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.

## Introduction to Optimal Transport

The theory of Optimal Transport finds its roots in the work of Gaspard Monge in 1781, whose interest was in finding the cheapest possible way to transfer some resources from producers to consumers.

After some major contributions due to Leonid Kantorovich (who was later awarded the Nobel Prize in Economics, partly for his work on the subject) in the 1940s, Optimal Transport has been blooming in the last thirty years, with applications covering partial differential equations, geometric analysis, mathematical finance, and machine learning, among the others.

## Spectral theory of deterministic and disordered systems

March 11-22 2024

The first week (possibly going into the second week as well) will provide an introduction to localization.

The proposed topics are:

## Introduction to numerical analysis and scientific computing with python

Syllabus 2023-2024

- Basics on Scientific Computing
- Vector spaces, vector norms, matrices, and matrix norms
- Basic linear algebra: direct solution of linear systems
- Not so basic linear algebra: iterative solution of linear systems
- Polynomial interpolation
- Interpolatory Quadrature rules
- L2 projection / Least square approximation
- Introduction to Finite Difference Methods
- Introduction to Finite Element Methods

Python laboratories

## Antonio Ambrosetti Medal Winners

**Edition 2021**

**Fabio Pusateri (University of Toronto)**, for his contributions to the field of non linear partial differential equations;

**Po-Lam Yung (Australian National University)**, for his work on the Sobolev spaces;