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BEGIN:VEVENT
SUMMARY:András Vasy (Stanford University)
DTSTART:20210517T150000Z
DTEND:20210517T154500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/1
DESCRIPTION:Title: On-spectrum Fredholm theory for the Laplacian on asymptotically
conic spaces\nby András Vasy (Stanford University) as part of Analys
is on Singular Spaces\n\n\nAbstract\nIn this talk I will discuss and compa
re two approaches via Fredholm theory to resolvent estimates for the Lapla
cian of asymptotically conic spaces (such as appropriate metric perturbati
ons of Euclidean space)\, including in the zero spectral parameter limit.\
n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yaiza Canzani (University of North Carolina at Chapel Hill)
DTSTART:20210517T160000Z
DTEND:20210517T164500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/2
DESCRIPTION:Title: Eigenfunction concentration via geodesic beams\nby Yaiza Ca
nzani (University of North Carolina at Chapel Hill) as part of Analysis on
Singular Spaces\n\n\nAbstract\nA vast array of physical phenomena\, rangi
ng from the propagation of waves to the location of quantum particles\, is
dictated by the behavior of Laplace eigenfunctions. Because of this\, it
is crucial to understand how various measures of eigenfunction concentrati
on respond to the background dynamics of the geodesic flow. In collaborati
on with J. Galkowski\, we developed a framework to approach this problem t
hat hinges on decomposing eigenfunctions into geodesic beams. In this talk
\, I will present these techniques and explain how to use them to obtain q
uantitative improvements on the standard estimates for the eigenfunction's
pointwise behavior\, Lp norms\, and Weyl Laws. One consequence of this me
thod is a quantitatively improved Weyl Law for the eigenvalue counting fun
ction on all product manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Guillarmou (Université Paris Saclay and CNRS)
DTSTART:20210517T170000Z
DTEND:20210517T174500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/3
DESCRIPTION:Title: Segal Axioms and modular bootstrap for Liouville CFT\nby Co
lin Guillarmou (Université Paris Saclay and CNRS) as part of Analysis on
Singular Spaces\n\n\nAbstract\nLiouville conformal field theory is a confo
rmal field theory quantizing the uniformization of Riemann surfaces. In jo
int work with Kupiainen\, Rhodes\, Vargas\, we show that Segal axioms are
satisfied for Liouville Conformal Field theory on Riemann surfaces\, i.e.
that the correlation/partition functions can be expressed by cutting the s
urfaces into surfaces with boundary. This is reminiscent to topological qu
antum field theory approaches where one associates Hilbert spaces H to bou
ndaries and trace class operators on H to manifolds with boundary\, with t
he property that operators compose when we glue two manifold along one com
mon boundary. Using our previous work on the conformal bootstrap for the 4
-point function on the sphere\, this allows to express the partition and c
orrelation functions as explicit functions on the moduli space of Riemann
surface with marked points in terms of the conformal blocks associated to
the Virasoro algebra and the structure constant (called DOZZ). The proof i
s a combination of probability methods\, scattering theory and the represe
ntation theory of Virasoro algebra.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafe Mazzeo (Stanford University)
DTSTART:20210518T220000Z
DTEND:20210518T224500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/4
DESCRIPTION:Title: The index of the deformation problem for Z_2 harmonic spinors.<
/a>\nby Rafe Mazzeo (Stanford University) as part of Analysis on Singular
Spaces\n\n\nAbstract\nZ_2 harmonic spinors arise as limiting objects in ga
uge theory\, and are solutions of an overdetermined boundary problem. I wi
ll describe some ongoing work (with Haydys and Takahashi) concerning the i
ndex of the associated deformation operator when the branching set is a ne
twork of curves in a 3-manifold.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadrian Quan (University of Illinois Urbana-Champaign)
DTSTART:20210518T230000Z
DTEND:20210518T234500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/5
DESCRIPTION:Title: Resolvent and Wave trace of Asymptotically Complex Hyperbolic M
anifolds\nby Hadrian Quan (University of Illinois Urbana-Champaign) as
part of Analysis on Singular Spaces\n\n\nAbstract\nIn this talk I will re
port on continuing work about the spectral geometry of asymptotically comp
lex hyperbolic manifolds. This class of non-compact spaces contain as exam
