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Research Groups.

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

Algebra Research Group (Group Theory)

Algebra is one of the fundamental areas of mathematics which studies, in a general sense, abstract structures arising as a generalization of ordinary arithmetic and its invariants. This area of pure mathematics also has numerous applications other branches of science and technology such as physics, chemistry or computer science. The research interest of the group is mainly group theory and  focuses on studying the internal structure of groups from their actions and representations, the lattice of its subgroups and arithmetical properties, both in finite groups and infinite groups with certain finiteness conditions, and its applications mainly in relation with automata and formal languages.

Head of the Group e-mail
Martínez Pastor, Ana anamarti@mat.upv.es
Alemany Martínez, Elena ealemany@mat.upv.es
Arroyo Jordá, Milagro parroyo@mat.upv.es
Arroyo Jordá, Paz marroyo@mat.upv.es
Camp Mora, Sergio scamp@mat.upv.es
Felipe Román, Mª José mfelipe@mat.upv.es
Pedraza Aguilera, Mª Carmen mpedraza@mat.upv.es
Pedraza Aguilera, Tatiana tapedraz@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 line: Algebra (Group Theory)

Applications of Functional Analysis to Engineering

Our work consists of applying the techniques from functional analysis to the rigorous solution of mathematical problems in engineering, by modelling them through ordinary differential equations and partial differential equations, and by the analysis of their solutions and the mathematical properties they possess.
Head of the Group e-mail
López Molina, Juan Antonio jalopez@mat.upv.es
Rivera Ortún, María José mjrivera@mat.upv.es

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

The research interest of the group is the geometry of Banach spaces and the infinite-dimensional complex analysis. In the first setting, we study differentiability of norms and renorming. In the second, we deal with properties of polynomials and multilinear mappings in Banach spaces.
Head 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

Celestial Mechanics and Reference Systems

Head of the Group e-mail
Martínez Usó, M.J. mjmartin@mat.upv.es

Functional Analysis and Applications to Physics (FUNAPHY)

Funaphy is an interdisciplinary research group mainly devoted to the study of mathematical problems in the area of the functional analysis and its applications to other areas, both of theoretical and applied science, such as Classical and Quantum Mechanics and signal analysis in Acoustics. Our group members are leading experts in functional analysis, physics and topology. Nowadays, regarding the research in mathematics, our publications deal with classical and new problems of the general theory of Banach lattices, operator theory, vector measures and integration, and scattering theory.

Also applications of the so called non symmetric topology in the context of the functional analysis have been developed by the members of the group in recent years. Simultaneously, an applied project for the signal analysis of acoustic spectra that gives mathematical support to a research group in experimental physics of our university is being developed at the moment.

Web: http://www.upv.es/funaphy/
Head of the Group e-mail
Garcia Raffi, Lluís Miquel lmgarcia@mat.upv.es
Calabuig Rodríguez, José Manuel jmcalabu@mat.upv.es
Jiménez Férnandez, Eduardo edjimfer@mat.upv.es
Sánchez Pérez, Enrique Alfonso easancpe@mat.upv.es
External Collaborators University
Blasco de la Cruz, Oscar Universitat de València
Ferrando Palomares, Irene Universitat de València
Juan Blanco, María Arantzazu Universitat de València
  Research Lines: Wave propagation

Hypercyclic Operators and Linear Chaos

Our main research area is the study of the chaotic dynamics of linear operators on infinite-dimensional spaces (Banach and Fréchet spaces). This is a topic which combines techniques of Dynamical Systems and operator theory. We are mainly concerned with the analysis of topological properties related to chaos, like the existence of dense orbits (hypercyclicity, within our framework), other stronger properties (mixing, weakly mixing, etc.), and general notions of irregularity for orbits (Li-Yorke chaos, distributional chaos,etc.). We also study notions from ergodic theory (given an infinite-dimensional linear dynamical system, the existence of invariant measures with certain additional properties, etc.) and their consequences in the frequently recurrent behaviour of dense orbits.

We are interested in discrete and continuous dynamical systems. In the latter case, we mainly concentrate our attention on continuous dynamical systems which come from solution semigroups of linear partial differential equations and of infinite systems of linear ordinary differential equations.

