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.

## POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder

## Reducibility for a fast-driven linear Klein–Gordon equation

## Dynamical systems and PDEs

Date | Time | Room | Speaker | Seminar |

October 26 | 17:00 | TBC | Qingtang Su (University of Southern California) | Nonlinear Modulational Instability of the Stokes Waves in 2d Full Water Waves |

November 9 | 14:00 | Zoom | Zhiwu Lin (Georgiatech) | Nonlinear Nonlinear Modulational Instability of Dispersive PDE Models |

## Dynamical systems and PDEs

## Theory and practice of Finite Element Methods

This is a shared course between the SISSA PhD track

on Mathematical Analysis, Modeling, and Applications

(math.sissa.it) and the Master in High Performance Computing

(www.mhpc.it). It is a course that follows two parallel lines:

theory of finite element methods (graduate students level, ~20 hours) and

practice of finite element methods (mhpc students levels, ~20 hours).

Date | Time | Room | Speaker | Seminar |

October 26 | 17:00 | TBC | Qingtang Su (University of Michigan) | Nonlinear Modulational Instability of the Stokes Waves in 2d Full Water Waves |

## Advanced Programming

The course aims to provide advanced knowledge of both theoretical and practical programming in C++14 and Python3, particularly the principles of object-oriented programming and best practices of software development.

**Syllabus:**

## A diagrammatic approach to perturbation theory

In this course I will present a diagrammatic approach which can be conveniently used to study perturbative series. After a general introduction, I will start by focusing on the classical KAM theorem in the "mechanical case'', and then discuss various generalizations, such as the case of more general hamiltonians, non-maximal tori, harmonic oscillators, depending on the audience preferences.