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BEGIN:VEVENT
SUMMARY:Martin Vogel (IRMA\, Université de Strasbourg)
DTSTART;VALUE=DATE-TIME:20210920T160000Z
DTEND;VALUE=DATE-TIME:20210920T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/1
DESCRIPTION:Title: Spectral asymptotics of noisy non-selfadjoint operator
s\nby Martin Vogel (IRMA\, Université de Strasbourg) as part of CRM-S
pectral geometry in the clouds\n\n\nAbstract\nThe spectral theory of non-s
elfadjoint operators is an old and highly developed subject. Yet it still
poses many new challenges crucial for the understanding of modern problem
s such as scattering systems\, open or damped quantum systems\, the analys
is of the stability of solutions to non-linear PDEs\, and many more. The
lack of powerful tools readily available for their selfadjoint counterpart
s\, such a general spectral theorem or variational methods\, makes the ana
lysis of the spectra of non-selfadjoint operators a subtle and highly vari
ed subject. One fundamental issue of non-selfadjoint operators is their i
ntrinsic sensitivity to perturbations\, indeed even small perturbations ca
n change the spectrum dramatically. This spectral instability\, also call
ed pseudospectral effect\, was initially considered a drawback as it can b
e at the origin of severe numerical errors. However\, recent works in sem
iclassical analysis and random matrix theory have shown that this pseudosp
ectral effect also leads to new and beautiful results concerning the spect
ral distribution and eigenvector localization of non-selfadjoint operators
with small random perturbations. In this talk\, I will discuss recent re
sults and some fundamental techniques involved in the analysis. The talk
is partly based on joint work with Anirban Basak\, St´ephane Nonnenmacher
\, Johannes Sj¨ostrand and Ofer Zeitouni\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Rivière (Université de Nantes)
DTSTART;VALUE=DATE-TIME:20210927T160000Z
DTEND;VALUE=DATE-TIME:20210927T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/2
DESCRIPTION:Title: Poincaré series and linking of Legendrian knots\n
by Gabriel Rivière (Université de Nantes) as part of CRM-Spectral geomet
ry in the clouds\n\n\nAbstract\nOn a compact surface of variable negative
curvature\, I will explain that the Poincar´e series associated to the ge
odesic arcs joining two given points has a meromorphic continuation to the
whole complex plane. This is achieved by using the spectral properties o
f the geodesic flow. Moreover\, the value of Poincar´e series value at 0
is rationnal in that case and it can be expressed in terms of the genus o
f the surface by interpreting it in terms of the linking of two Legendrian
knots. If time permits\, I will explain how this result extends when one
considers geodesic arcs orthogonal to two fixed closed geodesics. This i
s a joint work with N.V. Dang.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Charron (Technion)
DTSTART;VALUE=DATE-TIME:20211004T160000Z
DTEND;VALUE=DATE-TIME:20211004T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/3
DESCRIPTION:Title: Pleijel's theorem for Schrödinger operators\nby P
hilippe Charron (Technion) as part of CRM-Spectral geometry in the clouds\
n\n\nAbstract\nWe will discuss some recent results regarding the number of
nodal domains of Laplace and Schr¨odinger operators. Improving on Coura
nt’s seminal work\, Pleijel’s original proof in 1956 was only for doma
ins in R 2 with Dirichlet boundary conditions\, but it was later generaliz
ed to manifolds (Peetre and B´erard-Meyer) with Dirichlet boundary condit
ions\, then to planar domains with Neumann Boundary conditions (Polterovic
h\, L´ena)\, but also to the quantum harmonic oscillator (C.) and to Schr
¨odinger operators with radial potentials (C. - Helffer - Hoffmann-Osten
hof). In this recent work\, we proved Pleijel’s asymptotic upper bound
for a much larger class of Schr¨odinger operators which are not necessari
ly radial. In this talk\, I will explain the problems that arise from stu
dying Schr¨odinger operators as well as the successive improvements in th
e methods that led to the current results.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Stern (University of Chicago)
