# Colloquium: Milivoje Lukic (Rice University), KdV equation with almost periodic initial data.

### Event Description:

Speaker: Milivoje Lukic, Rice University.

Title: KdV equation with almost periodic initial data

Abstract: The KdV equation is known to be integrable for several

classes of initial data, such as decaying, periodic, and finite-gap

quasiperiodic. In this talk, we will describe recent progress for

almost periodic initial data, centered around a conjecture of Percy

Deift that the solution is almost periodic in time. We will discuss

the proof of existence, uniqueness, and almost periodicity in time, in

the regime of absolutely continuous and sufficiently "thick" spectrum.

In particular, this result proves Deift's conjecture for small

analytic quasiperiodic initial data with Diophantine frequency. The

talk is based on joint work with Ilia Binder, David Damanik, and

Michael Goldstein.