Fermionic inequalities

par Gontier David

lundi 23 sept. 2024, 11:00 → 12:00 Europe/Paris

A711 (Université Paris-Dauphine)

We present a family of minimization problems, where the minimization space is a set of N orthonormal functions in L2 (the fermions), which interact locally. These problems arise, for example, when we want to minimize the sum of eigenvalues (Lieb-Thirring inequality). We will explain how to show the existence of minimizers for this kind of problem, and give several examples.
In particular, we will study an ad hoc problem where the N = 2 fermion problem is well-posed, but the N = 1 fermion problem has no minimizer.

This is joint work with Mathieu Lewin, Rupert Frank (Part 1) and Salma Lahbabi, Simona Rota Nodari (Part 2).