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SUMMARY:Rigidity in the Ginzburg–Landau equation from S2 to S2 - Matilde
  Gianocca (ETH Zürich)
DTSTART:20260203T114500Z
DTEND:20260203T121500Z
UID:TALK239605@talks.cam.ac.uk
DESCRIPTION:The Ginzburg&ndash\;Landau energy is often used to approximate
  the Dirichlet energy. As the perturbation parameter tends to zero\, criti
 cal points of the Ginzburg&ndash\;Landau energy converge\, in an appropria
 te (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 so
 lutions of the associated nonlinear elliptic system from S2 to S2\, thereb
 y identifying exactly which harmonic maps can arise as Ginzburg&ndash\;Lan
 dau limits in this regime.
LOCATION:Seminar Room 1\, Newton Institute
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