DTSTART;VALUE=DATE-TIME:20211018T150000Z
DTEND;VALUE=DATE-TIME:20211018T160000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/4
DESCRIPTION:Title: Steklov-maximizing metrics on surfaces with many bound
ary components\nby Daniel Stern (University of Chicago) as part of CRM
-Spectral geometry in the clouds\n\n\nAbstract\nJust over a decade ago\, F
raser and Schoen initiated the study of metrics maximizing the first Stekl
ov eigenvalue among all metrics of fixed boundary length on a given surfac
e with boundary. Drawing inspiration from the maximization problem for La
place eigenvalues on closed surfaces--where maximizing metrics are induced
by minimal immersions into spheres--they showed that Steklov-maximizing m
etrics are induced by free boundary minimal immersions into Euclidean ball
s\, and laid the groundwork for an existence theory (recently completed by
important work of Matthiesen-Petrides). In this talk\, I'll describe joi
nt work with Mikhail Karpukhin\, characterizing the limiting behavior of t
hese metrics on surfaces of fixed genus g and k boundary components as k b
ecomes large. In particular\, I'll explain why the associated free bounda
ry minimal surfaces converge to the closed minimal surface of genus g in t
he sphere given by maximizing the first Laplace eigenvalue\, with areas co
nverging at a rate of (log k)/k.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Blomer (Universität Bonn)
DTSTART;VALUE=DATE-TIME:20211025T160000Z
DTEND;VALUE=DATE-TIME:20211025T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/5
DESCRIPTION:Title: Eigenvalue statistics of flat tori\nby Valentin Bl
omer (Universität Bonn) as part of CRM-Spectral geometry in the clouds\n\
n\nAbstract\nThe Berry Tabor conjecture predicts that the local statistics
of eigenvalues of a regular system is Poissonian\, at least in generic ca
ses. In this talk\, I consider the special case of flat tori which has th
e attractive feature that arithmetic tools become available. I will expla
in some ideas and methods from analytic number theory that shed light on t
his question\, in particular with respect to small gaps\, large gaps and t
riple correlation. This covers joint papers with Aistleitner\, Bourgain\,
Radziwill\, Rudnick.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Rohleder (Stockholms universitet)
DTSTART;VALUE=DATE-TIME:20211101T160000Z
DTEND;VALUE=DATE-TIME:20211101T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/6
DESCRIPTION:by Jonathan Rohleder (Stockholms universitet) as part of CRM-S
pectral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabine Boegli (Durham University)
DTSTART;VALUE=DATE-TIME:20211108T170000Z
DTEND;VALUE=DATE-TIME:20211108T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/7
DESCRIPTION:Title: On the discrete eigenvalues of Schrödinger operators
with complex potentials\nby Sabine Boegli (Durham University) as part
of CRM-Spectral geometry in the clouds\n\n\nAbstract\nIn this talk I shall
present constructions of Schr¨odinger operators with complexvalued poten
tials whose spectra exhibit interesting properties. One example shows tha
t for sufficiently large p\, namely p > (d + 1)/2 where d is the dimension
\, the discrete eigenvalues need not be bounded by the L p norm of the pot
ential. This is a counterexample to the Laptev–Safronov conjecture (Com
m. Math. Phys. 2009). Another construction proves optimality (in some
sense) of generalisations of Lieb–Thirring inequalities to the nonselfad
joint case - thus giving us information about the accumulation rate of the
discrete eigenvalues to the essential spectrum. This talk is based on jo
int works with Jean-Claude Cuenin and Frantisek Stampach.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Sharp (University of Leeds)
DTSTART;VALUE=DATE-TIME:20211115T170000Z
DTEND;VALUE=DATE-TIME:20211115T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/8
DESCRIPTION:by Ben Sharp (University of Leeds) as part of CRM-Spectral geo
metry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART;VALUE=DATE-TIME:20211122T170000Z
DTEND;VALUE=DATE-TIME:20211122T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/9
