Information is processed in physical devices. In the quantum regime the concept of classical bit is replaced by the quantum bit. We introduce quantum principles, and then quantum communications, key distribution, quantum entropy, and spin dynamics. No prio ...
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 ...
Stochastic PDEs are used to model systems that are spatially extended and include a random component. This course gives an introduction to this topic, including some general measure theory, some Gaussian measure theory and some linear semigroup theory. ...
The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...
Linear and nonlinear dynamical systems are found in all fields of science and engineering. After a short review of linear system theory, the class will explain and develop the main tools for the qualitative analysis of nonlinear systems, both in discrete-t ...
Le relevé numérique touche les trois disciplines de la faculté ENAC. De l'échelle territoriale à l'analyse structurelle en passant par la mesure du bâti, cela implique d'intégrer des méthodologies propres aux différents champs d'activités de chaque section ...
Quantum mechanics is one of the most successful physical theories. This course presents the mathematical formalism (functional analysis and spectral theory) that underlies quantum mechanics. It is simultaneously an introduction to mathematical physics and ...
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 ...