Brief description

 

The main goal in most problems of singularity theory is to understand the dependency upon parameters of some mathematical object, precisely at the point where small perturbations affect the behavior. Singularity theory is a transversal subject that has evolved in a continuous dialogue in algebra, geometry and topology. Classically, it has borrowed methods from algebraic and differential geometry and topology, commutative and homological algebra, dynamical systems... New methods coming from other fields such as non-Archimedean methods, arc spaces or symplectic topology have an important role nowadays. Recently, also the study of Lipschitz geometry of singularities has flourished. On the applications side, we focus on cryptographic methods which are able to resist quantum computation attacks. 

 

 

Researchers

• María Pe Pereira. Associate Professor (Profesora Contratada Doctora), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM (PI)
• Pedro Daniel González Pérez. Associate Professor (Profesor Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM (PI)
• Alejandro Melle Hernández. Professor (Catedrático), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• María Emilia Alonso García. Associate Professor (Profesora Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• Pilar Coscojuela Escanilla. PhD Student (Contratado Predoctoral), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM

 

External Collaborators

• Baldur Sigurdsson. Post-doc grant (Contratado Posdoctoral), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• Enrique Artal Bartolo. Professor (Catedrático), Department of Mathematics (Departamento de Matemáticas), Universidad de Zaragoza
• José Ignacio Cogolludo Agustín. Professor (Catedrático), Department of Mathematics (Departamento de Matemáticas), Universidad de Zaragoza
• Javier Fernández de Bobadilla De Olazabal (Ikerbasque Research Professor, Group Leader, BCAM)
• Ignacio Luengo Velasco. Professor (Catedrático), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• Martín Avendaño González. Associate Professor (Profesor Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• Jorge Martín Morales (Investigador Ramón y Cajal, Departamento de Matemáticas, Universidad de Zaragoza)
• Jorge Carmona Rúber. Associate Professor (Profesor Contratado Doctor), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• Raquel Díaz Sánchez. Associate Professor (Profesora Contratada Doctora), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
• Miguel Ángel Marco Buzunámiz. Associate Professor (Profesor Contratado Doctor), Department of Mathematics (Departamento de Matemáticas), Universidad de Zaragoza
• Juan Viu Sos. Assistant Professor (Profesor Ayudante Doctor), UPM
• Manuel González Villa. Postdoctoral Researcher María Zambrano, Department of Mathematics (Departamento de Matemáticas), Universidad de Zaragoza
• Patricio Almirón Cuadros. Postdoctoral Researcher, Institute of Mathematics (Instituto de Matemáticas), Universidad de Granada

 

Publications

• S. Gusein-Zade, I. Luengo, A. Melle-Hernández. Grothendieck Ring of Pairs of Quasi-Projective Varieties. Functional Analysis and its Applications, 58, (1), 33-38. 2024. DOI: 10.1134/S0016266324010040.
• P. D. González Pérez, M. González Villa, C. R. Guzmán Durán, M. Robredo Buces. Multiplier ideals of plane curve singularities via Newton polygons. Communications in Algebra, 2023. DOI: 10.1080/00927872.2023.2257799