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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

Applications of Topology and Analysis (APLANTOP)

We are concerned with specific problems on the relationship between topology and the functional analysis, for certain kinds of locally convex spaces, including spaces of Fréchet, their topological duals, spaces of continuous functions C(X) and the spaces of distributions and analytical functions. We study topological invariants, such as tightness, Lindelof, Souslin and Hewitt numbers with applications to the topological characterization of properties of concrete objects of functional analysis, to obtain new characterizations, applications and better understanding of certain properties. Combinative techniques of descriptive topology of sets as K-analiticity, analiticity, almost-Souslin, semicontinuity, etc with techniques of local convexity. This topics are in part developed in the monograph “Descriptive Topology in Selected Topics of Functional Analysis”, Developments in Mathematics 24, Springer 2011

Topological vector spaces.

Barrlledness and applications vector spaces with and without local convexity conditions and properties of strong and weak barrelledness. Countably additive vector measures, location properties and Banach spaces including spaces $L_p$ are also studied as well as the wavelets in solving differential models.

Integration of new technologies to the Mathematics education.

The different aspects that involve the use of new technologies, including the use of mathematical programs and educational platforms are studied.

Head of the Group e-mail
Sánchez Ruiz, Luis Manuel lmsr@mat.upv.es
López Pellicer, Manuel mlopezpe@mat.upv.es
Moll López, Santiago smoll@mat.upv.es
Morales González, Isabel mimorales@mat.upv.es

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, M.J. mjmartin@mat.upv.es
External Collaborators University
Marco, Francisco José Universitat Jaume I de Castelló
López, 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 their applications to several areas of mathematical analysis, like complex analysis, operator theory, Fourier analysis, dynamical systems and linear partial differential operators.

More precisely, we work in the following problems:

(1) Spaces of analytic functions and operators between them: weighted spaces of analytic functions, composition, superposition and Toeplitz operators, operators on spaces of real analytic functions.
(2) Localization operators and time-frequency analysis: Stockwell transform, uncertainty principles, weighted modulation spaces, frames for Fréchet spaces.
(3) Linear partial differential and convolution operators on spaces of ultradifferentiable functions and ultradistributions: solution operators, hypoellipticity, iterates of the operator, quasianalytic classes, extension of smooth functions, and
(4) Abstract functional analytic developments: splitting of short exact sequences, mean ergodic operators, topological algebras and linear dynamical systems.
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
Albanese, Ángela Università del Salento, Lecce, Italia
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: http://www.madphy.nicedaybranding.com/
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
Szwedek, Radoslaw
Romero Garcia, Vicent
Falciani, Hervé
Jonard, Natalia

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

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