DESCRIPTION:Title: The maximal spectral gap of a hyperbolic surface\n
by Michael Magee (Durham University) as part of CRM-Spectral geometry in t
he clouds\n\n\nAbstract\nA hyperbolic surface is a surface with metric of
constant curvature -1. The spectral gap between the first two eigenvalues
of the Laplacian on a closed hyperbolic surface contains a good deal of i
nformation about the surface\, including its connectivity\, dynamical prop
erties of its geodesic flow\, and error terms in geodesic counting problem
s. For arithmetic hyperbolic surfaces the spectral gap is also the subjec
t of one of the biggest open problems in automorphic forms: Selberg’s ei
genvalue conjecture. It was an open problem from the 1970s whether there
exist a sequence of closed hyperbolic surfaces with genera tending to infi
nity and spectral gap tending to 1/4. (The value 1/4 here is the asymptot
ically optimal one.) Recently we proved that this is indeed possible. I
’ll discuss the very interesting background of this problem in detail as
well as some ideas of the proof. This is joint work with Will Hide.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Sher (DePaul University)
DTSTART;VALUE=DATE-TIME:20211129T170000Z
DTEND;VALUE=DATE-TIME:20211129T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/10
DESCRIPTION:Title: Nodal counts for the Dirichlet-to-Neumann operator\nby David Sher (DePaul University) as part of CRM-Spectral geometry in t
he clouds\n\n\nAbstract\nNodal sets of Steklov eigenfunctions on manifolds
with boundary have been extensively studied in recent years. Somewhat le
ss well understood are the nodal sets of their restrictions to the boundar
y\, that is\, the eigenfunctions of the Dirichlet-to-Neumann operator. In
particular\, little is known about nodal counts. In this talk we explore
this problem and prove an asymptotic version of Courant’s nodal domain
theorem for Dirichlet-to-Neumann eigenfunctions. This is joint work with
Asma Hassannezhad (Bristol).\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Claude Cuenin (Loughborough University)
DTSTART;VALUE=DATE-TIME:20211206T170000Z
DTEND;VALUE=DATE-TIME:20211206T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/11
DESCRIPTION:Title: Schrödinger operators with complex potentials: Beyon
d the Laptev-Safronov conjecture\nby Jean-Claude Cuenin (Loughborough
University) as part of CRM-Spectral geometry in the clouds\n\n\nAbstract\n
I will report on recent progress concerning eigenvalues of Schr¨odinger o
perators with complex potentials. This talk can be seen as a continuation
of the recent talk by Sabine B¨ogli (Durham) in the same seminar series\
, where a counterexample to the Laptev-Safronov conjecture was presented.
I will explain how techniques from harmonic analysis\, particularly those
related to Fourier restriction theory\, can be used to prove upper and lo
wer bounds. Then I will present new results that show that in some cases
one can go beyond the threshold of the counterexample.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Chaubet (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20211213T170000Z
DTEND;VALUE=DATE-TIME:20211213T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/12
DESCRIPTION:Title: Closed geodesics with prescribed intersection numbers
\nby Yann Chaubet (Université Paris-Saclay) as part of CRM-Spectral g
eometry in the clouds\n\n\nAbstract\nOn a closed negatively curved surface
\, Margulis gave the asymptotic growth of the number of closed geodesics o
f bounded length\, when the bound goes to infinity. In this talk\, I will
present a similar asymptotic result for closed geodesics for which certai
n intersection numbers — with a given family of pairwise disjoint simple
closed geodesics — are prescribed. This result is obtained by introduc
ing a dynamical scattering operator related to the surface (with boundary)
obtained by cutting our original surface along the simple curves\, and by
proving a trace formula.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Berkolaiko (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20220117T170000Z
DTEND;VALUE=DATE-TIME:20220117T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/13
