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.

## Topics in Computational Fluid Dynamics

- Introduction to CFD, examples.
- Constitutive laws
- Incompressible flows.
- Numerical methods for potential and thermal flows
- Boundary layer theory
- Thermodynamics effects, energy equation, enthalpy and entropy
- Vorticity equations
- Introduction to turbulence
- Numerical methods for viscous flows: steady Stokes equations
- Stabilisation (SUPG) and inf-sup condition

## Reduced Order Methods for Computational Mechanics

**Mathematics Area, PhD in Mathematical Analysis, Modelling and Applications (AMMA)**

**Master in High Performance Computing (MHPC)**

**Lectures Prof Gianluigi Rozza, Tutorials coordinated by Dr Michele Girfoglio, Dr Niccolò Tonicello and Nicola Demo.**

## Introduction to dispersive equations

The goal of the course is to introduce several tools to study the existence of solutions of nonlinear dispersive PDEs such as the Schr ̈odinger and wave equations.

## Advanced topics on the analysis of Finite Element Methods

This course is meant to be complementary to the courses Numerical Solution of PDEs, Numerical Solution of PDEs Using the Finite Element Method, and Advanced FEM Techniques.

## An Introduction to modern tools for collaborative science

# An introduction to modern tools for collaborative science

## From CD to RCD spaces

Aim of the course is to provide an introduction to the world of synthetic description of lower Ricci curvature bounds, which has seen a tremendous amount of activity in the last decade: by the end of the lectures the student will have a clear idea of the backbone of the subject and will be able to navigate through the relevant literature.

## Mechanics of biological systems

The course focusses on mathematical tools for the study of the mechanics of continuous media, with applications to mechano-biology and bio-robotics, with topics extracted from the following syllabus.