Marco Veneroni

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Scientific Interests

Gradient Flows and Optimal Transportation Problems

  • Discrete Optimal Transport and applications to imaging
  • Unification of chemical reaction and diffusion processes as a Wasserstein Gradient Flow

Homogenization of nonlinear PDEs

  • Stochastic homogenization
  • Hysteresis, differential inclusions
  • Models of elasto-plasticity

Liquid crystals

  • Surface energies for nematic shells
  • Analysis, optimization, approximation

Modelling of multicomponent lipid membranes

  • Helfrich and Willmore functionals
  • Calculus of variations, geometric measure theory, differential geometry

Pattern formation

  • Line patterns in diblock copolymers
  • Eikonal equation for line fields
  • Geometric measure theory, varifolds
  • Gamma-convergence

Modelization of the cardiac electric field:

  • Homogenization, 2-scale convergence
  • Degenerate Parabolic PDEs
  • Reaction-Diffusion systems
  • Maximal regularity and analytic semigroups