DESCRIPTION:by Gregory Berkolaiko (Texas A&M University) as part of CRM-Sp
ectral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Berkolaiko (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20220124T170000Z
DTEND;VALUE=DATE-TIME:20220124T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/14
DESCRIPTION:Title: Towards Morse theory of dispersion relations\nby
Gregory Berkolaiko (Texas A&M University) as part of CRM-Spectral geometry
in the clouds\n\n\nAbstract\nThe question of optimizing an eigenvalue of
a family of self-adjoint operators that depends on a set of parameters ari
ses in diverse areas of mathematical physics. Among the particular motiva
tions for this talk are the FloquetBloch decomposition of the Schroedinger
operator on a periodic structure\, nodal count statistics of eigenfunctio
ns of quantum graphs\, and the minimal spectral partitions of domains and
graphs. In each of these problems one seeks to identify and/or count the
critical points of the eigenvalue with a given label (say\, the third lowe
st) over the parameter space which is often known and simple\, such as a t
orus. Classical Morse theory is a set of tools connecting the number of c
ritical points of a smooth function on a manifold to the topological invar
iants of this manifold. However\, the eigenvalues are not smooth due to p
resence of eigenvalue multiplicities or ”diabolical points”. We recti
fy this problem for eigenvalues of generic families of finite-dimensional
operators. The correct ”Morse indices” of the problematic diabolical
points turn out to be universal: they depend only on the total multiplicit
y at the diabolical point and on the relative position of the eigenvalue o
f interest in the eigenvalue group. Based on a joint work with I.Zelenko.
\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Savo (Sapienza University of Rome)
DTSTART;VALUE=DATE-TIME:20220131T170000Z
DTEND;VALUE=DATE-TIME:20220131T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/15
DESCRIPTION:Title: Isoperimetric inequalities for the lowest Aharonov-Bo
hm eigenvalue of the Neumann and Steklov problems\nby Alessandro Savo
(Sapienza University of Rome) as part of CRM-Spectral geometry in the clou
ds\n\n\nAbstract\nWe discuss isoperimetric inequalities for the magnetic L
aplacian on a bounded domain Ω endowed with an Aharonov-Bohm potential A
with pole at a fixed point x0 ∈ Ω. Since A is harmonic on Ω \\ {x0
}\, the magnetic field vanishes\; the spectrum for the Neumann condition (
or for the Steklov problem) reduces to that of the usual non-magnetic Lapl
acian\, but only when the flux of the potential A around the pole is an in
teger. When the flux is not an integer the lowest eigenvalue is actually
positive\, and the scope of the talk is to show how to generalize the clas
sical inequalities of Sz¨ego-Weinberger\, Brock and Weinstock to the lowe
st eigenvalue of this particular magnetic operator\, the model domain bein
g a disk with the pole at its center. We consider more generally domains
in the plane endowed with a rotationally invariant metric (which include t
he spherical and the hyperbolic case).\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Ferraresso (Cardiff University)
DTSTART;VALUE=DATE-TIME:20220207T170000Z
DTEND;VALUE=DATE-TIME:20220207T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/16
DESCRIPTION:Title: Neumann and intermediate biharmonic eigenvalue proble
ms on sigularly perturbed domains\nby Francesco Ferraresso (Cardiff Un
iversity) as part of CRM-Spectral geometry in the clouds\n\n\nAbstract\nSe
e the abstract here: https://archimede.mat.ulaval.ca/agirouard/SpectralClo
uds/2022/February7/February7.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fortier Bourque (Université de Montréal)
DTSTART;VALUE=DATE-TIME:20220214T170000Z
DTEND;VALUE=DATE-TIME:20220214T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/17
DESCRIPTION:Title: The multiplicity of λ 1 in genus 3\nby Maxime
Fortier Bourque (Université de Montréal) as part of CRM-Spectral geometr
y in the clouds\n\n\nAbstract\nSee the abstract here: https://archimede.ma
t.ulaval.ca/agirouard/SpectralClouds/2022/February14/February14.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malo Jézéquel (MIT)
