alabama
On Self-Extensions
Abstract:
Fix a positive integer n, a prime p, and look at square matrices of size n by n
whose entries are integers modulo p. Then take the subset of those matrices whose
determinants are not equal to zero and use the usual matrix multiplication as the operation.
We just construted a finite group. This group is just one example of an infinite family of
groups called Chevalley groups.
Now take the n-dimensional vector space consisting of vectors whose components are also
integers modulo p. Again the usual matrix operation defines an "action" of our
group on the vector space. Vector spaces that are equipped with such an
action are called modules.
In this talk we will give an introduction to the study of group
actions for finite Chevalley groups. In particular, we want to look at vector spaces
that contain no subspaces that are left invariant under the action of the group.
These are called simple modules.
Finally, we will give a partial answer to the following question: Is it possible
to build a new module out of two isomorphic simple ones?
Tuesday
January 16, 2001
3:30 PM in ILB 370
Please Notice Unusual
Day
Chris Bendel
University of Wisconsin, Stout
If you meet a module on the street, how can you tell if
it's projective?
Abstract:
It is well known that a module over a finite group is
projective if and only if it is injective. Indeed, this holds more
generally for any finite-dimensional cocommutative Hopf algebra over
a field. In general, however, these fundamental concepts are not the
same. In this talk, we will present a survey of methods for determining
the projectivity of a module over a class of algebras over a field of
prime characteristic. We will first note the differences between the
situation for finite groups and more general Hopf algebras. Then, we
will focus on a specific method based on a result of Chouinard, which
states that a module over a finite group is projective if and only if
it is projective upon restriction to every elementary abelian subgroup.
We present a generalization of this to a larger family of Hopf algebras
(or finite group schemes) which encompasses finite groups as well as
nipotent restricted Lie algebras (and more generally unipotent
infinitesimal group schemes).
Friday
February 9, 2001
3:30 PM in ILB 370
Please Notice Unusual
Day
Bimal K Sinha
University of Maryland Baltimore County
A statistical comparison of CMW and DPW for monitoring groundwater
pollutants
Abstract:
Monitoring of groundwater pollutants is performed by boring wells
at predetermined locations in the ground and assessing trace amounts of
certain chemicals. In this talk a statistical comparison between the
traditional conventionally monitored wells (CMW) and the more recent
direct push wells (DPW) based on actual data will be presented. The
problem is nontrivial because of the highly sparse nature of the data
arising out of many `flagged' cases. A Bayesian solution will be
indicated.
Monday
February 12, 2001
3:30 PM in ILB 370
Please Notice Unusual
Day
Daniel Shapiro
Ohio State University
Products of Sums of Squares
Abstract:No Title
An [r,s,n]-formula is defined to be an expression of the type:
where the 's and 's are indeterminates and each is a
bilinear form in X and Y. For example, norms of complex numbers
provide a [2,2,2]-formula while quaternions and octonions provide
[4,4,4] and [8,8,8]-formulas. In 1898 Hurwitz proved that there
is an [n,n,n]-formula iff n = 1, 2, 4 or 8, and he posed the
general question of determining when such formulas exist. In the
1920s Hurwitz and Radon settled the case s = n. The general
question seems very difficult, but many interesting aspects and
applications have been studied in the past few decades, touching on
algebra, combinatorics, topology, and geometry.
Monday
February 12, 2001 Mobile Mathematics Circle Lecture Sponsored by the Alabama Space Consortium
7 pm in ILB 430
Please Notice Unusual
Day and Time
Daniel Shapiro
Ohio State University
Scissors Congruence
Abstract:
Consider polygonal figures in the plane. If a figure is cut into a
finite number of pieces, those pieces can be rearranged without
overlapping (as in a jigsaw puzzle) to make another figure.
Certainly the new figure has the same area as the original. However
suppose we start with two figures of equal area. Must there be a way
to cut the first figure into pieces which can then be rearranged to
make the second figure? This question will be discussed, along with
various possibilities for generalization.
Monday
February 19, 2001
3:30 pm in ILB 370
Please Notice Unusual
Day
Titu Andreescu
University of Nebraska
Mathematical Induction: An Elegant and Powerful Method
Abstract:
My talk will feature essay-type, open-ended problems in undergraduate
mathematics in an attempt to move away from routine exercises and memorized
algorithms toward creative solutions to unconventional problems. I will
present examples and Olympiad problems from Algebra, Geometry, Number Theory,
and Combinatorics, because they are interesting, fun to solve, and they best
reflect mathematical ingenuity and elegant arguments.
Monday
February 19, 2001 Mobile Mathematics Circle Lecture Sponsored by the Alabama Space Consortium
7 pm in ILB 430
Please Notice Unusual
Day and Time
Titu Andreescu
University of Nebraska
Some of my favorite problems
Abstract:
A variety of examples and Olympiad problems from Algebra, Geometry, Number
Theory, and Combinatorics will be presented. They have been selected
because they are interesting, fun to solve and unconventional.
Thursday
March 22, 2001
3:30 PM in ILB 370
Ed Sandifer
Western Connecticut State University
Euler's Fourteen Problems
Abstract:
In 1755, Leonhard Euler sent a list of
14 "Quaestiones Mathematicae" to the St Petersburg Academy, with the intent
that those problems serve as a guide
for mathematical research for the next several years. Using these problems
as a model, we discuss the ways problems have been set before the
mathematical community and the role of problem lists, like Euler's and
Hilbert's. We also look at the particular problems Euler posed, in the
context of his times and the great mathematical, scientific and
philosophical issues of the day.
