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 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 ...
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire (pour les futurs mathématiciens) et de démontrer rigoureusement les résultats principaux de ce sujet. ...
The microstructure of many alloys and ceramics are constituted of very fine intricate domains (variants) created by diffusive or displacive phase transformations. The course introduces the crystallographic tools required to define, calculate and predict th ...
This course introduces the foundations of information retrieval, data mining and knowledge bases, which constitute the foundations of today's Web-based distributed information systems. ...
This course will provide an introduction to model category theory, which is an abstract framework for generalizing homotopy theory beyond topological spaces and continuous maps. We will study numerous examples of model categories and their applications in ...
Quantum computing has received wide-spread attention lately due the possibility of a near-term breakthrough of quantum supremacy. This course acts as an introduction to the area of quantum computing. After the course, the students will have an basic unders ...
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...). ...