Monday, April 15, 2002
| Title |
Monotonicity of Eigenvalues of Hermitian Matrices |
| Speaker |
Professor Mourad Ismail |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
We discuss various discrete techniques to describe how the eigenvalues of a
parameter-dependent Hermitian matrix change as a function of the parameter.
Monday, April 8, 2002
| Title |
Cocycle Knot Invariants, Alexander and Burau Matrices, Part
II |
| Speaker |
Marina Appiou-Nikiforou |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Monday, April 1, 2002
| Title |
Cocycle Knot Invariants, Alexander and Burau Matrices |
| Speaker |
Marina Appiou-Nikiforou |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
We will talk about extensions of quandles by 2-cocycles in relation to knot
colorings. We will also demonstrate relations between cocycle invariants and
Alexander and Burau matrices. Examples of the Whitehead link and Borromean rings
will be given.
Monday, March 25, 2002
| Title |
Using Circulant Matrices to Solve Low-Level Polynomials |
| Speaker |
Karol McIntosh |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
The idea is to construct a circulant matrix with a specified characteristic
polynomial. Roots of the polynomial become eigenvalues which are trivially found
for circulant matrices. This approach provides a beautiful unity to the solutions
of quadratic, cubic, and quartic polynomials. This is a talk on a paper by D.
Kalman & J. E. White.
Monday, March 18, 2002
| Title |
Distance-Regular Graphs, Part II |
| Speaker |
Dr. Brian Curtin |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
We continue with a gentle introduction to distance-regular graphs. This second
part will focus on the Bose-Mesner algebra of a distance-regular graph and its
representations. We shall also discuss the “Q-polynomial”
property (which is defined algebraically) and some its characterizations.
The script of the first part is available on my web page at
http://www.math.usf.edu/~bcurtin/DRG1.pdf.
Monday, March 4, 2002
| Title |
Distance-Regular Graphs |
| Speaker |
Dr. Brian Curtin |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
I will discuss some basic combinatorial and algebraic features of distance-regular
graphs, objects central to my research. This talk is intended to be a gentle
introduction to the subject. I will give some examples and briefly discuss some
connections to other topics as well as presenting some basic facts.
Monday, February 25, 2002
| Title |
Software to Generate Codes for DNA Computations |
| Speaker |
Mr. David Kephart |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
In DNA nontechnology and DNA based computations the design of DNA sequences
that are error resistant is of essential importance. The set of all sequences
that are generated by a biomolecular protocol forms a language over the four
letter alphabet {A,G,C,T}. This
alphabet is associated with a natural involution mapping h, h(A)
= T and h(G) = C. In order to avoid
undesirable Watson-Crick bonds between the words (undesirable hybridization),
the language has to satisfy certain variations of coding properties such as:
being a prefix (suffix) code, comma-free code, and more particular for DNA,
no involution of a word is a subword of another word, or no ivolution of a word
is a subword of a composition of two words.
We will demonstrate the alpha-test version of software that can either (1)
test whether a given set of code words satisfy any of these properties or (2)
design a set of code words that satisfy certain coding properties defined by
the user. Though the default alphabet for the program is the DNA alphabet of
{A,G,C,T} it is designed to accept
(or generate) words over arbitrary alphabet and as such it can be used for a
variety of applications.
Note: This work is joint with K. Mahalingam and N. Jonoska.
Monday, February 18, 2002
| Title |
Coloring Knots With a 4-Color Palette |
| Speaker |
Dr. Masahiko Saito |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
First I review a coloring scheme of knots and links. For a given 4-colored
link, I give a rule of changing the (underlying) colors by a yellow marker.
Whether or not you can consistently change colors this way depends on a given
link, and can be used to distinguish links.
Then I will discuss how to come up with such marker rules, and mention a
relation to the quandle cocycle knot invariants.
Monday, February 11, 2002
| Title |
Games, Logics, and Complexity III |
| Speaker |
Dr. Greg McColm |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
We will conclude with a look at second order logic, the polynomial hierarchy,
and other hallucinatory nonsense.
Monday, February 4, 2002
| Title |
Games, Logics, and Complexity II |
| Speaker |
Dr. Greg McColm |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
We continue with the game for PTIME, and move on to NLOGSPACE.
Monday, January 28, 2002
| Title |
Games, Logics, and Complexity |
| Speaker |
Dr. Greg McColm |
| Time |
9:00-10:00 a.m. |
| Place |
PHY 120 |
Abstract
There are a number of logics that are associated with famous complexity classes.
And there are a number of games that are associated with famous logics. This
gives us an opportunity for some representation theorems that may enable to
understand the complexity classes better.
We will start with our old friend PTIME …