Line Manager: María José Felipe Roman

Character theory and the study of conjugacy classes in finite groups are two closely related lines of research. Their main objective is to obtain information about the structural properties of the group, such as its normal structure, simplicity, and solvability. We are also interested in obtaining this type of structural information in factored groups. Many results in this framework require specific techniques in both fields, as well as in simple groups.

Line Manager: Mari Carmen Pedraza Aguilera

The study of factored groups is a productive area of research in finite group theory, where the structural impact of the factors on the whole group is a central issue. We address various problems in this context: extensions of the Kegel-Wielandt theorem through pi-decomposable or pi-soluble groups, or the influence of the conjugacy class sizes of the elements in the factors. We are particularly interested in factored groups with certain connectivity properties between the factors (total, mutual, conditional permutability; L-connection).

Line Manager: Ana Martínez Pastor

One of the most effective methods in the structural study of finite groups, parallel to the classification of simple groups, is the analysis of the interrelations between relevant families of subgroups and their embedding in the group, as well as their lattice properties. In this framework, we focus particularly on the influence of the normalizers of the Sylow subgroups on the group’s structure. Significant lattices of subgroups are also studied.

Line manager: Alfred Peris Manguillot

The following points are being worked on: Analysis of different concepts of chaos in operator dynamics, recurrence properties and combinatorial number theory in linear dynamics, and regularity properties (mean ergodicity, Cesàro boundedness, etc.) in operator dynamics.

Line manager: Marina Murillo Arcila

The following type of problems are considered: Study of the algebrability of sets of functions related to the dynamics of differential operators, analysis of the algebrability of sets of functions with certain pathological properties, and development of new techniques for the lineability/algebrability/spaciability of sets of functions, sequences, series, etc.

Line manager: Vicente Montesinos Santalucía.

Equivalent standards can enhance the properties of differentiation and convexity. Thus, functions become differentiable at many points, enabling differentiation techniques to analytically solve various problems. For example, computing shortest or farthest distances to subsets becomes feasible. The isomorphic characterization of spaces with good renormings is crucial. Lipschitz functions naturally appear in many functional analysis issues, as they allow for the linearization of nonlinear problems. In many cases, the Banach space structure becomes more transparent using these techniques.

Line manager: Pablo Sevilla Peris.

The study involves holomorphic functions in infinite-dimensional Banach spaces and the algebraic structure of such functions along with their analytic properties. The power series of such functions in a space with an unconditional basis may not converge everywhere. Describing the convergence points is related to the Bohr radius and the unconditional basis of the space of homogeneous polynomials. This includes Banach spaces of Dirichlet series, scalar and vector-valued, connecting holomorphic functions and Hardy spaces on the infinite-dimensional torus.

Line manager: Alfred Peris Manguillot.

Some of the stated objectives are: applying probabilistic and fuzzy methods in linear dynamics, analyzing various properties and their feedback between linear and nonlinear dynamics, and studying properties of topological dynamics in discrete dynamical systems.

Line manager: Enrique Jordá Mora.

We investigate linear partial differential operators that are hypoelliptic in classes of ultradifferentiable functions and tempered ultradistributions, the Wigner transform, and the linear and continuous extension of smooth functions from compact sets.

Line manager: José Bonet Solves.

We study Banach and locally convex spaces of analytic and differentiable functions, as well as operators between them. Various properties of integral operators, differential operators, and weighted composition operators are investigated.

Line manager: Manuel López Pellicer

In the space of continuous scalar functions C(X) defined on a Tychonoff space X, equipped with either the topology of pointwise convergence or the topology of compact-open convergence, there is current interest in studying covering properties by resolutions whose elements absorb certain predefined sets (such as finite subsets or compact sets). These resolutions are utilized in C(X) to characterize topological and cardinality properties of X.

Line manager: Manuel López Pellicer

The Banach space of bounded and finitely additive scalar measures defined on a σ-algebra of sets satisfies the Nikodym-Grothendieck and Valdivia boundedness theorems, as well as the Grothendieck and Vitali-Hahn-Saks sequential convergence theorems. Small subsets of the σ-algebra have been identified that satisfy the hypotheses of these four theorems, along with a partial solution to Valdivia’s problem concerning whether the boundedness property of Nikodym in a set algebra implies strong boundedness (2013).

Line manager: Jesús Rodríguez López

Fuzzy mathematical theory emerged to model situations of uncertainty where classical binary logic was not suitable. This led to the development of fuzzy logic, which is much more flexible. In this line of research, we work with certain connectives of fuzzy logic such as t-norms, t-conorms, fuzzy implications, etc. Additionally, we also study other fuzzy mathematical structures that give rise to topologies, such as fuzzy metrics, fuzzy uniformities, and fuzzy proximities.

