Vorlesung (Blockkurs): De Finetti theorems, meanfield limits and BoseEinstein condensation (N. Rougerie) (SoSe 2015)News (June 18th): Second version of the lecture notes is here (and at arXiv:1506.05263). News (June 18th): The students having handed in homework can pick up their 'Schein' at the secretary's office News (April 21th): You can find the slides from the first lecture here. News (April 10th): First version of the lecture notes is here. Lecturer: Nicolas Rougerie (CNRS / Université GrenobleAlpes). Time, room: This is a 'Blockkurs' consisting of 9 lectures each of two hours. It is an English version of N. Rougerie's 'Cours Peccot' at Collège de France. It takes place in B 134 at the following times: 20  24 April 2015 (MoFr) 1820Uhr & 27  30 April 2015 (MoThu) 1820Uhr. Exercises (Übungen): There will be a number of homeworks for students wishing to acquire a 'Schein'. Synopsis (Kurzbeschreibung): The course will adress the meanfield approximation for the equilibrium states of Nbody systems in classical and quantum statistical mechanics. The main goal is a rigorous derivation from first principles of effective models that are usually based on statistical independence assumptions. A general strategy to achieve this will be discussed in details. The main tools are structure theorems "à la de Finetti" which describe the possible largeN limits of the admissible states of statistical mechanics. The main application we have in mind is the BoseEinstein condensation phenomenon, which takes place in cold dilute Bose gases. Accordingly, the main emphasis of the course will be on the justification of the meanfield approximation for the ground state of large bosonic systems. We shall discuss topics such as the concentrationcompactness principle, localization methods in Fock space, the structure of bosonic density matrices, the Hartree and GrossPitaevskii functionals etc. Audience (Hörerkreis): Master students of Mathematics and Physics, TMPMaster. Credits: 2 ECTS. Exam (Prüfung): There will be a number of homeworks for students wishing to acquire a 'Schein'. The exact modus will be discussed by Prof. Rougerie in the lectures. Prerequisites: A basic knowledge of Mathematical Quantum Mechanics (corresponding to the course 'Mathematical Quantum Mechanics 1' (MQM1)) is an advantage. Language (Sprache): English. Literature: There will be lecture notes. These will be updated regularly. First version of the lecture notes is here (version 1: March 2015). Second version of the lecture notes is here (version 2: May 2015); see also arXiv:1506.05263. (A version (in French) of N. Rougerie's notes for the 'Cours Peccot' at Collège de France can be found here.)  Letzte Änderung: 26 June 2015 (no more updates). Thomas Østergaard Sørensen 
