Singularidades en Geometria Algebraica y sus interacciones con Topologia, Geometria Metrica y Geometria Simplectica
Objective:The coordinated reseach proposal contains a very comprehensive set of objectives and developments in Singularity Theory and its applications from a modern viewpoint. At BCAM node we will focus at: (1) Lipschitz Geometry (joint with Madrid team): developing further the recently introduced theory of MD-Homology and apply it to advance in the comprehension of Lipschitz Geometry of singularities. Connections with equisingularity theory and resolution of singularities will be explored. We expect to find connections and applications non-arquimedean geometry. (2) Floer and Contact Homology and their connections with arc spaces (joint with Madrid, Zaragoza and our parters in Leuven and Budapest). Recent discoveries of McLean, Budur, Bobadilla, Le?, Nguyen and Nemethi hint a new connection between Floer theories of symplectic and contact manifolds associated with singularities and algebro-geometric objets like arc spaces, line bundles and their cohomology, and intersection lattices. Precise an appealing conjectures are formulated, and many more are waiting for their discovery. Applications to long-standing problems like Le-Ramanujam and Zariski conjectures could be derived. (3) Characteristic classes on singular varieties. Recently Bobadilla and Pallares have designed a new method based on cubical hyperresolutions, perverse sheaves and Hodge theory and proved with it a conjecture of Brasselet-Schurman-Yokura on L-classes of singular varieties. The method can be further applied to get much finer information on the geometric significance of the various L-classes, and other charactristic classes of singular varieties. (4) Palka and Pelka have succeded to make significant progress in a set of long-standing conjectures on affine algebraic geometry using the Minimal Model Program. Such study is by no means complete, and Pelka will go further on it. The knowledge of Pelka on MMP can be combined with the expertise of Bobadilla and Pallares in perverse sheaves to study the sheaf of nearby cycles and approach the Le?- Ramanujam conjecture. (5) Bobadilla and Romano have recently classified special Maximal Cohen-Macaulay modules on Gorenstein normal surface singularities. The technique can be further applied to the non-Gorenstein/non-special classification, which would have impact in the study of derived categories of coherent sheaves at singularities. The technique also matches with the study of the Zaragoza team, Laszlo and Nemethi of embedded curves in surfaces via associated reflexive modules, and we plan to join forces to deepen in this relation.
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