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BEGIN:VEVENT
SUMMARY:Alexandre Girouard (Université Laval)
DTSTART:20200501T170000Z
DTEND:20200501T174500Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/1
DESCRIPTION:Title: Homogenization of Steklov problems with applications t
o sharp isoperimetric bounds\, part I\nby Alexandre Girouard (Universi
té Laval) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe que
stion to find the best upper bound for the first nonzero Steklov eigenvalu
e of a planar domain goes back to Weinstock\, who proved in 1954 that the
first nonzero perimeter-normalized Steklov eigenvalue of a simply-connecte
d planar domain is 2*pi\, with equality iff the domain is a disk. In a rec
ent joint work with Mikhail Karpukhin and and Jean Lagacé\, we were able
to let go of the simple connectedness assumption. We constructed a family
of domains for which the perimeter-normalized first eigenvalue tends to 8
π. In combination with Kokarev's bound from 2014\, this solves the isoper
imetric problem completely for the first nonzero eigenvalue. The domains a
re obtained by removing small geodesic balls that are asymptotically dense
ly periodically distributed as their radius tends to zero. The goal of thi
s talk will be to survey recent work on homogenisation of the Steklov prob
lem which lead to the above result. On the way we will see that many spect
ral problems can be approximated by Steklov eigenvalues of perforated doma
ins. A surprising consequence is the existence of free boundary minimal su
rfaces immersed in the unit ball by first Steklov eigenfunctions and with
area strictly larger than 2*pi. This talk is based on joint work with Anto
ine Henrot (U. de Lorraine)\, Mikhail Karpukhin (UCI) and Jean Lagacé(UCL
).\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Lagacé (University College London)
DTSTART:20200501T175000Z
DTEND:20200501T183500Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/2
DESCRIPTION:Title: Homogenization of Steklov problems with applications t
o sharp isoperimetric bounds\, part II.\nby Jean Lagacé (University C
ollege London) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nTra
ditionally\, deterministic homogenisation theory uses the periodic structu
re of Euclidean space to describe uniformly distributed perturbations of a
PDE. It has been known for years that it has many applications to shape
optimisation. In this talk\, I will describe how the lack of periodic str
ucture can be overcome to saturate isoperimetric bounds for the Steklov pr
oblem on surfaces. The construction is intrinsic and does not depend on a
ny auxiliary periodic objects or quantities. Using these methods\, we obt
ain the existence of free boundary minimal surfaces in the unit ball with
large area. I will also describe how the intuition we gain from the homog
enisation construction allows us to actually construct some of them\, part
ially verifying a conjecture of Fraser and Li. This talk is based on join
t work with Alexandre Girouard (U. Laval)\, Antoine Henrot (U. de Lorrai
ne) and Mikhail Karpukhin (UCI).\n\nEn ligne-Web: Veuillez communiquer ave
c l'organisateur/Please contat the organizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Zelditch (Northwestern University)
DTSTART:20200507T170000Z
DTEND:20200507T183500Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/3
DESCRIPTION:Title: Spectral asymptotics for stationary spacetimes\nby
Steve Zelditch (Northwestern University) as part of CRM-Montreal analysis
Seminar\n\n\nAbstract\nWe explain how to formulate and prove analogues of
the standard theorems on spectral asymptotics on compact Riemannian manif
olds -- Weyl's law and the Gutzwiller trace formula-- for stationary space
times. As a by-product we prove a semi-classical Weyl law for the Klein-G
ordon equation where the mass is the inverse Planck constant.\n\nSéminair
e en ligne / Web Seminar\nVeuillez communiquer avec l'organisateur pour to
ute question / Please contact the organizer for any questions at: dmitry.j
akobson@mcgill.ca\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malik Younsi (University of Hawaii)
DTSTART:20200515T183000Z
DTEND:20200515T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/4
DESCRIPTION:Title: Holomorphic motions\, conformal welding and capacity\nby Malik Younsi (University of Hawaii) as part of CRM-Montreal analysi
s Seminar\n\n\nAbstract\nThe notion of a holomorphic motion was introduced
by Mane\, Sad and Sullivan in the 1980's\, motivated by the observation t
hat Julia sets of rational maps often move holomorphically with holomorphi
c variations of the parameters. Even though the original motivation for th
eir study came from complex dynamics\, holomorphic motions have found over
the years to be of fundamental importance in other related areas of Compl
ex Analysis\, such as the theory of Kleinian groups and Teichmuller theory
for instance. Holomorphic motions also played a central role in the semin
al work of Astala on distortion of dimension and area under quasiconformal
mappings. In this talk\, I will first review the basic notions and result
s related to holomorphic motions\, including quasiconformal mappings and t
he (extended) lambda lemma. I will then present some recent results on the
behavior of logarithmic capacity and analytic capacity under holomorphic
motions. As we will see\, conformal welding (of quasicircle Julia sets) pl
ays a fundamental role. This is joint work with Tom Ransford and Wen-Hui A
i.\n\nEn ligne-Web: Veuillez communiquer avec l'organisateur/Please contat
the organizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Galkowski (University College London)
DTSTART:20200522T150000Z
DTEND:20200522T160000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/5
DESCRIPTION:Title: Viscosity limits for 0th order operators\nby Jeff
Galkowski (University College London) as part of CRM-Montreal analysis Sem
inar\n\n\nAbstract\nIn recent work\, Colin de Verdiere--Saint-Raymond and
Dyatlov--Zworski showed that a class of zeroth order pseudodifferential op
erators coming from experiments on forced waves in fluids satisfies a limi
ting absorption principle. Thus\, these operators have absolutely continu
ous spectrum with possibly finitely many embedded eigenvalues. In this ta
lk\, we discuss the effect of small viscosity on the spectra of these oper
ators\, showing that the spectrum of the operator with small viscosity con
verges to the poles of a certain meromorphic continuation of the resolvent
through the continuous spectrum. In order to do this\, we introduce spac
es based on an FBI transform which allows for the testing of microlocal an
alyticity properties. This talk is based on joint work with M. Zworski.\
n\nEn ligne-Web: Veuillez communiquer avec l'organisateur/Please contat th
e organizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blair Davey (The City College of New York)
DTSTART:20200528T160000Z
DTEND:20200528T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/6
DESCRIPTION:Title: A quantification of the Besicovitch projection theorem
and its generalizations\nby Blair Davey (The City College of New York
) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe Besicovitch
projection theorem asserts that if a subset E of the plane has finite leng
th in the sense of Hausdorff and is purely unrectifiable (so its intersect
ion with any Lipschitz graph has zero length)\, then almost every linear p
rojection of E to a line will have zero measure. As a consequence\, the p
robability that a line dropped randomly onto the plane intersects such a s
et E is equal to zero. Thus\, the Besicovitch projection theorem is conne
cted to the classical Buffon needle problem. Motivated by the so-called B
uffon circle problem\, we explore what happens when lines are replaced by
more general curves. We discuss generalized Besicovitch theorems and\, as
Tao did for the classical theorem (Proc. London Math. Soc.\, 2009)\, we
use multi-scale analysis to quantify these results. This work is joint w
ith Laura Cladek and Krystal Taylor.\n\nEn ligne-Web: Veuillez communiquer
avec l'organisateur/Please contat the organizer: dmitry.jakobson@mcgill.c
a\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sagun Chanillo (Rutgers\, School of Arts and Sciences)
DTSTART:20200603T173000Z
DTEND:20200603T183000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/7
DESCRIPTION:Title: Bourgain-Brezis inequalities\, applications and Border
line Sobolev inequalities on Riemannian Symmetric spaces of non-compact ty
pe\nby Sagun Chanillo (Rutgers\, School of Arts and Sciences) as part
of CRM-Montreal analysis Seminar\n\n\nAbstract\nBourgain and Brezis discov
ered a remarkable inequality which\nis borderline for the Sobolev inequali
ty in Eulcidean spaces. In this\ntalk we obtain these inequalities on nilp
otent Lie groups and on\nRiemannian symmetric spaces of non-compact type.
