Posted April 9, 2021

Applied Analysis Seminar Questions or comments?

3:30 pm
Rui Han, LSU

A Polynomial Roth Theorem for Corners in the Finite Field Setting

The investigation of polynomial extensions of the Roth''s theorem was started by Bourgain and Chang, and has seen a lot of recent advancements. The most striking of these are a series of results of Peluse and Prendiville which prove quantitative versions of the polynomial Roth and Szemerédi theorems in the integer setting. There is yet no corresponding result for corners, the two dimensional setting for polynomial Roth's Theorem, where one considers progressions of the form (x, y), (x+t, y), (x, y+t^2) in [1 ,..., N]^2, for example.

We will talk about a recent result on the corners version of the result of Bourgain and Chang, showing an effective bound for a three term polynomial Roth's theorem in the finite field setting. This is based on joint work with Michael Lacey and Fan Yang.

Posted March 22, 2021

Last modified March 26, 2021

Control and Optimization Seminar Questions or comments?

2:00 pm https://lsu.zoom.us/j/94269991036 (Click "Questions or comments?" to request password)
Jean-Michel Coron, Universite Pierre et Marie Curie, France

Boundary Stabilization of 1-D Hyperbolic Systems

Hyperbolic systems in one space dimension appear in various real life applications, such as navigable rivers and irrigation channels, heat exchangers, plug flow chemical reactors, gas pipe lines, chromatography, and traffic flow. This talk will focus on the stabilization of these systems by means of boundary controls. Stabilizing feedback laws will be constructed. This includes explicit feedback laws which have been implemented for the regulation of the rivers La Sambre and La Meuse. The talk will also deal with the more complicated case where there are source terms.

Posted April 7, 2021

3:30 pm - 4:30 pm https://lsu.zoom.us/j/99528757270?pwd=SUprWlJyczd3VUhEZ3Z3MTJjdjlwdz09
Egor Maximenko, National Polytechnic Institute, Mexico

Radial Toeplitz operators on the Fock space and square-root-slowly oscillating sequences

In this talk, based on a joint article with Kevin Esmeral (https://doi.org/10.1007/s11785-016-0557-0), we describe the C*-algebra generated by radial Toeplitz operators with bounded symbols acting on the Fock space.

We prove that this C*-algebra is isometrically isomorphic to the C*-algebra of bounded sequences uniformly continuous with respect to the square-root-metric $\rho(j,k)=|\sqrt(j)-\sqrt(k)|$.

More precisely, we show that the spectral sequences (i.e., the sequences of the eigenvalues) of radial Toeplitz operators form a dense subset of the latter C*-algebra of sequences.

The main idea is to approximate the spectral sequences by convolutions and apply an appropriate version of Wiener''s density theorem.