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 \(D^2\times I^1\) 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 \(D^2\times D^2\) 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 \(2\times 2\) 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