Abstract: The supercooled Stefan problem describes freezing of supercooled water. In contrast to the Stefan problem that describes melting of ice, the supercooled problem exhibits unstable behaviour which makes the usual PDE methods break down. We will discuss some recent progress which employs a stochastic version of optimal transport, involving optimal stopping times of the Brownian motion.

Bio: Young-Heon Kim earned his PhD from Northwestern University in 2005. He then had a postdoctoral position at Fields Institute and U. Toronto before joining at UBC in 2009 after a one-year membership at Institute for Advanced Study. His current research is on various aspects of optimal transport theory and its applications.