Algeria

Tropical Complex Analysis

Ilpo Laine

Summary:

Basic notions of tropical analysis and tropical functions
Nevanlinna functions for tropical functions
Tropical entire functions
First main theorem in tropical analysis
Tropical variants of some complex analysis results
Tropical analysis in a finite interval
Non-linear tropical functions
Clunie, Valiron etc. in the tropical setting

Algebraic curves over finite fields

Christophe Ritzenthaler

Summary: motivation sur l’exemple des courbes planes ; introduction des bases de géométrie algébriques (variétés, dimension, singularité, variété projective,…), problématique des courbes maximales sur les corps finis; présentation de 3 projets de recherches.

Deep learning methods for stochastic dynamics

Omar Kebiri

Summary:

Functional Analysis

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.

Complex Analysis

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.

Complex Analysis

Gabriele Benedetti

Functionnal Analysis

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.

Advanced algebra

Peter Stevenhagen

Summary: This is part of the regular International Master in Mathematics program.

Geometry and Dynamics

The general theme of this school lies at the intersection of geometry and dynamics, focusing on the interactions between Riemannian and Lorentzian geometries on the one hand, and dynamical systems on the other. For instance, a Lorentzian, Riemannian, or more generally semi-Riemannian metric naturally gives rise to dynamical objects such as:
• the action of its isometry and conformal groups,
• the geodesic flow (a differential equation on the tangent bundle), and
• the Ricci flow (an evolution PDE on the space of all metrics).

Numbers Theory

Francesco Pappalardi

Summary:

Elementary Numbers Theory:

Quadratic reciprocity
Arithmetic fonctions

Analytic Numbers Theory :

Dirichlet Arithmetic progression
Prime Number Theorem

Algeria