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SUMMARY:Joel Dahne (Uppsala University\, Sweden)
DTSTART:20210427T140000Z
DTEND:20210427T150000Z
DTSTAMP:20260423T024746Z
UID:CRM-CAMP/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/46/
 ">A computer assisted counterexample to Payne’s nodal line conjecture wi
 th few holes</a>\nby Joel Dahne (Uppsala University\, Sweden) as part of C
 RM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis\n\n\
 nAbstract\nPayne conjectured in 1967 that the nodal line of the second Dir
 ichlet eigenfunction must touch the boundary of the domain. In their 1997 
 breakthrough paper\, Hoffmann-Ostenhof\, Hoffmann-Ostenhof and Nadirashvil
 i proved this to be false by constructing a counterexample in the plane wi
 th an unspecified\, but large\, number of holes and raised the question of
  the minimum number of holes a counterexample can have. In this talk I wil
 l present a computer assisted counter example with 6 holes. This is joint 
 work with Javier Gómez-Serrano and Kimberly Hou.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/46/
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