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Research

Department of Mathematical Engineering

Research

Fundamental research

Applied research

Our research focuses on 5 fundamental areas and we actively participate in 6 applied research laboratories of the Center for Mathematical Modeling.

Fundamental research

Algorithms and combinatorics

We seek to understand structural aspects of graphs, centralized and distributed algorithms, and the behavior of certain processes in networks. The main lines of research are graph theory, random structures and algorithms, distributed computing, and discrete dynamical systems.

Researchers
  • Marcos Kiwi, Theory of computation, random structures and algorithms
  • Martín Matamala, Algorithms, graph theory, combinatorics
  • Iván Rapaport, Discrete mathematics, theory of computation, cellular automata, distributed computing
  • José Soto, Aproximation algorithms, combinatorial optimization
  • Maya Stein, Graph theory, combinatorics

Nonlinear Analysis and Partial Differential Equations

Our research is focused on the qualitative study of partial differential equations, with emphasis on those coming from mathematical physics. Our main contributions are focused on the study of nonlinear dispersive equations, mathematical methods of physics, variational inequalities, modeling of liquid crystals, metamaterials and problems associated with the p-Laplacian operator and crime modeling.

Researchers
  • Patricio Felmer, nonlinear analysis and fully nonlinear models
  • Michal Kowalczyk, singular perturbation problems, eliptic and parabolic models, dispersive equations
  • Raúl Manasevich, nonlinear analysis, nonlinear ordinary differential equations
  • María Eugenia Martínez, nonlinear Schrodinger and water wave models
  • Salomé Martínez, partial differential equations in ecology
  • Claudio Muñoz, nonlinear dispersive models
  • Gabrielle Nornberg, nonlinear and quasilinear elliptic equations
  • Hanne Van Den Bosch, mathematical physics, Sobolev inequalities

Mathematical mechanics and inverse problems

We study uniqueness and stability of solutions for inverse problems in partial differential equations, as well as algorithms for their reconstruction. We are also interested in the mathematical analysis and numerical methods associated with problems in solid and fluid mechanics, and in the control and homogenization of partial differential equations.

Researchers
  • Carlos Conca, mathematical mechanics, partial differential equations
  • Jaime Ortega, mathematical mechanics y inverse problems
  • Axel Osses, inverse problems, control and modeling in partial differential equations 
  • Jorge San Martín, mathematical mechanics

Optimization and equilibrium

We develop convex and nonlinear programming techniques, dynamical systems, stochastic optimization, semi-algebraic geometry, conic and semi-infinite programming, gradient flows, accelerated algorithms, variational analysis and game theory, along with industrial applications.

Researchers
  • Jorge Amaya, operations research 
  • Rafael Correa, variational analysis 
  • Aris Daniilidis, dynamical systems, differential geometry
  • Alejandro Jofré, variational analysis, energy modeling
  • Héctor Ramírez, conic programming, resource management 

Probability and ergodic theory

We conduct research in fundamental topics in probability theory, stochastic processes, statistical physics, and ergodic theory. We also develop applications in bioinformatics, astroinformatics, mining, natural and non-renewable resources, and data science.

Researchers
  • Sebastián Donoso, topological dynamics, ergodic theory 
  • Joaquín Fontbona, stochastic processes, stochastic modeling
  • Raúl Gouet, stochastic processes, stochastic modeling
  • Alejandro Maass, ergodic theory, systems biology
  • Servet Martínez, Markov chains, discrete potential theory, dynamical systems, stochastic modeling
  • Daniel Remenik, probability theory, mathematical physics
  • Jaime San Martín, stochastic calculus, potential theory, quasistationary distributions
  • Avelio Sepúlveda, probability theory, mathematical physics

Applied research at the CMM

The Department of Mathematical Engineering develops applied research in different topics of mathematics. In this context, the contribution of DIM researchers consists of solving applied problems via mathematical modeling. This work is developed in a strategic alliance with the Center for Mathematical Modeling (CMM).

Further information on the CMM website.

Climate & biodiversity

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Data Science

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Digital Health

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Digital Mining

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Mathematical education

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Researchers
  • Pablo Dartnell
  • Patricio Felmer
  • Salomé Martínez
  • Héctor Ramírez

Resource management

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Researchers

Investigación

Grupos de investigación fundamental

Investigación aplicada en el CMM