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.

Nonlinear potentials at the fractional scale: sharp regularity

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On the number of level sets of smooth Gaussian fields

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Statistical properties of free fermions

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Probability Seminars

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Towards a statistical theory for flows of rough vector fields

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An optimal transport approach to APB estimate on metric measure spaces

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Analysis Seminars 2023-2024

Analysis Seminars are held on Thursday from 14:00 to 15:30.

Organizers: Alberto Maspero, Nicola Gigli.

Linear and nonlinear bifurcation problems (Topics in Ad. Analysis 2)

After introducing the theory of analytic functions between Banach spaces, we shall present perturbative results for the spectrum of linear operators, in particular for separated eigenvalues of closed operators, with applications to the stability of traveling water waves. Then we shall present bifurcation results of periodic and quasi-periodic solutions of nonlinear dynamical systems as well as homoclinic solutions to hyperbolic equilibria of Hamiltonian systems.

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Topics in high order accurate time integration methods

Ordinary differential equations (ODEs) describe many physical, biological and chemical phenomena. It is, thus, important to find approximations of ODEs which are highly accurate and, in order to obtain it within reasonable computational times, high order accurate time integration methods are very often chosen to proceed in time. In this course, we will revise ODEs and the theoretical results that guarantee their existence and uniqueness [1, 2].

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Introduction to geometric control

The course of 10 lectures will provide an introduction to geometric control theory. The first part of the course will be devoted to controllability, the second part will discuss stabilization, while the last part will focus on optimal control. No prior knowledge of control theory is required.

Course program:
1. Some basic questions in the control formalism, some examples of control systems.
2. Controllability of linear systems. Lie brackets and their relation with controlled motions.

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Mathematics