Mathematical Analysis, Modelling, and Applications

The activity in mathematical analysis is mainly focussed on ordinary and partial differential equations, on dynamical systems, on the calculus of variations, and on control theory. Connections of these topics with differential geometry are also developed.The activity in mathematical modelling is oriented to subjects for which the main technical tools come from mathematical analysis. The present themes are multiscale analysis, mechanics of materials, micromagnetics, modelling of biological systems, and problems related to control theory.The applications of mathematics developed in this course are related to the numerical analysis of partial differential equations and of control problems. This activity is organized in collaboration with MathLab for the study of problems coming from the real world, from industrial applications, and from complex systems.

ERC-starting grant project 204979 “Hamiltonian PDEs: new connections between dynamical systems and PDEs with small divisors phenomena”

Read more about ERC-starting grant project 204979 “Hamiltonian PDEs: new connections between dynamical systems and PDEs with small divisors phenomena”

The relative heat content for submanifolds in sub-Riemannian geometry

Rossi T. The relative heat content for submanifolds in sub-Riemannian geometry. Actes du séminaire Théorie Spectrale et Géométrie. 2021 ;36.

Relative heat content asymptotics in sub-Riemannian manifolds

Agrachev AA, Rizzi L, Rossi T. Relative heat content asymptotics in sub-Riemannian manifolds. Analysis & PDE [Internet]. 2024 . Available from: https://doi.org/10.2140/apde.2024.17.2997

Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group

Rossi T. Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group . Advances in Calculus of Variations. 2021 ;16(1).

Heat content asymptotics in sub-Riemannian manifolds

Rizzi L, Rossi T. Heat content asymptotics in sub-Riemannian manifolds. Journal de Mathématiques Pures et Appliquées. 2021 ;148.

Infinitely many isolas of modulational instability for Stokes waves

Berti M, Corsi L, Maspero A, Ventura P. Infinitely many isolas of modulational instability for Stokes waves.; 2024.

First isola of modulational instability of Stokes waves in deep water

Berti M, Maspero A, Ventura P. First isola of modulational instability of Stokes waves in deep water.; 2024. Available from: https://arxiv.org/pdf/2401.14689

PRIN 2020XB3EFL, Hamiltonian and Dispersive PDEs

Read more about PRIN 2020XB3EFL, Hamiltonian and Dispersive PDEs

Do analytically one dimensional spheres exist?

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Interacting Diffusions, Optimal Transport and Extended Metric Measure Geometry

Abstract: The study of interacting particles has been a central subject in statistical physics. The goal of this course is to study interacting infinitely many Brownian motions with long range interaction by using methods from extended metric measure geometry and optimal transport theory. The lectures will cover several topics from the following subjects:

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Mathematics