Algebraic K-theory, which to any ring R associates a sequence of groups, can be viewed as a theory of linear algebra over an arbitrary ring. We will study in detail the first two of these groups and some of their applications to other areas of mathematics. ...
The course introduces the paradigm of quantum computating in an axiomatic way. We introduce the notions of quantum bits, gates, and circuits. We introduce themost important quantum algorithms. We also touch upon error-correcting codes. This course is indep ...
Algebraic geometry is the common language for many branches of modern research in mathematics. This course gives an introduction to this field by studying algebraic curves and their intersection theory. ...
Ce cours se focalise sur la conception de l'espace public et sur les rapports qu'il entretient avec les usages. Au prisme de la place de l'enfant en ville, les étudiant·es construiront des dispositifs ludiques dans le cadre d'un programme de revalorisation ...
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...). ...
The course will focus on a probabilistic construction of a conformal field theory related to random Riemann surfaces, called the Liouville conformal field theory. The symmetries of the theory allow to express the n-point correlation functions in terms of 3 ...