Fourier Analysis and Partial Differential Equations Conference
A conference in honor of Dorina Mitrea.
Friday, October 31, 2025
Department of Mathematics, Baylor University
Registration:
There is no registration fee but all participants should use the registration form on this page to register.
Featured Speakers:
Russell Brown (University of Kentucky)
- Title: Recovering polyharmonic operators from boundary information
- Abstract: We fix a domain and an operator L whose principal part is a polyharmonic operator and includes lower order terms and consider solutions of Lu=0 in our domain. The question we ask is if the coefficients of the lower order terms are uniquely determined by the space on the boundary of Cauchy data of all solutions. The first result establishing uniqueness is due to Krupchyk, Lassas and Uhlmann. Our contribution is to use a technique of Haberman and Tataru to establish uniqueness under reduced regularity assumptions on the coefficients. The results presented do not appear to be complete and I will discuss some open problems suggested by these results. The talk reports on work that is joint with Daniel Faraco and Landon Gauthier.
Alexander Koldobsky (University of Missouri)
- Title: Functions positively associated with integral transforms
- Abstract: We introduce the class of functions positively associated with a linear operator. We describe these classes for several integral operators including the spherical Radon transform and the cosine transform. We show that positively associated functions control the comparison problem for linear operators generalizing the Busemann-Petty problem for convex bodies.
Fritz Gesztesy (Baylor University)
- Title: The weak coupling spectral instability of Krein-type self-adjoint extensions
- Abstract: We discuss the spectral instability of Krein-von Neumann (and more generally, Krein-type) self-adjoint extensions of symmetric operators in a Hilbert space with respect to relatively form compact, negative (additive) perturbations. More precisely, we show the remarkable spectral instability that under relatively mild hypotheses on the negative perturbation, spectrum (in fact, eigenvalues) instantly, that is, for arbitrarily small (nonzero) coupling constants, appears below the spectrum of the Krein-type extension.
This is based on joint work with Jussi Behrndt and Henk de Snoo.
Local Organizing Committee:
- Fritz Gesztesy
- Marius Mitrea
- Julie Posey
Tentative Schedule:
- Location: MMSCI 301
- 1:30 - Coffee and Refreshments
- 2:00 - 2:15 - Introductory Remarks
- 2:15 - 3:00 - Russel Brown
- 3:15 - 4:00 - Alexander Koldobsky
- 4:00 - 4:30 - Break
- 4:30 - 5:15 - Fritz Gesztesy
- 6:00 - 9:00 Dinner
Venue:
The Department of Mathematics is located on the third floor of the Sid Richardson Science Building (Paul L. Foster Success Center).
The conference will be held in Marrs McLean Science Building 301.
The conference dinner will be held at the Baylor Club in the North Lounge.
Use the Campus Map to locate these buildings.
Baylor University lies in Waco, Texas on Interstate I-35 between Dallas/Fort Worth and Austin, Texas..
Lodging:
Holiday Inn Express Downtown Waco
101 Taylor Street, Waco, TX
254-236-6288
Room reservations available until October 22, 2025.
Practical information:
Wi-Fi connection: By all means plan on using eduroam if you have it. If you don't have it, get it now if your institution is a member. Other possibilities exist but are far inferior and cumbersome to organize.
Parking: If you plan to park a car on campus during the conference, please use the link below to register as a visitor.
The visiting parking slots comprise the first 3 rows starting from the left when confronting the main entrance of Sid Richardson, the mathematics building (between 3rd and 4th street); they are marked in green. (Faculty and Staff parking slots are to the right of the visitor slots and marked in yellow.) See the following map:
Sponsored by the Simons Foundation, College of Arts and Sciences and the Department of Mathematics of Baylor University.