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SUMMARY:Dimitris Xatzakos (Université de Bordeaux)
DTSTART;VALUE=DATE-TIME:20200429T130000Z
DTEND;VALUE=DATE-TIME:20200429T140000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044707Z
UID:HarmonicAnalysisAarhus/1
DESCRIPTION:Title: Quantum ergodicity on thin sets and closed geodesics on ari
thmetic 3-manifolds\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/
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SUMMARY:Jungwon Lee (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20200519T121500Z
DTEND;VALUE=DATE-TIME:20200519T134500Z
DTSTAMP;VALUE=DATE-TIME:20240804T044707Z
UID:HarmonicAnalysisAarhus/2
DESCRIPTION:Title: Dynamics of continued fractions and conjecture of Mazur-Rub
in\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;VALUE=DATE-TIME:20201209T140000Z
DTEND;VALUE=DATE-TIME:20201209T150000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044707Z
UID:HarmonicAnalysisAarhus/3
DESCRIPTION:Title: An Extension of a Theorem by Cheeger and Müller to Spaces
with Isolated Conical Singularities\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;VALUE=DATE-TIME:20210621T130000Z
DTEND;VALUE=DATE-TIME:20210621T140000Z
DTSTAMP;VALUE=DATE-TIME:20240804T044707Z
UID:HarmonicAnalysisAarhus/4
DESCRIPTION:Title: An integral formula for a Euclidean Jordan algebra and its
applications\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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