News and events

Patrick Tchepmo Djomegni

Mohamed MBEHOU

Summary: These notes are intended for first-year Master students. After having strengthened their knowledge on ordinary differential equations, students get in touch with partial differential equations and some of the methods and problems related to them. At the same time, it is hoped to strengthen the knowledge and skills of students in mathematical analysis. Learning basics techniques to solve first and second-order PDEs.

Sudhir GHORPADE

Summary:  The course covered the following topics: 

Linear Codes associated to higher dimensional varieties:

Geometric approach to linear codes via the language of projective systems. The following specific classes of linear codes and some of their fundamental properties including determination of basic parameters will be discussed. 

• Codes associated to Veronese varieties (Projective Reed-Muller Codes)
• Grassmann codes
• Schubert codes

Betti numbers of linear codes and matroids: 

Mesut ŞAHİN

Francesco Polizzi

Summary: Elements of commutative algebra, affine varieties, projective varieties.

Seyed Hamid Hassanzadeh

Summary: The course consists of the following sessions: 

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