We obtain applications\nto Navier Stokes eqn in 2D and to Strichartz inequ
alities for wave and\nSchrodinger equations and to the Maxwell equations f
or Electromagnetism.\nThese results were obtained jointly with Jean Van Sc
haftingen and Po-lam\nYung.\n\nJoint seminar with Geometric Analysis - En
ligne-Web: Veuillez communiquer avec l'organisateur/Please contat the orga
nizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spyros Alexakis (University of Toronto)
DTSTART:20200611T163000Z
DTEND:20200611T173000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/8
DESCRIPTION:Title: Singularity formation in Black Hole interiors\nby
Spyros Alexakis (University of Toronto) as part of CRM-Montreal analysis S
eminar\n\n\nAbstract\nThe prediction that solutions of the Einstein equati
ons in the interior of black holes must always terminate at a singularity
was originally conceived by Penrose in 1969\, under the name of "strong co
smic censorship hypothesis". The nature of this break-down (i.e. the asy
mptotic properties of the space-time metric as one approaches the terminal
singularity) is not predicted\, and remains a hotly debated question to t
his day. One key question is the causal nature of the singularity (space-
like\, vs null for example). Another is the rate of blow-up of natural ph
ysical/geometric quantities at the singularity. Mutually contradicting pr
edictions abound in this topic. Much work has been done under the assumpt
ion of spherical symmetry (for various matter models). We present a stabi
lity result for the Schwarzschild singularity under polarized axi-symmetri
c perturbations of the initial data\, joint with G. Fournodavlos). One k
ey innovation of our approach is a certain new way to treat the Einstein e
quations in axial symmetry\, which should have broader applicability.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Strohmaier (University of Leeds)
DTSTART:20200619T160000Z
DTEND:20200619T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/9
DESCRIPTION:Title: Scattering theory for difScattering theory for differe
ntial forms and its relation to cohomologyferential forms and its relation
to cohomology\nby Alexander Strohmaier (University of Leeds) as part
of CRM-Montreal analysis Seminar\n\n\nAbstract\nI will consider spectral t
heory of the Laplace operator on a manifold that is Euclidean outside a co
mpact set. An example of such a setting is obstacle scattering where seve
ral compact pieces are removed from $\\R^d$. The spectrum of the operator
on functions is absolutely continuous. In the case of general $p$-forms
eigenvalues at zero may exist\, the eigenspace consisting of L^2-harmonic
forms. The dimension of this space is computable by cohomological methods
. I will present some new results concerning the detailed expansions of g
eneralised eigenfunctions\, the scattering matrix\, and the resolvent near
zero. These expansions contain the L^2-harmonic forms so there is no cle
ar separation between the continuous and the discrete spectrum. This can
be used to obtain more detailed information about the L^2-cohomology as we
ll as the spectrum. If I have time I will explain an application of this
to physics. (joint work with Alden Waters)\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Logunov (Princeton University)
DTSTART:20200626T140000Z
DTEND:20200626T145000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/10
DESCRIPTION:Title: Nodal sets\, Quasiconformal mappings and how to apply
them to Landis' conjecture\nby Alexander Logunov (Princeton Universit
y) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nA while ago Nad
irashvili proposed a beautiful idea how to attack problems on zero sets of
Laplace eigenfunctions using quasiconformal mappings\, aiming to estimate
the length of nodal sets (zero sets of eigenfunctions) on closed two-dime
nsional surfaces. The idea have not yet worked out as it was planned. Ho
wever it appears to be useful for Landis' Conjecture. We will explain how
to apply the combination of quasiconformal mappings and zero sets to quan
titative properties of solutions to $\\Delta u + V u =0 on the plane\, whe
re $V$ is a real\, bounded function. The method reduces some questions ab
out solutions to Shrodinger equation $\\Delta u + V u =0$ on the plane to
questions about harmonic functions. Based on a joint work with E.Malinnik
ova\, N.Nadirashvili and F. Nazarov.\n\nSPECIAL SEMINAR ON THE OCCASION O
F THE 65TH BIRTHDAY OF N. NADIRASHVILI\nFRIDAY\, JUNE 26\, STARTS AT 10:00
AM EASTERN TIME\, ZOOM SEMINAR\nProgram: 11:00 - 11:50: Vladimir Sverak (
University of Minnesota)\nZoome banquet Analysis Seminar: 12:15-13:30\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sverak (University of Minnesota)
DTSTART:20200626T150000Z
DTEND:20200626T155000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/11
DESCRIPTION:Title: Liouville theorems for the Navier-Stokes equations\nby Vladimir Sverak (University of Minnesota) as part of CRM-Montreal an
alysis Seminar\n\n\nAbstract\nAssume u is a smooth\, bounded\, and diverge
nce-free field on R^3 satisfying the steady Navier-Stokes equation -\\Delt
a u +u\\nabla u + \\nabla p=0 (for a suitable function p). Does u have to
be constant? We still don't know. Interesting things are known and Nikolai
made important contributions to our knowledge concerning this question. S
imilar problems can also be considered for various model equations. The le
cture will concern various aspects of this problem.\n\nSPECIAL SEMINAR ON
THE OCCASION OF THE 65TH BIRTHDAY OF N. NADIRASHVILI\nFRIDAY\, JUNE 26\, S
TARTS AT 10:00 AM EASTERN TIME\, ZOOM SEMINAR\nProgram: 10:00 - 10:50: Ale
xander Logunov (Princeton University )\nZoome banquet Analysis Seminar: 12
:15-13:30\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART:20200715T150000Z
DTEND:20200715T160000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/12
DESCRIPTION:Title: The spectral a random hyperbolic surface\nby Mich
ael Magee (Durham University) as part of CRM-Montreal analysis Seminar\n\n
\nAbstract\nOn a compact hyperbolic surface\, the Laplacian has a spectral
gap between 0 and the next smallest eigenvalue if and only if the surface
is connected. The size of the spectral gap measures both how highly conne
cted the surface is\, and the rate of exponential mixing of the geodesic f
low on the surface. There is an analogous concept of spectral gap for grap
hs\, with analogous connections to connectivity and dynamics. Motivated by
theorems about the spectral gap of random regular graphs\, we proved that
for any $\\epsilon > 0$\, a random cover of a fixed compact connected hyp
erbolic surface has no new eigenvalues below 3/16 - $\\epsilon$\, with pro
bability tending to 1 as the covering degree tends to infinity. The number
3/16 is\, mysteriously\, the same spectral gap that Selberg obtained for
congruence modular curves. The talk is intended to be accessible to gradua
te students and is based on joint works with Frédéric Naud and Doron Pud
er.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Wilson (The University of Vermont)
DTSTART:20200807T150000Z
DTEND:20200807T160000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/13
DESCRIPTION:Title: Perturbed Haar function expansions\nby Mike Wilso
n (The University of Vermont) as part of CRM-Montreal analysis Seminar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malabika Pramanik (University of British Columbia)
DTSTART:20200828T160000Z
DTEND:20200828T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/14
DESCRIPTION:Title: Restriction of eigenfunctions to sparse sets on manif
olds\nby Malabika Pramanik (University of British Columbia) as part of
CRM-Montreal analysis Seminar\n\n\nAbstract\nGiven a compact Riemannian m
anifold $(M\, g)$ without boundary\, we consider the restriction of Laplac
e-Beltrami eigenfunctions to certain subsets $\\Gamma$ of the manifold. H
ow do the Lebesgue $L^p$ norms of these restricted eigenfunctions grow? Bu
rq\, Gerard\, Szvetkov and independently Hu studied this question when $\\
Gamma$ is a submanifold. In ongoing joint work with Suresh Eswarathasan\,
we extend earlier results to the setting where $\\Gamma$ is an arbitrary
Borel subset of $M$. Here differential geometric methods no longer apply.
