A natural problem in group theory is: what can we say about a group in which all subgroups of a relevant family of subgroups satisfy a certain property? We intend to make contributions along these lines.
When a factor group G=AB is considered as a product of two subgroups, related with certain permutability conditions, the natural question is to determine what we can say about G from the properties of A and B, and what we can say about A and B from properties of G.
The fathoms are associated to trifactor groups with structural properties that effectively determine solutions of the quantum Yang-Baxter equation.
Development of multivariate dynamic models and their analysis by Bayesian mehtodology, using MCMC simulation methods. Incorporation of spatial dependencies into the temporal structure of the models. Design and implementation in R of algorithms for their analysis, estimation and prediction.
Properties of holomorphic functions and Banach spaces and algebras whose elements are these functions are studied.
Development of models with compositional data. In environments such as biology, economics or geology, it is common to work with data vectors whose components reflect the relative contribution of different parts in relation to a total, obtaining compositional samples. Work will be done on the progress of statistical modelling of compositional data, its application and its mathematical foundations.
Development of Bayesian hierarchical models for the study of the geographical variability of diseases and their temporal evolution with the aim of aiding decision-making and the development of surveillance programmes.
Certain classes of groups are defined by the actions of the groups with regard to the main factors or other normal sections. Special importance is attached to subgroups that cover or avoid all the main factors of the group, as well as actions that determine flanges of special type.
Properties of bounded operators between Banach spaces are studied, as well as multilinear applications and polynomials in Banach spaces and the spaces formed by these applications.
Mathematical modelling of electroencephalographic (EEG) brain activity in relation to drug effects and from the paradigm of individual differences.
To develop new methods for non-linear partial differential equations that allow us to contribute to the solution of concrete problems, most of them suggested by applications.
In the field of computer science, there has been a growing interest in the study of semigroups and monoids in relation to automata and formal languages. We aim to apply techniques from group theory and universal algebra to the analysis of these objects.
In recent years, groups where all subnormal subgroups are normal, permutable, or Sylow-permutable have been of interest, both in terms of finite groups and extensions to classes of infinite groups. We have also developed computational techniques to study these groups with GAP.
The study of pseudo-differential operators with time-frequency analysis methods.
