Syllabus

Here is a preliminary plan for the lectures based on the table of contents of the lecture notes. The lecture number 1-17 is indicated in square brackets. Not all topics will be covered.

1. Introduction [1]2. Some preliminaries and notation [1,2]2.1. Hilbert spaces2.2. Lebesgue spaces2.3. Fourier transform2.4. Sobolev spaces2.5. Forms and operators3. A very brief mathematical formulation of classical and quantum mechanics [3,4]3.1. Some classical mechanics3.2. The instability of classical matter3.3. Some quantum mechanics4. Uncertainty principles [5,6,7,8]4.1. Heisenberg4.2. Hardy4.3. Sobolev4.4. Application to the stability of the hydrogen atom4.5. Poincaré4.6. Poincaré-Sobolev?4.7. IMS localization?4.8. Local uncertainty5. Exclusion principles [9,10]5.1. Fermions5.2. Repulsive bosons5.3. Local exclusion6. The Lieb–Thirring inequality [11,12,13]6.1. Some history6.2. Covering lemma6.3. Local proof of LT for fermions6.4. Local proof of LT for inverse-square repulsive bosons6.5. One-body formulations6.6. Applications of LT6.7. Connections between Hardy–Sobolev–LT?7. The stability of matter [14,15,16]7.1. Some history7.2. Stability of the first kind7.3. Some electrostatics7.4. Proof of stability of the second kind

Examination: There will be homework assignments and, if aiming for a higher grade, an individual project. More information will become available when the course starts.