BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Martin Vogel (IRMA\, Université de Strasbourg)
DTSTART:20210920T160000Z
DTEND:20210920T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/1
DESCRIPTION:Title: Spectral asymptotics of noisy non-selfadjoint o
perators\nby Martin Vogel (IRMA\, Université de Strasbourg) as part o
f CRM-Spectral geometry in the clouds\n\n\nAbstract\nThe spectral theory o
f non-selfadjoint operators is an old and highly developed subject. Yet i
t still poses many new challenges crucial for the understanding of modern
problems such as scattering systems\, open or damped quantum systems\, the
analysis of the stability of solutions to non-linear PDEs\, and many more
. The lack of powerful tools readily available for their selfadjoint coun
terparts\, such a general spectral theorem or variational methods\, makes
the analysis of the spectra of non-selfadjoint operators a subtle and high
ly varied subject. One fundamental issue of non-selfadjoint operators is
their intrinsic sensitivity to perturbations\, indeed even small perturbat
ions can change the spectrum dramatically. This spectral instability\, al
so called pseudospectral effect\, was initially considered a drawback as i
t can be at the origin of severe numerical errors. However\, recent works
in semiclassical analysis and random matrix theory have shown that this p
seudospectral effect also leads to new and beautiful results concerning th
e spectral distribution and eigenvector localization of non-selfadjoint op
erators with small random perturbations. In this talk\, I will discuss re
cent results and some fundamental techniques involved in the analysis. Th
e talk is partly based on joint work with Anirban Basak\, St´ephane Nonne
nmacher\, Johannes Sj¨ostrand and Ofer Zeitouni\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriel Rivière (Université de Nantes)
DTSTART:20210927T160000Z
DTEND:20210927T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/2
DESCRIPTION:Title: Poincaré series and linking of Legendrian knot
s\nby Gabriel Rivière (Université de Nantes) as part of CRM-Spectral
geometry in the clouds\n\n\nAbstract\nOn a compact surface of variable ne
gative curvature\, I will explain that the Poincar´e series associated to
the geodesic arcs joining two given points has a meromorphic continuation
to the whole complex plane. This is achieved by using the spectral prope
rties of the geodesic flow. Moreover\, the value of Poincar´e series val
ue at 0 is rationnal in that case and it can be expressed in terms of the
genus of the surface by interpreting it in terms of the linking of two Leg
endrian knots. If time permits\, I will explain how this result extends w
hen one considers geodesic arcs orthogonal to two fixed closed geodesics.
This is a joint work with N.V. Dang.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philippe Charron (Technion)
DTSTART:20211004T160000Z
DTEND:20211004T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/3
DESCRIPTION:Title: Pleijel's theorem for Schrödinger operators\nby Philippe Charron (Technion) as part of CRM-Spectral geometry in the
clouds\n\n\nAbstract\nWe will discuss some recent results regarding the nu
mber of nodal domains of Laplace and Schr¨odinger operators. Improving o
n Courant’s seminal work\, Pleijel’s original proof in 1956 was only f
or domains in R 2 with Dirichlet boundary conditions\, but it was later ge
neralized to manifolds (Peetre and B´erard-Meyer) with Dirichlet boundary
conditions\, then to planar domains with Neumann Boundary conditions (Pol
terovich\, L´ena)\, but also to the quantum harmonic oscillator (C.) and
to Schr¨odinger operators with radial potentials (C. - Helffer - Hoffman
n-Ostenhof). In this recent work\, we proved Pleijel’s asymptotic upper
bound for a much larger class of Schr¨odinger operators which are not ne
cessarily radial. In this talk\, I will explain the problems that arise f
rom studying Schr¨odinger operators as well as the successive improvement
s in the methods that led to the current results.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Stern (University of Chicago)
DTSTART:20211018T150000Z
DTEND:20211018T160000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/4
DESCRIPTION:Title: Steklov-maximizing metrics on surfaces with man
y boundary components\nby Daniel Stern (University of Chicago) as part
of CRM-Spectral geometry in the clouds\n\n\nAbstract\nJust over a decade
