Research

• Sobolev orthogonal polynomials
• Matrix polynomials
• Orthogonal polynomials variants and multiortogonales
• Rational approach and Fourier
• Complex analysis and operator theory
• Applications quadratures rational and simultaneous integration
• Applications physical
• Applications systems theory

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• Statistical mechanics and nonlinear dynamics
• Materials science and nanostructures
• Microfluidics and adsorption fluids structured substrates
• Ecology and Evolution theoretical
• Dynamics of socio-economic systems and game theory
• Theoretical biology

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• Elliptic and parabolic partial differential equations
• Numerical methods for partial differential equations
• Ordinary differential equations

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• Numerical solution of PDEs
• Monte Carlo methods for PDEs
• Numerical stochastic calculus
• Approximation theory
• Reverse problems
• Imaging
• Wave propagation
• Machine learning

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• Nonlinear electronic transport in nanostructures
• Nonequilibrium statistical mechanics
• Field theories and Statistical Mechanics
• Applications to biological systems. Blood vessel dynamics. Collective motion of cells in tissues. Collective motion: swarms, flocks. Biofilms
• Biomedicine: Age related macular degeneration, cancer
• Computational materials: Defects in solids and multiscale simulations. Graphene. Materials for nuclear fusion. Molecular dynamics, Monte Carlo, density functional theory
• Mathematical Physics. General Relativity. Combinatorics
• Astrodynamics and control of artificial satellites

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