# Philip Boyland

## Professor of Mathematics and Co-Director of the Center for Applied Mathematics, University of Florida

Philip Boyland

** **

**Date**: Thursday, March 5, 2015**Time**: 3:10 PM**Place**: Byker Auditorium, Chemistry and Biochemistry Building

**Title**: Topology, Tangling and Fluid Mixing

**Sponsoring department**: Mathematical Sciences

## Summary:

When we look at flowing water, our attention is drawn to the complicated patterns,
the swirls, eddies and flow lines that change and evolve,

but also maintain a kind of constancy. These images and structures have

fascinated artists and scientists for millennia.This lecture will begin with a description
of some of the morphology and mathematics of these structures, followed by a discussion
of their application to fluid mixing. Ideas and theorems from topology and chaotic
dynamical systems will yield principles to design efficient mixers. The main mathematical
idea is that the topological constraints give rise to the exponential growth of material
lines and thus of the gradients of transported quantities. The lecture will conclude
with a discussion of how the same collection of topological/dynamical ideas can be
used to quantify the entangling of such diverse entities as hair, ocean floats and
individual motion in crowds.

## About the speaker:

Philip Boyland is an expert in topological methods in dynamical systems, which is the mathematical study of system evolution. He has also made significant contributions to Hamiltonian and fluid dynamics. He is known for his discovery of a two-dimensional analogue of Sharkovki’s Theorem and his pioneering application of topological chaos in designing viscous fluid stirring protocols. A skilled expositor, he has given over 100 conference and seminar presentations. He was a Postdoctoral Fellow at Boston University and the Mathematical Science Research Institute in Berkeley. He was also a Visiting Research Fellow at the Institute for Mathematics and its Applications in Minneapolis, the IME at the University of Sao Paulo, and twice at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK. He is currently Professor of Mathematics and Co-Director of the Center for Applied Mathematics at the University of Florida.