In the machine learning research line we deal with data problems coming from different scenarios: industry, biosciences, health, economy, etc. We pursue the developments of new machine learning algorithms that can efficiently tackle these problems. Particularly, we consider problems that account for a variety of data types: from time series, to steaming data or images and speech, and a wide range of modelization techniques and mathematical formalisms such as: probabilistic graphical models, Bayesian approaches, deep learning, etc.

The aim of the research in Applied Statistics is to consolidate BCAM as a reference in areas such as biostatistics, demography, environmental modeling, medical statistics, epidemiology, business analytics, and biomedical research applications involving data-driven mathematical and statistical tools.

Current research is concerned with the analytical study of physically motivated systems of partial differential equations. So far it has concentrated on several major directions:

Modern harmonic analysis is a very active field of research which has reached a state of maturity that places itself in a central position within the mathematical sciences. Although the origin of harmonic analysis goes back to the study of the heat equation (through Fourier theory), harmonic analysis today has many interconnections with many areas of mathematics like PDEs, operator theory or complex analysis. Often, harmonic analysis plays an important role when the scenarios are not very friendly as those where there is a lack of smoothness.

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence Singularity Theory lies at the crossroads of the paths connecting applications of mathematics with its most abstract parts. For example, it connects the investigation of optical caustics with simple Lie algebras and regular polyhedra theory, while also relating hyperbolic PDE wavefronts to knot theory and the theory of the shape of solids to commutative algebra.

Since the advent of modern Single Particle Tracking (SPT) techniques, a large amount of data with great temporal and spatial accuracy has been produced. The emergence of anomalous diffusion has been confirmed by SPT statistics in many biological systems, with sub-diffusive behavior often associated to crowding, confinement phenomena, and strong heterogeneity of the environment. Recent experiments on molecular diffusion within the cell environment permit to distinguish the anomalous behavior caused by active mechanisms, from the one caused by crowding and confinement in the same system.