Using methods from geometric measure theory\, we obtain sharp growth est
imates for the restricted eigenfunctions that rely only on the size of $\\
Gamma$. Our results are sharp for large $p$\, and are realized for large
families of sets $\\Gamma$ that are random and Cantor-like.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Maria Martell (Instituto de Ciencias Matemáticas (ICMAT))
DTSTART:20200911T130000Z
DTEND:20200911T140000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/15
DESCRIPTION:Title: Uniform rectifiability and elliptic operators satisfy
ing a Carleson measure condition\nby Jose Maria Martell (Instituto de
Ciencias Matemáticas (ICMAT)) as part of CRM-Montreal analysis Seminar\n\
n\nAbstract\nIn this talk I will study the correspondence between the prop
erties of the solutions of a class of PDEs and the geometry of sets in Euc
lidean space. We settle the question of whether (quantitative) absolute c
ontinuity of the elliptic measure with respect to the surface measure and
uniform rectifiability of the boundary are equivalent\, in an optimal clas
s of divergence form elliptic operators satisfying a suitable Carleson mea
sure condition. Our setting is that of domains having an Ahlfors regular
boundary and satisfying the so-called interior Corkscrew and Harnack chain
conditions (these are respectively scale-invariant/quantitative versions
of openness and path-connectivity) and we show that for the class of Kenig
-Pipher uniformly elliptic operators (operators whose coefficients have co
ntrolled oscillation in terms of a Carleson measure condition) the solvabi
lity of the $L^p$-Dirichlet problem with some finite $p$ is equivalent to
the quantitative openness of the exterior domains or to the uniform rectif
iablity of the boundary. \n\nJoint work with S. Hofmann\, S. Mayboro
da\, T. Toro\, and Z. Zhao.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Wilson (The University of Vermont)
DTSTART:20200821T150000Z
DTEND:20200821T160000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/16
DESCRIPTION:Title: Perturbed Haar function expansions\nby Mike Wilso
n (The University of Vermont) as part of CRM-Montreal analysis Seminar\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Gibara (Université Laval)
DTSTART:20201211T143000Z
DTEND:20201211T153000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/17
DESCRIPTION:Title: Boundedness and continuity for rearrangements on spac
es defined by mean oscillation\nby Ryan Gibara (Université Laval) as
part of CRM-Montreal analysis Seminar\n\n\nAbstract\nIn joint work with Al
mut Burchard and Galia Dafni\, we study the boundedness and continuity of
rearrangement operators on the space BMO of functions of bounded mean osci
llation. Improved bounds are obtained for the BMO-seminorm of the decreasi
ng rearrangement\, and the symmetric decreasing rearrangement is shown to
be bounded on BMO. Both of these rearrangements are shown to be discontinu
ous as maps on BMO\, but sufficient normalization conditions are establish
ed to guarantee continuity on the subspace VMO of functions of vanishing m
ean oscillation.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renaud Raquepas (McGill University)
DTSTART:20201211T160000Z
DTEND:20201211T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/18
DESCRIPTION:Title: Entropy production in nondegenerate diffusions: large
times and small noises\nby Renaud Raquepas (McGill University) as par
t of CRM-Montreal analysis Seminar\n\n\nAbstract\nEntropy production (EP)
is a key quantity from thermodynamics which quantifies the irreversibility
of the time evolution of physical systems. I will start the presentation
with a general introduction to the different approaches to defining EP. Th
en\, I will focus on the context of nondegenerate diffusions and I will de
scribe the large-deviation properties of EP as time goes to infinity. I wi
ll also explain how the behaviour of the corresponding rate function boils
down to the study of the smallest eigenvalue for a family of differential
operators with a small parameter.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anush Tserunyan (McGill University)
DTSTART:20210115T190000Z
DTEND:20210115T200000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/19
DESCRIPTION:Title: Ergodic theorems along trees\nby Anush Tserunyan
(McGill University) as part of CRM-Montreal analysis Seminar\n\n\nAbstract
\nIn the classical pointwise ergodic theorem for a probability measure pre
serving (pmp) transformation $T$\, one takes averages of a given integrabl
e function over the intervals $\\{x\, T(x)\, T^2(x)\, \\hdots\, T^n(x)\\}$
in front of the point $x$. We prove a “backward” ergodic theorem for
a countable-to-one pmp $T$\, where the averages are taken over subtrees of
the graph of T that are rooted at $x$ and lie behind $x$ (in the directio
n of $T^{-1}$). Surprisingly\, this theorem yields forward ergodic theorem
s for countable groups\, in particular\, one for pmp actions of free group
s of finite rank\, where the averages are taken along subtrees of the stan
dard Cayley graph rooted at the identity. This strengthens Bufetov’s the
orem from 2000\, which was the most general result in this vein. This is j
oint work with Jenna Zomback.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Vig (CRM\, McGill)
DTSTART:20210212T160000Z
DTEND:20210212T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/20
DESCRIPTION:Title: Spectral invariants and Birkhoff Billiards\nby Am
ir Vig (CRM\, McGill) as part of CRM-Montreal analysis Seminar\n\n\nAbstra
ct\nConsider a smooth\, bounded\, strictly convex domain in the plane. The
re are two games one can play. The classical one is billiards\, in which a
billiard ball orbits around the domain and reflects elastically at the bo
undary. The “quantum” analogue involves the study of wave propagation
in the domain and understanding the frequencies at which such waves oscill
ate. In this talk\, we discuss recent progress on the inverse spectral pro
blem of determining a billiard table from its Laplace spectrum. In particu
lar\, we introduce a new class of spectral invariants for a generic class
of billiard tables obtained from an explicit Hadamard-Riesz type parametri
x for the wave propagator\, microlocally near geodesic loops of small rota
tion number. These same techniques also allow us to prove (infinitesimal)
Robin spectral rigidity of the ellipse\, when both the boundary and bounda
ry conditions are allowed to deform simultaneously. Finally\, we mention o
ngoing work together with Vadim Kaloshin to cancel singularities in the wa
ve trace for special types of domains.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Jaye (Georgia Tech)
DTSTART:20210305T160000Z
DTEND:20210305T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/21
DESCRIPTION:Title: Multi-scale analysis of Jordan curves\nby Benjami
n Jaye (Georgia Tech) as part of CRM-Montreal analysis Seminar\n\n\nAbstra
ct\nIn this talk we will describe how one can detect regularity in Jordan
curves through analysis of associated geometric square functions. We will
particularly focus on the resolution of a conjecture of L. Carleson. Joi
nt work with Xavier Tolsa and Michele Villa (https://arxiv.org/abs/1909.08
581).\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Ransford (Université Laval)
DTSTART:20210319T150000Z
DTEND:20210319T160000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/22
DESCRIPTION:Title: Failure of approximation of odd functions by odd poly
nomials\nby Thomas Ransford (Université Laval) as part of CRM-Montrea
l analysis Seminar\n\n\nAbstract\nWe construct a Hilbert holomorphic funct
ion space $H$ on the unit disk such that the polynomials are dense in $H$\
, but the odd polynomials are not dense in the odd functions in $H$. As a
consequence\, there exists a function $f$ in $H$ that lies outside the clo
sed linear span of its Taylor partial sums $s_n(f)$\, so it cannot be appr
oximated by any triangular summability method applied to the $s_n(f)$. We
also show that there exists a function $f$ in $H$ that lies outside the cl
osed linear span of its radial dilates $f_r\, r < 1$. (Joint work with Jav
ad Mashreghi and Pierre-Olivier Parise).\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Faifman (Tel Aviv University)
DTSTART:20210326T180000Z
DTEND:20210326T190000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/23
DESCRIPTION:Title: A Funk perspective on convex geometry\nby Dmitry
Faifman (Tel Aviv University) as part of CRM-Montreal analysis Seminar\n\n
\nAbstract\nThe Funk metric in the interior of a convex set is a lesser-kn
own cousin of the Hilbert metric. The latter generalizes the Beltrami-Klei
n model of hyperbolic geometry\, and both have straight segments as geodes
ics\, thus constituting solutions of Hilbert's 4th problem alongside norme
d spaces. Unlike the Hilbert metric\, the Funk metric is not projectively
invariant. I will explain how\, nevertheless\, the Funk metric gives rise
