Month: November 2023

Monday, February 26, 2024 - 11:15
Sala di Rappresentanza
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

---

SPEAKER: Emanuela Giacomelli (LMU München)

---

The low density Fermi gas in three dimensions

In recent decades, the study of many-body systems has been an active area of research in both physics and mathematics. In this talk we consider a system of N interacting fermions with spin 1/2 confined in a box in the dilute regime. We are interested in studying the correlation energy, defined as the difference between the energy of the fundamental state and that of the free Fermi gas. We will discuss some recent results on a first-order asymptotic for the correlation energy in the thermodynamic limit, where the number of particles and the size of the box are sent to infinity while keeping the density fixed. In particular, we will present some recent results for the correlation energy that go in the direction of a rigorous proof of the well-known Huang-Yang formula of 1957.

Monday, January 15, 2024 - 11:15
Aula 9
Dipartimento di Matematica
Università degli Studi di Milano
Via Cesare Saldini 50

---

SPEAKER: Clara Torres Latorre (Universitat de Barcelona)

---

Regularity theory for elliptic and parabolic PDE

In this talk, we’ll explore how regularity theory is crucial for understanding partial differential equations (PDEs), and how it has consequences in physics and numerical analysis. We’ll first focus on why regularity matters, then take elliptic and parabolic PDEs as examples to talk about classical and recent regularity results. The goal is to give a practical overview, explaining when PDE solutions are smooth or singular.