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SUMMARY:Dimitris Xatzakos (Université de Bordeaux)
DTSTART:20200429T130000Z
DTEND:20200429T140000Z
DTSTAMP:20260422T225842Z
UID:HarmonicAnalysisAarhus/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarmonicAnal
 ysisAarhus/1/">Quantum ergodicity on thin sets and closed geodesics on ari
 thmetic 3-manifolds</a>\nby Dimitris Xatzakos (Université de Bordeaux) as
  part of Harmonic Analysis Seminar Aarhus\n\n\nAbstract\nIn this talk I wi
 ll discuss our work about two problems on hyperbolic manifolds\, the QUE c
 onjecture of Rudnick and Sarnak and the Prime geodesic theorem. For arithm
 etic manifolds\, using triple product formulas and the Kuznetsov trace for
 mula the study of these two problems can be reduced to subconexity estimat
 es for related L-functions. I will describe some of our recent results wit
 h a focus on the case of arithmetic 3-manifolds.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysisAarhus/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jungwon Lee (Sorbonne Université)
DTSTART:20200519T121500Z
DTEND:20200519T134500Z
DTSTAMP:20260422T225842Z
UID:HarmonicAnalysisAarhus/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarmonicAnal
 ysisAarhus/2/">Dynamics of continued fractions and conjecture of Mazur-Rub
 in</a>\nby Jungwon Lee (Sorbonne Université) as part of Harmonic Analysis
  Seminar Aarhus\n\n\nAbstract\nMazur and Rubin established several conject
 ural statistics for modular symbols. We show that the conjecture holds on 
 average. We plan to introduce the approach based on spectral analysis of t
 ransfer operator associated to a certain skew-product Gauss map and conseq
 uent result on mod p non-vanishing of modular L-values with Dirichlet twis
 ts (joint with Hae-Sang Sun).\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysisAarhus/2/
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SUMMARY:Ursula Ludwig (Universität Duisburg-Essen)
DTSTART:20201209T140000Z
DTEND:20201209T150000Z
DTSTAMP:20260422T225842Z
UID:HarmonicAnalysisAarhus/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarmonicAnal
 ysisAarhus/3/">An Extension of a Theorem by Cheeger and Müller to Spaces 
 with Isolated Conical Singularities</a>\nby Ursula Ludwig (Universität Du
 isburg-Essen) as part of Harmonic Analysis Seminar Aarhus\n\n\nAbstract\nA
 n important comparison theorem in global analysis is the comparison of ana
 lytic and topological torsion for smooth compact manifolds equipped with a
  unitary flat vector bundle. It has been conjectured by Ray and Singer and
  has been independently proved by Cheeger and Müller in the 70ies. Bismut
  and Zhang combined the Witten deformation and local index techniques to g
 eneralise the result of Cheeger and Müller to arbitrary flat vector bundl
 es with arbitrary Hermitian metrics.The aim of this talk is to present an 
 extension of the Cheeger-Müller theorem to spaces with isolated conical s
 ingularities by generalising the proof of Bismut and Zhang to the singular
  setting. In the first part of the talk I will recall the classical Cheege
 r-Müller theorem on a compact smooth manifold.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysisAarhus/3/
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SUMMARY:Siddhartha Sahi (Rutgers University)
DTSTART:20210621T130000Z
DTEND:20210621T140000Z
DTSTAMP:20260422T225842Z
UID:HarmonicAnalysisAarhus/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarmonicAnal
 ysisAarhus/4/">An integral formula for a Euclidean Jordan algebra and its 
 applications</a>\nby Siddhartha Sahi (Rutgers University) as part of Harmo
 nic Analysis Seminar Aarhus\n\n\nAbstract\nWe introduce a one-parameter in
 tegral associated with a Euclidean Jordan algebra\, and we give an explici
 t evaluation as a power series in spherical polynomials. We use the integr
 al to bound certain Gaussian functions on the Jordan algebra introduced by
  Sahi\, which play a key role in the construction of small unitary represe
 ntations of the Tits-Kantor-Koecher conformal group of the Jordan algebra.
  This application involves only very special values of the parameter\, and
  for those values we establish a formula for the integral as an algebraic 
 function\, which in particular implies that the Gaussian functions are squ
 are-integrable with respect to a natural measure.\n\nThis is joint work wi
 th Alexander Dvorsky.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysisAarhus/4/
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