Seminars usually take place either at
UPV/EHU, Seminar Room of the Mathematics Department, Facultad de Ciencias, on Thursdays at 12:00, or
BCAM, Seminar Room, on Thursdays at 17:00.
Some seminars were recorded, and the videos can be found together with the description of the seminar on the subpage related to the year the talk happened. You can also find them here.
To subscribe to the seminar mailing list, contact one of the organizers.
As of October 2nd, 2025, the count of talks reached 264.
BCAM, Thursday, October 16th, 2025, 17:00 - 18:00
Title: Convex integration for the Monge-Ampere system.
Marta Lewicka - University of Pittsburgh
The Monge-Ampere system (MA) is the multi-dimensional version of the Monge-Ampere equation, arising from the prescribed curvature problem and closely related to the problems of isometric immersions and the minimization of elastic energies of thin shells.
In case of dimension d=2 and codimension k=1, (MA) reduces to the classical Monge-Ampere equation as the prescription of the Gaussian curvature of a shallow surface in R^3, whereas (MA) prescribes the full Riemann curvature of a shallow d-dimensional manifold in R^{d+k}.
(MA) takes its weak formulation, called the Von Karman system (VK). When d= 2, k= 1, (VK) arises in the theory of elasticity as the the Von Karman stretching content a thin film.
Closely related to (MA) and (VK) is the system (II) for an isometric immersion of the given d-dimensional Riemannian metric into R^{d+k}. (II) yields (VK) when equating the leading order terms along a perturbation of the Euclidean metric.
This lecture will concern the ongoing study of existence, regularity, and multiplicity of solutions to systems (MA), (VK), (II) through the method of convex integration, building on the prior fundamental results due to Nash, Kuiper, Kallen, Borisov, the more recent approach due to Conti, Delellis and Szekelyhidi, and the parallel analysis of Cao, Hirsch and Inauen.
We will also explore relation to the scaling of the non-Euclidean energies of elastic deformations and the quantitative isometric immersion problem.
UPV/EHU, Thursday, October 23rd, 2025, 12:00 - 13:00
Title: An optimal fractional Hardy inequality on the discrete half-line
Rubén de la Fuente - BCAM
Hardy type inequalities have been a widely studied field since the first proofs in the early 20th century. The interest in these inequalities comes from their many applications in functional analysis, PDEs, spectral theory, or probability.
In this context, we prove a discrete fractional Hardy’s inequality. In particular, a Hardy inequality concerning the fractional Laplacian in the discrete half-line with a weight that is optimal, in the sense that it cannot be substituted by any pointwise larger weight and its decay is as slow as possible. The strategy of the proof relies mainly on spectral properties of the aforementioned operator and criticality theory for graph Laplacians. As an immediate application, we derive some unique continuation results for positive Schrödinger operators involving the fractional Laplacian on the discrete half-line. Joint work with Ujjal Das.
BCAM, Thursday, October 30th, 2025, 17:00 - 18:00
Title: TBA
Emmanuel Russ
TBA
BCAM, Thursday, November 6th, 2025
Title: TBA
Cole Jeffrey Jeznach - cancelled
TBA
UPV/EHU, Thursday, November 13th, 2025
Title: Fourier analytic methods in the spectral theory of Schrödinger operators
Dr. Konstantin Merz - Institute of Analysis and Algebra and Institute for Partial Differential Equations
Estimating the location and accumulation of eigenvalues for Schrödinger operators is a classical problem at the intersection of spectral theory and mathematical physics. In this talk, we illustrate how Fourier analysis, in particular Fourier restriction, yields sharp eigenvalue estimates for Schrödinger-type operators with short-range potentials. We highlight the limitations of such methods for long-range potentials and show how they can be overcome by introducing randomness. Our results shed new light on the critical temperature for superconductivity in BCS theory and on the energy and lifetime of resonances in nuclear physics.