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SUMMARY:Dimitris Xatzakos (Université de Bordeaux)
DTSTART:20200429T130000Z
DTEND:20200429T140000Z
DTSTAMP:20260404T111246Z
UID:HarmonicAnalysisAarhus/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Harmo
 nicAnalysisAarhus/1/">Quantum ergodicity on thin sets and closed geodesics
  on arithmetic 3-manifolds</a>\nby Dimitris Xatzakos (Université de Borde
 aux) as part of Harmonic Analysis Seminar Aarhus\n\n\nAbstract\nIn this ta
 lk I will discuss our work about two problems on hyperbolic manifolds\, th
 e QUE conjecture of Rudnick and Sarnak and the Prime geodesic theorem. For
  arithmetic manifolds\, using triple product formulas and the Kuznetsov tr
 ace formula the study of these two problems can be reduced to subconexity 
 estimates for related L-functions. I will describe some of our recent resu
 lts with a focus on the case of arithmetic 3-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysisAarhus/1
 /
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jungwon Lee (Sorbonne Université)
DTSTART:20200519T121500Z
DTEND:20200519T134500Z
DTSTAMP:20260404T111246Z
UID:HarmonicAnalysisAarhus/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Harmo
 nicAnalysisAarhus/2/">Dynamics of continued fractions and conjecture of Ma
 zur-Rubin</a>\nby Jungwon Lee (Sorbonne Université) as part of Harmonic A
 nalysis Seminar Aarhus\n\n\nAbstract\nMazur and Rubin established several 
 conjectural statistics for modular symbols. We show that the conjecture ho
 lds on average. We plan to introduce the approach based on spectral analys
 is of transfer operator associated to a certain skew-product Gauss map and
  consequent result on mod p non-vanishing of modular L-values with Dirichl
 et twists (joint with Hae-Sang Sun).\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysisAarhus/2
 /
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BEGIN:VEVENT
SUMMARY:Ursula Ludwig (Universität Duisburg-Essen)
DTSTART:20201209T140000Z
DTEND:20201209T150000Z
DTSTAMP:20260404T111246Z
UID:HarmonicAnalysisAarhus/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Harmo
 nicAnalysisAarhus/3/">An Extension of a Theorem by Cheeger and Müller to 
 Spaces with Isolated Conical Singularities</a>\nby Ursula Ludwig (Universi
 tät Duisburg-Essen) as part of Harmonic Analysis Seminar Aarhus\n\n\nAbst
 ract\nAn important comparison theorem in global analysis is the comparison
  of analytic and topological torsion for smooth compact manifolds equipped
  with a unitary flat vector bundle. It has been conjectured by Ray and Sin
 ger and has been independently proved by Cheeger and Müller in the 70ies.
  Bismut and Zhang combined the Witten deformation and local index techniqu
 es to generalise the result of Cheeger and Müller to arbitrary flat vecto
 r bundles with arbitrary Hermitian metrics.The aim of this talk is to pres
 ent an extension of the Cheeger-Müller theorem to spaces with isolated co
 nical singularities by generalising the proof of Bismut and Zhang to the s
 ingular setting. In the first part of the talk I will recall the classical
  Cheeger-Müller theorem on a compact smooth manifold.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysisAarhus/3
 /
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SUMMARY:Siddhartha Sahi (Rutgers University)
DTSTART:20210621T130000Z
DTEND:20210621T140000Z
DTSTAMP:20260404T111246Z
UID:HarmonicAnalysisAarhus/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/Harmo
 nicAnalysisAarhus/4/">An integral formula for a Euclidean Jordan algebra a
 nd its applications</a>\nby Siddhartha Sahi (Rutgers University) as part o
 f Harmonic Analysis Seminar Aarhus\n\n\nAbstract\nWe introduce a one-param
 eter integral associated with a Euclidean Jordan algebra\, and we give an 
 explicit evaluation as a power series in spherical polynomials. We use the
  integral to bound certain Gaussian functions on the Jordan algebra introd
 uced by Sahi\, which play a key role in the construction of small unitary 
 representations of the Tits-Kantor-Koecher conformal group of the Jordan a
 lgebra. This application involves only very special values of the paramete
 r\, and for those values we establish a formula for the integral as an alg
 ebraic function\, which in particular implies that the Gaussian functions 
 are square-integrable with respect to a natural measure.\n\nThis is joint 
 work with Alexander Dvorsky.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysisAarhus/4
 /
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