Francesco Pappalardi

Summary:

Elementary Numbers Theory: 

• Quadratic reciprocity
• Arithmetic fonctions 

Analytic Numbers Theory : 

• Dirichlet Arithmetic progression
• Prime Number Theorem

Maciej Dunajski

Summary: Integrable systems are nonlinear differential equations which ‘in principle’ can be solved analytically. This means that the solution can be reduced to a finite number of algebraic operations and integrations. Such systems are very rare - most nonlinear differential equations admit chaotic behaviour and no explicit solutions can be written down. Integrable systems nevertheless lead to a very interesting mathematics ranging from differential geometry and complex analysis to quantum field theory and fluid dynamics.

Abdulhakeem Yusuf

Summary: The following topics were covered during the period of stay 

1. GENERAL FIRST-ORDER EQUATION i. General Introduction of ODE ii. iii. Equivalence of an Initial Value Problem Existence & Uniqueness Theorem 

2. LINEAR SYSTEM OF FIRST-ORDER EQUATION i. Characrerisation of the Fundamental Matrix ii. iii. iv. v. vi. vii. Properties of Linear Systems Adjoint systems Homogeneous and non-homogeneous system Autonomous Differential equations LINEAR SYSTEMS WITH PERIODIC COEFFICIENTS THEORY OF OSCILLATION 

Patrick Tchepmo Djomegni

Patrick Tchepmo Djomegni

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:

Born in a letter of Robert Langlands to André Weil in 1967, the Langlands program seeks to establish a far-reaching web of conjectures relating seemingly distant areas of mathematics, primarily number theory, representation theory, and algebraic geometry

This thematic month will focus on some of the most important current directions of this program: the geometric Langlands program, the p-adic Langlands program, the geometrization of the Langlands program, and relative Langlands duality.

Titre: FOUVRY - 73

Week 1-2 (17 August- 28 August 2026): Summer school
Week 3 (31 August -4 September 2026): Workshop
Week 4 (7-11 September 2026): Scientific collaborations

General summary: