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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.

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.

Comunicato stampa

Edition 2023

Javier Gomez-Serrano (Brown University), for fundamental contributions to long standing and important problems in fluid dynamics;

Alessandro Carlotto (University of Trento), for groundbreaking contributions to several different areas of geometric analysis, such as geometric relativity, minimal surface theory, and the study of manifolds with positive scalar curvature.

Comunicato stampa

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