The seminars take place on Wednesday afternoon, usually at 14:30 Italian time.
November 4th, 2026, 16:30 Italian time
Rupert Frank (Ludwig-Maximilians Universität München)
From Bogoliubov-de Gennes to Ginzburg-Landau: Critical Points Near Tc in the Non-Magnetic Case
We study the relation between the Bogoliubov-de Gennes (BdG) equation and the Ginzburg-Landau (GL) equation for a BCS model without external fields. While previous rigorous derivations of GL theory from BCS theory have focused on energies and minimizers, here we consider arbitrary critical points in the relevant energy regime. For temperatures close to the critical temperature, we prove that every sufficiently small solution of the BdG equation admits an asymptotic factorization into a microscopic Cooper-pair profile and a macroscopic order parameter. The latter satisfies the GL equation up to an error that vanishes in the scaling limit. We also prove the opposite direction, going from a solution of the GL equation to an approximate solution of the BdG equation. Our analysis relies on a Birman-Schwinger reformulation of the BdG equation, a Lyapunov-Schmidt type reduction, and semiclassical estimates at low regularity.
The talk is based on joint work with C. Hainzl. and Dong Hao Ou Yang.
December 2nd, 2026
Beatrice Pelloni (Heriot-Watt University, Maxwell Institute for Mathematical Sciences)
TBA
TBA
January 13th, 2027
Benjamin Schlein (Universität Zürich)
TBA
TBA
March, 2027
TBD (TBD)
TBA
TBA
April, 2027
TBD (TBD)
TBA
TBA
May, 2027
TBD (TBD)
TBA
TBA
