Mathematical Engineering Department

Main training and research areas

Non-linear partial differential equations

The research activity of the area is oriented to the analysis of partial differential equations, parabolic, elliptic and dispersive. Studied problems concern various areas of modern analysis of differential equations, ranging from the functional analysis and modeling of nonlinear problems to the qualitative study of solutions to specific problems and their application to particular problems of mathematical physics and biology. The analytical techniques include perturbation theory, bifurcation theory, non-linear analysis and critical points theory.

Discrete mathematics

The research area focuses on the study of objects of finite nature. The issues addressed concern various fields such as theoretical computer science, graph theory, random structures, the design and analysis of algorithms, as well as more specific applications of computing, operational research, social sciences, etc. Mathematical tools include combinatorics, polyhedral and linear programming theory, probabilistic methods and coding theory.

Mathematical mechanics, control and inverse problems

The research is centered around mathematical and numerical analysis, including computational simulation, of systems governor two partial differential equations appearing in applied mathematics and engineering sciences such as mechanics, metallurgy, biomechanics and geophysics among others fields. The studies range from basic theoretical aspects to applied research aimed at solving problems of industrial origin. Specific topics include: inverse problems, homogenization theory, control theory, Navier-Stokes equations, mechanics of continuous media.

Probability and ergodic theory

This area is devoted to central problems in the theory of probabilities, and contributes to the development of other areas such as differential equations, linear algebra, dynamic systems and statistical physics. The research covers topics such as: Markov chains, stochastic differential equations, discrete potential theory, ergodic theory, packing problems, random structures, cellular automata, particle systems and stochastic models in mathematical physics. The activities in this area also provide theoretical basis for applied research in mathematical modeling of the genome, bioinformatics, forestry and fragmentation in mining.

Optimization and equilibrium

The research is aimed at theoretical analysis and numerical resolution of optimization and equilibrium problems using linear and non-linear programming, variational inequalities, game theory, convex analysis, calculus of variations and optimal control. Studies range from the analysis of the stability and sensitivity of abstract variational problems to the development of numerical algorithms for the resolution of specific models in applied sectors such as mining, geo-mechanics, economy, transport, energy, telecommunications, and natural resources (forestry, fishing).

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