seminar

• IMAG Functional Analysis Seminar
• Title: Tingley's Problem(s): Positive answers and insightful results
• By Pedro Saavedra Ortiz (UGR)
• Abstract: Banach spaces play a key role in mathematics due to their structural richness and wide applications. Classical results link isometries of normed spaces, unit balls, and spheres to linear isometries, with Tingley's Problem (1987) focusing on whether sphere isometries extend isometrically and R-linearly - a question still open in dimensions ≥ 3. A variant of this problem studies spheres of positive elements, reducing even further the available information about the considered spaces. In this talk, we will show the interplay between Algebra, Analysis and Geometry that is suggested by Tingley's Problem, and we will explore some of the tools utilised to provide a positive answer in certain spaces (such as C(K) with K compact or JBW*-algebras).

• IMAG Functional Analysis Seminar
• Title: The Daugavet property is equivalent to the polynomial Daugavet property
• By Sheldon Dantas (UGR)
• Abstract: In this talk we will show that the Daugavet property implies the polynomial Daugavet property. The central argument relies on a geometric characterization due to Shvidkoy: we will prove that this characterization, originally formulated in terms of the weak topology, remains valid when replacing it with the weak polynomial topology. Finally, we will discuss other results obtained with close related techniques. This talk is based on a recent joint work with Miguel Martín and Yoël Perreau (University of Tartu, Estonia).

Author : Dong-Hwi Seo, University of Granada

Title : Free boundary minimal surfaces in a ball and eigenvalue problems

Where : Seminario 1, IMAG

When : September 19th, 12h - 13h

Abstract : Eigenvalue problems have played a pivotal role in the study of minimal surface theory. In this talk, I will provide an overview, starting with basic concepts and progressing to recent development. Specifically, I will explain free boundary minimal surfaces in the unit ball and their connection to eigenvalue problems. Key conjectures in this area will be highlighted, along with a discussion of my recent contribution.

Author : David Kalaj, University of Montenegro

Title : The Schwarz lemma for holomorphic and minimal disks at the boundary.

Where : Seminario 1 (IMAG)

When : 12h - 14h

Abstract : We first prove a Boundary Schwarz lemma for holomorphic disks on the unit ball in ${\mathbb{C}}^n$. Further by using a Schwarz lemma for minimal conformal disks of Forstnerič and Kalaj, we prove the boundary Schwarz lemma for such minimal disks.

Conferenciante : Antonio Hidalgo (Max Planck Institute for Mathematics in the Sciences)

Título : Pathological solutions of 2D Navier-Stokes equations with gradients in Hardy spaces.

Localización : Aula A24, Facultad de Ciencias

Resumen : In this talk, we will review the main results and limitations in the use of convex integration for the unforced Euler and Navier-Stokes equations in 2D. We will then present a new sharp result that establishes a threshold between rigidity and flexibility in the 2D Navier-Stokes equations. This is a joint work with Jan Burczak.

FIRST TALK: 11:30h

Author : Rabia Aktas-Karaman, Ankara University, Turkey

Title : Fourier transforms of orthogonal polynomials on the cone and on the paraboloid

Abstract : The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal polynomials on the cone such as Laguerre polynomials on the cone and Jacobi polynomials on the cone and to define two new families of multivariate orthogonal functions by using Parseval's identity. Also, the obtained results are expressed in terms of the continuous Hahn polynomials. Moreover, we present similar results for the orthogonal polynomials on the paraboloid.

References:
1. Koelink, H.T. On Jacobi and continuous Hahn polynomials, Proc. Amer. Math. Soc., 124(3), 887-898, 1996.
2. Aktas Karaman, R., Area, I. Fourier transforms of orthogonal polynomials on the cone, Numerical Algorithms, https://doi.org/10.1007/s11075-025-02112-x , 2025.
3. Güldogan Lekesiz, E., Aktas, R., Area, I. Fourier transform of the orthogonal polynomials on the unit ball and continuous Hahn polynomials, Axioms, 11(10), 558, 2022.
4. Cetin, H.O., Aktas Karaman, R. Fourier transforms of orthogonal structures on the paraboloid, submitted for publication

SECOND TALK:

Author : Miguel Piñar, Universidad de Granada

Title : A fully diagonalized spectral method on the unit ball

Abstract : Our main objective in this work is to demonstrate how orthogonal Sobolev polynomials emerge as a useful tool within the framework of spectral methods for boundary-value problems. The solution of a boundary-value problem for a stationary Schr\"odinger equation on the unit ball can be studied from a variational perspective. In this variational formulation, a Sobolev inner product naturally arises. As test functions, we consider the linear space of polynomials satisfying the boundary conditions on the sphere, and a basis of mutually orthogonal polynomials with respect to the Sobolev inner product is provided. The basis of the proposed method is provided in terms of spherical harmonics and univariate Sobolev orthogonal polynomials. The connection formula between these orthogonal Sobolev polynomials and classical orthogonal polynomials on the ball is established. Consequently, the Sobolev Fourier coefficients of a function satisfying the boundary value problem are recursively derived. Finally, numerical experiments were presented.

Location: Seminario 2, IMAG.
When: Thursday, September 11th 2025

• IMAG Functional Analysis Seminar
• Title: El problema de Mackey-Gleason-Bunce-Wright: Morfismos de estructuras unitarias
• By Gerardo Martín Escolano (UGR)
• Abstract: En esta charla hablaremos sobre la reciente resolución del problema de Mackey-Gleason-Bunce-Wright y su aplicación en el estudio los llamados "piecewise Jordan homomorphisms" sobre el conjunto de unitarios de una JBW$^*$-álgebra.

Granada, Spain, May 28-29, 2026

Reliability, maintenance and safety in the data-driven era

Topics of interest include, but are not limited to:

• Data-driven reliability and maintenance.
• Stochastic processes for reliability and failure modelling.
• Condition monitoring, diagnostics, and prognostics.
• Predictive maintenance and digital twins.
• Machine learning and neural networks in reliability engineering.
• Structural health monitoring and sensor system design.
• Uncertainty and sensitivity analysis for safety evaluation of critical structures.
• Value of information analysis for improved decision-making in structural safety.
• Resilience engineering and infrastructure systems management.
• Sustainable maintenance.
• Bayesian methods in reliability and maintenance modelling.
• Partially Observable Markov Processes for Condition-Based Maintenance.
• Deep Learning for Remaining Useful Life (RUL) Prediction.
• Hybrid AI-Statistical Models for Fault Diagnosis.
• Reliability and Maintenance Strategies for Industry 5.0.

More information in the conference web: https://conferences.enbis.org/event/79/overview

Fecha y hora: martes 1 de julio, 12:00

Lugar: Seminario 2, IMAG

Ponente: Andrés Riveros Valdevenito

Title: Monotonicity in Quadratically Regularized Optimal Transport

Abstract: In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the unregularized counterpart as the regularization parameter is relaxed. We find it useful to investigate this monotonicity more abstractly for linear programs over polytopes, regularized with the squared norm. Here, monotonicity can be stated as an invariance property of the curve mapping the regularization parameter to the solution: once the curve enters a face of the polytope, does it remain in that face forever? We show that this invariance is equivalent to a geometric property of the polytope, namely that each face contains the minimum norm point of its affine hull. Returning to the optimal transport problem and its associated Birkhoff polytope, we verify this property for low dimensions, but show that it fails for marginals with five or more point masses. As a consequence, the conjectured monotonicity of the support fails in general, even if experiments suggest that monotonicity holds for many cost matrices.