Skip to main content

Analysis and PDE Seminar

Analysis and Partial Differential Equations Seminar

Talks take place at 11:00-12:00 noon, Tuesday in POT 745, unless otherwise noted. For updates and more information, please visit: http://ms.uky.edu/~mhto224/seminar/PDEseminarS2018.html

If you have any questions about a particular seminar, please contact the speaker's host. For general questions about the seminar, please contact Mihai Tohaneanu using the email address mihai.tohaneanu@uky.edu

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and Partial Differential Equations Seminar

Talks take place at 11:00-12:00 noon, Tuesday in POT 745, unless otherwise noted. For updates and more information, please visit: http://ms.uky.edu/~mhto224/seminar/PDEseminarS2018.html

If you have any questions about a particular seminar, please contact the speaker's host. For general questions about the seminar, please contact Mihai Tohaneanu using the email address mihai.tohaneanu@uky.edu

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and Partial Differential Equations Seminar

Talks take place at 11:00-12:00 noon, Tuesday in POT 745, unless otherwise noted. For updates and more information, please visit: http://ms.uky.edu/~mhto224/seminar/PDEseminarS2018.html

If you have any questions about a particular seminar, please contact the speaker's host. For general questions about the seminar, please contact Mihai Tohaneanu using the email address mihai.tohaneanu@uky.edu

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and Partial Differential Equations Seminar

Talks take place at 11:00-12:00 noon, Tuesday in POT 745, unless otherwise noted. For updates and more information, please visit: http://ms.uky.edu/~mhto224/seminar/PDEseminarS2018.html

If you have any questions about a particular seminar, please contact the speaker's host. For general questions about the seminar, please contact Mihai Tohaneanu using the email address mihai.tohaneanu@uky.edu

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and Partial Differential Equations Seminar

Talks take place at 11:00-12:00 noon, Tuesday in POT 745, unless otherwise noted. For updates and more information, please visit: http://ms.uky.edu/~mhto224/seminar/PDEseminarS2018.html

If you have any questions about a particular seminar, please contact the speaker's host. For general questions about the seminar, please contact Mihai Tohaneanu using the email address mihai.tohaneanu@uky.edu

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and Partial Differential Equations Seminar

TITLE: Localization and spectral statistics for Schr\"odinger operators with random point interactions

Talks take place at 11:00-12:00 noon, Tuesday in POT 745, unless otherwise noted. For updates and more information, please visit: http://ms.uky.edu/~mhto224/seminar/PDEseminarS2018.html

If you have any questions about a particular seminar, please contact the speaker's host. For general questions about the seminar, please contact Mihai Tohaneanu using the email address mihai.tohaneanu@uky.edu

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and PDE Seminar

 

The Bernstein Problem in Two Dimensions

 

I will outline a complete solution to the weighted approximation problem for polynomials

on an arbitrary bounded simply connected domain  in the complex plane. In that setting

the problem was first studied extensively by Keldysh prior to 1941 in the context of L2-

approximation, and more than four decades later by Beurling where, in the latter instance,

the emphasis was on uniform approximation. Here, Beurling obtains the sharper result

with respect to the weight w, but at the expense of limiting the type of region to which

his argument applies. Ironically, however, the two problems turned out to be essentially

equivalent, but neither Beurling nor Keldysh obtained what might be considered a definitive

solution. My presentation will focus on the L2-case, where the theory of Sobolev spaces and

its associated potential theory is available. It is a simple matter to pass from there to a

solution in the case of uniform approximation.

 

 

Date:
-
Location:
POT 745
Tags/Keywords:
Event Series:

Analysis and PDE Seminar

TITLE:  Complete Integrability of the Benjamin-Ono Equation
 
ABSTRACT: The Benjamin-Ono equation (BO) is a model for deep gravity waves in stratified fluids. It was discovered to be completely integrable by Nakamura, Bock and Kruskal, and Fokas and Ablowitz. Unlike many other completely integrable equations, the direct and inverse scattering transform (IST) for BO is only established on a formal level. In this talk, we will discuss several results aiming at a rigorous analysis of the foundation of the IST for BO. Such a problem will require spectral analysis of a certain singular integral perturbation of the derivative operator, together with a good understanding of a non-local Riemann-Hilbert problem. 
Date:
-
Location:
745 Patterson Office Tower
Event Series:

Analysis and PDE Seminar

TITLE:  Boundary Korn Inequality and Neumann Problems in Homogenization of Elliptic Systems of Elasticity
 
ABSTRACT:  This talk concerns with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coecients, arising in the theory of homogenization. We establish uniform optimal egularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate. This is a joint work with Jun Geng and Liang Song.
Date:
-
Location:
745 Patterson Office Tower
Event Series:

Analysis and PDE Seminar-Master's Talk

TITLE:  Upper Bounds for the Eigenvalue Counting Function of the Laplacian and Schrodinger Operators
 
ABSTRACT:  TheWeyl asymptotics provide information about the asymptotic distribution of the eigenvalues of the Laplacian in a bounded domain. Polya conjectured that the Weyl asymptotics actually provide an upper bound for the eigenvalue counting function. In the late 70's, Cwickel, Rosenbljum and Lieb independently (and with di erent techniques) proved an upper bound on the number of negative eigenvalues of a Schrodinger operator on Rd. I will give a motivated presentation of Lieb's technique, which uses path integrals and the Feynman- Kac formula. Lieb also used this bound to get a bound proportional to Polya's conjecture.
Date:
-
Location:
745 Patterson Office Tower
Event Series:
Subscribe to Analysis and PDE Seminar