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Fall 2006
Algebra Seminar
Analysis Seminar
Topology-Geometry Seminar
Math & CS Club
Algebra Seminar
Thursdays, 2:10 - 3:00 in Ritter Hall 222
| DATE |
SPEAKER |
TITLE |
Sept. 14
|
Dave Jackson
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"The Layer Lemma"
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Abstract: It is well-known
that the (left or right) Cayley graph
for a finitely generated group has 0,1,2 or infinitely many ends.
In joint work over recent years, Vesna Kilibarda and I have defined
the number of ends for finitely generated semigroups and monoids.
For arbitrary m,n we have constructed examples of monoids T such that
the left Cayley graph for T has m ends while the right Cayley graph
for T has n ends. In this talk, I will present the Layer Lemma which
provides a reasonably transparent and uniform construction for vast
numbers of such examples. I will outline a proof of the Layer Lemma.
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Sept. 21
|
Greg Marks
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"An application of calculus to ring
theory"
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Abstract: To check that every
ideal of a commutative ring is
finitely generated, it is enough to test the prime ideals. To
check that every ideal is principal, again it is enough to test
the prime ideals. We will show that neither statement is true
if the word "prime" is changed to "maximal"; using freshman calculus we
will construct a commutative ring in which every maximal ideal
is principal but in which certain ideals are not even finitely
generated,
thus establishing that calculus has important practical applications.
This talk is geared toward graduate students (though faculty are
obviously welcome too) and will assume only a knowledge of calculus
and some basic commutative ring theory.
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Sept. 28
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Greg Marks
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"On quasi-duo rings"
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Abstract: The speaker will be
discussing some recent
joint work with A. Leroy and J. Matczuk.
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Oct. 5
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Greg Marks
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"On quasi-duo rings" Part
II
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Oct. 12
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Greg Marks
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"On quasi-duo rings"
Part III
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Oct.
19
|
Greg
Marks
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"On
quasi-duo rings" Part IV
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Oct. 26
|
Greg Marks
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"On quasi-duo rings"
Part V
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Nov. 2
|
Greg Marks
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"On quasi-duo rings"
Part VI
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Nov. 9
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Greg Marks
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"On quasi-duo rings"
Part VII
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Nov. 16
|
Kevin Scannell
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"On largeness"
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Abstract: I will define
various notions of largeness for discrete groups and
indicate why they might be of interest to 3-manifold topologists. I
will
illustrate some techniques for verifying largeness by looking at the
so-called
"Fibonacci groups".
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Analysis Seminar
Tuesdays, 2:10 - 3:00 in Ritter Hall 316
| DATE |
SPEAKER
|
TITLE |
Sept. 26
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Tom McNamara
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Intro to Non-Commutative
Harmonic Analysis
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Abstract: We
begin with a review of classical Fourier
analysis, with an empahsis on its group theoretic interpretations.
From here we seek to investigate one of the fundamental themes
of harmonic analysis: Try to decompose a space of functions on
a group (or a set on which a group acts) in terms of the most
elementary
functions we can find which mirror the group operation. We start our
investigation by looking at a finite group actions on a finite set,
then move on to the group SO(3).
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Oct. 3
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Tom McNamara
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Intro to Non-Commutative
Harmonic Analysis, Part II
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Oct. 10
|
Myung-Sin Song,
Assistant Professor,
SIU Edwardsville
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Wavelet Image Compression
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Abstract: While
wavelet analysis is perhaps a chapter in function
theory, we show that the algorithms that result from it is the key
to the processing of numbers, or more precisely of digitized
information,
signals, digital images, etc. Thus, applications of the wavelets
include
substantial parts of signal and image processing, and many other fields
of science and engineering. My talk focuses on the processing of images
with the use of custom designed wavelet algorithms, and threshold
filters
with their mathematical properties. This is to outline various
connections between Hilbert space geometry and image processing. That
is, referring a digital image as a matrix and show how the low-pass
filter and high-pass filter as operators are digitized and are being
used in a computer program to compress the image.
