Looking for Roots and Finding Chaos

UA Huntsville Distinguished Lecture Series

Dr. Davar Khoshnevisan

Department of Mathematics
University of Utah

11:30 Friday, 5 March 2010
001 Auditorium, Wilson Hall
Pizza at 11:00

Abstract

In this talk we will argue that our number system is profoundly complex, and that this complexity is tied intimately to the nature of the notions of "randomness" and "chaos."

Over 4000 years ago, Babylonians discovered an iterative method, or "algorithm" for computing the square root of an arbitrary positive number. Their method is extremely efficient; in fact, small variations of their method are still being used in modern computational machines.

In order to keep the technical requirements of this talk to a minimum, we concentrate on a concrete, though instructive, example: Namely, the square root of 2, whose analysis dates at least as far back as 5 BC in the work of Hipassus. We introduce a close variation of the Babylonian algorithm, and see concretely how it leads us naturally to chaos.

This is a self-contained discussion, with few if any, requirements from university-level mathematics and/or physics.

Biographical Sketch

Dr. Davar Khoshnevisan is Professor of Mathematics at University of Utah. He has made significant contributions in random fields, stochastic differential equations, Levy processes and dimension estimation and geometric measure theory for high-dimensional data. Among his achievements, he was a winner of The 1998 Rollo Davidson Prize awarded by University of Cambridge, UK and he was an elected council member of Institute of Mathematical Statistics in 2009. He has published more than 80 research papers and 3 books. He will be a plenary speaker on the 34th Conference on Stochastic Processes and Their Application in 2010, one of the most important conferences in the field.