Our group has made contributions to the mathematical analysis, numerical simulation and modeling of a variety of topics in applied sciences:
Biomedicine: analysis of gene expression data and cell migration data in cancer processes, data studies for immune disorders, pattern formation in biofilms, protein folding and unfolding, nerve impulse propagation, angiogenesis.
Optimization, inverse problems and imaging: noninvasive imaging of biological samples by digital holography techniques, constrained optimization methods and Bayesian approaches to inverse scattering problems in acoustics, photodetection and electromagnetism.
Materials science: defects and ripples in graphene, dislocation nucleation and motion in crystals, nucleation of bubbles in radioactive waste, aggregation processes to form particles, domain walls and oscillations in semiconductor superlattices.
Nonlinear waves in oscillator networks and discrete reaction-diffusion systems.
Long time behavior and well posedness in: fluid mechanics equations, nonlinear wave equations, integrodifferential kinetic models for plasmas, semiconductors and cellular systems.
Biomedicine and nanotechnology are currently active areas of research in need of new ideas and adequate mathematical techniques, goal to which we plan to devote our efforts for the next years.