9–14 Feb 2025
Gran Sasso Science Institute, L'Aquila (IT)
Europe/Rome timezone

Lectures

Topological states of matters

Sven Bachmann 
The University of British Columbia

Abstract: In these lectures, I will provide an overview of the mathematical understanding of topological states of condensed matter systems, focussing on the quantum Hall effect as a prototypical example. While very much is known for non-interacting electrons, the interacting situation has long been a challenge. The lectures will focus on some of the new techniques that allow to deal with interacting systems and the results that have come with them. I will discuss the general problem of the classification of topological phases at zero temperature and if time permits its relation to classifying anyonic quasi-particles. 

 



T.B.A.

Caroline Lasser
Technische Universität München

Abstract: T.B.A.
 



Gross-Pitaevskii theory of supersolids

Mathieu Lewin
CEREMADE - Université Paris Dauphine

Abstract: We consider the stationary Gross-Pitaevskii equation for an extended function not tending to 0 at infinity, which describes the condensate part of an infinite Bose gas. The goal of the talk will be to explain how to mix tools from PDEs and statistical mechanics to study the phase diagram of this model. In particular, we will prove that there is a unique freezing transition for interaction potentials that are stable but not positive definite. The conjecture is that the solutions in the solid phase are periodic. Those describe a supersolid, a state of matter that has been the subject of much recent experimental work. Work in collaboration with Phan Thành Nam (Munich).