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.

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 : 

• Introduction to lattices and geometry of numbers
• Introduction to linear codes and lattices from codes
• Introduction to number fields and lattices from number fields
• Introduction to quaternion algebras and codes from quaternion algebras
• Practical aspects : channel modeling

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.