2022-2023

The organizers of this seminar are Ovidiu Costin, Jan Lang, and Jonathan Stanfill.

The regular time for the seminar will be Thursday from 11:20 a.m. – 12:20 p.m. eastern time. For more information, to request the Zoom meeting link, or if you are interested in giving a talk at the seminar, please contact Jonathan Stanfill or Jan Lang.

Date/Time Location Speaker Institution Title (click to see abstract) Slides
December 1 at 11:30am MW 154 Nobuaki Obata Tohoku University, Japan
A quantitative approach to quadratic embedding of graphs

It is known in the Euclidean distance geometry tracing
back to Schoenberg (1935-37) that a graph admits a quadratic
embedding in a Euclidean space if and only if the distance matrix
$D=[d(x,y)]$ is conditionally negative definite. This condition,
being equivalent to that the q-matrix $Q=[q^{d(x,y)}]$ is positive
definite for all $0\le q\le 1$, appears also in quantum probability.
A new numerical invariant of a graph called the quadratic embedding
constant (QEC) was introduced in 2017 for a quantitative approach.
In this talk we will review the basic ideas and recent results and
propose some questions.
References: arXiv:2207.13278, arXiv:2206.05848, arXiv:1904.08059

Slides AOTS Dec 1, 2022
*December 8 at 10am Zoom Marcus Waurick TU Bergakademie Freiberg, Germany
Sign-indefinite divergence form problems in multi-d

In the talk, we recall a characterisation of well-posedness for abstract divergence form problems that provides a more detailed picture than the classical Lax—Milgram theorem. With this we analyse well-posedness of 1-dimensional divergence form problems with bounded, measurable, possibly sign-changing coefficients and $H^{-1}$-right-hand sides. Lifting this result to an operator equation in $L_2$, we provide a solution theory for multi-d divergence form problems with real coefficients piecewise constant on slabs. As it turns out, the condition for continuous invertibility of the corresponding operator equation in $L_2$ can be conveniently characterised looking at the zeros of a certain explicit polynomial expression. This leads to a genericity result for solving these kind of equations.

Slides AOTS Dec 8, 2022
January 12
TBD

TBD

January 19 TBD Ahmad Barhoumi University of Michigan
TBD

TBD

January 26 TBD Yidong Chen University of Illinois Urbana-Champaign
TBD

TBD

February 2
TBD

TBD

February 9 TBD Giorgio Young University of Michigan
TBD

TBD

February 16
TBD

TBD

February 23
TBD

TBD

March 2
TBD

TBD

March 9 TBD Chris Marx Oberlin College
TBD

TBD

March 23 Zoom Roger Nichols The University of Tennessee at Chattanooga
TBD

TBD

March 30
TBD

TBD

April 6 TBD Guglielmo Fucci East Carolina University
TBD

TBD

April 13
TBD

TBD

April 20 TBD Tao Mei Baylor University
TBD

TBD

April 27
TBD

TBD

TBD TBD Gino Biondini University at Buffalo, The State University of New York
TBD

TBD

* Joint PDE Seminar talk