Head of the Group e-mail
Peris Manguillot, Alfred aperis@mat.upv.es
Barrachina Civera, Xavier xabarci@doctor.upv.es
Conejero Casares, Alberto aconejero@mat.upv.es
Martínez Jiménez, Félix fmartinez@mat.upv.es
Murillo Arcila, Marina mamuar1@posgrado.upv.es
Puig de Dios, Yunied yupuide@posgrado.upv.es
Ródenas Escribà, Francisco frodenas@mat.upv.es
PhD Students
Aroza Benlloch, Javier jaarben@upvnet.upv.es
Bartoll Arnau, Salud sbartoll@mat.upv.es
Galán, Víctor
Jiménez Munguía, Ronald
Nogués Martínez, Rafael ranomar@posgrado.upv.es
External Collaborators University
Bernardes, Nilson
Bès, Juan Bowling Green State University
Bonilla, Antonio
Grosse-Erdmann, Karl G. Université de Mons
Müller, Vladimir
Oprocha, Piotr

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 UVEG; biotechnology, with researchers form Universidad Católica de Valencia; or in the advanced modelling in energetic engineering. As a result of the research activities of the group an 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
Fuente Herraiz, David dafueher@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
Martínez Molada, Eulalia eumarti@mat.upv.es
Pérez Quiles, María Jezabel jperezq@mat.upv.es
Sanchis Llopis, José María jmsanchis@mat.upv.es
Siurana paula, María masiupau@upv.es
Soler Fernández, David dsoler@mat.upv.es
Urchueguía Schölzel,Javier Fermín jfurchueguia@fis.upv.es
    Research Lines: Mathematical modelsNumerical methods,  PhotonicsSynthetic Biology.

Methods of Functional Analysis for Mathematical 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 Carme mcgomez@mat.upv.es
Jorda Mora, Enrique ejorda@mat.upv.es
Jornet Casanova, David djornet@mat.upv.es
PhD Students
Beltrán Meneu, María José mabelme@csa.upv.es
Castillo Medina, Jaime jaicasme@upvnet.upv.es
Primo Tárraga, Eva atirpe.23@gmail.com
External Collaborators University
Albanese, Ángela Università del Salento
Domański, Pawel Adam Mickiewicz University
Fernández Rosell, Carmen Universitat de València
Frerick, Leonhard Universität Trier
Galbis Verdú, Antonio Universitat de València
Ribera Puchades, Juan Miguel Universitat de València

Singularity Theory and its Applications

The research topics of our group focus on the study of the singularities of real and complex maps, both from the algebraic and the differential point of view. Therefore, our research topics include current problems of algebraic geometry, commutative algebra and differential geometry. We also consider the applications of singularity theory to other fields, like the theory of error correcting codes.
Head of the Group e-mail
Bivià Ausina, Carles carbivia@mat.upv.es
Monserrat Delpalillo, Francisco José framonde@mat.upv.es

Research Lines: Geometry

Topology and its Applications

Our research group is mainly interested in several branches of general topology (asymmetric topology, fixed point theory, fuzzy distances, topological algebra, hyperspaces, etc.) as well as its applications to other fields: domain theory, construction of quantitative models in theoretical computer science, image processing, approximation of functions, applications of denotational semantics to the complexity analysis of algorithms, etc.

Head of the Group e-mail
Romaguera Bonilla, Salvador sromague@mat.upv.es
Alegre Gil, Carmen calegre@mat.upv.es
Gregori Gregori, Valentín vgregori@mat.upv.es
Marín Molina, Josefa jomarinm@mat.upv.es
Morillas Gómez, Samuel smorillas@mat.upv.es
Rodríguez López, Jesús jrlopez@mat.upv.es
Sapena Piera, Almanzor alsapie@mat.upv.es
Tirado Peláez, Pedro pedtipe@mat.upv.es
External collaborators University
Castro Company, Francisco Universitat de València
Sánchez Granero, Miguel Ángel Universidad de Almería
Sanchis, Manuel Universitat Jaume I

Research Lines: Topology