to many projective invariants\, which moreover enjoy a duality extending r
esults of Holmes-Thompson and Alvarez Paiva on spheres of normed spaces an
d Gutkin-Tabachnikov on Minkowski billiards. I will also discuss how the m
aximal volume problem in Funk geometry yields an extension of the Blaschke
-Santalo inequality.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Khanin (University of Toronto)
DTSTART:20210409T180000Z
DTEND:20210409T190000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/24
DESCRIPTION:Title: On Stationary Solutions to the Stochastic Heat Equati
on\nby Konstantin Khanin (University of Toronto) as part of CRM-Montre
al analysis Seminar\n\n\nAbstract\nI plan to discuss the problem of unique
ness of global solutions to the random Hamilton-Jacobi equation. I will f
ormulate several conjectures and present results supporting them. Then I
will discuss a new uniqueness result for the Stochastic Heat equation in t
he regime of weak disorder.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Krylov (University of Minnesota)
DTSTART:20210416T140000Z
DTEND:20210416T150000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/25
DESCRIPTION:Title: A review of some new results in the theory of linear
elliptic equations with drift in $L_{d}$\nby Nicolai Krylov (Universit
y of Minnesota) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nWe
present an overview of recent results related to the Aleksandrov type est
imates with power of summability of the free term $d_0 < d$\, the Harnack
inequality for $u\\in W^{2}_{d_{0}\,loc}$\, Holder continuity of $L$-harmo
nic and $L$-caloric functions. Under the assumption that the main coeffici
ents are almost in VMO (and $b\\in L_{d}$) we also present the results abo
ut solvability of the elliptic equations in $W^{2}_{d_{0}}$ in domains and
in the whole space. A few relates issues are discussed as well.\n\nVia zo
om: https://ulaval.zoom.us/j/62869112863?pwd=dndUME9ORmRVQWxGRklvcmFmL3Fyd
z09\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitali Vougalter (University of Toronto)
DTSTART:20210423T180000Z
DTEND:20210423T190000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/26
DESCRIPTION:Title: Solvability of some integro-differential equations wi
th anomalous diffusion and transport\nby Vitali Vougalter (University
of Toronto) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe wo
rk deals with the existence of solutions of an integro-differential equati
on in the case of the anomalous diffusion with the negative Laplace operat
or in a fractional power in the presence of the transport term. The proof
of existence of solutions is based on a fixed point technique. Solvability
conditions for elliptic operators without Fredholm property in unbounded
domains are used. We discuss how the introduction of the transport term im
pacts the regularity of solutions.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nages Shanmugalingam (University of Cincinnati)
DTSTART:20210507T180000Z
DTEND:20210507T190000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/27
DESCRIPTION:Title: Prime ends for domains in metric measure spaces and t
heir use in potential theory and QC theory\nby Nages Shanmugalingam (U
niversity of Cincinnati) as part of CRM-Montreal analysis Seminar\n\n\nAbs
tract\nPrime ends were first developed by Caratheodory in order to underst
and the boundary behavior of conformal mappings from the disk. As such\, t
he construction of Caratheodory and Ahlfors worked for simply connected pl
anar domains\, but had to be modified for more general domains. In this ta
lk we will focus on a construction in the setting of domains in metric spa
ces\, and describe their use in potential theory (Dirichlet problem for th
e p-energy minimizers) and in studying boundary behavior of QC maps.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Germain Gendron (Université de Nantes (1/3))
DTSTART:20210322T150000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/28
DESCRIPTION:Title: Uniqueness and stability for an inverse Steklov probl
em\nby Germain Gendron (Université de Nantes (1/3)) as part of CRM-Mo
ntreal analysis Seminar\n\n\nAbstract\nIn this talk\, we present results f
or an inverse Steklov problem for a particular class of 2-dimensional mani
folds having the topology of a hollow sphere and equipped with a warped pr
oduct metric. We prove that the knowledge of the Steklov spectrum determi
nes uniquely the associated warping function up to a natural invariance.
Then\, we study the continuous dependence of the warping function defining
the warped product with respect to the Steklov spectrum.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Monk (IRMA Strasbourg (2/3))
DTSTART:20210322T150000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/29
DESCRIPTION:Title: Geometry and spectrum of random hyperbolic surfaces\nby Laura Monk (IRMA Strasbourg (2/3)) as part of CRM-Montreal analysis
Seminar\n\n\nAbstract\nThe main aim of this talk is to present geometric
and spectral properties of typical hyperbolic surfaces. More precisely\,
I will: \n• introduce a probabilistic model\, first studied by Mirzakhan
i\, which is a natural and convenient way to sample random hyperbolic surf
aces \n• describe the geometric properties of these random surfaces \n
• explain how one can deduce from this geometric information estimates o
n the number of eigenvalues of the Laplacian in an interval [a\,b]\, using
the Selberg trace formula.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhichao Wang (University of Toronto (3/3))
DTSTART:20210322T150000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/30
DESCRIPTION:Title: Conformal upper bounds for the volume spectrum\nb
y Zhichao Wang (University of Toronto (3/3)) as part of CRM-Montreal analy
sis Seminar\n\n\nAbstract\nIn this talk\, we prove upper bounds for the vo
lume spectrum of a Riemannian manifold that depend only on the volume\, di
mension\, and a conformal invariant.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Saez (Pontificia Universidad Cat´olica de Chile)
DTSTART:20210329T160000Z
DTEND:20210329T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/31
DESCRIPTION:Title: Eigenvalue bounds for the Paneitz operator and its as
sociated boundary operator\nby Mariel Saez (Pontificia Universidad Cat
´olica de Chile) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\n
In this talk I will discuss bounds for the first eigenvalue of the Paneitz
operator P and its associated third-order boundary operator B3 on fourman
ifolds. We restrict to orientable\, simply connected\, locally confomally
flat manifolds that have at most two umbilic boundary components. The pr
oof is based on showing that under the hypotheses of the main theorems\, t
he considered manifolds are confomally equivalent to canonical models. Th
e fact that P and B3 are conformal in four dimensions is key in the proof.
This is joint work with Maria del Mar Gonzalez\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hakim Boumaza (Université Paris 13)
DTSTART:20210402T153000Z
DTEND:20210402T163000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/32
DESCRIPTION:Title: Integrated density of states of the periodic Airy-Sch
rödinger operator\nby Hakim Boumaza (Université Paris 13) as part of
CRM-Montreal analysis Seminar\n\n\nAbstract\nIn this talk I present\, in
the semiclassical regime\, an explicit formula for the integrated density
of states of the periodic Airy-Schrodinger operator on the real line. The
potential of this Schrödinger operator is periodic\, continuous and piec
ewise linear. For this purpose\, the spectrum of the Schrödinger operato
r whose potential is the restriction of the periodic Airy-Schrödinger pot
ential to a finite number of periods is studied. We prove that all the ei
genvalues of the operator corresponding to the restricted potential are in
the spectral bands of the periodic Airy-Schrodinger operator and none of
them are in its spectral gaps. In the semiclassical regime\, we count the
number of these eigenvalues in each of the spectral bands. Note that in
these results there are explicit constants which characterize the semiclas
sical regime. This is joint work with Olivier Lafitte (USPN - CRM Montrea
l).\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederic Naud (Sorbonne Université)
DTSTART:20210505T173000Z
DTEND:20210505T183000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/33
DESCRIPTION:Title: The spectral gap of random hyperbolic surfaces\nb
y Frederic Naud (Sorbonne Université) as part of CRM-Montreal analysis Se
minar\n\n\nAbstract\nWe will start with a survey on (some very recent) res
ults on the low spectrum of random compact hyperbolic surfaces\, for vario
us models including discrete and continuous Teichmuller spaces. We will th
en give some ideas of the proofs by emphasizing the analogy with radom gra
phs. We will also dicuss non compact situations where similar results on r
esonances can be obtained. Joint works with Michael Magee and Doron Puder.