Line manager: Francisco José Monserrat Delpalillo

We work in various areas within singularity theory and valuation theory using methods from algebraic geometry as our main tool. This includes topics such as convex cones associated with algebraic varieties, multiplier ideals, flat valuations, and Newton-Okounkov bodies. Additionally, we consider applications to related areas such as error-correcting codes theory or algebraic foliations theory.

Line manager: Carles Bivià Ausina.

We study numerical invariants associated with maps and complex analytic varieties. These invariants are based on intersection theory and consequently lead to the study of fundamental concepts in singularity theory, such as the integral closure of ideals and submodules of a free module. One of our main interests lies in describing numerical invariants and integral closures in terms of Newton polyhedra and monomial ideals. We also investigate the geometry and topology of complex polynomial maps and their connection with the Jacobian conjecture.

Line manager: Pedro Tirado Peláez

The objective of this research line is to obtain fixed point theorems in the context of quasi-metric spaces, as well as to characterize various notions of completeness in quasi-metric spaces in terms of the existence of fixed points. Additionally, we also study these problems in the context of fuzzy quasi-metric spaces.

Line manager: Carmen Alegre Gil

Asymmetric topology is a branch of topology that studies topological structures which do not satisfy the symmetry axiom, such as asymmetric norms, quasi-metrics, quasi-proximities, and quasi-uniformities. The study of these structures has increased in recent years not only due to their purely theoretical interest but also because of their applications in Computer Science. The aim of our research is to investigate properties of asymmetric topological structures that can contribute to the development of the mentioned applications.

Line manager: Alfred Peris Manguillot

Some of the objectives are: the study of financial time series (stocks, stock indices, etc.) using deep learning and artificial intelligence operators and techniques; the analysis of industrial electric induction motors for the diagnosis of bar breaks using wavelet transform and operator theory techniques.

Line manager: Jesús Rodríguez López

Aggregation refers to any process by which a certain number of numbers are combined to obtain a single representative value. This aggregation process is carried out through so-called aggregation functions. These types of functions have become an important object of study due to their applications in various fields such as statistics, decision theory, artificial intelligence, etc. However, these types of functions can be used not only to aggregate numbers but also to aggregate certain topological structures such as metrics. It is in these types of aggregation processes that we are interested.

Line manager: Alberto Conejero Casares

Line manager: Marina Murillo Arcila

In this line of research, we focus on: studying continuous dynamical systems, especially those related to linear PDEs and infinite systems of linear ODEs, analyzing qualitative properties of fractional models in continuous and discrete time, and studying numerical schemes corresponding to discretizations of continuous-time fractional operators.

Line manager: David Jornet.

We investigate Fourier integral operators in modulation spaces, Gabor transform, and biomedical signal processing with time-frequency analysis. Collaboration has taken place with the Hospital Universitari Politècnic La Fe (Valencia).

Line manager: Alberto Conejero Casares

We are currently collaborating with the BDS (ITACA) laboratory on the following topics: modeling of glioblastoma, designing apps for patient data collection to feed predictive models, and data quality in clinical records repositories. Additionally, we are working on synthetic biology modeling of specific plants in collaboration with Diego Orzáez’s laboratory (IBMCP), and at the cellular level with Guillermo Rodrigo (I2SysBio).

Line manager: Alberto Conejero Casares

We are proud members of the Data Science against COVID-19 Task Force, led by Nuria Oliver. We have specialized in outbreak modeling and predicting the evolution of the COVID-19 pandemic using Recurrent Neural Networks.

Regarding complex network modeling, we are interested in applications across various disciplines, including network communications, image processing, linguistics, and more. We are also working on data visualization for the so-called Scientific Maps in collaboration with E. Orduña and M. Rebollo.

Line manager: Pedro J. Fernández de Córdoba Castellá.

Search for Statistical Regularities in Human Behavior Based on Heuristics Inspired by Statistical Physics, where Age and Gender are Fundamental Parameters. Development of Indices for Classifying Individuals in Different Contexts, with a Special Emphasis on Social and Health Sciences. Development of Models to Describe the Evolution of Human Collectivities Throughout the Life Cycle. The physical models used in our work include: the Ideal Gas Model, the van der Waals Model for Real Gases, and Planck’s Law to Describe Black Body Behavior. Additionally, we utilize general principles such as the Maximum Entropy Principle from Physics and the Laws of Thermodynamics.

Line manager: Antonia Ferrer Sapena

The definition of information indices has become a fundamental tool for evaluating research, much like economic indices are central to modern economic theory. The mathematical structure of these indices is related to abstract integration, utilizing universal integrals and integrals in the scalar case, and generally integration with respect to fuzzy capacities. These theoretical issues and their specific applications for bibliometric analysis of data, journals, and open information, for example, have become the focus of this new line of research.

