2023-2024 FSU Mathematics Distinguished Lecture
Colloquium
Distinguished Lecture Series
Abstract
Title: On the stability of solitons and topological solitons in one-dimensional field theories
Solitons are particle-like solutions to dispersive evolution equations whose shapes persist as time evolves. In some situations, these solitons appear due to the balance between nonlinear effects and dispersion, in other situations their existence is related to topological properties of the model. Broadly speaking, they form the building blocks for the long-time dynamics of dispersive equations. In this talk I will present joint work with J. Luehrmann (TAMU) on long-time decay estimates for perturbations of the soliton for the 1D focusing cubic Klein-Gordon equation (up to exponential time scales), and I will discuss our previous work on the asymptotic stability of the sine-Gordon kink under odd perturbations. While these two problems are quite similar at first sight, we will see that they differ by a subtle cancellation property, which has significant consequences for the long-time dynamics of the perturbations of the respective solitons.
Wilhelm Schlag obtained his PhD at the California Institute of Technology in 1996 under the supervision of Thomas Wolff. Since then, he has held positions at Princeton University, California Institute of Technology and the University of Chicago where he was H. J. Livingston Professor of Mathematics. Since 2018 he is Professor at Yale University, where he currently serves as the Chair of the Department of Mathematics. He has done extensive work in Fourier Analysis, Spectral theory and dispersive partial differential equations. For his work he has received numerous awards, including the Sloan Fellowship, the Guggenheim Fellowship and an Invited Lecture at the International Congress of Mathematics in 2014. In addition he is currently one of the managing editors of Inventiones Mathematicae, one of the leading publications in the Mathematical Sciences.