\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Moonens (Paris-Saclay)
DTSTART:20210519T173000Z
DTEND:20210519T183000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/34
DESCRIPTION:Title: Solving the divergence equation with measure data in
non-regular domains\nby Laurent Moonens (Paris-Saclay) as part of CRM-
Montreal analysis Seminar\n\n\nAbstract\nIn this talk\, we shall present a
recent joint work with E. Russ (Grenoble) concerning the equation $\\math
rm{div}\\\,v=\\mu$ in a (rather general) open domain $\\Omega$\, where $\\
mu$ is a (signed) Radon measure in $\\Omega$ satisfying $\\mu(\\Omega)=0$.
We show in particular that\, under mild assumptions on the geometry of $\
\Omega$ (and some assumptions on $\\mu$)\, one can provide a constructive
way to build solutions $v$ in a weighted $L^\\infty$ space enjoying weak N
eumann-type boundary conditions.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svitlana Mayboroda (University of Minnesota)
DTSTART:20210412T160000Z
DTEND:20210412T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/35
DESCRIPTION:Title: The landscape law for the integrated density of state
s\nby Svitlana Mayboroda (University of Minnesota) as part of CRM-Mont
real analysis Seminar\n\n\nAbstract\nWe establish non-asymptotic estimates
from above and below on the integrated density of states of the Schr¨odi
nger operator L = −∆ + V \, using a counting function for the minima o
f the localization landscape\, a solution to the equation Lu = 1.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Helffer (Université Paris Sud)
DTSTART:20210419T160000Z
DTEND:20210419T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/36
DESCRIPTION:Title: Semi-classical edge states for the Robin Laplacian (a
fter Helffer-Kachmar)\nby Bernard Helffer (Université Paris Sud) as p
art of CRM-Montreal analysis Seminar\n\n\nAbstract\nMotivated by the study
of high energy Steklov eigenfunctions\, we examine the semi-classical Rob
in Laplacian. In the two dimensional situation\, we determine an effectiv
e operator describing the asymptotic distribution of the negative eigenval
ues\, and we prove that the corresponding eigenfunctions decay away from t
he boundary\, for all dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Bogdan (Wroclaw University)
DTSTART:20210430T180000Z
DTEND:20210430T190000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/37
DESCRIPTION:Title: Optimal Hardy identities and inequalites for the frac
tional Laplacian on $L^p$\nby Krzysztof Bogdan (Wroclaw University) as
part of CRM-Montreal analysis Seminar\n\n\nAbstract\nWe will present a ro
ute from symmetric Markovian semigroups to Hardy inequalities\, to nonexpl
osion and contractivity results for Feynman-Kac semigroups on $L^p$. We wi
ll focus on the fractional Laplacian on $\\mathbb{R}^d$\, in which case th
e constants\, estimates of the Feynman-Kac semigroups and tresholds for co
ntractivity and explosion are sharp. Namely we will discuss selected resul
ts from arXiv:2103.06550\, joint with Bartl omiej Dyda\, Tomasz Grzywny\,
Tomasz Jakubowski\, Panki Kim\, Julia Lenczewska\, Katarzyna Pietruska-Pa\
\l uba or Dominika Pilarczyk.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karl-Mikael Perfekt (University of Reading)
DTSTART:20210426T160000Z
DTEND:20210426T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/38
DESCRIPTION:Title: Infinitely many embedded eigenvalues for the Neumann-
Poincaré operator in 3D\nby Karl-Mikael Perfekt (University of Readin
g) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nI will discuss
the spectral theory of the Neumann-Poincar´e operator for 3D domains with
rotationally symmetric singularities\, which is directly related to the p
lasmonic eigenvalue problem for such domains. I will then describe the co
nstruction of some special domains for which the problem features infinite
ly many eigenvalues embedded in the essential/continuous spectrum. Severa
l questions and open problems will be stated. \nBased on joint papers wit
h Johan Helsing and with Wei Li and Stephen Shipman.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lipnowski (McGill University)
DTSTART:20210514T150000Z
DTEND:20210514T160000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/39
DESCRIPTION:Title: Towards optimal spectral gaps in large genus\nby
Michael Lipnowski (McGill University) as part of CRM-Montreal analysis Sem
inar\n\n\nAbstract\nI'll discuss recent joint work with Alex Wright (arXiv
: 2103.07496) showing that typical large genus hyperbolic surfaces have fi
rst Laplacian eigenvalue at least 3/16−epsilon.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Chen (Louisiana State University)
DTSTART:20210528T180000Z
DTEND:20210528T190000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/40
DESCRIPTION:Title: BV functions and some functional inequalities on nest
ed fractals\nby Li Chen (Louisiana State University) as part of CRM-Mo
ntreal analysis Seminar\n\n\nAbstract\nIn this talk\, we discuss functions
of bounded variations (BV) on fractals which satisfy sub-Gaussian heat ke
rnel bounds. We also prove isoperimetric inequalities and Poincare inequal
ities on some nested fractals. Our proofs use heat kernel methods and the
key ingredient is a weak Bakry-Emery curvature type condition. The talk ar
e based on joint works with Patricia Alonso-Ruiz\, Fabrice Baudoin\, Luke
Rogers\, Nageswari Shanmugalingam and Alexander Teplyaev.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Wunsch (Northwestern University)
DTSTART:20210503T160000Z
DTEND:20210503T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/41
DESCRIPTION:Title: Semiclassical analysis and the convergence of the fin
ite element method\nby Jared Wunsch (Northwestern University) as part
of CRM-Montreal analysis Seminar\n\n\nAbstract\nAn important problem in nu
merical analysis is the solution of the Helmholtz equation in exterior dom
ains\, in variable media\; this models the scattering of time-harmonic wav
es. The Finite Element Method (FEM) is a flexible and powerful tool for o
btaining numerical solutions\, but difficulties are known to arise in obta
ining convergence estimates for FEM that are uniform as the frequency of w
aves tends to infinity. I will describe some recent joint work with David
Lafontaine and Euan Spence that yields new convergence results for the FE
M which are uniform in the frequency parameter. The essential new tools c
ome from semiclassical microlocal analysis and the use of the functional c
alculus. Another ingredient is a slightly surprising new resolvent estima
te.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ram Band (Technion)
DTSTART:20210510T160000Z
DTEND:20210510T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/42
DESCRIPTION:Title: Neumann domains on manifolds and graphs\nby Ram B
and (Technion) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe
nodal set of a Laplacian eigenfunction forms a partition of the underlyin
g manifold or graph. Another natural partition is based on the gradient v
ector field of the eigenfunction (on a manifold) or on the extremal points
of the eigenfunction (on a graph). The submanifolds (or subgraphs) of th
is partition are called Neumann domains (you may guess the reason for this
name\, and it would also be mentioned in the talk \;) We present results
for Neumann domains on manifolds and on graphs - their count\, geometric p
roperties and spectral positions. The Neumann domain results are compared
to those of the nodal domain study. \nThe talk is based on joint works w
ith Lior Alon\, Michael Bersudsky\, Graham Cox\, Sebastian Egger\, David F
ajman and Alexander Taylor.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Girouard (Université Laval)
DTSTART:20210517T160000Z
DTEND:20210517T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/43
DESCRIPTION:Title: Free boundary minimal surfaces and large Steklov eige
nvalues\nby Alexandre Girouard (Université Laval) as part of CRM-Mont
real analysis Seminar\n\n\nAbstract\nA free boundary minimal surface (FBMS
) in the unit ball is a minimal surface Ω ⊂ B ⊂ R 3 which satisfies
one of the two following equivalent conditions: • Ω meets the boundary
∂B orthogonally\, • The coordinate functions xi : Ω → R are Stekl
ov eigenfunctions with eigenvalue σ = 1. The study of FBMS is witnessing
a renaissance thanks to the fundamental work of Fraser and Schoen\, who d
iscovered that isoperimetric optimizers for the first nonzero Steklov eige
nvalue σ1(Ω) of surfaces lead to the existence of FBMS with prescribed
topology. For surfaces of genus 0\, they proved existence of maximizers f
or the perimeter-normalized σ1(Ω) and thereby obtained several new FBMS
. In this talk I will show how this link can be used to obtain a sequence
of FBMS Ωn ⊂ B such that area(Ωn ) n→∞ −−−→ 4π. This
is based on a construction of domains in the sphere S 2 with perimeter-nor
malized σ1(Ω) converging to 8π. These domains are obtained by removin
g small disks from the sphere\, in the spirit of homogenization theory. I
will also dicuss a conjecture by Fraser and Li\, stating that σ1(Ω) =
1 for each FBMS Ω ⊂ B. More precisely\, I will show that the conjectu
re is true for some FBMS which are invariant under the action of the symme
try group of some platonic solids. This talk is based on joint work with
Jean Lagac´e (UCL).\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Genqian Liu (Beijing Institute of Technology)
DTSTART:20210524T160000Z
DTEND:20210524T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/44
DESCRIPTION:Title: Geometric invariants of spectrum of the Navier-Lame o
perator\nby Genqian Liu (Beijing Institute of Technology) as part of C
RM-Montreal analysis Seminar\n\n\nAbstract\nIn this talk\, we review the a
symptotic expansions of the heat traces for various operators including th
e Laplace operator\, the poly-Laplace operator\, the Maxwell operator\, th
e Stokes operator\, etc. Then for the elastic Navier-Lame operator (a non
-Laplace type operator) on a compact connected Riemannian n-manifold M wit
h smooth boundary\, we explicitly obtain the first two coefficients of the
asymptotic expansion of the heat trace for NavierLame operator with Diric
hlet and Neumann boundary conditions. These two coefficients provide prec
ise information for the volume of the elastic body M and the surface area
of the boundary in terms of the spectrum of the NavierLame operator. This
gives an answer to an interesting and open problem mentioned by Avramidi.
