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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.

Modern mathematics: AI, numerical computations, computer-assisted proofs and applications

In this course I will explain a combination of theoretical and applied paradigms that, together, yield new results in mathematics that are not attainable using traditional methods. Specific emphasis will be put in problems coming from PDE, although some of the techniques might be amenable to broad areas of mathematics. 

Introduction to Alexandrov geometry across signatures

This course should serve as an introduction to the field of Alexandrov geometry, the study of metric spaces with (a non-smooth analogue of) bounded sectional curvature. We discuss same basic metric geometry and introduce a variety of different formulations of these curvature bounds. We then go on to showcase several theorems, including: Hopf--Rinow--Cohn--Vossen, Majorisation, Gluing, and the Collision Theorem. 

Mechanics of biological systems

Course topics:

- A primer on the biophysics of the cell

- Fluid-structure interaction problems in biophysics

- Shape control and active elasticity of unicellular organisms

- Swimming motility of unicellular organisms

- Beating of eukaryotic cilia 

Schedule

26 March 9.00 11.00 (aula 134)

Organizational meeting and First Introductory lecture

 

The course will continue according to the following schedule:

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