The Øresund Seminar on Analysis, PDEs & Related Topics Spring 2025

All lectures are held in Auditorium 10, which is on the 1st floor in the H.C. Ørsted Building (walk up the stairs inside, next to the mathematics library).

Entering the H.C. Ørsted Building is easiest from the park side e.g. at GPS coordinates 55.700609, 12.560782:
https://maps.google.com/?q=55.700609,12.560782

The precise location of Auditorium 10 is at GPS coordinates 55.700015, 12.560734 as shown here on Google Maps:
https://maps.google.com/?q=55.700015,12.560734

Before the event, many of us plan to walk for lunch, at 12.00, at the new Niels Bohr Building canteen, just a short walk from the department - the entrance to canteen is at these GPS coordinates: 55.7010424,12.5573901.
 https://maps.google.com/?q=55.7010424,12.5573901

Please see, for more program details:
https://sites.google.com/view/oeresunds-seminar 

13.15-14.00: Julie Rowlett (Chalmers/University of Gothenburg)

Title: Geometric deformations and spectral invariants

Abstract: How does geometry affect physics, or conversely, do physical phenomena have geometric implications? Several physical processes, including the diffusion of heat and the propagation of waves, are governed by the Laplace spectrum. When a certain geometry hosting a physical process is deformed, how does this deformation affect the Laplace spectrum and in turn affect the physical process? I will talk about smooth-to-singular geometric deformations and singular-to-smooth geometric deformations and the behavior of the Laplace spectrum and some of its spectral invariants under these deformations. This is based on joint work with G. Mårdby.

14.15-15.00: Helmut Abels (University of Regensburg)

Title: Nonlocal Cahn-Hilliard Type Equations and their Local Limits

Abstract: Cahn-Hilliard type equations are used to describe phase separations in various physical systems. Besides the classical ``local'' Cahn-Hilliard equation, which leads a fourth order parabolic equation with non-monotone nonlinearity, there is a ``nonlocal'' counter-part, which involves a non-convolution type operator instead of a Laplacian in the equation of the so-called chemical potential. It has the advantage that it can be derived as a limit of micro-scopic models. We discuss known analytic results for both types of Cahn-Hilliard equations and corresponding Navier-Stokes/Cahn-Hilliard systems, which describe diffuse interface models for the two-phase flow of viscous incompressible fluids. Moreover, we present results on convergence of the nonlocal systems to their local counterparts.

15.00-15.30 Coffee break

15.30-16.15: Léo Morin (University of Copenhagen)

Title: Quantum Unique Ergodicity for Magnetic Laplacians

Abstract: This talk is about the high energy limit for Magnetic Laplacians on the 2 dimensional Torus. Under a geometric control condition on the magnetic field, we prove a Quantum Unique Ergodicity result : every sequence of high energy eigenfunctions is uniformly distributed on the torus. Such result is not true for the standard Laplacian. Despite the magnetic field being small in this limit, it is still strong enough to ensure uniform distribution. This work relies on semiclassical and microlocal techniques. In fact, we show uniform distribution in phase space. (Joint work with G. Rivière)

16.30-17.15: Adem Limani (Lund University)

Title: Aspects of regularity for normalized Cauchy integrals

Abstract: The normalized Cauchy integral is a fundamental device in complex function theory, with deep connections to spectral theory of linear contractions on Hilbert spaces and to completeness problems involving certain classes of Schrödinger operators. While originally motivated by spectral theoretical considerations, the normalized Cauchy integrals also exhibit subtle function theoretical behavior. In this talk, we shall discuss a class of uniqueness problems for normalized Cauchy integrals and explore their intimate connection to simultaneous approximation phenomenon and other classical problems in Harmonic analysis.

 18.30 Dinner at Food Club Amager (don't forget to register)