ago\, Fraser and Schoen initiated the study of metrics maximizing the firs
t Steklov eigenvalue among all metrics of fixed boundary length on a given
surface with boundary. Drawing inspiration from the maximization problem
for Laplace eigenvalues on closed surfaces--where maximizing metrics are
induced by minimal immersions into spheres--they showed that Steklov-maxim
izing metrics are induced by free boundary minimal immersions into Euclide
an balls\, and laid the groundwork for an existence theory (recently compl
eted by important work of Matthiesen-Petrides). In this talk\, I'll descr
ibe joint work with Mikhail Karpukhin\, characterizing the limiting behavi
or of these metrics on surfaces of fixed genus g and k boundary components
as k becomes large. In particular\, I'll explain why the associated free
boundary minimal surfaces converge to the closed minimal surface of genus
g in the sphere given by maximizing the first Laplace eigenvalue\, with a
reas converging at a rate of (log k)/k.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Blomer (Universität Bonn)
DTSTART:20211025T160000Z
DTEND:20211025T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/5
DESCRIPTION:Title: Eigenvalue statistics of flat tori\nby Vale
ntin Blomer (Universität Bonn) as part of CRM-Spectral geometry in the cl
ouds\n\n\nAbstract\nThe Berry Tabor conjecture predicts that the local sta
tistics of eigenvalues of a regular system is Poissonian\, at least in gen
eric cases. In this talk\, I consider the special case of flat tori which
has the attractive feature that arithmetic tools become available. I wil
l explain some ideas and methods from analytic number theory that shed lig
ht on this question\, in particular with respect to small gaps\, large gap
s and triple correlation. This covers joint papers with Aistleitner\, Bou
rgain\, Radziwill\, Rudnick.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Rohleder (Stockholms universitet)
DTSTART:20211101T160000Z
DTEND:20211101T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sabine Boegli (Durham University)
DTSTART:20211108T170000Z
DTEND:20211108T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/7
DESCRIPTION:Title: On the discrete eigenvalues of Schrödinger ope
rators with complex potentials\nby Sabine Boegli (Durham University) a
s part of CRM-Spectral geometry in the clouds\n\n\nAbstract\nIn this talk
I shall present constructions of Schr¨odinger operators with complexvalue
d potentials whose spectra exhibit interesting properties. One example sh
ows that for sufficiently large p\, namely p > (d + 1)/2 where d is the di
mension\, the discrete eigenvalues need not be bounded by the L p norm of
the potential. This is a counterexample to the Laptev–Safronov conjectu
re (Comm. Math. Phys. 2009). Another construction proves optimality (i
n some sense) of generalisations of Lieb–Thirring inequalities to the no
nselfadjoint case - thus giving us information about the accumulation rate
of the discrete eigenvalues to the essential spectrum. This talk is base
d on joint works with Jean-Claude Cuenin and Frantisek Stampach.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Sharp (University of Leeds)
DTSTART:20211115T170000Z
DTEND:20211115T180000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART:20211122T170000Z
DTEND:20211122T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/9
DESCRIPTION:Title: The maximal spectral gap of a hyperbolic surfac
e\nby Michael Magee (Durham University) as part of CRM-Spectral geomet
ry in the clouds\n\n\nAbstract\nA hyperbolic surface is a surface with met
ric of constant curvature -1. The spectral gap between the first two eige
nvalues of the Laplacian on a closed hyperbolic surface contains a good de
al of information about the surface\, including its connectivity\, dynamic
al properties of its geodesic flow\, and error terms in geodesic counting
problems. For arithmetic hyperbolic surfaces the spectral gap is also the
subject of one of the biggest open problems in automorphic forms: Selberg
’s eigenvalue conjecture. It was an open problem from the 1970s whether
there exist a sequence of closed hyperbolic surfaces with genera tending
to infinity and spectral gap tending to 1/4. (The value 1/4 here is the a
symptotically optimal one.) Recently we proved that this is indeed possibl
e. I’ll discuss the very interesting background of this problem in deta
il as well as some ideas of the proof. This is joint work with Will Hide.
