Seminario di Analisi
Martedì 7 Novembre 2023 – Sala Professori I Livello, h. 14.30
DOTT. GIACOMO CANEVARI

VARIATIONAL CONVERGENCE FOR THE GINZBURG-LANDAU FUNCTIONAL ON
COMPLEX LINE BUNDLES

ABSTRACT. The Ginzburg-Landau functional was originally proposed as a model
for superconductivity in Euclidean domains. However, invariance with respect to gauge
transformations – which is one of the most prominent features of the model -suggests
that the functional can be naturally defined in the setting of complex line bundles, where
it can be regarded as an Abelian Yang-Mills-Higgs theory. In this talk, we shall consider
the Ginzburg-Landau functional on a Hermitian line bundle over a closed Riemannian
manifold, in the scaling inherited from superconductivity theory. We shall focus on the
variational aspects of the problem (and describe the main ideas without going too much
into the technicalities). In particular, we shall discuss the asymptotic behaviour, in the
so-called ”London limit”, of minimisers and critical points whose energy grows at most
logarithmically in the Ginzburg-Landau coupling parameter. The talk is based on a joint
work with Federico Dipasquale (Scuola Superiore Meridionale) and Giandomenico Orlandi (Verona).