DTSTART;VALUE=DATE-TIME:20220221T170000Z
DTEND;VALUE=DATE-TIME:20220221T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/18
DESCRIPTION:by Malo Jézéquel (MIT) as part of CRM-Spectral geometry in t
he clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Lucardesi (IECL)
DTSTART;VALUE=DATE-TIME:20220228T170000Z
DTEND;VALUE=DATE-TIME:20220228T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/19
DESCRIPTION:Title: On the maximization of the first (non trivial) Neuman
n eigenvalue of the Laplacian under perimeter constraint\nby Ilaria Lu
cardesi (IECL) as part of CRM-Spectral geometry in the clouds\n\n\nAbstrac
t\nIn this talk I will present some recent results obtained in collaborati
on with A. Henrot and A. Lemenant (both in Nancy\, France)\, on the maxi
mization of the first (non trivial) Neumann eigenvalue\, under perimeter c
onstraint\, in dimension 2. Without any further assumption\, the problem
is trivial\, since the supremum is +∞. On the other hand\, restricting
to the class of convex domains\, the problem becomes interesting: the maxi
mum exists\, but neither its value nor the optimal shapes are known. In 2
009 R.S. Laugesen and B.A. Siudeja conjectured that the maximum among co
nvex sets should be attained at squares and equilateral triangles. We pro
ve that the conjecture is true for convex planar domains having two axes o
f symmetry.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nelia Charalambous (University of Cyprus)
DTSTART;VALUE=DATE-TIME:20220307T170000Z
DTEND;VALUE=DATE-TIME:20220307T180000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/20
DESCRIPTION:by Nelia Charalambous (University of Cyprus) as part of CRM-Sp
ectral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Freitas (University of Lisbon)
DTSTART;VALUE=DATE-TIME:20220314T160000Z
DTEND;VALUE=DATE-TIME:20220314T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/21
DESCRIPTION:by Pedro Freitas (University of Lisbon) as part of CRM-Spectra
l geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Young researchers in spectral geometry IV
DTSTART;VALUE=DATE-TIME:20220321T160000Z
DTEND;VALUE=DATE-TIME:20220321T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/22
DESCRIPTION:Title: Young researchers in spectral geometry IV\nby You
ng researchers in spectral geometry IV as part of CRM-Spectral geometry in
the clouds\n\n\nAbstract\n(1/3) Title: Convexity Properties for Harmonic
Functions on Riemannian Manifolds \n\nAbstract: In the 70’s Almgren noti
ced that for a harmonic real-valued function defined on a ball\, its L 2 -
norm over a sub-sphere will have an increasing logarithmic derivative with
respect to the radius of mentioned sphere. We examined similar integrals
over a more general class of parameterized surfaces by studying harmonic
functions defined on compact subdomains of Riemannian manifolds. The inte
grals over spheres are also generalized to level sets of a given function
satisfying certain conditions. If we consider the L 2 norms over these le
vel sets parametrized by a generalization of the radius\, we again reprodu
ce Almgren’s convexity property. We will sketch the proof of this resul
t and illustrate the usefulness of the convexity result by examining some
explicit parameterized families of surfaces\, e.g. geodesic spheres and e
llipses. \n\n(2/3) Title: Steklov conformally extremal metrics in higher
dimensions \n\nAbstract: Steklov extremal metrics on surfaces have been m
uch studied due to their connection to free-boundary minimal surfaces foun
d by Fraser and Schoen. In this talk\, I will present a characterization
of higher dimensional Steklov conformally extremal metrics\, highlighting
its similarities with the same problem for Laplace eigenvalues. To this e
nd\, I will answer the question of which normalization to use and show how
the Steklov problem with boundary density appears natural in this context
. This is joint work with Mikhail Karpukhin. \n\n(3/3) Title: Many noda
l domains in random regular graphs \n\nAbstract: If we partition a graph a
ccording to the positive and negative components of an eigenvector of the
adjacency matrix\, the resulting connected subcomponents are called nodal
