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BEGIN:VEVENT
SUMMARY:Alexandre Girouard (Université Laval)
DTSTART;VALUE=DATE-TIME:20200501T170000Z
DTEND;VALUE=DATE-TIME:20200501T174500Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/1
DESCRIPTION:Title: Homogenization of Steklov problems with applications to sharp
isoperimetric bounds\, part I\nby Alexandre Girouard (Université Lav
al) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe question t
o find the best upper bound for the first nonzero Steklov eigenvalue of a
planar domain goes back to Weinstock\, who proved in 1954 that the first n
onzero perimeter-normalized Steklov eigenvalue of a simply-connected plana
r domain is 2*pi\, with equality iff the domain is a disk. In a recent joi
nt work with Mikhail Karpukhin and and Jean Lagacé\, we were able to let
go of the simple connectedness assumption. We constructed a family of doma
ins for which the perimeter-normalized first eigenvalue tends to 8π. In c
ombination with Kokarev's bound from 2014\, this solves the isoperimetric
problem completely for the first nonzero eigenvalue. The domains are obtai
ned by removing small geodesic balls that are asymptotically densely perio
dically distributed as their radius tends to zero. The goal of this talk w
ill be to survey recent work on homogenisation of the Steklov problem whic
h lead to the above result. On the way we will see that many spectral prob
lems can be approximated by Steklov eigenvalues of perforated domains. A s
urprising consequence is the existence of free boundary minimal surfaces i
mmersed in the unit ball by first Steklov eigenfunctions and with area str
ictly larger than 2*pi. This talk is based on joint work with Antoine Henr
ot (U. de Lorraine)\, Mikhail Karpukhin (UCI) and Jean Lagacé(UCL).\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Lagacé (University College London)
DTSTART;VALUE=DATE-TIME:20200501T175000Z
DTEND;VALUE=DATE-TIME:20200501T183500Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/2
DESCRIPTION:Title: Homogenization of Steklov problems with applications to sharp
isoperimetric bounds\, part II.\nby Jean Lagacé (University College
London) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nTraditiona
lly\, deterministic homogenisation theory uses the periodic structure of E
uclidean space to describe uniformly distributed perturbations of a PDE.
It has been known for years that it has many applications to shape optimis
ation. In this talk\, I will describe how the lack of periodic structure
can be overcome to saturate isoperimetric bounds for the Steklov problem o
n surfaces. The construction is intrinsic and does not depend on any auxi
liary periodic objects or quantities. Using these methods\, we obtain the
existence of free boundary minimal surfaces in the unit ball with large a
rea. I will also describe how the intuition we gain from the homogenisati
on construction allows us to actually construct some of them\, partially v
erifying a conjecture of Fraser and Li. This talk is based on joint work
with Alexandre Girouard (U. Laval)\, Antoine Henrot (U. de Lorraine) and
Mikhail Karpukhin (UCI).\n\nEn ligne-Web: Veuillez communiquer avec l'org
anisateur/Please contat the organizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Zelditch (Northwestern University)
DTSTART;VALUE=DATE-TIME:20200507T170000Z
DTEND;VALUE=DATE-TIME:20200507T183500Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/3
DESCRIPTION:Title: Spectral asymptotics for stationary spacetimes\nby Steve
Zelditch (Northwestern University) as part of CRM-Montreal analysis Semina
r\n\n\nAbstract\nWe explain how to formulate and prove analogues of the st
andard theorems on spectral asymptotics on compact Riemannian manifolds --
Weyl's law and the Gutzwiller trace formula-- for stationary spacetimes.
As a by-product we prove a semi-classical Weyl law for the Klein-Gordon e
quation where the mass is the inverse Planck constant.\n\nSéminaire en li
gne / Web Seminar\nVeuillez communiquer avec l'organisateur pour toute que
stion / Please contact the organizer for any questions at: dmitry.jakobson
@mcgill.ca\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malik Younsi (University of Hawaii)
DTSTART;VALUE=DATE-TIME:20200515T183000Z
DTEND;VALUE=DATE-TIME:20200515T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/4
DESCRIPTION:Title: Holomorphic motions\, conformal welding and capacity\nby
Malik Younsi (University of Hawaii) as part of CRM-Montreal analysis Semin
ar\n\n\nAbstract\nThe notion of a holomorphic motion was introduced by Man
e\, Sad and Sullivan in the 1980's\, motivated by the observation that Jul
ia sets of rational maps often move holomorphically with holomorphic varia
tions of the parameters. Even though the original motivation for their stu
dy came from complex dynamics\, holomorphic motions have found over the ye
ars to be of fundamental importance in other related areas of Complex Anal
ysis\, such as the theory of Kleinian groups and Teichmuller theory for in
stance. Holomorphic motions also played a central role in the seminal work
of Astala on distortion of dimension and area under quasiconformal mappin
gs. In this talk\, I will first review the basic notions and results relat
ed to holomorphic motions\, including quasiconformal mappings and the (ext
ended) lambda lemma. I will then present some recent results on the behavi
or of logarithmic capacity and analytic capacity under holomorphic motions
. As we will see\, conformal welding (of quasicircle Julia sets) plays a f
undamental role. This is joint work with Tom Ransford and Wen-Hui Ai.\n\nE
n ligne-Web: Veuillez communiquer avec l'organisateur/Please contat the or
ganizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeff Galkowski (University College London)
DTSTART;VALUE=DATE-TIME:20200522T150000Z
