Frédérique Oggier
Summary: In this course, we taught show how lattices and codes, both independently and jointly, are used in the context of communication systems. The course was structured as follows :
Jorge Mozo Fernández
Summary: The idea of this course is to give an introduction to the theory of real dynamical systems from scratch, focusing on the main elements of qualitative theory: equilibria, periodic orbits, limit cycles, … An outline of the contents is as follows:
Ibrahima Drame
Summary: In this course, we will study Galton- Watson processes, which are the simplest prototype of branching processes and are characterized by the fact that time is discrete and represents successive generations. On the other hand, we will consider branching processes in continuous time, that is, populations that reproduce and die at random times, continuously over time.
Chiara Franceschini
Frédéric van Wijland
Summary: High dimensional data are everywhere, from physical systems to the spreading of epidemics, the world of economic agents or that of neural networks and machine learning. The course aims at stressing the basic techniques underpinning our understanding of the emergence of collective behaviors in very large assemblies of interacting agents.
Gabriela Alexandra Estevez Jacinto
Summary: We study the space of compact operators defined in Hilbert spaces. We saw some examples and the relation of this space with the other spaces such as the space of operators of finite rank, the set of self-adjoint operators, the set of operators with non-empty eigenvalues. We also studied some of the main properties of compact operators such as the characterization of self-adjoint and compact operators (Spectral Theorem) and some applications.
Anna Benini
Summary: Anna Miriam Benini introduced topics such as conformal mappings, Riemann surfaces, Riemann mapping theorem, classification of Riemann surfaces, and meromorphic functions on the Riemann sphere.
Gabriele Benedetti
Charlene Kalle
Summary: A comprehensive review on Banach and Hilbert spaces, covering foundational concepts and structural properties essential to understanding these spaces. In addition, we presented major theorems in functional analysis, including the Hahn-Banach Theorem, Banach-Steinhaus Theorem, and Riesz Representation Theorem, explaining their implications and applications. All lectures were accompanied by tutorial sessions, a homework was given to be sent by email by students.
Peter Stevenhagen
Summary: This is part of the regular International Master in Mathematics program.