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Research Groups
Research Groups.
Internal organization of the Institute in research groups based on their area of expertise…
Our research group is mainly interested in Group Theory, which is one of the fundamental branches of Algebra, with numerous applications inside Mathematics, as well as in other areas of science and technology such as physics, chemistry, computer science, or ICT. Our goal is to advance the knowledge of the structure of groups, through the analysis of their factorizations, representations, the lattice of their subgroups and arithmetical properties. This analysis uses techniques of the theory of classes, simple groups, graphs and lattice theory. In the applied side, we are concerned with the interaction of semigroups with automata and formal languages.
| External Collaborators | University |
| Beltrán Felip, Antonio | Universitat Jaume I de Castellón |
| Hauck, Peter | Universidad de Tübingen, Alemania |
| Kazarin, Lev S. | Universidad de Yaroslavl, Rusia |
| Pérez Ramos, Mª Dolores | Universitat de València |
Research lines:
-Factorised groups
-Lattice and subgroup embedding properties
-Conjugacy classes and characters in finite groups
Banach Spaces and Infinite-Dimensional Holomorphy
Research in the geometry of Banach spaces (structure and renorming, differentiability properties of convex functions, Lipschitz functions and Lipschitz-free spaces, optimization in Banach spaces, weak compactness). Research in holomorphy in infinite-dimensional Banach spaces (Dirichlet series in Banach spaces, multilineal mappings, polynomials in Banach spaces).
| Heads of the Group | |
| Montesinos Santalucía, Vicente | vmontesinos@mat.upv.es |
| Sevilla Peris, Pablo | psevilla@mat.upv.es |
| Researchers | |
| Guirao Sánchez, Antonio José | anguisa@mat.upv.es |
| Aliaga Varea, Ramón | raalva@upvnet.upv.es |
| External Collaborators | University |
| Zizler, Václav | University of Alberta, Canada |
| Fabian, Marian | Czech Academy of Science, Czech Republic |
| Carando, Daniel | Universidad de Buenos Aires, Argentina |
| Defant, Andreas | Universität de Oldenburg, Germany |
Research lines:
-Geometry of Banach spaces
-Infinite-dimensional holomorphy
Celestial Mechanics and Reference Systems
This research group is interested in Celestial Mechanics and Reference Systems, and also in the History of Astronomy.
Research line
-Homogenization and correction of celestial reference frames
| Head of the Group | |
| Martínez Usó, María José | mjmartin@mat.upv.es |
| External Collaborators | University |
| Marco Castillo, Francisco José | Universitat Jaume I de Castelló |
| López Ortí, José Antonio | Universitat Jaume I de Castelló |
Research line
-Homogenization and correction of celestial reference frames
Our group investigates different notions of dynamics (mainly, notions of chaos) for
operators and semigroups of operators on spaces of infinite dimension. Precisely, we work on:
(1) Dynamics of C_0-semigroups and applications,
(2) Dynamics of fractional differential (difference) equations,
(3) Li-Yorke chaos and distributional chaos,
(4) Lineability, algebrability and spaceability,
(5) Recurrence in the dynamics of operators,
(6) Dynamics of m-isometries,
(7) Topological and mesure-theoretic properties in linear dynamics,
(8) Numerical simulation and analysis of the dynamics of linear models.
Foreign members: Nilson Bernardes, Juan Bes, Karl Grosse-Erdmann, Carlos Lizama and Piotr Oprocha.
(1) Dynamics of C_0-semigroups and applications,
(2) Dynamics of fractional differential (difference) equations,
(3) Li-Yorke chaos and distributional chaos,
(4) Lineability, algebrability and spaceability,
(5) Recurrence in the dynamics of operators,
(6) Dynamics of m-isometries,
(7) Topological and mesure-theoretic properties in linear dynamics,
(8) Numerical simulation and analysis of the dynamics of linear models.
