# Colloquium-Ken McLaughlin

**Speaker:**Ken McLaughlin, Colorado State University

**Location:**LD 229

## Some interesting phenomena, limits, and a few open questions regarding integrable PDEs (linear and nonlinear)

ABSTRACT:

I will describe some surprising phenomena related to the KdV equation in the periodic setting (related to fractal dimension), and also the whole-line case (infinite accumulation of solitons and asymptotic behavior). For the case of periodic boundary conditions, I will motivate things with explicit calculations regarding linear PDEs, and explain how for the (integrable) nonlinear equation, some extensions have been obtained by PDE analysts without using integrability, which leads to a few open problems for folks working in integrable systems.

ABOUT THE SPEAKER:

Ken McLaughlin is a professor and the department chair at Colorado State University. He studied mathematics at New York University and went on to earn his Ph.D. from that school's Courant Institute in 1994. After graduation, he was a National Science Foundation Postdoctoral Fellow and has also been on the faculty at the University of North Carolina at Chapel Hill. He has held positions at the Universite de Bourgogne in Dijon, France, the Mathematical Sciences Research Institute in Berkeley, California, the Pontificial Universidade Catolica de Rio de Janeiro in Brazil, the Katholieke Unversiteit in Leuven, Belgium, the Ecole Normale Superieur in Paris, France, and the Universite de Paris VII.

Hosted by: M. Yattselev and A. Its