Fields Colloquium

This aim of this talk is to give an overview of results obtained in the recently emerged field of nonlinear quantum graphs.

Quantum graphs are metric graphs, i.e. graphs whose edges have a length, equipped with a Hamiltonian operator. A nonlinear quantum graph is a quantum graph endowed with a nonlinear Schrödinger equation. Over the last 15 years, the study of nonlinear quantum graphs has gained a considerable momentum, with particular emphasis on the study of existence and properties of stationary states. In this talk, I will outline the main mathematical features of nonlinear quantum graphs, review the most significant results obtained so far and discuss possible future developments.

Stefan Le Coz has been Maître de conférences at the University of Toulouse since September 2010. He obtained his PhD in Mathematics from the University of Franche-Comté in 2007, before holding postdoctoral positions at SISSA and Paris 6 for two years. His research focuses on nonlinear dispersive PDEs, with particular interest in solitons, multi-solitons, blow-up solutions, and, more recently, nonlinear quantum graphs.