University of South Florida

College of Arts and Sciences

Search

Menu

Give Now

Title: The Symbolic Dynamics of Tiling the Integers Speaker: Ethan Coven Time: TBA Place: TBA

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.

Title: An Unusual Way to Generate Conic Sections and two Related Euclidean Constructions Speaker: Sam Sakmar, Department of Physics, USF Time: 3:00pm‐4:00pm Place: PHY 130

Title: Braids of surfaces in \(4\)-space Speaker: Seiichi Kamada, U. of South Alabama (and Osaka City U.) Time: 3:00pm‐4:00pm Place: PHY 130

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.

Title: The Dangers of Near-Earth Asteroids Speaker: Rudy Dvorak, Astronomy Department University of Vienna Vienna, Austria Time: 2:00pm‐3:00pm Place: PHY 108

Title: Some Asymptotic Results and Exponential Approximations in Semi-Markov Models Speaker: George Roussas, Professor and Associate Dean Department of Mathematics & Statistics University of California, Davis Time: 2:00pm‐3:00pm Place: PHY 118

Title: A Rayleigh-Ritz Method Applied to a Two-Dimensional Inverse Spectral Problem Speaker: C. Maeve McCarthy, Murray State University Time: 3:00pm‐4:00pm Place: PHY 120

Title: Groups of \(2\times 2\) Matrices Speaker: Ross Geoghegan, SUNY at Binghamton Time: 2:00pm‐3:00pm Place: PHY 108

Title: Estimation With Meyer Types and Wavelets Speaker: Marianna Pensky Time: 2:00pm‐3:00pm Place: PHY 118