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SUMMARY:Giada Franz — Minimal surfaces via equivariant eigenvalue optimi
 zation\, after Karpukhin\, Kusner\, McGrath\, and Stern
DTSTART:20251129T090000Z
DTEND:20251129T100000Z
DTSTAMP:20260424T050700Z
UID:indico-event-15200@indico.math.cnrs.fr
DESCRIPTION:In 1996\, Nadirashvili discovered a beautiful connection betwe
 en minimal surfaces in round spheres and an optimization problem for Lapla
 ce eigenvalues on a surface. This gave a surprising analytic perspective o
 n minimal surfaces and opened the way for many important results.\nHere\, 
 we will focus on the recent paper from 2024 by Karpukhin–Kusner–McGrat
 h–Stern\, who use equivariant eigenvalue optimization to construct many 
 new examples of minimal surfaces in the three-dimensional unit sphere. Usi
 ng similar methods\, they also find many new free boundary minimal surface
 s in the three-dimensional unit ball\, in particular obtaining examples fo
 r every topological type. This was a central open problem in the field\, p
 osed by Fraser–Li in 2014\, whose analogue in the three dimensional sphe
 re was solved by Lawson in 1970. Note that free boundary minimal surfaces 
 in round balls enjoy a connection with another eigenvalue problem\, namely
  the Steklov problem\, by a result of Fraser–Schoen.\nIn the talk\, we w
 ill give an overview of the results. We will present the ingredients in th
 e proof of Karpukhin–Kusner–McGrath–Stern (including previous result
 s by Petrides from 2014 and Karpukhin–Stern from 2020) and we will focus
  on the novel techniques of the paper. These have already spurred importan
 t advances in the study of Laplace eigenvalue optimization by Petrides (20
 24) and Karpukhin–Petrides–Stern (2025).\n\nhttps://indico.math.cnrs.f
 r/event/15200/
LOCATION:Amphithéâtre Charles Hermite (IHP - Bâtiment Borel)
URL:https://indico.math.cnrs.fr/event/15200/
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