\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maziej Zworski (Berkeley)
DTSTART:20210531T160000Z
DTEND:20210531T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/45
DESCRIPTION:Title: Spectral theory of internal waves in fluids\nby M
aziej Zworski (Berkeley) as part of CRM-Montreal analysis Seminar\n\n\nAbs
tract\nThe connection between the formation of internal waves in fluids\,
spectral theory and the dynamics of homeomorphisms of the circle was inves
tigated by oceanographers in the 90s and resulted in novel experimental ob
servations (Maas et al\, 1997). The specific homeomorphism is given by a
chess billiard and has been considered by many authors (John 1941\, Arnold
1957\, Ralston 1973\, ... \, Lenci et al 2021). The relation between th
e nonlinear dynamics of this homeomorphism and linearized internal waves p
rovides a striking example of classical/quantum correspondence (in a class
ical and surprising setting of fluids!). Using a model of tori and of zer
oth order pseudodifferential operators\, it has been a subject of recent r
esearch\, first by Colin de Verdi`ere-Saint Raymond 2020 and then by Dyatl
ov\, Galkowski\, Wang and the speaker. In this talk I will review those r
esults and present new work\, with Dyatlov and Wang\, on the more physical
ly relevant boundary value problem.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kapukhin (California Institute of Technology)
DTSTART:20210607T160000Z
DTEND:20210607T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/46
DESCRIPTION:Title: Stability of isoperimetric eigenvalue inequalities\nby Mikhail Kapukhin (California Institute of Technology) as part of CRM
-Montreal analysis Seminar\n\n\nAbstract\nStability questions for sharp in
equalities are important problems in analysis. Recently\, these questions
have been investigated for the first eigenvalue of the Laplacian on Eucli
dean domains. Optimal stability estimates for Faber-Krahn and Szego-Weinb
erger inequalities were obtained by BrascoDe Philippis-Velichkov and Nadir
ashvili\, Brasco-Pratelli respectively. In the present talk we first cons
ider the stability of another fundamental inequality in spectral geometry:
Hersch inequality for the first eigenvalue on the 2-dimensional sphere.
We then present generalizations to other surfaces and the related problems
from harmonic maps and minimal surfaces. Finally\, if time permits\, pot
ential applications to Steklov eigenvalue problem will be discussed. Base
d on the joint work with M. Nahon\, I. Polterovich and D. Stern.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gomez-Serrano (University of Barcelona)
DTSTART:20210614T160000Z
DTEND:20210614T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/47
DESCRIPTION:Title: Computer-assisted proofs and counterexamples in spect
ral geometry\nby Javier Gomez-Serrano (University of Barcelona) as par
t of CRM-Montreal analysis Seminar\n\n\nAbstract\nIn this talk I will expl
ain how to construct counterexamples for two problems in spectral geometry
. The main novelty is that parts of the proofs will be done via a rigorou
s computer-assisted proof. In the first part of the talk\, I will explain
how to prove that a triangle is not determined by its first\, second and
fourth (Dirichlet) eigenvalues\, solving a conjecture by Antunes and Freit
as. In the second part I will construct a planar domain with 6 holes for
which the nodal line is closed and does not touch the boundary. In partic
ular\, this domain does not satisfy Payne’s nodal line conjecture. This
gives a partial answer on a question posed by Hoffmann-Ostenhof\, Hoffman
n-Ostenhof and Nadirashvili asking what should be the minimal number of ho
les of such domains. The results are joint work with Joel Dahne\, Kimberl
y Hou and Gerard Orriols.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Luzzini (EPFL)
DTSTART:20210621T160000Z
DTEND:20210621T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/48
DESCRIPTION:Title: On the spectral asymptotics for the buckling problem<
/a>\nby Paolo Luzzini (EPFL) as part of CRM-Montreal analysis Seminar\n\n\
nAbstract\nSince the seminal works of Hermann Weyl at the beginning of the
20th century\, several authors have investigated the spectral asymptotics
of partial differential operators. Following this tradition\, in this ta
lk I will first present a recent result on a new proof of Weyl’s law for
the buckling eigenvalues requiring minimal assumptions on the domain. Th
e proof relies on asymptotically sharp lower and upper bounds that we deve
lop for Riesz means. Moreover\, we compute the second term in Weyl’s la
w in the case of balls and bounded intervals. This\, together with some fo
rmal considerations\, leads us to state a conjecture for the second term i
n general domains. The talk is based on a joint work with Davide Buoso (U
PO)\, Luigi Provenzano (Sapienza Universit`a di Roma)\, and Joachim Stubbe
(EPFL).\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Laptev (Imperial College London)
DTSTART:20210628T160000Z
DTEND:20210628T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/49
DESCRIPTION:Title: Spectral inequalities for Jacobi matrices following H
undertmark and Simon\nby Ari Laptev (Imperial College London) as part
of CRM-Montreal analysis Seminar\n\n\nAbstract\nWe shall proof of a Lieb-T
hirring type inequality for Jacobi matrices originally conjectured by Hund
ertmark and Simon. In particular\, we show that the estimate on the sum o
f eigenvalues does not depend on the off-diagonal terms as long as they ar
e smaller than their asymptotic value. An interesting feature of the proo
f is that it employs a technique originally used by Hundertmark-Laptev-Wei
dl concerning sums of singular values for compact operators. \nThis is a
joint work with M.Loss and L.Schimmer.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ivrii (University of Toronto)
DTSTART:20210726T160000Z
DTEND:20210726T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/50
DESCRIPTION:Title: Pointwise Spectral Asymptotics out of the Diagonal\nby Victor Ivrii (University of Toronto) as part of CRM-Montreal analysi
s Seminar\n\n\nAbstract\nWe establish semiclassical asymptotics or estimat
es for the Schwartz kernel eh(x\, y\; τ ) of spectral projector for a sec
ond order elliptic operator on a manifold with a boundary. While such asy
mptotics for its restriction to the diagonal eh(x\, x\, τ ) and\, especia
lly\, for its trace Nh(τ ) = R eh(x\, x\, τ ) dx are well-known\, the ou
t-of-diagonal asymptotics are much less explored. Our main tools: improve
d successive approximations and geometric optics. Our results would also
lead to classical asymptotics of eh(x\, y\, τ ) for fixed h (say\, h = 1)
and τ → ∞.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M University)
DTSTART:20210823T160000Z
DTEND:20210823T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/51
DESCRIPTION:Title: Small denominators and large numerators of quasiperio
dic Schroedinger operators\nby Wencai Liu (Texas A&M University) as pa
rt of CRM-Montreal analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jürgen Jost (University of Leipzig)
DTSTART:20210830T160000Z
DTEND:20210830T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/52
DESCRIPTION:Title: Spectra of graphs and hypergraphs\nby Jürgen Jos
t (University of Leipzig) as part of CRM-Montreal analysis Seminar\n\n\nAb
stract\nThe spectral theory of the Laplace operator on graphs offers many
analogies with that of Riemannian manifolds\, like Cheeger type inequaliti
es\, but also shows some different phenomena. For hypergraphs\, a main st
ep consists in the definition of a Laplace operator that can also offer su
ch analogies. Lovasz extensions of Rayleigh quotients can uncover some de
eper reasons behind such analogies.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nalini Anantharaman (IRMA\, Université de Strasbourg)
DTSTART:20210906T160000Z
DTEND:20210906T170000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/53
