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.
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:
Analytic Numbers Theory :
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
Lecturer: Christophe RITZENTHALER
This mini-course is a motivated introduction to the problematic of number of rational points on curves over finite fields. It will serve as a pretext to introduce the basics of algebraic geometry (Nullstellensatz, projective geometry,...) with a far-away open problem in mind (distribution of the number of points on genus 4 curves). We will in particular try to reduce the number of coefficients of these curves to be able to run some experiments with a computer.