\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Sher (DePaul University)
DTSTART:20211129T170000Z
DTEND:20211129T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/10
DESCRIPTION:Title: Nodal counts for the Dirichlet-to-Neumann oper
ator\nby David Sher (DePaul University) as part of CRM-Spectral geomet
ry in the clouds\n\n\nAbstract\nNodal sets of Steklov eigenfunctions on ma
nifolds with boundary have been extensively studied in recent years. Some
what less well understood are the nodal sets of their restrictions to the
boundary\, that is\, the eigenfunctions of the Dirichlet-to-Neumann operat
or. 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 wor
k with Asma Hassannezhad (Bristol).\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Claude Cuenin (Loughborough University)
DTSTART:20211206T170000Z
DTEND:20211206T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/11
DESCRIPTION:Title: Schrödinger operators with complex potentials
: Beyond the Laptev-Safronov conjecture\nby Jean-Claude Cuenin (Loughb
orough University) as part of CRM-Spectral geometry in the clouds\n\n\nAbs
tract\nI will report on recent progress concerning eigenvalues of Schr¨od
inger operators with complex potentials. This talk can be seen as a conti
nuation of the recent talk by Sabine B¨ogli (Durham) in the same seminar
series\, where a counterexample to the Laptev-Safronov conjecture was pres
ented. I will explain how techniques from harmonic analysis\, particularl
y those related to Fourier restriction theory\, can be used to prove upper
and lower 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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yann Chaubet (Université Paris-Saclay)
DTSTART:20211213T170000Z
DTEND:20211213T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/12
DESCRIPTION:Title: Closed geodesics with prescribed intersection
numbers\nby Yann Chaubet (Université Paris-Saclay) as part of CRM-Spe
ctral geometry in the clouds\n\n\nAbstract\nOn a closed negatively curved
surface\, Margulis gave the asymptotic growth of the number of closed geod
esics of bounded length\, when the bound goes to infinity. In this talk\,
I will present a similar asymptotic result for closed geodesics for which
certain intersection numbers — with a given family of pairwise disjoint
simple closed geodesics — are prescribed. This result is obtained by i
ntroducing a dynamical scattering operator related to the surface (with bo
undary) obtained by cutting our original surface along the simple curves\,
and by proving a trace formula.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Berkolaiko (Texas A&M University)
DTSTART:20220117T170000Z
DTEND:20220117T180000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregory Berkolaiko (Texas A&M University)
DTSTART:20220124T170000Z
DTEND:20220124T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/14
DESCRIPTION:Title: Towards Morse theory of dispersion relations\nby Gregory Berkolaiko (Texas A&M University) as part of CRM-Spectral g
eometry in the clouds\n\n\nAbstract\nThe question of optimizing an eigenva
lue of a family of self-adjoint operators that depends on a set of paramet
ers arises in diverse areas of mathematical physics. Among the particular
motivations for this talk are the FloquetBloch decomposition of the Schro
edinger operator on a periodic structure\, nodal count statistics of eigen
functions of quantum graphs\, and the minimal spectral partitions of domai
ns and graphs. In each of these problems one seeks to identify and/or cou
nt the critical points of the eigenvalue with a given label (say\, the thi
rd lowest) over the parameter space which is often known and simple\, such
as a torus. Classical Morse theory is a set of tools connecting the numb
er of critical points of a smooth function on a manifold to the topologica
l invariants of this manifold. However\, the eigenvalues are not smooth d
