(Non-)quantization phenomena for higher-dimensional Ginzburg-Landau vortices

Abstract: The Ginzburg-Landau energies for complex-valued maps, initially introduced to model superconductivity, were later found to approximate the area functional in codimension two.

While the pioneering works of Lin-Rivière and Bethuel-Brezis-Orlandi (2001) showed that, for families of critical maps, energy does concentrate along a codimension-two minimal submanifold, it has been an open question whether this happens with integer multiplicity. In this talk, based on joint work with Daniel Stern, we show that, in fact, the set of all possible multiplicities is precisely $\{1\} \cup [2,\infty)$.

analysis of PDEsdifferential geometry

Audience: researchers in the topic

( paper )

Comments: Get-together (30 min) $\cdot$ presentation Alessandro Pigati (60 min) $\cdot$ questions and discussions (30 min).

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NCTS international Geometric Measure Theory seminar

Series comments: We envisage an event built around virtual presentations on progress in geometric measure theory by external speakers. Every researcher is free to register as a participant and thus gain access to a virtual facility which is complete with lobby, lecture hall, and areas with boards for discussion. Thus, it shall recreate the exchange possibilities found at international conferences.

Focus: regularity and singularity theories for submanifolds of Riemannian manifolds and some of its applications.

Frequency: one presentation every other month.

Registration: required for new participants, go to the seminar website (allow at least one working day for processing).

Virtual venue: HyHyve space NCTS iGMT seminar (only for registered participants, opened one hour before the events).

You might want to consult the description of the premises and instructions.

Former organiser: Guido De Philippis (till March 2022).

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