The Øresund Seminar - Copenhagen 25/4, 2025

Information about the Øresund Seminar in Copenhagen 25/4, 2025

We are happy to announce that the next Øresund Seminar will be held in the Spring of 2025. It will this time take place in Copenhagen, at the Department of Mathematical Sciences at University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen. The talks take place in Auditorium 10.

The Øresund seminar starts after a joint lunch at 12.00 on April 25th, at the new Niels Bohr Building canteen, just a short walk from the department - the entrance is at these GPS coordinates: 55.7010424, 12.5573901.

Please register to the event on this link before April 15th.

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

Title: Geometric deformations and spectral invariants
Abstract: Click to expand →

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: Click to expand →

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: Click to expand →

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: Click to expand →

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)

Current organizers and contact:

U Copenhagen:

Søren Fournais

Niels Martin Møller

Jan Philip Solovej

Lund U:

Magnus Goffeng [magnus dot goffeng (at) math dot lth dot se (responsible for the homepage)]

Jacob Stordal Christiansen

Erik Wahlén

Information about the Øresund Seminar in Copenhagen 25/4, 2025

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

Title: Geometric deformations and spectral invariants Abstract: Click to expand →

Abstract:

14.15-15.00: Helmut Abels (University of Regensburg)

Title: Nonlocal Cahn-Hilliard Type Equations and their Local LimitsAbstract: Click to expand →

Abstract:

15.00-15.30 Coffee break

15.30-16.15: Léo Morin (University of Copenhagen)

Title: Quantum Unique Ergodicity for Magnetic LaplaciansAbstract: Click to expand →

Abstract:

16.30-17.15: Adem Limani (Lund University)

Title: Aspects of regularity for normalized Cauchy integralsAbstract: Click to expand →

Abstract:

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

Current organizers and contact:

U Copenhagen:

Lund U:

Title: Geometric deformations and spectral invariants
Abstract: Click to expand →

Title: Nonlocal Cahn-Hilliard Type Equations and their Local Limits
Abstract: Click to expand →

Title: Quantum Unique Ergodicity for Magnetic Laplacians
Abstract: Click to expand →

Title: Aspects of regularity for normalized Cauchy integrals
Abstract: Click to expand →