Company Profile
Centre de Recerca Matemàtica
Company Overview
The Centre de Recerca Matemàtica (CRM) was created in the year 1984 with the aim of promoting research and advanced training in mathematics with the collaboration and synergies of the university and other research institutes, thereby becoming a centre of international scientific reference in mathematics research.
The centre's activities are divided into two very different categories. The first category places the centre as organiser of international competitions (intensive research programmes, advances courses, conferences, etc.) and as a centre for long-term visiting researchers working in collaboration with the research community of Catalonia. Secondly, since 2008 CRM includes its own research groups, which allows it to open lines of research in different applied areas.
Strategic research areas
Complex systems. Many of today's challenges facing humanity originated in complex systems, which are those in which many parts interact, such as climate, the economy, society, the human brain, cells, etc. This line of research focuses especially on natural disasters (earthquakes, hurricanes, fires, etc.), human language structure, and mobility of individuals, and uses both the analysis of real data and model simulations to carry out its research.
Computational & Mathematical Biology. Biological systems are defined by the complex interaction of processes at highly different scales where those involving the population as a whole are affected by individual processes.
Computational Neuroscience. This group was created with the purpose of applying numerical and analytical modelling techniques as well as data analysis to the study of brain function. One of the main areas of interest is to explore how the dynamics of large numbers of neurons are shaped by the patterns of synaptic connectivity in cortical micro-circuits. This modelling work will be constrained by and compared to the increasing amount of experimental data available on cortical connectivity in rodents.
Financial Mathematics and Risk Control. In this research line, both theoretical and applied problems appearing in quantitative finance are studied: numerical computation of exotic options in Lévy-based financial models, numerical simulation of stochastic differential equations governed by general processes, inversion of the stochastic processes, Monte Carlo variance reduction methods, rating protocols, etc.
Approximation Theory and Harmonic Analysis. Harmonic analysis studies the representation of functions or signals as the superposition of basic waves and has several applications: signal processing, geomatics, electronic engineering, analysis of time series, numerical analysis, etc. Basic research is conducted in harmonic analysis and fundamental mathematical study, within the theory of nonlinear approximation, of many of these applications.
Industrial Mathematics. Industrial mathematics covers applied research in this field focused on future industrial applications. CRM focuses on modelling phase change and heat transmission, flow of fluids, monitoring of blood pressure, aerodynamics, etc. in its applications: ice formation in aircrafts, design of microvalves, flows in nanotubes and microchannels, automatic interpretation of blood pressure signals, etc.
Mathematical Epidemiology. Mathematical modelling of infectious diseases of the humans, domestic and wild animals and plants is a rapidly expanding and a highly practically relevant area of research. This general area includes a number of sub-sectors such as the emergence and invasion of new pathogens, the evolution of pathogens, the dynamics of the infectious disease in a population, as well as dynamics of microparasites within a host. It also deals with the mathematical description of immune response, as well as with its failure, as in the case of HIV infection. The most important area is, however, assisting epidemiologists and biologists in the development of rational strategies for the control of infectious diseases, at both a population and a single host levels.
Numerical Analysis and Scientific Computing. This group focuses on the development, theoretical analysis and implementation of new methodologies working towards the numerical solution of partial derivative equations in problems in fluid mechanics, structural mechanics, kinetic equations in statistical mechanics, etc. (finite element methods. multigrid and multiscale techniques, stabilisation methods, solution methods for resulting discrete systems).
Notable Clients
Notable Accomplishments / Recognition
The CRM, established in 1984, has as a mission statement to “improve research and advanced training in Mathematics, in collaboration with Universities and other research institutions in Catalunya”.
This concretises in three aspects:
- Attract recognized mathematicians to the Catalan R+D system, enhance collaborative interdisciplinary research, and promote research training at all levels.
- Support the local community in the international arena, by hosting visiting researchers from all over the world and organizing scientific events of various formats.
- Transfer mathematical knowledge and technology to society.