Colloquia — Spring 1999
Friday, January 22, 1999
| Title: |
The Symbolic Dynamics of Tiling the Integers |
| Speaker: |
Ethan Coven |
| Time: |
TBA |
| Place: |
TBA |
Abstract
A finite collection of finite sets tiles the integers if and only if the
integers can be expressed as a disjoint union of translates of members of the
collection. We associate with such a tiling a doubly infinite sequence with
symbols the sets in the collection. The set of all such sequences is a sofic
system, called a tiling system.
For example, if P consists of the sets {0} and {0,1}, then the
tiling system is the collection of all doubly infinite sequences with symbols
R (red, the “color” of {0}) and B (blue, the
“color” of {0,1}) such that between any two consecutive appearances of
R, there are an even number of B, i.e., the “even
system”. This sofic system is closely related to the
“Golden Mean” shift of finite type. Many transitive shifts of finite
type, e.g., the full 2-shift, cannot be realized (up to topological conjugacy) as
tiling systems. However, we show that, up to powers of the shift, every shift of
finite type can be realized as a tiling system.
Friday, February 12, 1999
| Title: |
An Unusual Way to Generate Conic Sections and two Related Euclidean
Constructions |
| Speaker: |
Sam Sakmar
Department of Physics, USF |
| Time: |
3:00-4:00 p.m. |
| Place: |
PHY 130 |
Friday, February 26, 1999
| Title: |
Braids of surfaces in 4-space |
| Speaker: |
Prof. Seiichi Kamada
U. of South Alabama (and Osaka City U.) |
| Time: |
3:00-4:00 p.m. |
| Place: |
PHY 130 |
Abstract
An m-braid is a collection of m strings in a cylinder
D2 × I1 satisfying a certain
condition. The set of m-braids forms a group, called the
m-braid group. This group plays an important role in knot theory. Knot
theory treats of embedded closed curves in Euclidean 3-space, and 2-dimensional
knot theory treats of embedded closed surfaces in 4-space. In this talk, a
generalization of m-braids is introduced, which is called a
2-dimensional m-braid or a surface braid. That is a surface in a
bi-disk D2 × D2 satisfying a certain
condition. The set of 2-dimensional m-braids forms a monoid (a
semi-group with identity). 2-dimensional braids are related with 2-dimensional
knot theory by the following two theorems.
Generalized Alexander's theorem. Any closed surface in 4-space is
described by a closed 2-dimensional braid.
Generalized Markov's theorem. Such a braid description is unique up to
braid isotopy, conjugation and stabilization.
Monday, March 1, 1999
| Speaker: |
Professor Rudy Dvorak
Astronomy Department
University of Vienna
Vienna, Austria |
| Title: |
The Dangers of Near-Earth Asteroids |
| Time: |
2:00-3:00 p.m. |
| Place: |
PHY 108 |
Thursday, March 4, 1999
| Title: |
Some Asymptotic Results and Exponential Approximations in Semi-Markov Models |
| Speaker: |
Dr. George Roussas
Professor and Associate Dean
Department of Mathematics & Statistics
University of California, Davis |
| Time: |
2:00-3:00 p.m. |
| Place: |
PHY 118 |
Monday, March 15, 1999
| Title: |
A Rayleigh-Ritz Method Applied to a Two-Dimensional Inverse Spectral Problem |
| Speaker: |
C. Maeve McCarthy
Murray State University |
| Time: |
3:00-4:00 p.m. |
| Place: |
PHY 120 |
Tuesday, March 16, 1999
| Title: |
Groups of 2×2 Matrices |
| Speaker: |
Ross Geoghegan
SUNY at Binghamton |
| Time: |
2:00-3:00 p.m. |
| Place: |
PHY 108 |
Friday, March 19, 1999
| Title: |
Estimation With Meyer Types and Wavelets |
| Speaker: |
Marianna Pensky |
| Time: |
3:00-4:00 p.m. |
| Place: |
PHY 118 |