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Oct. 17
|
Paul Koester,
Ph.D. Candidate,
Wash. Univ. St. Louis
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Fourier Analytic Methods in
Additive Combinatorics
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Abstract: Additive
combinatorics is that branch of number theory
concerned with finding arithmetic patterns in sets of integers. A
beautiful example of a result in this subject is the Green-Tao theorem,
that the prime numbers contain arbitrarily long sequences whose
consectutive
differences are all the same. While the statements of the theorems in
additive combinatorics have a very strong number theory flavor, the
proofs typically require tools from many subjects. One of the most
fruitful
tools is the discrete Fourier transform. In this talk, we will survey
some of the basic results in additive combinatorics, emphasizing the
role of Fourier analytic methods.
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Oct. 24
|
Tom McNamara
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Intro to Non-Commutative
Harmonic Analysis, Part III
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Abstract: We will continue with our examination SO(3) acting
on the two-sphere. The spherical harmonics will be shown to decompose
the function space L^2(S^2). Particular attention will be given to the
role played by the fact that S^2 is compact. From there we move on to
a non- compact, non-abelian Lie group G, investigating the action of
this
group on a normal subgroup N. We will look for a relationship between
L^2(N) and L^2(G), drawing parallels to the compact case.
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Oct. 31
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Cristina Draghici
(Washington University)
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Rearrangements on the
unit circle
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Abstract: In this talk I will present two types of rearrangements:
polarization, which is a very simple rearrangement of a function, also
called two-point rearrangement, and the symmetric decreasing
rearrangement.
Then I will talk about integral inequalities of functions. Some of
these
inequalities can be proved using the polarization technique, other
cannot.
I will mainly focus on inequalities which cannot be proved by
polarization,
and present an inequality on the unit circle involving two
diffeomorphisms,
and I will give a complete characterization of these diffeomorphisms.
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Nov. 7
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Mark Pedigo
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"Continuous functions are dense
in L1(T)"
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Abstract: A measurable function f is said to be in L1(R)
if ∫ |f| < ∞. These
functions play an important role in analysis. We show that any function
in L1(R) can be approximated by a continuous
function in the L1 norm. More precisely, for any L1(R)
function f, given ε > 0 there exists a continuous
function g in L1(R) such that the L1
norm of (f-g) is less than ε. We present a proof of
this
fact, along with a running example to illustrate the concepts of the
proof. The talk concludes with an application which sets the stage for
the November
14th seminar.
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Nov.14
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Ashley Reynolds
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"Trigonometric
polynomials are dense in L1(T)"
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Abstract: In this talk, we will show that the trigonometric
polynomials are dense in L1(T) using techniques from
Fourier
analysis. The material in this talk will follow the work of
Katznelson's
text An Introduction to Harmonic Analysis.
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Nov.21
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Morten Nielsen,
Aalborg University
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"Sparse Representation
of Data"
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Abstract: Sparse
approximation techniques have been at the core of a
rapidly evolving and very active area of research since the 1990s.
Their
most visible technological success has certainly been in the
compression
of high-dimensional data with wavelets. However, approximating a signal
or
an image with a sparse linear expansion from a possibly overcomplete
dictionary
of basis functions (called atoms) has turned out to be an extremely
useful
tool to solve many other signal processing problems. In this talk, I
will
discuss some of the mathematical and computational aspects of sparse
representations
using redundant dictionaries in a finite dimensional space.
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Topology-
Geometry Seminar
Thursdays, 3:00 - 4:00 in Ritter Hall 222
| DATE |
SPEAKER |
TITLE |
Sept.7
|
Steve Harris
|
"Topology in the Causal Boundary
of a Spacetime:
(1) Quasi-Compactness in General and
(2) Non-Hausdorffness for Simple Product Spacetimes"
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Abstract: (1)
Adding the future causal boundary to a strongly causal spacetime
results in a topological space with causal structure which
has this quasi-compact property: Any sequence of points has
a subsequence with a limit point so long as there is an event
in the common past of infinitely many of those points.
