Talks/Seminars

Abstract. Dynamical systems from physics are often continuous time systems, whereas the mathematical models often use discrete time. When does a discrete-time system embed in a continuous-time system?

In the late 1960's, Ornstein constructed the first system with no square root, thus providing an example which not only did not embed in an R-action, it didn't even embed in a rational action.

In the 1950's, Halmos initiated a study of which dynamical properties were generic, in the topological sense. What I plan to do in this talk is discuss some of the elementary ideas needed to show that the generic map has a square root; indeed, roots of all orders. The argument uses a nice topological lemma by Randall Dougherty and a topological Zero-One Law due to Glasner and yours-truly.

The argument seems tantalizingly close to showing that generically a map extends to a Q-action. However, an example that I will discuss (due to a graduate student, Blair Madore) suggests that it may not be so easy to close the gap.

(30Oct1998:  I gave 4 talks on this subject. Professor Vince will continue the topic starting on 04Nov1998, at 12:50PM.)

On Thursday, I will be giving gave a gentle introduction to Dissection Theory. No blood will be spilt.

Date: 20 Nov., 1997, at 7PM.
Title: "Dissection theory, Dehn's Theorem and Scissor Congruence"
Place: The Univ. of Florida Math Dept. Lounge, 3^rd floor, room 358.

The entire talk will be pictures. I plan to show how to go from any polygon to any other (of equal area) by straight-line cuts. In contrast, Dehn -answering Hilbert's Third Problem- showed that for 3-dimensional polyhedra, the analogous statement is false. In modern language, this is a nice application of linear algebra.

I'll give the modern short proof of this, skipping a detail about the dihedral angle of a tetrahedron. See my Dehn's solution to Hilbert's third problem (pdf) for a complete languorous solution, in only 2+epsilon pages.

Talks/Seminars Page