domains. Examining the structure of nodal domains has been used for more
than 150 years to deduce properties of eigenfunctions. Dekel\, Lee\, and
Linial observed that according to simulations\, most eigenvectors of the a
djacency matrix of random regular graphs have many nodal domains\, unlike
dense Erd˝os-R´enyi graphs. In this talk\, we show that for the most ne
gative eigenvalues of the adjacency matrix of a random regular graph\, the
re is an almost linear number of nodal domains. Joint work with Shirshend
u Ganguly\, Sidhanth Mohanty\, and Nikhil Srivastava.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Cherdantsev (Cardiff University)
DTSTART;VALUE=DATE-TIME:20220328T160000Z
DTEND;VALUE=DATE-TIME:20220328T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/23
DESCRIPTION:by Mikhail Cherdantsev (Cardiff University) as part of CRM-Spe
ctral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Colbois (Université de Neuchâtel)
DTSTART;VALUE=DATE-TIME:20220404T160000Z
DTEND;VALUE=DATE-TIME:20220404T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/24
DESCRIPTION:Title: Upper bounds for Steklov eigenvalues\nby Bruno Co
lbois (Université de Neuchâtel) as part of CRM-Spectral geometry in the
clouds\n\n\nAbstract\nI will explain two upper bounds for the Steklov eige
nvalues of a compact Riemannian manifold with boundary. The first is in t
erms of the extrinsic diameters of the boundary\, its injectivity radius a
nd the volume of the manifold. By applying these bounds to cylinders over
closed manifold\, we obtain new bounds for eigenvalues of the Laplace ope
rator on closed manifolds\, in the spirit of Berger–Croke. The second i
nvolves the volume of the manifold and of its boundary\, as well as packin
g and volume growth constants of the boundary and its distortion. I will
take time to give examples in order to explain why the quantities appearin
g in the inequalities are necessary. This is a joint work with Alexandre
Girouard.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Lagacé (King's College London)
DTSTART;VALUE=DATE-TIME:20220411T160000Z
DTEND;VALUE=DATE-TIME:20220411T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/25
DESCRIPTION:Title: Variations on the Weyl law for the Steklov problem on
surfaces\nby Jean Lagacé (King's College London) as part of CRM-Spec
tral geometry in the clouds\n\n\nAbstract\nSee abstract here: https://arch
imede.mat.ulaval.ca/agirouard/SpectralClouds/2022/April11/April11.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Karpukhin and Daniel Stern (Caltech and University of Chic
ago)
DTSTART;VALUE=DATE-TIME:20220425T160000Z
DTEND;VALUE=DATE-TIME:20220425T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/27
DESCRIPTION:Title: GEMSTONE mini-course: Harmonic maps\, minimal surface
s\, and shape optimization in spectral geometry\nby Mikhail Karpukhin
and Daniel Stern (Caltech and University of Chicago) as part of CRM-Spectr
al geometry in the clouds\n\n\nAbstract\nLecture 1\nApril 25 \nIntroductio
n to eigenvalue optimisation problems for surfaces. Hersch's theorem: roun
d metric on the sphere maximizes the first eigenvalue. Li-Yau's conformal
volume with an application to the sharp eigenvalue bounds on the projectiv
e plane.\n\nLecture 2\nApril 27\nMin-max theory for the energy of sphere-v
alue valued maps. Regularity of conformally maximizing metrics.\n\nLecture
3\nApril 29 \nStability of maximizing metrics. Applications to the optimi
zation of Steklov eigenvalues on surfaces with many boundary components.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Freitas (University of Lisbon)
DTSTART;VALUE=DATE-TIME:20220502T160000Z
DTEND;VALUE=DATE-TIME:20220502T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/28
DESCRIPTION:Title: Pólya-type inequalities on spheres and hemispheres\nby Pedro Freitas (University of Lisbon) as part of CRM-Spectral geomet
ry in the clouds\n\n\nAbstract\nWe consider the spectra of (round) spheres
and hemispheres with the aim of characterising which eigenvalues satisfy
P´olya’s conjecture and which do not. We then determine correction ter
ms to the first term in the Weyl asymptotics allowing us to provide sharp.