Friday
April 6, 2001
3:30 pm in ILB 370
Please Notice Unusual
Day
Noel Brady
University of Oklahoma
Finding Surfaces in Free-by-Cyclic Groups
Abstract:
Groups arise whenever we see symmetry in mathematics. For example,
you see lots of symmetries in a wallpaper pattern in your home.
The group in this instance consists of rigid motions of the plane
which move the wallpaper pattern in such a way that it superimposes
perfectly on itself. Such rigid motions are called symmetries of the
pattern. We may translate or shift the pattern one unit
to the right and see that it superimposes on itself. If we shift it
a further 2 units to the right, then we have shifted it a total of
3 units. There is a basic algebra at work here similar to the algebra
of numbers under addition: $1+2=3$. This algebraic object, the collection
of all symmetries of the pattern together with the operation of
composition, is called a group. Groups have a formal definition in
mathematics, and have been studied independently of geometry for a
long time.
Geometric group theory is a new branch of mathematics which advocates
a return to geometry when dealing with groups. An abstract group can be
viewed as a group of symmetries of some geometric object. We can study and
try to classify groups by studying these geometric objects. Gromov
achieved remarkable success with this approach when he defined the
notion of a hyperbolic group, and showed that hyperbolic groups have
some very beautiful properties.
In this talk, we'll give a brief survey of hyperbolic groups, and then
talk about some ideas for finding closed hyperbolic surface groups inside
other hyperbolic groups.
Friday
April 13, 2001
3:30 pm in ILB 370
Please Notice Unusual
Day
Subhash C. Bagui
University of West Florida
Breast Cancer Detection Using Rank Nearest Neighbor Classification Rules
Abstract:
In this article we propose a new generalization
of the rank
nearest neighbor (RNN) classification rule for multivariate data for
diagnosis of breast cancer. We study the performance of this rule using
two
well known databases and compare the results with the conventional k-NN
rule. We observe that this rule performed remarkably well, and the
computational complexity of the proposed k-RNN rule is much less than the
conventional k-NN rule.
Tuesday
April 17, 2001
2:00 pm in ILB 370
Please Notice Unusual
Day and Time
Pedro Lopez
Kansas State University and IST in Lisbon, Portugal
Quandle Cohomology and Invariants for Embeddings of
Codimension 2
Abstract:
In [1] quandle cocycles are used to concoct invariants for
embeddings of codimension two; 2-cocycles give rise to invariants for
(classical) knots and 3-cocycles give rise to invariants for knotted
surfaces.
Refining the ideas in [1] we are able to derive new invariants.
References:
[1] J. S. Carter et al, Quandle Cohomology and State-Sum Invariants of
Knotted Curves and Surfaces, math>GT/9903135, 1999
Wednesday
April 18, 2001 Keynote Address at the USA Research Forum
1:10 pm in the Student Center Ballroom
David S. Moore
Purdue University
Statistical Thinking: How to Tell the Facts from the Artifacts
Abstract:
Statistics in its technical dress has miraculous properties: it makes
invisible effects visible, appeases hostile editors, and sets shared
standards for many fields of science. Yet a few elements of statistical
thinking can help any educated person assess most ``statistical''
controversies. Are we dealing with data or anecdotes? How were the
data obtained? How large is the advertised effect relative to variation
among individuals? What lurking variables were considered (or ignored)?
This nontechnical talk illustrates the principles of statistical
thinking through examples.
Wednesday
April 18, 2001
3:30 pm in ILB 140
David S. Moore
Purdue University
Statistical Literacy and Statistical Competence
for the New Century
Abstract:
In an environment in which much that once required thought is
automated, what should all educated people know about data, variation,
and chance? That's statistical literacy. What should someone who works
with data now and then in her job remember from the statistics course
she took 5 years ago? That's statistical competence. Both statistical
literacy and statistical competence are important to knowledge workers,
more important in most settings than the detailed mastery that
constitutes statistical professionalism. This informal talk offers one
opinion on the nature of statistical literacy and statistical
competence, and indirectly on the teaching of statistics to beginners.
Wednesday
May 30, 2001
3:30 pm in ILB 370
Please Notice Unusual
Day
Ilia Kapovich
University of Illinois at Urbana-Champaign
On the Poenaru condition and almost convexity.
Abstract:
Poenaru condition P(n) generalizes Cannon's almost convexity
condition for a finitely generated group and says that balls
in the Cayley graph of the group have some mild convexity
properties. We generalize the Poenaru condition and prove,
in particular, that Poenaru P(2)-groups are finitely presentable,
have word problem solvable in exponential time and that they satisfy
linear isodiametric and double exponential isoperimetric inequalities.
Department of Mathematics and Statistics
ILB 325
University of South Alabama Mobile, AL 36688
phone: (251) 460-6264 (voice), (251) 460-7969 (fax)
dept e-mail:
current page:
http://www.southalabama.edu/mathstat/colloquia/colloq-00-01.shtml
's and 
's are indeterminates and each 
is a
bilinear form in X and Y. For example, norms of complex numbers
provide a [2,2,2]-formula while quaternions and octonions provide
[4,4,4] and [8,8,8]-formulas. In 1898 Hurwitz proved that there
is an [n,n,n]-formula iff n = 1, 2, 4 or 8, and he posed the
general question of determining when such formulas exist. In the
1920s Hurwitz and Radon settled the case s = n. The general
question seems very difficult, but many interesting aspects and
applications have been studied in the past few decades, touching on
algebra, combinatorics, topology, and geometry.
