Thursday,
Feb 22nd
Adam
Dreibelbis – SU ’07 (Senior Colloquium)
Three-Dimensional Finite
Difference Time-Domain Modeling of the Schumann Resonances on
Earth and Mars
ABSTRACT: Schumann Resonances are extremely low
frequency electromagnetic waves that resonate between the highly conducting
Earth's surface (or Mars', etc.) and the highly conducting ionosphere.
The observation of these resonances can provide information about solar flares
and other atmospheric events. The three-dimensional finite difference
time-domain modeling is a technique developed by Yang and Pasko
that relies on numerical analysis to provide realistic solutions to Schumann
Resonance problems.
Mon.,
March 12th
Derek
Smith,
Quaternions
for Fun and Profit
ABSTRACT: Here's an SAT ``analogy'' question
from 1988.
(Problem
42) real numbers :
complex numbers :: complex numbers :
____?_____
The answer, (D) quaternions, was missed by more than 85%
percent of the examinees, which I find troubling. One of the goals of my presentation will be
to ensure that you won't miss this question, should it ever arise on any
standardized test you have to take. Just
as the complex numbers double the single dimension of the real number line, the
quaternions double again to give dimension 4.
This might suggest that they skipped the chance for application in our
3-dimensional world, but in fact quaternions are often the algebraic tools of
choice to represent 3-dimensional rotations, which leads to applications from
computer graphics to wireless communication.
In this introductory presentation, you will learn the mathematics of the
quaternion and related algebras, with several applications presented along the
way. (NOTE NEW DATE!)
Mon.,
March 19th,
Alex Wilce,
SU
Background
to Quantum Information Theory
ABSTRACT: In
preparation for Wednesday’s visit by Chris Fuchs, I’ll outline the standard
mathematical apparatus of quantum mechanics, stressing analogies (and
disanalogies) with classical probability theory. (NOTE
NEW DATE!)
Wed.,
March 21st
Chris Fuchs, Lucent Technologies/Bell Labs
Math
Problems from the Far Side of Quantum Information
ABSTRACT: The field of Quantum Information has recently rightly
attracted great interest for the technological fruits it may bear. But there is a sect of its practitioners who
think it stands a chance to bring us much more than that---namely, that its
theoretical tools will give us a means for exploring what quantum mechanics is
really all about and for settling some of the deepest problems in physics. The roots of this optimism come from a very
old thought: that a quantum state has
more to do with representing its user's information, than any inherent physical
property of the system to which it is ascribed.
What is new and nice is that quantum information teaches us how to
formulate this idea precisely and even check its consistency. Nicer still for the mathematics community is
the number of juicy mathematical problems the consistency-checking process
poses. In this talk, I will review some
of the history of this and then quickly settle on a sample problem that has
been annoying me a lot lately: the
question of the existence of symmetric informationally complete
positive-operator-valued measures for finite dimensional Hilbert spaces. I'm not alone---it turns out to be equivalent
to a 30-year-old problem in coding theory---but I will say some things about it
that you may not have heard before. (The talk should be accessible to students
who’ve had linear algebra.)
Wed.,
March 28th
Cornelius Pillen,
Group
Representations
ABSTRACT: Many areas of modern mathematics and
the sciences explore the actions of groups on other mathematical objects. In
particular, one might be interested in groups acting on vector spaces. This
allows for group elements to be "represented" as matrices. In this
talk we will use some easy examples to introduce the audience to the various
flavors of representation theory of finite groups. We will compare ordinary
representations to modular representations and give some historical background.
Only some basic knowledge of linear algebra is needed in order to enjoy the
presentation.
Thurs., March 29th
Introduction
to Bioinformatics Sequence and genome analysis
ABSTRACT: We describe various tools for DNA, RNA, and protein
sequence analysis. We also describe some of the underlying algorithms based on
global, local and multiple sequence alignments with scoring block substitution
matrices motivated by biological and evolutionary considerations. We will also
discuss tools for finding protein coding regions in DNA sequences based on
statistical approaches.
(NOTE SPECIAL ROOM: This colloquium will be held in SEIBERT 108.)
Mon., April 16th
Jay Stine,
Pre-Hausdorff
Spaces CANCELLED
The notion of using open sets to separate
points or closed sets from other points or closed sets is fundamental in
general topology. The classical T2 (a.k.a. Hausdorff) separation axiom is often
assumed in a first course in topology, and even in practice by working
mathematicians. Consequently, separation
conditions weaker than T2 are often given little consideration. However, there are many interesting and
useful topological spaces which are not Hausdorff. In this talk I will introduce a separation
axiom called pre-Hausdorff. This new
separation condition generalizes the Hausdorff axiom, and has advantages over
it topologically which I will discuss. I
will give some characterizations of pre-Hausdorff spaces, and a
characterization of Hausdorff spaces in terms of pre-Hausdorff. I will also discuss some classical Theorems
of general topology which can or cannot be generalized by replacing the
Hausdorff condition by pre-Hausdorff. (NOTE NEW DAY!)
Unless otherwise noted, colloquia will begin at 4:15 p.m., in Seibert 017. (Light refreshments will be served at 4:05.)
For further information, contact Alex Wilce (wilce@susqu.edu) or Jeff Graham (graham@susqu.edu )