New methods and interactions in Singularity Theory and beyond
Objective:This project is centred in Singularity Theory and its interactions and applications to Complex and Algebraic Geometry, Differential/symplectic/Contact Topology, Hodge Theory and Algebraic Topology. This subject is still at the core of various developments (Mori's Theory, Symplectic and Contact Geometry, algebro-geometric Donaldson-Thomas Theory, Hodge Theory and D-modules...) In the present project we propose several directions of development in singularity theory, designed in order to approach the solution of several classical conjectures, and explore new interactions with the latest developments in nearby areas. New problems and conjectures are formulated, which are interesting bottlenecks whose solution would open new development perspectives in the theory, and whose study will need significantly new ideas. We have taken care of finding feasible starting points and interesting classes of singularities where the initial development is less steep. And to find links among the seemingly difernt techniques and problems which we propose. We deal with the following specific topics: vanishing cohomology of isolated and non-isolated singularities. Rational homotopy generalisations of Hodge Theory and rational vanishing homotopy. Applications to Equisingularity questions. Disentanglement theory and its relation with vanishing homology and homotopy. Symplectic and contact geometry of milnor fibrations. A vast programme in topological equisingularity including a multifaceted attack to Lê-Ramanujan problem. Generalisations of McKay correspondence. Banagl Intersection spaces. Topological and analytic invariants of normal surface singularities. Arc spaces and Nash correspondence. Compactified Jacobians.
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