Line manager: Jose María Isidro San Juan

The current topics of interest at the interface between mathematics and physics constitute the main research focus of this group. Specifically, two contemporary issues are being investigated: The foundations of quantum theory, particularly from a thermodynamic perspective (referred to as the “emergence of quantum theory”). A differential-geometric approach to thermodynamics, as a byproduct of the former but also interesting in its own right.

Line manager: María José Martínez Usó

Positions and movements in the celestial sphere must be expressed in a well-defined reference system, embodied in various reference structures (catalogs). Their precise definition, determination, and correction over time are crucial to ensure accurate positioning, such as in satellite navigation. The study and homogenization of these catalogs, as well as their adaptation to the reference materialized in Gaia, are goals of this line of work.

We propose methods to enhance integration techniques used in studying problems related to orbital motion, both in satellite theory and in the planetary theories of the solar system. Additionally, we aim to catalog and utilize ancient astronomical observations (mainly from the Middle Ages) to update and improve current astronomical parameters.

Line manager: Lluis M. García Raffi

This line of research focuses on the propagation of waves through heterogeneous media composed of a supporting material with inserted elements of another material or geometric discontinuities that represent a change in physical properties. These changes modulate transport phenomena within the medium, imparting specific properties such as transparency over a wide bandwidth, isotropic diffusion, isotropic filtering, and more.

Line manager: Carles Milian

The primary focus of this research line is on nonlinear dynamics and the formation of spatiotemporal solitons in dissipative media of various natures, with particular emphasis on dynamics and control (such as multiple-frequency combs). Additional closely related interests revolve around physical effects associated with inelastic laser-matter interactions, including ionization and the Raman effect. This research involves extensive numerical study of complex mathematical models developed from fundamental principles of physics.

Line manager: Sergio Hoyas Calvo

Wall turbulence is responsible for approximately 5% of humanity’s CO2 emissions. Despite the fact that the equations governing this phenomenon have been known for over 150 years, the problem remains open. Through direct numerical simulations (DNS), we study the dynamics of turbulent flows in simple domains, aiming for the largest possible Reynolds numbers.

Line manager: Enrique A. Sánchez Pérez

This line of research is developed within the context of mathematical analysis, utilizing two different mathematical theories: The theory of integration with respect to vector measures, which is applied in the study of function spaces, functional approximation, operator theory (optimal domains), and Banach lattices (representation). Secondly, quasi-metrics are employed in multi-objective optimization, and within the context of machine learning, Lipschitz extensions of functions are used. Both lines of work, centered around function theory, are studied from both theoretical perspectives and in their practical applications.

Line manager: Jose M. Calabuig Rodríguez

The main objective of this line of research is the creation of indicators and machine learning algorithms for predictive analysis based on data collected from football matches. Through a framework agreement with Levante UD and LaLiga Professional Football, we have access to data (both event-based and tracking data) from matches. This research lies at the intersection of mathematics and data science.

Line manager: Alberto Conejero Casares

We analyze the structure and behavior of optimization algorithms that, in their configuration, utilize tensor products, and their connections with Quantum Computing.

Line manager: Pedro J. Fernández de Córdoba Castellá.

The field of Industrial Mathematics focuses on solving problems of industrial interest. Within this scope, examples include numerical simulation of energy efficiency issues in buildings, analysis of geothermal heating and cooling systems, and studies on heat transfer in LED bulbs. Additionally, the group is keen on fostering relationships with businesses and promoting the transfer of mathematical technology to the industry.

Line manager: Miguel Ángel García March

The main objective of this line is to harness Applied Mathematics to drive sophisticated models and appropriate computational techniques in various areas of quantum technologies: quantum simulators and computers. The aim is to explore new realistic systems for quantum simulators and computers, based on, for example, systems of few interacting ultra-cold atoms, systems exploiting quantum random numbers in optimization problems, annealers, machine learning protocols, etc.; or systems that can be used for quantum reservoir computing and quantum machine learning.

Quantum metrology/thermometry: The goal is to study quantum devices for this purpose. For instance, systems based on impurities within Bose-Einstein condensates.

Quantum machines, phononic and quantum thermodynamics: Problems akin to open quantum systems oriented towards these applications.

Quantum chaos and thermalization in isolated quantum systems.

Photonic emulators of interacting quantum systems and condensed matter (via, for example, solitons in optical networks or vortex systems – singular and nonlinear optics).

Line manager: Samuel Morillas Gómez

Fuzzy logic and fuzzy metrics have proven effective in enhancing various image processing methods such as image enhancement, smoothing, or filtering. Recently, there has been increasing interest in the study of image appearance models, which concern how images are perceived by the human visual system. This area of research has applications in a wide range of topics including camera technology, image reproduction, and even augmented and virtual reality. These issues are also investigated within this research group.