(2) For a simple product spacetime, R x N (N Riemannian), adding the
causal boundary produces a result (the causal completion) which is
related to a simple product on a compactification of N (formed from
adding its Busemann boundary). Either that Busemann compactification is
Hausdorff and the causal completion of the spacetime is essentially a
simple product of
R with the Busemann compactification of N; or the Busemann
compactification is non-Hausdorff, requiring more convergence than is
naively expected, and the causal completion of the spacetime is more
complicated than a product structure.
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Sept.14
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Steve Harris
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"Topology in the Causal
Boundary of a Spacetime" II
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Sept.21
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Steve Harris
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"Topology in the Causal
Boundary of a Spacetime" III
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Sept.28
|
Steve Harris
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"Topology in the Causal
Boundary of a Spacetime" IV
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Oct. 5
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Robert Huff
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"Flat Structures on Minimal
Surfaces"
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Abstract:
A powerful technique in minimal surface theory
involves using meromorphic one-forms on a Riemann surface to prove the
existence of previously undiscovered minimal surfaces in space. The
one-forms are typically chosen to be compatible with a pre-existing
visual image of the surface. Such images are quite common due to
the development of computer graphics packages, and there are dozens of
images of minimal surfaces available on the internet for which
there is no mathematical existence proof.
In this series of talks, we will define a
minimal surface and discuss some examples, both new and old. Then, we
will outline the technique of finding flat stuctures
on minimal surfaces. Two particular flat structures will then
be discussed in more detail in an attempt to show how broadly this
technique can be applied. Finally, we will conclude with a specific
application in an effort to communicate the mathematical ideas involved
in an existence proof.
|
Oct. 12
|
Robert Huff
|
"Flat Structures on Minimal
Surfaces" Part II
|
Abstract: See
above.
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Oct. 19
|
Bryan Clair
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"Ricci flow and 3-manifolds"
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Abstract: Hamilton's
Ricci flow program was recently completed by Perelman to prove the
Poincare conjecture, and possibly Thurston's geometrization conjecture
as well. In what promises to be a rather long and occasionally
misguided
series of seminars, we will attempt to understand the Ricci flow and
its applications to 3-manifold topology.
This first week we'll look at Ricci curvature and some of the basics of
Ricci flow.
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Oct. 26
|
Bryan Clair
|
"Ricci flow and 3-manifolds"
II
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Abstract: This week: basics of Ricci flow
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Nov. 9
|
Bryan Clair
|
"Ricci flow and 3-manifolds"
III
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Abstract: This week: more basics of Ricci flow
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tba
|
David Letscher
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Abstract: -----
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Math & CS Club
Wednesdays, 4:10 - 5:00 in Ritter Hall 316
| DATE |
SPEAKER
|
TITLE |
Tues. Sept 26
|
-----
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Fall Semester BBQ
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Abstract: From
3:30 - ca 5:00 pm the department will host
a BBQ in the lobby of Ritter Hall. Students and faculty are welcome
to encouraged to attend this event.
|
Wedn. Oct. 18
4:00-5:30 RH200
|
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Steve Harris
|
Wormholes, Time Machines, and
What Happens If I Shoot Grandma
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Abstract: What
does a wormhole in space mean? What, mathematically, is a time machine?
Are they related? The Math and CS Club invites
everyone interested to join us for a talk by Dr. Harris on space-time
geometry.
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Wedn. Nov. 15
4:00-5:30 RH200
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David Letscher
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Football Statistics and BCS
Rankings
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Abstract: Dr.
Letscher will present an interesting perspective
on extracting information from football statistics and identifying the
team
with the best chance of winning from the numbers.
Anyone who has interest is invited to join us for this discussion.
Refreshments
will be provided.
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