Mathematical Physics and Harmonic Analysis Seminar

Date: February 6, 2020

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Darren Ong, XIAMEN UNIVERSITY MALAYSIA

Title: Restrictions on the existence of a canonical system flow hierarchy

Abstract: The KdV hierarchy is a family of evolutions on a Schr\"odinger operator that preserves its spectrum. Canonical systems are a generalization of Schr\"odinger operators, that nevertheless share many features with Schr\"odinger operators. Since this is a very natural generalization, one would expect that it would also be straightforward to build a hierarchy of isospectral evolutions on canonical systems analogous to the KdV hierarchy. Surprisingly, we show that there are many obstructions to constructing a hierarchy of flows on canonical systems that obeys the standard assumptions of the KdV hierarchy. This is joint work with Injo Hur.