• Speaker: Peter Yuditskii, Johannes Kepler University Linz
• Title: The Deift conjecture
• Date: 03/31/2021
• Time: 4:00 PM - 5:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

At his 60th birthday conference in 2005, Percy Deift was asked to present a list of unsolved problems. This list was updated ten years later, on his 70th birthday conference. As the number one unsolved problem in both lists we still have the following conjecture. Problem 1.1 (KdV with almost periodic initial data). Consider the Korteweg–de Vries (KdV) equation $$u_t +uu_x +u_{xxx} =0 $$ with initial data $$u(x,t=0)=q(x),\quad x\in\mathbb{R}.$$ In the 1970’s, McKean and Trubowitz proved the remarkable result that if the initial data $q(x)$ is periodic, $q(x + T ) = q(x)$ for some $T > 0$, then the solution $u(x, t)$ is almost periodic in time. This result leads to the following natural conjecture: The same is true if $q(x)$ is almost periodic, i.e., if the initial data is almost periodic in space, the solution evolves almost periodically in time. Zoom Link: https://msu.zoom.us/j/94297154840 Passcode: the same as the last time

• Speaker: Ilya Kachkovskiy, MSU
• Title: Spectral bands of two-dimensional periodic elliptic operators
• Date: 04/14/2021
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Dapeng Zhan (zhan@msu.edu)

I will give an overview of spectral theory of second order elliptic operators on $\mathbb R^2$ on the example of Schrodinger operators and explain the main steps of the proof that spectral band edged are attained at finitely many values of the quasimomenta. If time permits, I will discuss related result and work in progress. The talk is based on joint work with N. Filonov. Note: The meeting time is 3:00 pm instead of 4:00 pm. We use the same zoom link and passcode as before.