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BEGIN:VEVENT
SUMMARY:András Vasy (Stanford University)
DTSTART:20210517T150000Z
DTEND:20210517T154500Z
DTSTAMP:20260422T185127Z
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 Analysis on S
ingular Spaces\n\n\nAbstract\nIn this talk I will discuss and compare two
approaches via Fredholm theory to resolvent estimates for the Laplacian of
asymptotically conic spaces (such as appropriate metric perturbations of
Euclidean space)\, including in the zero spectral parameter limit.\n
LOCATION:https://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:20260422T185127Z
UID:CMO_21w5222/2
DESCRIPTION:Title: Eigenfunction concentration via geodesic beams\nby Yaiza Canzani (
University of North Carolina at Chapel Hill) as part of Analysis on Singul
ar Spaces\n\n\nAbstract\nA vast array of physical phenomena\, ranging from
the propagation of waves to the location of quantum particles\, is dictat
ed by the behavior of Laplace eigenfunctions. Because of this\, it is cruc
ial to understand how various measures of eigenfunction concentration resp
ond to the background dynamics of the geodesic flow. In collaboration with
J. Galkowski\, we developed a framework to approach this problem that hin
ges on decomposing eigenfunctions into geodesic beams. In this talk\, I wi
ll present these techniques and explain how to use them to obtain quantita
tive improvements on the standard estimates for the eigenfunction's pointw
ise behavior\, Lp norms\, and Weyl Laws. One consequence of this method is
a quantitatively improved Weyl Law for the eigenvalue counting function o
n all product manifolds.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Guillarmou (Université Paris Saclay and CNRS)
DTSTART:20210517T170000Z
DTEND:20210517T174500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/3
DESCRIPTION:Title: Segal Axioms and modular bootstrap for Liouville CFT\nby Colin Gui
llarmou (Université Paris Saclay and CNRS) as part of Analysis on Singula
r Spaces\n\n\nAbstract\nLiouville conformal field theory is a conformal fi
eld theory quantizing the uniformization of Riemann surfaces. In joint wor
k with Kupiainen\, Rhodes\, Vargas\, we show that Segal axioms are satisfi
ed for Liouville Conformal Field theory on Riemann surfaces\, i.e. that th
e correlation/partition functions can be expressed by cutting the surfaces
into surfaces with boundary. This is reminiscent to topological quantum f
ield theory approaches where one associates Hilbert spaces H to boundaries
and trace class operators on H to manifolds with boundary\, with the prop
erty that operators compose when we glue two manifold along one common bou
ndary. Using our previous work on the conformal bootstrap for the 4-point
function on the sphere\, this allows to express the partition and correlat
ion functions as explicit functions on the moduli space of Riemann surface
with marked points in terms of the conformal blocks associated to the Vir
asoro algebra and the structure constant (called DOZZ). The proof is a com
bination of probability methods\, scattering theory and the representation
theory of Virasoro algebra.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafe Mazzeo (Stanford University)
DTSTART:20210518T220000Z
DTEND:20210518T224500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/4
DESCRIPTION:Title: The index of the deformation problem for Z_2 harmonic spinors.\nby
Rafe Mazzeo (Stanford University) as part of Analysis on Singular Spaces\
n\n\nAbstract\nZ_2 harmonic spinors arise as limiting objects in gauge the
ory\, and are solutions of an overdetermined boundary problem. I will desc
ribe some ongoing work (with Haydys and Takahashi) concerning the index of
the associated deformation operator when the branching set is a network o
f curves in a 3-manifold.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hadrian Quan (University of Illinois Urbana-Champaign)
DTSTART:20210518T230000Z
DTEND:20210518T234500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/5
DESCRIPTION:Title: Resolvent and Wave trace of Asymptotically Complex Hyperbolic Manifold
s\nby Hadrian Quan (University of Illinois Urbana-Champaign) as part o
f Analysis on Singular Spaces\n\n\nAbstract\nIn this talk I will report on
continuing work about the spectral geometry of asymptotically complex hyp
erbolic manifolds. This class of non-compact spaces contain as examples ce
rtain quotients of complex hyperbolic space\, as well as pseudoconvex doma
ins in Stein manifolds. My focus will be on the resolvent and wave kernel\
