Variational convergence for the Ginzburg-Landau functional on complex line bundles

Regular seminar of the Department of Mathematics
10 October 2023
Start time 
2:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room "1"
Target audience: 
University community
UniTrento students
Contact person: 
Andrea Pinamonti, Andrea Marchese, Giorgio Saracco, Gian Paolo Leonardi
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3786-1980
Giacomo Canevari (University of Verona)


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 (Università Federico II, Napoli) and Giandomenico Orlandi (Verona).

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