The MCEN research group develops innovative research at the interface between Mathematical, Computational and Experimental Neuroscience. This involves developing novel theoretical and algorithmic tools, multiscale parsimonious models (biophysical and data-driven), neuroscientific experiments and data analytical tools to extract of invariant patterns from experimental and clinical observations.

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,

The Quantum Mechanics group is strongly based on J.-B. Bru and W. de Siqueira Pedra’s mathematical works on quantum many-body theory, which is an important domain of mathematical physics. It mainly refers to rigorously understand the close connection between microscopic, mesoscopic and macroscopic properties of quantum systems. In mathematics, it is reminiscent of Hilbert's sixth problem, among his 23 problems which have been authoritative for the twentieth century mathematics.

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.