, and how the behavior of closed geodesics in the interior can influence t
hese spectral invariants. Our study of these operators will include discus
sion of different techniques in microlocal analysis\, including radial est
imates\, complex absorption\, and a Fourier Integral Operator calculus mod
eled on the Theta-calculus of pseudodifferential operators introduced by E
pstein-Mendoza-Melrose.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Tacy (University of Auckland)
DTSTART:20210519T000000Z
DTEND:20210519T004500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/6
DESCRIPTION:Title: Filament structure in random plane waves\nby Melissa Tacy (Univers
ity of Auckland) as part of Analysis on Singular Spaces\n\n\nAbstract\nNum
erical studies of random plane waves\, functions where the coefficients ar
e chosen ``at random''\, have detected an apparent filament structure. The
waves appear enhanced along straight lines. There has been significant di
fference of opinion as to whether this structure is indeed a failure to eq
uidistribute\, numerical artefact or an illusion created by the human desi
re to see patterns. In this talk I will present some recent results that g
o some way to answering the question. First we consider the behaviour of a
random variable given by where is a unit ray from the point in direction
. We will see that this random variable is uniformly equidistributed. That
is\, the probability that for any \, differs from its equidistributed val
ue 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 p
icture and study a random variable where is a semiclassical localiser at P
lanck scale around we do see a failure to equidistribute. This suggests th
at the observed filament structure is a configuration space reflection of
the phase space concentrations.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Rochon (Université du Québec à Montréal)
DTSTART:20210520T220000Z
DTEND:20210520T224500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/7
DESCRIPTION:Title: Quasi-fibered boundary pseudodifferential operators\nby Frédéric
Rochon (Université du Québec à Montréal) as part of Analysis on Singu
lar Spaces\n\n\nAbstract\nQuasi-fibered boundary (QFB) metrics form a natu
ral class of complete metrics generalizing the quasi-asymptotically locall
y Euclidean (QALE) metrics of Joyce. After recalling what those metrics ar
e\, 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 harm
onic forms. This in turn can be used to study the reduced L2 cohomology of
some QFB metrics. This is a joint work with Chris Kottke.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (IMATE-UNAM Oaxaca)
DTSTART:20210520T230000Z
DTEND:20210520T234500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/8
DESCRIPTION:Title: Convergence of manifolds under volume convergence\, a tensor and a dia
meter bound\nby Raquel Perales (IMATE-UNAM Oaxaca) as part of Analysis
on Singular Spaces\n\n\nAbstract\nGiven a closed and oriented manifold an
d Riemannian tensors on that satisfy and we will see that converges to in
the volume preserving intrinsic flat sense. We note that under these condi
tions we do not necessarily obtain smooth\, or even Gromov-Hausdorff conve
rgence. Nonetheless\, this result can be applied to show stability of a cl
ass of tori. That is\, any sequence of tori in this class with almost nonn
egative scalar curvature converge to a flat torus. We will also see that a
n analogous convergence result to the stated above but for manifolds with
boundary can be applied to show stability of the positive mass theorem for
a particular class of manifolds. [Based on joint works with Allen\, Allen
-Sormani\, Cabrera Pacheco - Ketterer\, and Huang - Lee]\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kiril Datchev (Purdue University)
DTSTART:20210521T000000Z
DTEND:20210521T004500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/9
DESCRIPTION:Title: Resonances for thin barriers on the half-line.\nby Kiril Datchev (
Purdue University) as part of Analysis on Singular Spaces\n\n\nAbstract\nT
he analysis of scattering by thin barriers arises in the study of physical
problems involving the confinement of individual electrons by small numbe
rs of atoms. Motivated by work of Galkowski in higher dimensions\, we cons
ider a simplified model of such a barrier in the form of a delta function
potential on the half-line. Our main results compute quantum decay rates (
imaginary parts of resonances) for particles confined by such a potential.
