Date: March 10th, 4-5pm
Location: Klaus 1443 Lecture Auditorium

Title: Nonlinear waves, spectra, and dynamics in infinite dimensions.

Abstract: 

Waves are ubiquitous in nature. Some wave phenomena are conspicuous, most notably in elastic objects, and in bodies of water. In electro-dynamics, quantum mechanics, and gravity, waves play a fundamental role but are much more difficult to find. Over the past centuries, major scientific breakthroughs have been associated with the discovery of hidden wave phenomena in nature. Engineering has enabled our modern information based society by developing sophisticated methods which allow us to harness wave propagation. Seismic exploration relies on wave scattering in the discovery of natural resources. Medicine depends heavily on wave-based imaging technology such as MRI and CAT scans.

Mathematics has played a major role in the understanding of wave propagation, and its many intricate phenomena including reflection, diffraction, and refraction. In its most basic form, the wave equation is a linear partial differential equation (PDE). However, modern science and engineering rely heavily on nonlinear PDEs which can exhibit many surprising and delicate properties. Mathematical analysis continues to evolve rapidly driven in part by the many open questions surrounding nonlinear PDEs and their solutions. This talk will survey some of the mathematics involved in our understanding of waves, both linear and nonlinear. 

About the speaker:

Professor Wilhelm Schlag is the Phillips Professor of Mathematics and the Chair of the Department of Mathematics at Yale University. A world-leading expert in harmonic analysis, mathematical physics, and partial differential equations, much of Schlag’s work has been devoted to the study of wave propagation, both in structured as well as in disordered media.

Schlag is a recipient of Sloan and Guggenheim fellowships, among others. He was a plenary speaker at the International Congress of Mathematical Physics in 2012 as well as an invited speaker at the International Congress of Mathematicians in 2014. Prior to joining the Yale faculty, he was the Holmer J. Livingston Professor of Mathematics at the University of Chicago. Before that, he served as professor at the California Institute of Technology, and as assistant professor at Princeton University.

Wilhelm Schlag will also give a colloquium talk on March 14th. Details can be found on the seminar page.