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DTSTART:20260329T030000
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DTSTAMP:20260424T143429Z
UID:1762336800@ist.ac.at
DTSTART:20251105T110000
DTEND:20251105T120000
DESCRIPTION:Speaker: Yunzhe Li\nhosted by Kaloshin Group\nAbstract: I will 
 present a joint work with Joscha Henheik\, Vadim Kaloshin and Amir Vig on 
 the deformationa spectral rigidty of Liouville metrics. The Liouville metr
 ics refer to a class of Riemannian metrics on the 2-torus of the form ds2 
 = (f(x) + g(y))(dx2+dy2). Liouville metrics are special partly because the
 y are conjectured to be the only class of metrics whose geodesic flow is i
 ntegrable in the Liouville-Arnold sense. We consider the Laplace spectrum 
 of such metrics\, i.e.\, the set of eigenvalues λ of the PDE  –Δu = 
 λu where Δ is the Laplace-Beltrami operator associated with the metric. 
 We prove that\, for generic f and g\, if a deformation of the form (f(x) +
  g(y) + εU(x\,y))(dx2+dy2) preserves the Laplace spectrum\, then U = 0. I
  will review the background of this problem and explain some key ideas of 
 the proof.
LOCATION:Mondi 3/ Central Building\, ISTA
ORGANIZER:
SUMMARY:Yunzhe Li: Informal dynamical systems discussion: Liouville Metrics
  and Spectral Rigidity
URL:https://talks-calendar.ista.ac.at/events/6107
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