Minimality of the vortex solution for Ginzburg-Landau systems

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• Radu Ignat (Université Paul Sabatier Toulouse III)
• Wednesday 20 August 2025, 11:00-11:45
• Seminar Room 1, Newton Institute.

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DNMW06 - Recent challenges in the mathematical design of new materials

We consider the standard Ginzburg-Landau system for N-dimensional maps defined in the unit ball for some parameter eps>0. For a boundary data corresponding to a vortex of topological degree one, the aim is to prove the (radial) symmetry of the ground state of the system. We show this conjecture in any dimension N≥7 and for every eps>0, and then, we also prove it in dimension N=4,5,6 provided that the admissible maps are curl-free. This is part of several joint works with Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu, Mickael Nahon and Mircea Rus.

This talk is part of the Isaac Newton Institute Seminar Series series.

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