The Basque Center for Applied Mathematics – BCAM

The Basque Center for Applied Mathematics – BCAM is an international research center in the field of Applied Mathematics that was founded in 2008 by the Basque Government, the UVP/EHU and Ikerbasque. It is also supported by the Provincial Council of Bizkaia and Innobasque. One of its main objectives is to put mathematics at the service of society through the transfer of knowledge, making the results of its research available to sectors such as biosciences, health, energy or advanced manufacturing, and working together with local and international institutions and companies.

Research proposals shall cover the following lines:

• Computational Mathematics (CM): We analyse modern numerical methods such as advanced Finite Element (AFE) and Finite Volume (FV) techniques applied to stationary and time-dependent problems. In addition, we develop new meshless multi- scale methods such as Smoothed Particle Hydrodynam- ics (SPH) or Dissipative Particle Dynamics (DPD) applied to complex fluids and mesoscopic flow problems.
• Mathematical Modelling with Multidisciplinary Applications (M3A): We push the boundaries of mathematics and develop analytical frameworks, multiscale parsimonious models, advanced algorithms and novel measuring techniques to extract invariant patterns hidden within the multi-spatial-temporal scales involved in biological and physical systems. A closed loop between hypothesis testing, HPC, high throughput data and data management, enable quantitative and qualitative knowledge discovery.
• Mathematical Physics (MP): We study several questions of classical physics that although long known, are still not understood from the mathematical perspective, microscopic origin of macroscopic laws (like in electricity) and natural phenomena of front motion embedded into random environments. More theoretically, we study the geometry of Singularities appearing in Algebraic Geometry.
• Analysis of Partial Differential Equations (APDE): The attempt to efficiently describe real-life phenomena leads to mathematical models, often expressed in terms of PDEs, capturing the essential features of the phenomena. Solving these equations implies the use and development of sophisticated techniques of analysis together with the realisation of numerical simulations to eventually determine the validity of the models.
• Data Science (DS): In the applied statistics field, the main topics of our research are semi-parametric regression, multidimensional smoothing, (Bayesian) hierarchical models, computational statistics… Regarding Machine learning, we work on supervised and unsupervised classification of massive data, probabilistic graphical models, time series, Bayesian optimisation, etc. In optimisation we pursue the developments of efficient metaheuristics methods.
• Model building and data analysis for COVID: prediction-evolution models, analysis of RX images, pronostic prediction, traceability analysis.