DESCRIPTION:by Nalini Anantharaman (IRMA\, Université de Strasbourg) as p
art of CRM-Montreal analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Medvedev\; Marco Michetti\; William Hide (Higher School o
f Economics (HSE University) (1/3)\; Université de Lorraine (2/3)\; Durha
m University (3/3))
DTSTART:20210913T123000Z
DTEND:20210913T165000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/54
DESCRIPTION:Title: Young researchers in spectral geometry III - 3 short
talks\nby Vladimir Medvedev\; Marco Michetti\; William Hide (Higher Sc
hool of Economics (HSE University) (1/3)\; Université de Lorraine (2/3)\;
Durham University (3/3)) as part of CRM-Montreal analysis Seminar\n\n\nAb
stract\n(1/3) On the index of the critical Moebius band in the 4-ball \n\
nIn this talk I will show that the Morse index of the critical Moebius ban
d in the 4-dimensional Euclidean ball equals 5. This result makes use of
the quartic Hopf differential technique and a comparison theorem between t
he index of a free boundary minimal surface in the Euclidean ball and its
spectral index. The latter also enables us to reprove a well-known result
that the index of the critical catenoid in the 3-ball equals 4. These re
sults are obtained in my paper in progress. \n\n(2/3) A comparison betw
een Neumann and Steklov eigenvalues \n\nIn this talk we present a compari
son between the normalized first (non-trivial) Neumann eigenvalue |Ω|µ1
(Ω) for a Lipschitz open set Ω in the plane\, and the normalized first
(non-trivial) Steklov eigenvalue P(Ω)σ1(Ω). More precisely\, we stu
dy the ratio F(Ω) := |Ω|µ1(Ω)/P(Ω)σ1(Ω). We prove that this r
atio can take arbitrarily small or large values if we do not put any restr
iction on the class of sets Ω. Then we restrict ourselves to the class
of plane convex domains for which we get explicit bounds. We also study t
he case of thin convex domains for which we give more precise bounds. In
the last part of the talk we present the corresponding Blaschke-Santal´o
diagrams (x\, y) = (|Ω|µ1(Ω)\, P(Ω)σ1(Ω)) and we state some open
problems. This talk is based on a joint work with Antoine Henrot. \n\n(
3/3) Spectral gaps for random hyperbolic surfaces with cusps \n\nWe shall
study the discrete spectrum of the Laplacian on random non-compact finite-
area hyperbolic surfaces\, focusing on the size of the first non-zero eige
nvalue i.e. the spectral gap. We shall introduce a model for random surf
aces\, arising from the Weil-Petersson metric on moduli space. Then we sh
all discuss some recent results in this model for compact surfaces and the
ir extension to the non-compact case. In particular\, we prove the existe
nce of a positive uniform spectral gap of explicit size for random large g
enus non-compact surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins)
DTSTART:20211022T183000Z
DTEND:20211022T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/55
DESCRIPTION:Title: Some results on harmonic maps with free boundary and
beyond\nby Yannick Sire (Johns Hopkins) as part of CRM-Montreal analys
is Seminar\n\n\nAbstract\nThe theory of harmonic maps with free boundary i
s an old topic in geometric analysis. I will report on recent results on
their Ginzburg-Landau approximation\, regularity theory\, and their heat f
low. I will also describe several models in the theory of liquid crystals
where the heat flow of those maps appears\, emphasizing on some well-pose
dness issues and some hints on the construction of blow-up solutions. Sev
eral important results in geometric analysis such as extremal metrics for
the Steklov eigenvalues for instance make a crucial use of such maps. I
’ll give some open problems and will try to explain how to attack few op
en questions in the field using tools recently developed.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Roysdon (Tel Aviv)
DTSTART:20211029T183000Z
DTEND:20211029T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/56
DESCRIPTION:Title: On measure theoretic projection bodies\nby Michae
l Roysdon (Tel Aviv) as part of CRM-Montreal analysis Seminar\n\n\nAbstrac
t\nThe inequalities of Petty and Zhang are affine isoperimetric-type inequ
alities providing sharp bounds for voln−1 n (K)voln(Π◦K)\, where ΠK
is a projection body of a convex body K is the convex body with support fu
nction given by hΠK(θ) = voln−1(K|θ ⊥)\, θ ∈ S n−1 \, where θ
⊥ denotes the hyperplane orthogonal to the direction θ. The upper bou
nd\, due to Petty\, and referred to as Petty’s projection inequality att
ains equality only when K is an ellipsoid\, and the lower bound is due to
Zhang and equality occurs only when K is a simplex. In this talk\, we pre
sent a number of generalizations of Zhang’s inequality to the setting of
measures. In addition\, we introduce extensions of the projection body o
perator Π to the setting of arbitrary measures\, that is\, given a measur
e µ on R n with continuous density ϕ\, ΠµK is the convex bodies whose
support function is given by hΠµK(θ) = 1 2 Z ∂K |hθ\, nK(y)i|φ(y)dy
\, where ∂K denotes the boundary of K and nK(y) denotes the outer unit n
ormal of ∂K at y. We remark that the support function hπµK has been d
eeply studied in the literature\, and is an example of a generalized zonio
d when ϕ is taken to be even. Authors: Dylan Langharst\; Kent State Univ
ersity Michael Roysdon\; Tel Aviv University Artem Zvavitch\; Kent State U
niversity\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fortier Bourque (Universite de Montreal)
DTSTART:20211112T193000Z
DTEND:20211112T203000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/57
DESCRIPTION:Title: The extremal length systole of the Bolza surface\
nby Maxime Fortier Bourque (Universite de Montreal) as part of CRM-Montrea
l analysis Seminar\n\n\nAbstract\nThe extremal length of a curve on a Riem
ann surface is a conformal invariant that has a nice geometric description
but is not so simple to compute in practice. The extremal length systole
is defined as the infimum of the extremal lengths of all non-contractible
closed curves. I will discuss joint work with Didac Martinez-Granado and
Franco Vargas Pallete in which we compute the extremal length systole of
the Bolza surface\, the most symmetric surface of genus two. The calculat
ion involves certain identities for elliptic integrals called the Landen t
ransformations. We also prove that the Bolza surface is a local maximizer
for the extremal length systole and conjecture that it is the unique glob
al maximizer.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrios Ntalampekos (Stony Brook)
DTSTART:20211119T193000Z
DTEND:20211119T203000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/58
DESCRIPTION:Title: Rigidity theorems for circle domains\nby Dimitrio
s Ntalampekos (Stony Brook) as part of CRM-Montreal analysis Seminar\n\n\n
Abstract\nA circle domain $\\Omega$ in the Riemann sphere is a domain each
of whose boundary components is either a circle or a point. A circle dom
ain $\\Omega$ is called conformally rigid if every conformal map from $\\O
mega$ onto another circle domain is the restriction of a Mobius transforma
tion. In this talk I will present some new rigidity theorems for circle d
omains satisfying a certain quasihyperbolic condition. As a corollary\, J
ohn and Holder circle domains are rigid. This provides new evidence for a
conjecture of He and Schramm\, relating rigidity and conformal removabili
ty. This talk is based on joint work with Malik Younsi.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suresh Eswarathasan (Dalhousie)
DTSTART:20211126T193000Z
DTEND:20211126T203000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/59
DESCRIPTION:Title: Fractal uncertainty principle for discrete Cantor set
s for random alphabets\nby Suresh Eswarathasan (Dalhousie) as part of
CRM-Montreal analysis Seminar\n\n\nAbstract\nThe fractal uncertainty princ
iple (FUP) introduced by Dyatlov-Zahl’16 has seen some powerful applicat