\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorin Bucur (Université de Savoie)
DTSTART;VALUE=DATE-TIME:20220523T160000Z
DTEND;VALUE=DATE-TIME:20220523T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/29
DESCRIPTION:Title: Maximization of Neumann eigenvalues\nby Dorin Buc
ur (Université de Savoie) as part of CRM-Spectral geometry in the clouds\
n\n\nAbstract\nAbstract here: https://archimede.mat.ulaval.ca/agirouard/Sp
ectralClouds/2022/May23/May23.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Petrides (Institut de mathématiques de Jussieu)
DTSTART;VALUE=DATE-TIME:20220530T160000Z
DTEND;VALUE=DATE-TIME:20220530T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/30
DESCRIPTION:Title: Minimizing combinations of Laplace eigenvalues and ap
plications\nby Romain Petrides (Institut de mathématiques de Jussieu)
as part of CRM-Spectral geometry in the clouds\n\n\nAbstract\nWe give a v
ariational method for existence and regularity of metrics which minimize c
ombinations of eigenvalues of the Laplacian among metrics of unit area on
a surface. We show that there are minimal immersions into ellipsoids para
metrized by eigenvalues\, such that the coordinate functions are eigenfunc
tions with respect to the minimal metrics. As one of the applications\, w
e explain a new method to construct non-planar minimal spheres into 3d-ell
ipsoids after Haslhofer-Ketover and Bettiol-Piccione.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaoyang Huang (Courant Institute)
DTSTART;VALUE=DATE-TIME:20220606T160000Z
DTEND;VALUE=DATE-TIME:20220606T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/31
DESCRIPTION:Title: Extreme eigenvalues of random d -regular graphs\
nby Jiaoyang Huang (Courant Institute) as part of CRM-Spectral geometry in
the clouds\n\n\nAbstract\nAbstract here: https://archimede.mat.ulaval.ca/
agirouard/SpectralClouds/2022/June6/June6.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Kriventsov (Rutgers University)
DTSTART;VALUE=DATE-TIME:20220613T160000Z
DTEND;VALUE=DATE-TIME:20220613T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/32
DESCRIPTION:by Dennis Kriventsov (Rutgers University) as part of CRM-Spect
ral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220620T160000Z
DTEND;VALUE=DATE-TIME:20220620T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/33
DESCRIPTION:Title: Optimal transport and quantitative geometric inequali
ties\nby Andrea Mondino (University of Oxford) as part of CRM-Spectral
geometry in the clouds\n\n\nAbstract\nAbstract here: https://archimede.ma
t.ulaval.ca/agirouard/SpectralClouds/2022/June20/June20.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadine Große (Universität Freiburg)
DTSTART;VALUE=DATE-TIME:20220704T160000Z
DTEND;VALUE=DATE-TIME:20220704T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/34
DESCRIPTION:Title: Boundary value problems on domain with cusps\nby
Nadine Große (Universität Freiburg) as part of CRM-Spectral geometry in
the clouds\n\n\nAbstract\nWe consider boundary value problems of the Lapla
cian with Dirichlet (or mixed) boundary conditions on domains with singula
rities. In two dimensions these singularities include also cusps. Our ap
proach is by blowing up the singularities via a conformal change to transl
ate the boundary problem to one on a noncompact manifold with boundary tha
t is of bounded geometry and of finite width. This gives a natural geomet
ric interpretation in the appearing weights and additional conditions need
ed to obtain well-posedness results. This is joint work with Bernd Ammann
(Regensburg) and Victor Nistor (Universite de Lorraine).\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Rupflin (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220711T160000Z
DTEND;VALUE=DATE-TIME:20220711T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/35
DESCRIPTION:by Melanie Rupflin (University of Oxford) as part of CRM-Spect