In the semiclassical limit\, the energy dependence of the decay rates is
logarithmic when the barrier is weaker and polynomial when the barrier is
stronger. For our computation\, we derive a formula for resonances in term
s of the Lambert W function and apply a series expansion. This project is
joint work with Nkhalo Malawo.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuwen Zhu (Northeastern University)
DTSTART:20210521T150000Z
DTEND:20210521T154500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/10
DESCRIPTION:Title: The Fredholm theory and L^2 cohomology of Tian--Yau metrics\nby X
uwen Zhu (Northeastern University) as part of Analysis on Singular Spaces\
n\n\nAbstract\nWe will discuss a family of four-dimensional non-compact hy
perK\\"ahler metrics called Tian--Yau metrics\, modelled by the Calabi ans
atz with inhomogeneous collapsing near infinity. Such metrics were used re
cently as the scaling bubble limits for codimension-3 collapsing of K3 sur
faces\, where the study of its Laplacian played a central role. In this ta
lk I will talk about the Fredholm mapping property and L^2 cohomology of s
uch metrics. This is ongoing work joint with Rafe Mazzeo.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Núñez-Zimbrón (Centro de Investigación en Matemáticas)
DTSTART:20210521T160000Z
DTEND:20210521T164500Z
DTSTAMP:20260422T185127Z
UID:CMO_21w5222/11
DESCRIPTION:Title: Harmonic functions on spaces with Ricci curvature bounded below\n
by Jesús Núñez-Zimbrón (Centro de Investigación en Matemáticas) as p
art of Analysis on Singular Spaces\n\n\nAbstract\nThe so-called spaces wit
h the Riemannian curvature-dimension condition (RCD spaces for short) are
metric measure spaces which are non-necessarily smooth but admit a notion
of "Ricci curvature bounded below and dimension bounded above". These aris
e naturally as Gromov-Hausdorff limits of Riemannian manifolds with these
conditions and\, in contrast to manifolds\, RCD spaces may have topologica
l or metric singularities. Nevertheless\, several properties and results f
rom Riemannian geometry can be extended to this non-smooth setting. In thi
s talk I will present recent work\, joint with Guido de Philippis\, in whi
ch we show that the gradients of harmonic functions vanish at the singular
points of the space. I will mention two consequences of this result on sm
ooth manifolds: it implies that there does not exist an a priori estimate
on the modulus of continuity of the gradient of harmonic functions dependi
ng only on lower bounds of the sectional curvature and that there is no a
priori Calderón-Zygmund inequality for the Laplacian with bounds that dep
end only on lower bounds of the sectional curvature.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semyon Dyatlov (MIT)
DTSTART:20210521T170000Z
DTEND:20210521T174500Z
DTSTAMP:20260422T185127Z
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 function
of its geodesic flow is defined for as a convergent product over the perio
ds of primitive closed geodesics and extends meromorphically to the entire
complex plane. If is hyperbolic (i.e. has sectional curvature )\, then th
e order of vanishing of at can be expressed in terms of the Betti numbers
. In particular\, Fried proved in 1986 that when is a hyperbolic 3-manifol
d\, I will present a recent result joint with Mihajlo Ceki\\'c\, Benjamin
K\\"uster\, and Gabriel Paternain: when and is a generic perturbation of t
he hyperbolic metric\, the order of vanishing of the Ruelle zeta function
jumps\, more precisely This is in contrast with dimension~2 where for all
negatively curved metrics. The proof uses the microlocal approach of expre
ssing as an alternating sum of the dimensions of the spaces of generalized
resonant Pollicott--Ruelle currents and obtains a detailed picture of the
se spaces both in the hyperbolic case and for its perturbations.\n
LOCATION:https://researchseminars.org/talk/CMO_21w5222/12/
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