ions in the last few years and become a hot topic in harmonic analysis. I
n this talk\, we study the FUP for discrete Cantor sets from a probabilist
ic perspective. We show that randomizing our alphabets gives a quantifiab
le improvement over the current “zero” and “pressure” bounds. In
turn\, this provides the best possible exponent when the Cantor sets enjoy
either the strongest Fourier decay or additive energy assumptions. This
is joint work with Xiaolong Han (Cal. State Northridge)\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bishop (Stony Brook)
DTSTART:20220211T193000Z
DTEND:20220211T203000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/60
DESCRIPTION:Title: Dessins and Dynamics\nby Chris Bishop (Stony Broo
k) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nAfter defining
harmonic measure on a planar domain\, I will discuss "true trees"\, i.e.\,
trees drawn in the plane so that every edge has equal harmonic measure an
d so that these measures are symmetric on each edge. True trees on the 2-
sphere are a special case in Grothendieck's theory of dessins d'enfant\, w
here a graph on a topological surface induces a conformal structure on tha
t surface. I will recall the connection between dessins\, equilateral tri
angulations and branched coverings (Belyi's theorem). I will also describ
e some recent applications of these ideas to holomorphic dynamics: approxi
mating sets by polynomial Julia sets\, finding meromorphic functions with
prescribed postcritical orbits\, constructing finite type dynamical system
s on hyperbolic Riemann surfaces\, building wandering domains for entire f
unctions\, and estimating the fractal dimensions of transcendental Julia s
ets. There will be many pictures and few proofs.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Wang (Indiana University)
DTSTART:20220225T193000Z
DTEND:20220225T203000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/61
DESCRIPTION:Title: Slope Gap Distributions of Veech Translation Surfa
ces\nby Jane Wang (Indiana University) as part of CRM-Montreal analysi
s Seminar\n\n\nAbstract\nTranslation surfaces are surfaces that are locall
y Euclidean except at finitely many points called cone points\, an example
being the regular octagon with opposite sides identified (the vertices ar
e identified and become a single cone point). A saddle connection is then
a straight trajectory that begins and ends at a cone point. It is known
that on almost every translation surface\, the set of angles of saddle con
nections on the surface is equidistributed in the circle. A finer notion
of how random the saddle connection directions are is given by something c
alled the gap distribution of the surface. In this talk\, we will expl
ain what the slope gap distribution of a translation surface is and su
rvey some known results about slope gap distributions\, including how o
ne can use properties of the horocycle flow to compute the slope gap di
stributions of special translation surfaces called Veech surfaces. We'll
then discuss recent results showing that the slope gap distributions
of Veech surfaces have to satisfy some nice analytic properties. This pro
ject is joint work with Luis Kumanduri and Anthony Sanchez.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Pilgrim (Indiana University)
DTSTART:20220325T183000Z
DTEND:20220325T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/62
DESCRIPTION:Title: Conformal surface embeddings and extremal length\
nby Kevin Pilgrim (Indiana University) as part of CRM-Montreal analysis Se
minar\n\n\nAbstract\nGiven two Riemann surfaces with boundary and a homoto
py class of topological embeddings between them\, we show there is a confo
rmal embedding in the homotopy class if and only if the extremal length of
every simple multi-curve is decreased under the embedding. For applicatio
ns to dynamical systems\, we need an additional fact: if the ratio is boun
ded above away from one\, then it remains so under passing to any finite c
over. I will also briefly mention how under natural conditions the techniq
ue of quasiconformal surgery promotes so-called rational-like maps f:f^{-1
}(S)→S\, where f^{−1}(S)⊂S are planar Riemann surfaces\, to rational
maps. This is joint work of Jeremy Kahn\, Kevin M. Pilgrim\, and Dylan P.
Thurston\; https://arxiv.org/abs/1507.05294 .\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norm Levenberg (Indiana University)
DTSTART:20220415T183000Z
DTEND:20220415T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/63
DESCRIPTION:Title: Zeros of Random Polynomial Mappings in Several Comple
x Variables\nby Norm Levenberg (Indiana University) as part of CRM-Mon
treal analysis Seminar\n\n\nAbstract\nWe discuss some results on random po
lynomials with an eye towards obtaining universality results under the mos
t general assumptions on the random coefficients. In particular\, we gener
alize and strengthen some previous results on asymptotic distribution of n
ormalized zero measures and currents associated to random polynomials and
random polynomial mappings in several complex variables. The talk is based
on joint work with Turgay Bayraktar and Tom Bloom.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro Romaniega (ICMAT)
DTSTART:20220520T183000Z
DTEND:20220520T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/64
DESCRIPTION:Title: Nodal sets of monochromatic waves from a deterministi
c and random point of view\nby Álvaro Romaniega (ICMAT) as part of CR
M-Montreal analysis Seminar\n\n\nAbstract\nIn this talk we present recent
results on the nodal set (i.e.\, the zero level set) of monochromatic wave
s (i.e.\, solutions of the Helmholtz equation) on the Euclidean space. Fol
lowing the breakthrough work of F. Nazarov and M. Sodin\, a growing litera
ture gives us powerful probabilistic results for the number of connected c
omponents of the nodal set of random monochromatic waves. The aim of this
talk is to explore the properties of these standard random monochromatic w
aves and\, consequently\, define a more general class of random monochroma
tic waves depending on a parameter \, which includes the standard definiti
on as a particular case. This parameter controls some regularity (of the F
ourier transform) and decay properties of these waves. Given that\, we stu
dy the structure of the nodal set depending on that parameter from a deter
ministic and from a random point of view. Finally\, we show how to constru
ct deterministic realizations or examples of monochromatic waves satisfyin
g the probabilistic Nazarov-Sodin volumetric growth for the number of conn
ected components of the nodal set and similarly for the volume of the noda
l set. This is a joint work with A. Enciso\, D. Peralta-Salas and A. Sarto
ri.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norm Levenberg (Indiana University)
DTSTART:20220422T183000Z
DTEND:20220422T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/65
DESCRIPTION:Title: Zeros of Random Polynomial Mappings in Several Comple
x Variables\nby Norm Levenberg (Indiana University) as part of CRM-Mon
treal analysis Seminar\n\n\nAbstract\nWe discuss some results on random po
lynomials with an eye towards obtaining universality results under the mos
t general assumptions on the random coefficients. In particular\, we gene
ralize and strengthen some previous results on asymptotic distribution of
normalized zero measures and currents associated to random polynomials and
random polynomial mappings in several complex variables. The talk is bas
ed on joint work with Turgay Bayraktar and Tom Bloom.\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Decio (Norwegian University of Science and Technology)
DTSTART:20220506T183000Z
DTEND:20220506T193000Z
DTSTAMP:20260404T095207Z
UID:MathematicalAnalysis/66
DESCRIPTION:by Stefano Decio (Norwegian University of Science and Technolo
gy) as part of CRM-Montreal analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/MathematicalAnalysis/66/
END:VEVENT
END:VCALENDAR