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Research Fields

  • geometry, in particular algebraic, differential, and noncommutative geometry, also with applications to quantum field and string theory
  • mathematical analysis, in particular partial differential equations, topological and variational methods in nonlinear analysis, dynamical systems, conservation laws, transport problems, geometric measure theory, calculus of variations, control theory, and subriemannian geometry
  • mathematical analysis of models from continuum mechanics, thin structures, homogenization techniques for composite materials, fracture mechanics, effective models for materials with microstructures, pattern formation from rough energy landscapes
  • mathematical modelling, in particular mechanics of solids and fluids, mechanics of new materials, modeling of complex and biological systems, multi scale analysis, mechano-biology and cell motility
  • mathematical physics, in particular integrable systems and their applications, nonlinear partial differential equations and mathematical aspects of quantum physics
  • numerical analysis and scientific computing, applied to partial differential equations and to control problems with the development of innovative computational algorithms, numerical methods for geometrical and computational reduction, and applications to design, optimization, inverse problems and uncertainty quantification

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