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SUMMARY:Zeta determinants aligned with Zeta [Oberseminar Global Analysis a
 nd Operator Algebras]
DTSTART:20260703T090000Z
DTEND:20260703T100000Z
DTSTAMP:20260706T084400Z
UID:indico-event-1479@math-events.uni-bonn.de
DESCRIPTION:Speakers: Henri Moscovici (Ohio State University)\n\nThe prola
 te spheroidal wave operator\, whose underlying ODE goes back to classicalw
 ork on heat conduction in ellipsoids through separation of variables in pr
 olatespheroidal coordinates for the Helmholtz equation\, has played a surp
 risingly rich andunexpected role across several fields. After gaining cons
 iderable visibility throughits ”lucky accident” role in the 1960s solu
 tion by Slepian\, Landau\, and Pollak ofthe time- and band-limiting proble
 m for signals\, it reappeared in the late 1990s as acutoff mechanism in Co
 nnes’ trace-formula framework recovering the Riemann–Weilexplicit form
 ula in number theory. Connes also observed that\, when extended tothe whol
 e real line\, the prolate wave operator admits a unique self-adjoint exten
 sioncommuting both with the Fourier transform and with its truncation to t
 he finitetime interval. This extension turned out to be unexpectedly signi
 ficant: in 2022\, Connes and myself discovered that it possesses a purely 
 discrete negative spectrumconfined to the Sonin subspace\, whose eigenvalu
 es display a striking resemblanceto the zeros of the Riemann zeta function
 . Recent work of Ramis\, Richard–Jung\,and Thomann (2025) shows that the
  Sonin space is precisely the repository of thisnegative spectrum. The aim
  of this talk is to show that the restrictions of the prolateoperators to 
 the cor- responding Sonin spaces possess zeta determinants naturallyaligne
 d with the Riemann zeta function. Moreover\, they also admit semi-adelicex
 tensions whose zeta determinants exhibit the same phenomenon. Interestingl
 y\,the Sonin prolate operators are closely related to a class of Sturm–L
 iouville operatorsstudied extensively by Matthias Lesch and his collaborat
 ors.\n\nhttps://math-events.uni-bonn.de/event/1479/
LOCATION:Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1479/
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