Calculus of variations and applications
Calculus of Variations is a fundamental tool in the study of problems in physics and in engineer. Variational methods are successful to treat geometric problems and continuum mechanics, among a multitude of other applications. Within this line of research we are interested in: minimal surfaces and the study of functionals depending on curvatures; periodic homogenization and stochastic homogenization; theory of structured deformations; defects (dislocations and disclinations) in crystals; rate-independent evolutions; minimization of functionals of second order; optimal transport (multimarginal) with applications to DFT.
The technical tools that are mostly used are direct method of the Calculus of Variations, variational convergences (such as Gamma-convergence) and asymptotic analysis, relaxation techniques, and geometric measure theory.