June 26, 2016
The Fields Institute, Toronto, Canada
Tuesday, October 1, 2013
7:00 – 9:00 p.m. at the Fields Institute, 222 College Street, Toronto
The 2013 Fields Medal Symposium is centred on the work of 2010 Fields Medallist Elon Lindenstrauss, and its current and potential impact. The goal is bring Lindenstrauss' work to a broader public audience. This special program brings together students and mathematics professionals for an evening of discussion and inspiration, giving students the opportunity to ask questions and learn new ideas. Ralf Spatzier (University of Michigan) and Dmitry Jakobson (McGill University) will stir students' curiosity with talks about their work. Later in the evening, Elon Lindenstrauss will join Ralf, Dmitry, and Peter Sarnak for a panel discussion, moderated by Zach Paikin.
Public Talks

Dynamical Systems, Spectra and Geometry
Dmitry Jakobson, McGill University (slides)

The Laplace operator (or Laplacian) is a differential operator that arises in celestial mechanics, heat and wave propagation, and quantum mechanics. Eigenfunctions of the Laplacian describe vibrations of a string or a drum, pure states in quantum mechanics (atoms and molecules), and many other phenomena.

We will discuss how eigenfunctions behave when their energy (or their frequency) is increasing; the simplest example is provided by the functions sin(nx), when n increases. Certain properties of eigenfunctions of Laplacians on surfaces depend on the properties of motion along geodesics (geodesic flow) on the surfaces; geodesics are the shortest paths from one point on the surface to another (light travels along geodesics). We will also discuss how curvature of the surface influences the geodesic flow.

Dynamical Systems and Periodic Orbits
Ralf Spatzier, University of Michigan

In science we often consider systems that change with time. This could be the solar system, or a population of viruses or the weather. Dynamical systems theory in mathematics considers such systems abstractly. Of particular importance are periodic orbits. These are positions or states which return to themselves time and again. For example the earth revolves around the sun year after year. We will give precise mathematical formations of these concepts, discuss examples and questions like: When do periodic points exist? How many periodic points are there? Counting periodic points is closely related to entropy which is a measure of the speed of "mixing" of a system. I will touch on this fundamental idea which is one of the most important in dynamics.

Panel Discussion: From Number Theory to Chaos and Back. Where Do Mathematical Ideas Come From?

Have you ever wondered what mathematicians do? Or how they approach a problem? Do they set out the try to win a Fields Medal? How do mathematicians know what problems are important? These questions and more will be answered during the panel discussion.

Panellists: Dmitry Jakobson (McGill University), Elon Lindenstrauss (Hebrew University), Peter Sarnak (Institute for Advanced Study), Ralf Spatzier (University of Michigan) Moderator: Zach Paikin (Munk School of Global Affairs, University of Toronto)

Gold Level Sponsor

Silver Level Sponsor

James Stewart, Prof Emeritus, McMaster University; textbook author, donor of the Fields Institute Library
Bronze Level Sponsors

Edward Bierstone, Fields Institute and the University of Toronto
George Elliott, Fields Institute and the Unviersity of Toronto
John R. Gardner
Dan Rosen, R2 Financial Technologies
Philip Siller, BroadRiver Asset Management, L.P.