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 ...
Cet enseignement est une introduction à la théorie et la pratique de la médiation scientifique.
Cette année, ce cours aboutira à la création et l'animation d'un atelier pédagogique et interactif avec un groupe de jeunes. ...
This course is an introduction to intersection theory on algebraic varieties.An important aim of the course is to develop geometric intuition while using the language of schemes developed in the basic algebraic geometry course, thus building a solid foun ...
Des communautés shakers aux USA à la question du logement à Bâle, le semestre interroge l'habitat comme lieu intime et collectif, en explorant la transformation des espaces de travail en nouveaux lieux de partage. ...
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 ...
In this course we will describe in numerous examples how methods from l-adic cohomology as developed by Grothendieck, Deligne and Katz can interact with methods from analytic number theory (prime numbers, modular forms etc...). ...
Given a quadratic equation, e.g. x^2 + 2*y^2 = 81, how can we decide whether there is a rational solution (x,y)? This basic question is what the theory of Rational Quadratic Forms is all about. The course gives an introduction and highlights fundamental te ...
This course is a modern exposition of "Duke's Theorems" which describe the distribution of representations of large integers by a fixed ternary quadratic form. It will be the occasion to introduce the students to the adelic language, the theory of automorp ...