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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 analysismechanics of materialsmicromagneticsmodelling 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.

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 17:00TBC Qingtang Su (University of Michigan) Nonlinear Modulational Instability of the Stokes Waves in 2d Full Water Waves
Date Speaker Seminar
October 8 Daniele Tiberio Geodesic distances on Banach manifolds
October 15 Martina Zizza Properties of mixing BV vector fields
October 22 Simone Carano The relaxed area with respect to the strict convergence in BV
October 29 Moaad Khamlich Model order reduction for bifurcating phenomena in fluid-structure interaction problems
November 05 Daniela Di Donato C^1 submanifolds and Lipschitz graphs in Carnot groups
November 12 Giulio Ortali Subgrid Closure for the Shell Model of Turbulence using Deep Learning
November 19 Emanuele Caputo Parallel transport on ncRCD(K,N) spaces
November 26 Francesco Nobili Progress on the independence on p of p weak gradients
December 3 Niccolò Tonicello High-order spectral element methods for the simulation of compressible turbulent flows
December 10 Moreno Pintore Progress on the independence on p of p weak gradients
December 17 Mattia Manucci Contour Integral Methods and Reduced Basis for parametric dynamical problems
January 14 Davide Manini Localization via disintegration and isoperimetric inequality in non-compact MCP spaces
January 21 Jose Raul Bravo Martinez KratosMultiphysics and Local ROM
January 28 Luigi De Masi Min-max theory for minimal surfaces

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.

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