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 spaces
2.2. Lebesgue spaces
2.3. Fourier transform
2.4. Sobolev spaces
2.5. Forms and operators
3. A very brief mathematical formulation of classical and quantum mechanics [3,4]
3.1. Some classical mechanics
3.2. Some quantum mechanics
4. Uncertainty principles [5,6,7,8]
4.1. Heisenberg
4.2. Hardy
4.3. Sobolev
4.4. Application to the stability of the hydrogen atom
4.5. Poincaré
4.6. Poincaré-Sobolev?
4.7. IMS localization?
4.8. Local uncertainty
5. Exclusion principles [9,10]
5.1. Fermions
5.2. Repulsive bosons
5.3. Local exclusion
6. The Lieb–Thirring inequality [11,12,13]
6.1. Some history
6.2. Covering lemma
6.3. Local proof of LT for fermions
6.4. Local proof of LT for inverse-square repulsive bosons
6.5. Connections between Hardy–Sobolev–LT?
7. The stability of matter [14,15,16]
7.1. Some history
7.2. Stability of the first kind
7.3. Some electrostatics
7.4. Proof of stability of the second kind