ue to presence of eigenvalue multiplicities or ”diabolical points”. W
e rectify this problem for eigenvalues of generic families of finite-dimen
sional operators. The correct ”Morse indices” of the problematic diab
olical points turn out to be universal: they depend only on the total mult
iplicity at the diabolical point and on the relative position of the eigen
value of interest in the eigenvalue group. Based on a joint work with I.Z
elenko.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Savo (Sapienza University of Rome)
DTSTART:20220131T170000Z
DTEND:20220131T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/15
DESCRIPTION:Title: Isoperimetric inequalities for the lowest Ahar
onov-Bohm eigenvalue of the Neumann and Steklov problems\nby Alessandr
o Savo (Sapienza University of Rome) as part of CRM-Spectral geometry in t
he clouds\n\n\nAbstract\nWe discuss isoperimetric inequalities for the mag
netic Laplacian on a bounded domain Ω endowed with an Aharonov-Bohm pote
ntial 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 cond
ition (or for the Steklov problem) reduces to that of the usual non-magnet
ic Laplacian\, but only when the flux of the potential A around the pole i
s an integer. When the flux is not an integer the lowest eigenvalue is ac
tually positive\, and the scope of the talk is to show how to generalize t
he classical inequalities of Sz¨ego-Weinberger\, Brock and Weinstock to t
he lowest eigenvalue of this particular magnetic operator\, the model doma
in being a disk with the pole at its center. We consider more generally d
omains in the plane endowed with a rotationally invariant metric (which in
clude the spherical and the hyperbolic case).\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Ferraresso (Cardiff University)
DTSTART:20220207T170000Z
DTEND:20220207T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/16
DESCRIPTION:Title: Neumann and intermediate biharmonic eigenvalue
problems on sigularly perturbed domains\nby Francesco Ferraresso (Car
diff University) as part of CRM-Spectral geometry in the clouds\n\n\nAbstr
act\nSee the abstract here: https://archimede.mat.ulaval.ca/agirouard/Spec
tralClouds/2022/February7/February7.pdf\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fortier Bourque (Université de Montréal)
DTSTART:20220214T170000Z
DTEND:20220214T180000Z
DTSTAMP:20260404T095207Z
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
geometry in the clouds\n\n\nAbstract\nSee the abstract here: https://archi
mede.mat.ulaval.ca/agirouard/SpectralClouds/2022/February14/February14.pdf
\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malo Jézéquel (MIT)
DTSTART:20220221T170000Z
DTEND:20220221T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/18
DESCRIPTION:by Malo Jézéquel (MIT) as part of CRM-Spectral geometry in t
he clouds\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Lucardesi (IECL)
DTSTART:20220228T170000Z
DTEND:20220228T180000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/19
DESCRIPTION:Title: On the maximization of the first (non trivial)
Neumann eigenvalue of the Laplacian under perimeter constraint\nby Il
aria Lucardesi (IECL) as part of CRM-Spectral geometry in the clouds\n\n\n
Abstract\nIn this talk I will present some recent results obtained in coll
aboration with A. Henrot and A. Lemenant (both in Nancy\, France)\, on t
he maximization of the first (non trivial) Neumann eigenvalue\, under peri
meter constraint\, in dimension 2. Without any further assumption\, the p
roblem is trivial\, since the supremum is +∞. On the other hand\, restr
icting to the class of convex domains\, the problem becomes interesting: t
he maximum exists\, but neither its value nor the optimal shapes are known
. In 2009 R.S. Laugesen and B.A. Siudeja conjectured that the maximum a
mong convex sets should be attained at squares and equilateral triangles.
