Objective:This scientific proposal addresses research in the fields of harmonic analysis and inverse problems, and explores certain interactions. The suggested plan of investigation in these areas is natural as there is a high degree of commonality in the tools required to address the problems in hand, which vary from purely theoretical questions in harmonic analysis to more concrete ones in the theory of inverse problems. In harmonic analysis we are interested in research related to Kakeya and restriction phenomena. In the first case, questions are motivated by determining a certain notion of dimension, the Hausdorff dimension, of sets that contain a unit line segment in every direction. The study of these special sets has a long history and is connected to a host of central questions and conjectures in harmonic analysis. Our point of view is that of the analysis of suitable directional operators, namely, we consider averaging operators whose mapping properties capture the behaviour of these sets. The study of these operators, as well as of the closely related directional singular integrals, is also motivated by the problem of differentiation of functions along directions in a given set, or even along directions dictated by a suitable vector field. Again these objects are related to some long-standing conjectures in harmonic analysis and even conditional results are known to imply, for example, the Carleson theorem on the convergence of partial sums of Fourier series. The approach we suggest is in line with recent developments in harmonic analysis and is strongly influenced by the polynomial method. Restriction phenomena refer to the possibility of restricting the Fourier transform of a function to hypersurfaces with curvature. Such results can be used to deduce fine convergence properties of solutions of equations, like the Schrödinger equation, or wave equations. Our interest is in an appropriate notion of size of the exceptional sets, namely the sets where these convergence results fail.
MATH4SPORTS - Modelización matemática para la industria deportiva: salud y rendimiento
MATH4SPORTS seeks to transfer applied mathematics as a driving technology to the field of the sports industry, with a high potential for technology transfer to start-ups, professional clubs, researchers and other agents in the innovative environment of Bizkaia.
M-KONTAK - Investigación de los Fenómenos Asociados al Contacto Metal-Metal en Tecnologías de H2 a Alta Presión
The main objective of the M-KONTAK project is to gain an in-depth understanding of the failure modes and their effect on metallic materials and the surfaces of threaded joints in candidate technologies for high-pressure H2 effect on the metallic materials and surfaces that make up the threaded jo
KAIROS - Digitalización predictiva del comportamiento a largo plazo de materiales poliméricos composites. Empleo de IA, modelización basada en la física y metodologías de aceleración de ensayos
KAIROS was created with the main objective of researching and obtaining a solution that allows multi-scale digitisation combined with ML and accelerated testing methodologies, for the study of the long-term behaviour (creep, fatigue, ageing) of polymeric materials applicable, for example, to the
CHARGER+ - Nueva Generación de Puntos de Recarga de Vehículo Eléctrico con Funcionalidades Autónomas y Colaborativas e Impacto Cero
The general objective of the CHARGER+ project is to generate the necessary knowledge to define a new generation of electric vehicle (EV) charging points, so that the related Basque companies (electricity companies, charging post installation companies and charger manufacturers) will be in an adva