ples certain quotients of complex hyperbolic space\, as well as pseudoconv
ex domains in Stein manifolds. My focus will be on the resolvent and wave
kernel\, and how the behavior of closed geodesics in the interior can infl
uence these spectral invariants. Our study of these operators will include
discussion of different techniques in microlocal analysis\, including rad
ial estimates\, complex absorption\, and a Fourier Integral Operator calcu
lus modeled on the Theta-calculus of pseudodifferential operators introduc
ed by Epstein-Mendoza-Melrose.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Tacy (University of Auckland)
DTSTART:20210519T000000Z
DTEND:20210519T004500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/6
DESCRIPTION:Title: Filament structure in random plane waves\nby Melissa Tacy (
University of Auckland) as part of Analysis on Singular Spaces\n\n\nAbstra
ct\nNumerical studies of random plane waves\, functions where the coeffici
ents are chosen ``at random''\, have detected an apparent filament structu
re. The waves appear enhanced along straight lines. There has been signifi
cant difference of opinion as to whether this structure is indeed a failur
e to equidistribute\, numerical artefact or an illusion created by the hum
an desire to see patterns. In this talk I will present some recent results
that go some way to answering the question. First we consider the behavio
ur of a random variable given by where is a unit ray from the point in dir
ection . We will see that this random variable is uniformly equidistribute
d. That is\, the probability that for any \, differs from its equidistribu
ted value is small (in fact exponentially small). This result rules out a
strong scarring of random waves. However\, when we look at the full phase
space picture and study a random variable where is a semiclassical localis
er at Planck scale around we do see a failure to equidistribute. This sugg
ests that the observed filament structure is a configuration space reflect
ion of the phase space concentrations.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Rochon (Université du Québec à Montréal)
DTSTART:20210520T220000Z
DTEND:20210520T224500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/7
DESCRIPTION:Title: Quasi-fibered boundary pseudodifferential operators\nby Fr
édéric Rochon (Université du Québec à Montréal) as part of Analysis
on Singular Spaces\n\n\nAbstract\nQuasi-fibered boundary (QFB) metrics for
m a natural class of complete metrics generalizing the quasi-asymptoticall
y locally Euclidean (QALE) metrics of Joyce. After recalling what those me
trics are\, I will explain how to construct a suitable pseudodifferential
calculus containing good parametrices for operators like the Hodge-deRham
operator of a QFB metric\, allowing us to show that they are Fredholm when
acting on suitable Sobolev spaces and yielding results about the decay of
L2 harmonic forms. This in turn can be used to study the reduced L2 cohom
ology of some QFB metrics. This is a joint work with Chris Kottke.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (IMATE-UNAM Oaxaca)
DTSTART:20210520T230000Z
DTEND:20210520T234500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/8
DESCRIPTION:Title: Convergence of manifolds under volume convergence\, a tensor an
d a diameter bound\nby Raquel Perales (IMATE-UNAM Oaxaca) as part of A
nalysis on Singular Spaces\n\n\nAbstract\nGiven a closed and oriented mani
fold and Riemannian tensors on that satisfy and we will see that converges
to in the volume preserving intrinsic flat sense. We note that under thes
e conditions we do not necessarily obtain smooth\, or even Gromov-Hausdorf
f convergence. Nonetheless\, this result can be applied to show stability
of a class of tori. That is\, any sequence of tori in this class with almo
st nonnegative scalar curvature converge to a flat torus. We will also see
that an analogous convergence result to the stated above but for manifold
s with boundary can be applied to show stability of the positive mass theo
rem for a particular class of manifolds. [Based on joint works with Allen\
, Allen-Sormani\, Cabrera Pacheco - Ketterer\, and Huang - Lee]\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiril Datchev (Purdue University)
DTSTART:20210521T000000Z
DTEND:20210521T004500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/9
DESCRIPTION:Title: Resonances for thin barriers on the half-line.\nby Kiril Da
tchev (Purdue University) as part of Analysis on Singular Spaces\n\n\nAbst
ract\nThe analysis of scattering by thin barriers arises in the study of p