We prove that the conjecture is true for convex planar domains having two
axes of symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nelia Charalambous (University of Cyprus)
DTSTART:20220307T170000Z
DTEND:20220307T180000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Freitas (University of Lisbon)
DTSTART:20220314T160000Z
DTEND:20220314T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Young researchers in spectral geometry IV
DTSTART:20220321T160000Z
DTEND:20220321T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/22
DESCRIPTION:Title: Young researchers in spectral geometry IV\
nby Young researchers in spectral geometry IV as part of CRM-Spectral geom
etry in the clouds\n\n\nAbstract\n(1/3) Title: Convexity Properties for Ha
rmonic Functions on Riemannian Manifolds \n\nAbstract: In the 70’s Almgr
en noticed that for a harmonic real-valued function defined on a ball\, it
s L 2 -norm over a sub-sphere will have an increasing logarithmic derivati
ve with respect to the radius of mentioned sphere. We examined similar in
tegrals over a more general class of parameterized surfaces by studying ha
rmonic functions defined on compact subdomains of Riemannian manifolds. T
he integrals over spheres are also generalized to level sets of a given fu
nction satisfying certain conditions. If we consider the L 2 norms over t
hese level sets parametrized by a generalization of the radius\, we again
reproduce Almgren’s convexity property. We will sketch the proof of thi
s result and illustrate the usefulness of the convexity result by examinin
g some explicit parameterized families of surfaces\, e.g. geodesic sphere
s and ellipses. \n\n(2/3) Title: Steklov conformally extremal metrics in
higher dimensions \n\nAbstract: Steklov extremal metrics on surfaces have
been much studied due to their connection to free-boundary minimal surfac
es found by Fraser and Schoen. In this talk\, I will present a characteri
zation of higher dimensional Steklov conformally extremal metrics\, highli
ghting its similarities with the same problem for Laplace eigenvalues. To
this end\, I will answer the question of which normalization to use and s
how how the Steklov problem with boundary density appears natural in this
context. This is joint work with Mikhail Karpukhin. \n\n(3/3) Title: Ma
ny nodal domains in random regular graphs \n\nAbstract: If we partition a
graph according 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 fo
r more than 150 years to deduce properties of eigenfunctions. Dekel\, Lee
\, and Linial observed that according to simulations\, most eigenvectors o
f the adjacency 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 negative eigenvalues of the adjacency matrix of a random regular grap
h\, there is an almost linear number of nodal domains. Joint work with Sh
irshendu Ganguly\, Sidhanth Mohanty\, and Nikhil Srivastava.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Cherdantsev (Cardiff University)
DTSTART:20220328T160000Z
DTEND:20220328T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Colbois (Université de Neuchâtel)
DTSTART:20220404T160000Z
DTEND:20220404T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/24
DESCRIPTION:Title: Upper bounds for Steklov eigenvalues\nby B
runo Colbois (Université de Neuchâtel) as part of CRM-Spectral geometry
in the clouds\n\n\nAbstract\nI will explain two upper bounds for the Stekl
ov eigenvalues of a compact Riemannian manifold with boundary. The first
is in terms of the extrinsic diameters of the boundary\, its injectivity r
adius and the volume of the manifold. By applying these bounds to cylinde
rs over closed manifold\, we obtain new bounds for eigenvalues of the Lapl
ace operator on closed manifolds\, in the spirit of Berger–Croke. The s
econd involves the volume of the manifold and of its boundary\, as well as
packing and volume growth constants of the boundary and its distortion.
