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Research Groups.

Internal organization of the Institute in research groups based on their area of ​​expertise…

Algebra (Group Theory)

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.

Heads of the Group e-mail
Martínez Pastor, Ana anamarti@mat.upv.es
Felipe Román, Mª José mfelipe@mat.upv.es
Arroyo Jordá, Milagros marroyo@mat.upv.es
Arroyo Jordá, Paz parroyo@mat.upv.es
Esteban Romero, Ramón resteban@mat.upv.es
Ortiz Sotomayor, Víctor Manuel vicorso@doctor.upv.es
Pedraza Aguilera, Mª Carmen mpedraza@mat.upv.es
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 e-mail
Montesinos Santalucía, Vicente vmontesinos@mat.upv.es
Sevilla Peris, Pablo psevilla@mat.upv.es
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.  
Head of the Group e-mail
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

Dynamics of operators (DYNOP)

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.
Heads of the Group e-mail
Peris Manguillot, Alfred aperis@mat.upv.es
Conejero Casares, Alberto aconejero@mat.upv.es
Bartoll Arnau, Salud sbartoll@mat.upv.es
Martínez Jiménez, Félix fmartinez@mat.upv.es
Ródenas Escribà, Francisco frodenas@mat.upv.es
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:

(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/
Head of the Group e-mail
Bonet Solves, José jbonet@mat.upv.es
Gómez Collado, María del Carmen mcgomez@mat.upv.es
Jordá Mora, Enrique ejorda@mat.upv.es
Jornet Casanova, David djornet@mat.upv.es
Ortigosa Araque, Nuria nuorar@upv.es
PhD Students
Asensio López, Vicent viaslo@doctor.upv.es
Gómez Orts, Esther esgoor@upvnet.upv.es
Rodríguez Arenas, Alberto alrodar3@posgrado.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

  Research lines

-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.    
Head of the Group e-mail
Fernández de Córdoba Castellá, Pedro José pfernandez@mat.upv.es
Abraham Ibrahim, Sergio sabraham@mat.upv.es
Giménez Palomares, Fernando fgimenez@mat.upv.es
Hoyas Calvo, Sergio sergio.hoyas@mot.upv.es
Isidro San Juan, José María joissan@mat.upv.es
Pérez Quiles, María Jezabel jperezq@mat.upv.es
Sanchis Llopis, José María jmsanchis@mat.upv.es
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/
Heads of the Group e-mail
Calabuig Rodríguez, José Manuel jmcalabu@mat.upv.es
Garcia Raffi, Lluís Miquel lmgarcia@mat.upv.es
Sánchez Pérez, Enrique Alfonso easancpe@mat.upv.es
Ferrer Sapena, Antonia anfersa@har.upv.es
Peset Mancebo, María Fernanda mpesetm@upvnet.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.

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.

Web: http://prometeo2013058.blogs.upv.es
Head of the Group e-mail
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 e-mail
Bivià Ausina, Carles carbivia@mat.upv.es
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

Topology and its Applications

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.

Head of the Group e-mail
Jesús Rodríguez López jrlopez@mat.upv.es
Alegre Gil, Carmen calegre@mat.upv.es
Marín Molina, Josefa jomarinm@mat.upv.es
Morillas Gómez, Samuel smorillas@mat.upv.es
Pedraza Aguilera, Tatiana tapedraz@mat.upv.es
Tirado Peláez, Pedro pedtipe@mat.upv.es
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