Ibrahima Drame

Summary: Galton Watson process :

                       - without immigration

                       - with immigration

                       - multitype (with a finite number of types)

Continuous time branching process :

    - with exponential lifetime distributions, i.e markovian branching process

Patrick Tchepmo Djomegni

Summary: In this course, students will be introduced to the mathematical modeling of infectious diseases. Basic knowledge on certain diseases (tuberculosis, HIV/AIDS, hepatitis, malaria…) will be provided. Only deterministic mathematical models will be studied. Since the models are expressed in the form of ordinary differential equations, most of them cannot be solved explicitly. The qualitative characteristics of the solutions will be studied.
 

Coordinator: Ramesh Gautam, Mathematical Biology Research Centre (MBRC), Nepal

Gourav Arora (India), Youcef Mammeri (France)

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

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.