Foreign members: Nilson Bernardes, Juan Bes, Karl Grosse-Erdmann, Carlos Lizama and Piotr Oprocha.
| External Collaborators | University |
| Bermúdez de León, Teresa | Universidad de la Laguna, Spain |
| Bonilla Ramírez, Antonio | Universidad de la Laguna, Spain |
| Murillo Arcila, Marina | Universitat Jaume I, Spain |
Research lines
-Li-Yorke chaos, distributional chaos, and recurrence properties
-Lineability, algebrability and spaceability
-Topological and measure-theoretic properties in linear dynamics, and non-linear dynamics
-Semigroup theory and fractional calculus applied to PDE's
-Biological and biomedical mathematical modeling (B2M2)
-Signal processing methods for financial time series
Functional Analysis, Operator Theory and Time Frequency Analysis
Our main research area is the study of methods of functional analysis and operator theory and their applications to several areas of mathematical analysis, like complex analysis, Fourier analysis, dynamical systems, ergodic theory and linear partial differential operators.More precisely, we work in the following problems:
Research lines
-Operators on functions and sequence spaces
-Time frequency analysis and applications
-Partial differential operators and extension of smooth functions
(1) Spaces of analytic and differentiable functions and operators between them: weighted spaces of analytic functions, weighted composition operators, integral operators, Cesàro and Volterra operators.
(2) Time-frequency analysis: Gabortransform, Fourier integral operators, weighted modulation spaces and applications to biomedical nonstationary signals.
(3) Linear partial differential and pseudo-differential operators on spaces of ultradifferentiable functions and ultradistributions: hypoellipticity, regularity of solutions, wave front set and extension of smooth functions.
Webpage: http://jbonet.webs.upv.es/
| External Collaborators | University |
| Beltrán Meneu, María José | Universitat Jaume I, Castellón |
| Fernández Rosell, Carmen | Universitat de València |
| Galbis Verdú, Antonio | Universitat de València |
| Tárraga Primo, Eva | Universitat de València |
-Operators on functions and sequence spaces
-Time frequency analysis and applications
-Partial differential operators and extension of smooth functions
Interdisciplinary Modelling Group-InterTech
InterTech (www.intertech.upv.es) activities are based on collaborations from researchers of different areas aiming at the creation of new ideas of scientific and technological value. The interdisciplinary nature of the group allows to cover various fields like non-linear optics, in collaboration with the optics department of the Universitat de València; biotechnology; or in the advanced modelling in energetic engineering. As result of the research activities of the group a spin off, Energesis Ingeniería (www.energesis.es), was created fulfilling one of the main goals of InterTech members of transferring the scientific findings to society.
| External Collaborators | University |
| Ferrando Cogollos, Albert | Universitat de València |
| Finster, Felix | Universitaet Regensburg |
| Michinel Álvarez, Humberto | Universidad de Vigo |
| Navarro Pardo, Esperanza | Universitat de València |
Research Lines:
-Industrial Mathematics
-Mathematical modelling and numerical methods
-Mathematical Physics
MADPhy: Mathematics and Applications to Data and Physics
The group's activity is focused on the application of the concepts and methods of pure and applied mathematics to different areas of knowledge, which are grouped into two main blocks, Data Science and Physics. It is a multidisciplinary group that involves Mathematicians, Physicists, Documentation Specialists and Engineers. The argument thread of the activity is the elaboration of mathematical models for the analysis of related problems in Functional Analysis and Topology, Bibliometric Indices, Acoustics and Metamaterials, Non-linear Physics, Graph-based databases and Fraud Detection Algorithms, among others.
