Tony EZOME
Summary: I started by recalling the needed background from commutative algebra (noetherian modules and rings, finitely generated algebras, Hilbert basis theorem, integral/algebraic elements in a ring/field extension, transcendence degree of a field extension, the algebraic closure of a field) with useful exercice sessions.
Christian Maire
Summary: In this course one gave the proof of the following result. Theorem. Let p be a prime number, and let G be a p-group. Then there exists a Galois extension K/Q such that G=Gal(K/Q). The course aimed to give the key arguments, and explained the difficulty for p=2. During the last part of the course, I also explained some basic properties regarding class group, and the philosophy of Class Field Theory.
Florian Luca
Summary: Average orders of arithmetic functions, maximal orders, normal orders, the Turan-Kubilius Theorem Introduction to probabilistic number theory, density of sets of integers. Smooth numbers, Applications: there are fewer pseudoprimes than primes. Carmichael numbers. also explained some basic properties regarding class group, and the philosophy of Class Field Theory
JOAN-CARLES LARIO
Summary: Introduction to Cyclotomic Number Fields and Cyclotomic Function
Fields with some of their applications to Diophantine and Algebraic Geometric problems, respectively.
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.
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: