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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.

Optimal Control: tools and applications

The course will provide a brief introduction to the theory of optimal control, existence, necessary and sufficient optimality conditions, focusing on analytical tools and some specific applications.

Compressible Turbulence

Turbulence plays a fundamental role in many different applications varying from aeronautical to environmental simulations. This course aims at giving an overview of the phenomenology and mathematical modelling of compressible turbulent flows. We will start from a first part focused on gas dynamics (thermodynamics, compressible Navier-Stokes equations, speed of sound, shock waves). The second part of the course will instead be focused on turbulence phenomenology and modelling.

Advanced reduced order models in scientific machine learning

This course aims to provide a wide overview on novel strategies combining ideas from Reduced Order Modeling (ROM) and Scientific Machine Learning (SciML). The main goal is to investigate the great potential and the possible limitations of state-of-the-art methodologies to efficiently retrieve solutions of parametrized PDEs for computational mechanics problems.

Advanced Programming

Course material can be found here: https://github.com/pcafrica/advanced_programming_2025-2026

Tue 30 Sep 2025 14:00 - 16:00 128-129

Wed 01 Oct 2025 11:00 - 13:00 005

Tue 07 Oct 2025 14:00 - 16:00 005

Wed 08 Oct 2025 11:00 - 13:00 005

Tue 14 Oct 2025 14:00 - 16:00 005

Wed 15 Oct 2025 11:00 - 13:00 005

Tue 21 Oct 2025 14:00 - 16:00 005

Wed 22 Oct 2025 11:00 - 13:00 005

Tue 28 Oct 2025 14:00 - 16:00 005

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