Susquehanna Mathematics Colloquium

SU Math/CS Colloquium Archive

Spring, 2007

Feb 22^nd – 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.

March 12^th – Derek Smith, Lafayette College

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!)

March 19^th – 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!)

March 21^st – 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.)

March 28^th – Cornelius Pillen, University of South Alabama

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.

March 29^th – Zdzislaw Jackiewicz, Arizona State University

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.)

April 16^th – Jay Stine, College of Misericordia

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!)