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SUMMARY:On common roots of Legendre polynomials - Dan Mangoubi (Hebrew Uni
 versity of Jerusalem)
DTSTART:20260121T110000Z
DTEND:20260121T120000Z
UID:TALK241675@talks.cam.ac.uk
DESCRIPTION:It was shown by Bourgain and Rudnick in 2010 that for a curve 
 of non-vanishing curvature on the standard flat 2-torus there are no eigen
 functions of arbitrarily large eigenvalues which vanish on it.&nbsp\; We s
 how that for any small circle on the 2-sphere there are no&nbsp\; zonal sp
 herical harmonics of arbitrarily large eigenvalues which&nbsp\; vanish on 
 it. Equivalently\, only&nbsp\; a finite number of Legendre polynomials can
  share a&nbsp\; non-zero root. The conjecture by Stieltjes is that Legendr
 e polynomials have no common non-zero roots. The talk is based on joint wo
 rks with Adi Weller Weiser and Borys Kadets.
LOCATION:Seminar Room 2\, Newton Institute
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