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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.

Advanced Programming

The course aims to provide advanced knowledge of both theoretical and practical programming in C++11 and Python3, with particular regard to the principles of object-oriented programming and best practices of software development.

Due to covid-19 containement rules, this year, videos with pre-recorded lectures will be uploaded weekly, starting from the week of October 5, 2020.

Real Geometry

The course will be an introduction to the study of the topology of real algebraic varieties. 
 
The list of topics includes:
- Thom-Smith theory (allows to compute the Betti numbers of the fixed point set of an involution, the complex conjugation in our case)
- Morse Theory on algebraic sets 
- Semialgebraic geometry 
- Quantitative Thom's isotopy lemma

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