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Rigidity in the Ginzburg–Landau equation from S2 to S2

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GSTW05 - Emerging Horizons in Geometric Spectral Theory: an ECRs workshop

The Ginzburg–Landau energy is often used to approximate the Dirichlet energy. As the perturbation parameter tends to zero, critical points of the Ginzburg–Landau energy converge, in an appropriate (bubbling) sense, to harmonic maps. In this talk I will first explain key analytical properties of this approximation procedure, then show that not every harmonic map can be approximated in this way. This is based on a rigidity theorem: under the energy threshold of 8pi, we classify all solutions of the associated nonlinear elliptic system from S2 to S2, thereby identifying exactly which harmonic maps can arise as Ginzburg–Landau limits in this regime.

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

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Room FW26, Computer Laboratory, William Gates Building BITS-VIZAG Donald McIntyre Building, Faculty of Education, 184 Hills Road, room 2S8

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