We organize a masterclass in Angers, France, from December 19 to 21, 2023. The masterclass is mainly intended for second-year master students and PhD students. There will be two parallel lectures, each consisting of 6 one hour and a half sessions. The two lectures are:
- Semiclassical analysis and Bloch-Floquet theory, by Clotilde Fermanian Kammerer
The aim of these lectures is to discuss different PDEs technics related with a Schrödinger equation describing the dynamics of an electron in a crystal in presence of impurities. Because the size of the cells of the crystal are supposed to be very small comparatively with the macroscopic scale, it is a multi-scale problem with periodic aspects. We shall use semi-classical measures (also called Wigner measures) to take care of the multi-scale features, and Bloch theory to deal with the periodicity. These notions will be explained and used for calculating the density of probability of presence of the electron in the limit where the size of the cells is much smaller than the macroscopic scale.
- Regulous functions, by Jean-Philippe Monnier
When we develop real algebraic geometry in a classical way, many defects appear: no classical Nullstellensatz and Cartan's Theorems A and B no longer work. A recent theory consists of replacing the use of regular functions with continuous rational functions (otherwise called regulous). This course is an introduction to regulous algebraic geometry. We will show that this new geometry repairs many defects of real algebraic geometry.
The lectures will be in english.
Updtate (november 19) : Registration is now closed
The organisation board will pay for accommodation, including breakfast and lunches. Dinners are not included. We will do our best to cover travel costs, within the limit of our budget.
The number of participants is limited to 30. When registering to the masterclass, don't forget to indicate which lecture you will attend. The registration deadline is November 19, 2022.