I will take time to give examples in order to explain why the quantities a
ppearing in the inequalities are necessary. This is a joint work with Ale
xandre Girouard.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Lagacé (King's College London)
DTSTART:20220411T160000Z
DTEND:20220411T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/25
DESCRIPTION:Title: Variations on the Weyl law for the Steklov pro
blem on surfaces\nby Jean Lagacé (King's College London) as part of C
RM-Spectral geometry in the clouds\n\n\nAbstract\nSee abstract here: https
://archimede.mat.ulaval.ca/agirouard/SpectralClouds/2022/April11/April11.p
df\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Karpukhin and Daniel Stern (Caltech and University of Chic
ago)
DTSTART:20220425T160000Z
DTEND:20220425T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/27
DESCRIPTION:Title: GEMSTONE mini-course: Harmonic maps\, minimal
surfaces\, and shape optimization in spectral geometry\nby Mikhail Kar
pukhin and Daniel Stern (Caltech and University of Chicago) as part of CRM
-Spectral geometry in the clouds\n\n\nAbstract\nLecture 1\nApril 25 \nIntr
oduction to eigenvalue optimisation problems for surfaces. Hersch's theore
m: round metric on the sphere maximizes the first eigenvalue. Li-Yau's con
formal volume with an application to the sharp eigenvalue bounds on the pr
ojective plane.\n\nLecture 2\nApril 27\nMin-max theory for the energy of s
phere-value valued maps. Regularity of conformally maximizing metrics.\n\n
Lecture 3\nApril 29 \nStability of maximizing metrics. Applications to the
optimization of Steklov eigenvalues on surfaces with many boundary compon
ents.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Freitas (University of Lisbon)
DTSTART:20220502T160000Z
DTEND:20220502T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/28
DESCRIPTION:Title: Pólya-type inequalities on spheres and hemisp
heres\nby Pedro Freitas (University of Lisbon) as part of CRM-Spectral
geometry in the clouds\n\n\nAbstract\nWe consider the spectra of (round)
spheres and hemispheres with the aim of characterising which eigenvalues s
atisfy P´olya’s conjecture and which do not. We then determine correct
ion terms to the first term in the Weyl asymptotics allowing us to provide
sharp.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dorin Bucur (Université de Savoie)
DTSTART:20220523T160000Z
DTEND:20220523T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/29
DESCRIPTION:Title: Maximization of Neumann eigenvalues\nby Do
rin Bucur (Université de Savoie) as part of CRM-Spectral geometry in the
clouds\n\n\nAbstract\nAbstract here: https://archimede.mat.ulaval.ca/agiro
uard/SpectralClouds/2022/May23/May23.pdf\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romain Petrides (Institut de mathématiques de Jussieu)
DTSTART:20220530T160000Z
DTEND:20220530T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/30
DESCRIPTION:Title: Minimizing combinations of Laplace eigenvalues
and applications\nby Romain Petrides (Institut de mathématiques de J
ussieu) as part of CRM-Spectral geometry in the clouds\n\n\nAbstract\nWe g
ive a variational method for existence and regularity of metrics which min
imize combinations of eigenvalues of the Laplacian among metrics of unit a
rea on a surface. We show that there are minimal immersions into ellipsoi
ds parametrized by eigenvalues\, such that the coordinate functions are ei
genfunctions with respect to the minimal metrics. As one of the applicati
ons\, we explain a new method to construct non-planar minimal spheres into
3d-ellipsoids after Haslhofer-Ketover and Bettiol-Piccione.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiaoyang Huang (Courant Institute)
DTSTART:20220606T160000Z
DTEND:20220606T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/31
DESCRIPTION:Title: Extreme eigenvalues of random d -regular grap
hs\nby Jiaoyang Huang (Courant Institute) as part of CRM-Spectral geom
etry in the clouds\n\n\nAbstract\nAbstract here: https://archimede.mat.ula
val.ca/agirouard/SpectralClouds/2022/June6/June6.pdf\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Kriventsov (Rutgers University)
DTSTART:20220613T160000Z
DTEND:20220613T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART:20220620T160000Z
DTEND:20220620T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/33
DESCRIPTION:Title: Optimal transport and quantitative geometric i
nequalities\nby Andrea Mondino (University of Oxford) as part of CRM-S
pectral geometry in the clouds\n\n\nAbstract\nAbstract here: https://archi
mede.mat.ulaval.ca/agirouard/SpectralClouds/2022/June20/June20.pdf\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadine Große (Universität Freiburg)
DTSTART:20220704T160000Z
DTEND:20220704T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/34
DESCRIPTION:Title: Boundary value problems on domain with cusps\nby Nadine Große (Universität Freiburg) as part of CRM-Spectral geome
try in the clouds\n\n\nAbstract\nWe consider boundary value problems of th
e Laplacian with Dirichlet (or mixed) boundary conditions on domains with
singularities. In two dimensions these singularities include also cusps.
