Galois theory lies at the interface of Field Theory and Group Theory. It aims to describe the algebraic symmetries of fields. We will focus on Galois theory for finite field extensions and some applications. ...
Algebraic number theory is the study of the properties of solutions of polynomial equations with integral coefficients; Starting with concrete problems, we then introduce more general notions like algebraic number fields, algebraic integers, units, ideal c ...
P-adic numbers are a number theoretic analogue of the real numbers, which interpolate between arithmetics, analysis and geometry. In this course we study their basic properties and give various applications, notably we will prove rationality of the Weil Ze ...
Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative algebra. We study an algebraic version, namely group coho ...
This course introduces the basics of cryptography. We review several types of cryptographic primitives, when it is safe to use them and how to select the appropriate security parameters. We detail how they work and sketch how they can be implemented. ...