ral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polyxeni Spilioti (Aarhus University)
DTSTART;VALUE=DATE-TIME:20220725T160000Z
DTEND;VALUE=DATE-TIME:20220725T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/37
DESCRIPTION:by Polyxeni Spilioti (Aarhus University) as part of CRM-Spectr
al geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nunzia Gavitone (Università degli Studi di Napoli Federico II)
DTSTART;VALUE=DATE-TIME:20220627T160000Z
DTEND;VALUE=DATE-TIME:20220627T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/38
DESCRIPTION:by Nunzia Gavitone (Università degli Studi di Napoli Federico
II) as part of CRM-Spectral geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Ingremau (Université de Nice Sophia-Antipolis)
DTSTART;VALUE=DATE-TIME:20220912T160000Z
DTEND;VALUE=DATE-TIME:20220912T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/39
DESCRIPTION:Title: How Lagrangian states evolve into random waves\nb
y Maxime Ingremau (Université de Nice Sophia-Antipolis) as part of CRM-Sp
ectral geometry in the clouds\n\n\nAbstract\nIn 1977\, Berry conjectured t
hat eigenfunctions of the Laplacian on manifolds of negative curvature beh
ave\, in the high-energy (or semiclassical) limit\, as a random superposit
ion of plane waves. This conjecture\, central in quantum chaos\, is still
completely open. In this talk\, we will consider a much simpler situatio
n. On a manifold of negative curvature\, we will consider a Lagrangian st
ate associated to a generic phase. We show that\, when evolved during a l
ong time by the Schr¨odinger equation\, these functions do behave\, in th
e semiclassical limit\, as a random superposition of plane waves. This ta
lk is based on joint work with Alejandro Rivera\, and on work in progress
with Martin Vogel.\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semyon Dyatlov (Massachusetts Institute of Technology)
DTSTART;VALUE=DATE-TIME:20220926T160000Z
DTEND;VALUE=DATE-TIME:20220926T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/40
DESCRIPTION:Title: Ruelle zeta at zero for nearly hyperbolic 3-manifolds
\nby Semyon Dyatlov (Massachusetts Institute of Technology) as part of
CRM-Spectral geometry in the clouds\n\n\nAbstract\nAbstract here: https:/
/archimede.mat.ulaval.ca/agirouard/SpectralClouds/2022/Septembre26/Septemb
re26.pdf\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bram Petri (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20221003T160000Z
DTEND;VALUE=DATE-TIME:20221003T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/41
DESCRIPTION:Title: How do you efficiently chop a hyperbolic surface in t
wo?\nby Bram Petri (Sorbonne Université) as part of CRM-Spectral geom
etry in the clouds\n\n\nAbstract\nThe Cheeger constant of a Riemannian man
ifold measures how hard it is to cut out a large part of the manifold. If
the Cheeger constant of a manifold is large\, then\, through Cheeger’s
inequality\, this implies that Laplacian of the manifold has a large spect
ral gap. In this talk\, I will discuss how large Cheeger constants of hyp
erbolic surfaces can be. In particular\, I will discuss recent joint work
with Thomas Budzinski and Nicolas Curien in which we prove that the Cheeg
er constant of a closed hyperbolic surface of large genus cannot be much l
arger than 2/pi (approximately 0.6366). This in particular proves that th
ere is a uniform gap between the maximal possible Cheeger constant of a hy
perbolic surface of large enough genus and the Cheeger constant of the hyp
erbolic plane (which is equal to 1).\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mostafa Sabri (University Abu Dhabi)
DTSTART;VALUE=DATE-TIME:20221010T160000Z
DTEND;VALUE=DATE-TIME:20221010T170000Z
DTSTAMP;VALUE=DATE-TIME:20240423T120013Z
UID:Spectralgeometryintheclouds/42
DESCRIPTION:by Mostafa Sabri (University Abu Dhabi) as part of CRM-Spectra
l geometry in the clouds\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Spectralgeometryintheclouds/42/
END:VEVENT
END:VCALENDAR