With a highly interdisciplinary team, our research addresses significant mathematical problems and fundamental questions in medicine and biology.

In the CFD-MS group we develop novel multiscale models and high-performance simulation algorithms to describe the dynamics of simple and complex fluids from microfluidics up to macroscopic flow conditions.

Combinatorial optimization problems are ubiquitous in the real-world. Routing, scheduling, location, or cutting/packing, are examples of common problems in this area. Most of these problems are characterized for having a complexity that makes it impossible to solve high-dimensional instances to optimality, and here is where metaheuristics algorithms come to play. Metaheuristic algorithms are a set of techniques and algorithms that, although in most of occasions do not guarantee to find the global optimal solutions, they provide high-quality solutions in affordable computation times.

What these three topics have in common is that they will be studied making a modern use of classical techniques of Harmonic Analysis, such as: Oscillatory Integrals and Gauss Sums to describe the dynamics of vortex filaments, Singular Integral Operators like the Cauchy Integral to study shell interactions for Dirac equations and confinement, and Carleman estimates to obtain lower bounds that eventually lead to prove new uncertainty principles. More concretely,

Since its origins in the 1920s, Quantum Mechanics has remained one of the most vibrant and intellectually rich areas of research in both Physics and Mathematics. However, since the early 2000s, and with a significant acceleration in recent years, we have witnessed a turning point with the rise of what is now called the second quantum revolution, or Quantum 2.0.

Principal Investigators:
Michael Barton and David Pardo

Our research spans areas of Deep Learning, Inverse Problems, Finite Elements, Massive Computations, Numerical Analysis, Geometric Modeling, Computer Aided Design, and Modeling of Manufacturing Processes. We work in close interaction with industrial partners and institutions to promote transfer of knowledge and obtain feedback from real-life applications.

MSLMS activities include the development of efficient numerical methods and algorithms, computational models, software and computational kits for simulations of complex systems, with an ultimate goal of applying them to real life problems. Multidisciplinary research and multitasking are two of the defining features of the MSLMS group.