Web: https://www.madphy.webs.upv.es/
Research Lines:
-Functional Analysis, Topology and applications
-Mathematical physics of periodic and non-periodic structures
-Bibliometric Indices in Scientific Research
-Graph-based databases and Fraud Detection
Web: https://www.madphy.webs.upv.es/
| External Collaborators | University |
| Mastyło, Mieczysław | Adam Mickiewicz University (Polonia) |
| Szwedek, Radoslaw | Adam Mickiewicz University (Polonia) |
| Romero Garcia, Vicent | Le Mans Université, France |
| Falciani, Hervé | GRC Advisor |
| Jonard, Natalia | Universidad Nacional Autónoma de México |
Research Lines:
-Functional Analysis, Topology and applications
-Mathematical physics of periodic and non-periodic structures
-Bibliometric Indices in Scientific Research
-Graph-based databases and Fraud Detection
New Functional and Descriptive Methods in Functional Analysis (NUMAF)
The group is working on:
1.- The Separable Quotient Problem, open problem that states wether a infinite dimensional Banach space admits a Separable Infinite Dimensional Quotient. It is well known that small Banach spaces, I mean with denseness less than the bounding cardinal, as well as the big Banach spaces in the sense of Todorcevic, have separable quotient. Our aim is to get new characterizations of the separable quotient problem and to apply these characterizations to Banach Spaces with denseness between the bounding cardinal and the continuum cardinal, as well as to apply the new obtained characterizations to proof rapididly the existence of Separable quotient problem, in known cases like in the case of WCG spaces.
Research lines
-The separable quotient problem
-Nikodym properties on rings and algebras
1.- The Separable Quotient Problem, open problem that states wether a infinite dimensional Banach space admits a Separable Infinite Dimensional Quotient. It is well known that small Banach spaces, I mean with denseness less than the bounding cardinal, as well as the big Banach spaces in the sense of Todorcevic, have separable quotient. Our aim is to get new characterizations of the separable quotient problem and to apply these characterizations to Banach Spaces with denseness between the bounding cardinal and the continuum cardinal, as well as to apply the new obtained characterizations to proof rapididly the existence of Separable quotient problem, in known cases like in the case of WCG spaces.
2.- The second line of research is the determination of rings and algebras os subsets of a set such that Nikodym property implies more strong Nikodym properties. In other words: When Nikodym property is equivalent to strong and web Nikodym properties? It is well known that this equivalence holds in an sigma-algebra.
| Head of the Group | |
| López Pellicer, Manuel | mlopezpe@mat.upv.es |
| External Collaborators | University |
| Kakol, Jerzy | Adam Mikiewicz University, Polonia |
| Ferrando Pérez, Juan Carlos | Universidad Miguel Hernández de Elche |
Research lines
-The separable quotient problem
-Nikodym properties on rings and algebras
Singularity Theory and its Applications
The research topics of our group focus on the study of algebraic and complex analytic singularities. Our research topics include current problems of algebraic geometry, commutative algebra and also some applications to other fields, like the theory of error correcting codes and the theory of foliations. We also deal with the effective computation of numerical invariants of complex analytic maps and the study of notions like equisingularity and topological triviality of deformations of maps.
| Head of the Group | |
| Bivià Ausina, Carles | carbivia@mat.upv.es |
| Researchers | |
| Monserrat Delpalillo, Francisco José | framonde@mat.upv.es |
| External Collaborators | University |
| Galindo Pastor, Carlos | Universitat Jaume I de Castelló |
| Toshizumi Fukui | Saitama University, Japan |
Research Lines:
-Algebraic Geometry, Singularity Theory and Applications
-Complex Analytic Singularities
Our research group is mainly interested in several branches of general topology (asymmetric topology, fixed point theory, fuzzy topological structures, topological algebra, hyperspaces, etc.) as well as its applications to other fields as Computer Science (domain theory, construction of quantitative models, complexity analysis of algorithms) and Image Modelling (image smoothing, image filtering, etc.). We are also concerned with fuzzy set theory always with a topological flavour.
| External collaborators | University |
| D. Fairchild, Mark | Rochester Institute of Technology, USA |
| A. Künzi, Hans-Peter | University of Cape Town, South Africa |
| Valero, Óscar | Universitat de les Illes Balears, Spain |
Research Lines:
-Asymmetric topology
-Fixed point theory
-Fuzzy topological structures
-Fuzzy and metric tools for image modelling
Convocatorias
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FROM THE LIBRARY
Cours de calcul mathématique moderne. Théorie et exercices
- Laboureur, Maurice -- Cardot, Claude -- Chossat, Maurice ;
- Dunod