Our approach is by blowing up the singularities via a conformal change to
translate the boundary problem to one on a noncompact manifold with bound
ary that is of bounded geometry and of finite width. This gives a natural
geometric interpretation in the appearing weights and additional conditio
ns needed to obtain well-posedness results. This is joint work with Bernd
Ammann (Regensburg) and Victor Nistor (Universite de Lorraine).\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melanie Rupflin (University of Oxford)
DTSTART:20220711T160000Z
DTEND:20220711T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polyxeni Spilioti (Aarhus University)
DTSTART:20220725T160000Z
DTEND:20220725T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nunzia Gavitone (Università degli Studi di Napoli Federico II)
DTSTART:20220627T160000Z
DTEND:20220627T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Ingremau (Université de Nice Sophia-Antipolis)
DTSTART:20220912T160000Z
DTEND:20220912T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/39
DESCRIPTION:Title: How Lagrangian states evolve into random waves
\nby Maxime Ingremau (Université de Nice Sophia-Antipolis) as part of
CRM-Spectral geometry in the clouds\n\n\nAbstract\nIn 1977\, Berry conjec
tured that eigenfunctions of the Laplacian on manifolds of negative curvat
ure behave\, in the high-energy (or semiclassical) limit\, as a random sup
erposition of plane waves. This conjecture\, central in quantum chaos\, i
s still completely open. In this talk\, we will consider a much simpler s
ituation. On a manifold of negative curvature\, we will consider a Lagran
gian state associated to a generic phase. We show that\, when evolved dur
ing a long time by the Schr¨odinger equation\, these functions do behave\
, in the semiclassical limit\, as a random superposition of plane waves.
This talk is based on joint work with Alejandro Rivera\, and on work in pr
ogress with Martin Vogel.\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semyon Dyatlov (Massachusetts Institute of Technology)
DTSTART:20220926T160000Z
DTEND:20220926T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/40
DESCRIPTION:Title: Ruelle zeta at zero for nearly hyperbolic 3-ma
nifolds\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/
Septembre26.pdf\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bram Petri (Sorbonne Université)
DTSTART:20221003T160000Z
DTEND:20221003T170000Z
DTSTAMP:20260404T095207Z
UID:Spectralgeometryintheclouds/41
DESCRIPTION:Title: How do you efficiently chop a hyperbolic surfa
ce in two?\nby Bram Petri (Sorbonne Université) as part of CRM-Spectr
al geometry in the clouds\n\n\nAbstract\nThe Cheeger constant of a Riemann
ian manifold measures how hard it is to cut out a large part of the manifo
ld. If the Cheeger constant of a manifold is large\, then\, through Cheeg
er’s inequality\, this implies that Laplacian of the manifold has a larg
e spectral gap. In this talk\, I will discuss how large Cheeger constants
of hyperbolic surfaces can be. In particular\, I will discuss recent joi
nt work with Thomas Budzinski and Nicolas Curien in which we prove that th
e Cheeger constant of a closed hyperbolic surface of large genus cannot be
much larger than 2/pi (approximately 0.6366). This in particular proves
that there is a uniform gap between the maximal possible Cheeger constant
of a hyperbolic surface of large enough genus and the Cheeger constant of
the hyperbolic plane (which is equal to 1).\n
LOCATION:https://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mostafa Sabri (University Abu Dhabi)
DTSTART:20221010T160000Z
DTEND:20221010T170000Z
DTSTAMP:20260404T095207Z
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://stable.researchseminars.org/talk/Spectralgeometryintheclo
uds/42/
END:VEVENT
END:VCALENDAR