hysical problems involving the confinement of individual electrons by smal
l numbers of atoms. Motivated by work of Galkowski in higher dimensions\,
we consider a simplified model of such a barrier in the form of a delta fu
nction potential on the half-line. Our main results compute quantum decay
rates (imaginary parts of resonances) for particles confined by such a pot
ential. In the semiclassical limit\, the energy dependence of the decay ra
tes is logarithmic when the barrier is weaker and polynomial when the barr
ier is stronger. For our computation\, we derive a formula for resonances
in terms of the Lambert W function and apply a series expansion. This proj
ect is joint work with Nkhalo Malawo.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuwen Zhu (Northeastern University)
DTSTART:20210521T150000Z
DTEND:20210521T154500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/10
DESCRIPTION:Title: The Fredholm theory and L^2 cohomology of Tian--Yau metrics\nby Xuwen Zhu (Northeastern University) as part of Analysis on Singular
Spaces\n\n\nAbstract\nWe will discuss a family of four-dimensional non-com
pact hyperK\\"ahler metrics called Tian--Yau metrics\, modelled by the Cal
abi ansatz with inhomogeneous collapsing near infinity. Such metrics were
used recently as the scaling bubble limits for codimension-3 collapsing of
K3 surfaces\, where the study of its Laplacian played a central role. In
this talk I will talk about the Fredholm mapping property and L^2 cohomolo
gy of such metrics. This is ongoing work joint with Rafe Mazzeo.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Núñez-Zimbrón (Centro de Investigación en Matemáticas)
DTSTART:20210521T160000Z
DTEND:20210521T164500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/11
DESCRIPTION:Title: Harmonic functions on spaces with Ricci curvature bounded belo
w\nby Jesús Núñez-Zimbrón (Centro de Investigación en Matemática
s) as part of Analysis on Singular Spaces\n\n\nAbstract\nThe so-called spa
ces with the Riemannian curvature-dimension condition (RCD spaces for shor
t) are metric measure spaces which are non-necessarily smooth but admit a
notion of "Ricci curvature bounded below and dimension bounded above". The
se arise naturally as Gromov-Hausdorff limits of Riemannian manifolds with
these conditions and\, in contrast to manifolds\, RCD spaces may have top
ological or metric singularities. Nevertheless\, several properties and re
sults from Riemannian geometry can be extended to this non-smooth setting.
In this talk I will present recent work\, joint with Guido de Philippis\,
in which we show that the gradients of harmonic functions vanish at the s
ingular points of the space. I will mention two consequences of this resul
t on smooth manifolds: it implies that there does not exist an a priori es
timate on the modulus of continuity of the gradient of harmonic functions
depending only on lower bounds of the sectional curvature and that there i
s no a priori Calderón-Zygmund inequality for the Laplacian with bounds t
hat depend only on lower bounds of the sectional curvature.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semyon Dyatlov (MIT)
DTSTART:20210521T170000Z
DTEND:20210521T174500Z
DTSTAMP:20260404T041458Z
UID:CMO_21w5222/12
DESCRIPTION:Title: Ruelle zeta at zero for nearly hyperbolic 3-manifolds\nby
Semyon Dyatlov (MIT) as part of Analysis on Singular Spaces\n\n\nAbstract\
nFor a compact negatively curved Riemannian manifold \, the Ruelle zeta fu
nction of its geodesic flow is defined for as a convergent product over th
e periods of primitive closed geodesics and extends meromorphically to the
entire complex plane. If is hyperbolic (i.e. has sectional curvature )\,
then the order of vanishing of at can be expressed in terms of the Betti n
umbers . In particular\, Fried proved in 1986 that when is a hyperbolic 3-
manifold\, I will present a recent result joint with Mihajlo Ceki\\'c\, Be
njamin K\\"uster\, and Gabriel Paternain: when and is a generic perturbati
on of the hyperbolic metric\, the order of vanishing of the Ruelle zeta fu
nction jumps\, more precisely This is in contrast with dimension~2 where f
or all negatively curved metrics. The proof uses the microlocal approach o
f expressing as an alternating sum of the dimensions of the spaces of gene
ralized resonant Pollicott--Ruelle currents and obtains a detailed picture
of these spaces both in the hyperbolic case and for its perturbations.\n
LOCATION:https://stable.researchseminars.org/talk/CMO_21w5222/12/
END:VEVENT
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