Barbara Roos, "Superconductivity from a Mathematical Perspective"

Thursday 28 May 2026, 14:30 → 15:30 Europe/Rome

Ex-ISEF/Building-Main Lecture Hall (GSSI)

Abstract:

Superconductivity, despite having been discovered over a century ago, remains only partially understood, with many fundamental mathematical and physical questions still open.

 

Two central theoretical models for superconductivity are the microscopic Bardeen-Cooper-Schrieffer (BCS) theory and the macroscopic Ginzburg-Landau (GL) theory. In particular, GL theory is often applied to describe surface superconductivity, a phenomenon in which a material exhibits superconducting behavior near its surface while remaining a normal metal in the bulk. It is expected that GL theory can be derived from BCS theory as an effective macroscopic description, and in fact there is a rigorous derivation for domains without surfaces. However, for domains that have a surface, this is still an open problem.

 

After an introduction to superconductivity and the theoretical models, I will discuss mathematical results for BCS theory in the presence of surfaces and explain the mathematical challenges that arise in understanding the connection between BCS and GL theory in this setting.