DTEND;VALUE=DATE-TIME:20200522T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/5
DESCRIPTION:Title: Viscosity limits for 0th order operators\nby Jeff Galkows
ki (University College London) as part of CRM-Montreal analysis Seminar\n\
n\nAbstract\nIn recent work\, Colin de Verdiere--Saint-Raymond and Dyatlov
--Zworski showed that a class of zeroth order pseudodifferential operators
coming from experiments on forced waves in fluids satisfies a limiting ab
sorption principle. Thus\, these operators have absolutely continuous spe
ctrum with possibly finitely many embedded eigenvalues. In this talk\, we
discuss the effect of small viscosity on the spectra of these operators\,
showing that the spectrum of the operator with small viscosity converges
to the poles of a certain meromorphic continuation of the resolvent throug
h the continuous spectrum. In order to do this\, we introduce spaces base
d on an FBI transform which allows for the testing of microlocal analytici
ty properties. This talk is based on joint work with M. Zworski.\n\nEn l
igne-Web: Veuillez communiquer avec l'organisateur/Please contat the organ
izer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Blair Davey (The City College of New York)
DTSTART;VALUE=DATE-TIME:20200528T160000Z
DTEND;VALUE=DATE-TIME:20200528T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/6
DESCRIPTION:Title: A quantification of the Besicovitch projection theorem and it
s generalizations\nby Blair Davey (The City College of New York) as pa
rt of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe Besicovitch project
ion theorem asserts that if a subset E of the plane has finite length in t
he sense of Hausdorff and is purely unrectifiable (so its intersection wit
h any Lipschitz graph has zero length)\, then almost every linear projecti
on of E to a line will have zero measure. As a consequence\, the probabil
ity that a line dropped randomly onto the plane intersects such a set E is
equal to zero. Thus\, the Besicovitch projection theorem is connected to
the classical Buffon needle problem. Motivated by the so-called Buffon c
ircle problem\, we explore what happens when lines are replaced by more ge
neral curves. We discuss generalized Besicovitch theorems and\, as Tao di
d for the classical theorem (Proc. London Math. Soc.\, 2009)\, we use mu
lti-scale analysis to quantify these results. This work is joint with Lau
ra Cladek and Krystal Taylor.\n\nEn ligne-Web: Veuillez communiquer avec l
'organisateur/Please contat the organizer: dmitry.jakobson@mcgill.ca\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sagun Chanillo (Rutgers\, School of Arts and Sciences)
DTSTART;VALUE=DATE-TIME:20200603T173000Z
DTEND;VALUE=DATE-TIME:20200603T183000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/7
DESCRIPTION:Title: Bourgain-Brezis inequalities\, applications and Borderline So
bolev inequalities on Riemannian Symmetric spaces of non-compact type\
nby Sagun Chanillo (Rutgers\, School of Arts and Sciences) as part of CRM-
Montreal analysis Seminar\n\n\nAbstract\nBourgain and Brezis discovered a
remarkable inequality which\nis borderline for the Sobolev inequality in E
ulcidean spaces. In this\ntalk we obtain these inequalities on nilpotent L
ie groups and on\nRiemannian symmetric spaces of non-compact type. We obta
in applications\nto Navier Stokes eqn in 2D and to Strichartz inequalities
for wave and\nSchrodinger equations and to the Maxwell equations for Elec
tromagnetism.\nThese results were obtained jointly with Jean Van Schafting
en and Po-lam\nYung.\n\nJoint seminar with Geometric Analysis - En ligne-W
eb: Veuillez communiquer avec l'organisateur/Please contat the organizer:
dmitry.jakobson@mcgill.ca\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spyros Alexakis (University of Toronto)
DTSTART;VALUE=DATE-TIME:20200611T163000Z
DTEND;VALUE=DATE-TIME:20200611T173000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/8
DESCRIPTION:Title: Singularity formation in Black Hole interiors\nby Spyros
Alexakis (University of Toronto) as part of CRM-Montreal analysis Seminar\
n\n\nAbstract\nThe prediction that solutions of the Einstein equations in
the interior of black holes must always terminate at a singularity was ori
ginally conceived by Penrose in 1969\, under the name of "strong cosmic ce
nsorship hypothesis". The nature of this break-down (i.e. the asymptotic
properties of the space-time metric as one approaches the terminal singul
arity) is not predicted\, and remains a hotly debated question to this 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 physical/
geometric quantities at the singularity. Mutually contradicting predictio
ns abound in this topic. Much work has been done under the assumption of
spherical symmetry (for various matter models). We present a stability re
sult for the Schwarzschild singularity under polarized axi-symmetric pertu
rbations of the initial data\, joint with G. Fournodavlos). One key inno
vation of our approach is a certain new way to treat the Einstein equation
s in axial symmetry\, which should have broader applicability.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Strohmaier (University of Leeds)
DTSTART;VALUE=DATE-TIME:20200619T160000Z
DTEND;VALUE=DATE-TIME:20200619T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/9
DESCRIPTION:Title: Scattering theory for difScattering theory for differential f
orms and its relation to cohomologyferential forms and its relation to coh
omology\nby Alexander Strohmaier (University of Leeds) as part of CRM-
Montreal analysis Seminar\n\n\nAbstract\nI will consider spectral theory o
f the Laplace operator on a manifold that is Euclidean outside a compact s
et. An example of such a setting is obstacle scattering where several com
pact pieces are removed from $\\R^d$. The spectrum of the operator on fun
ctions is absolutely continuous. In the case of general $p$-forms eigenva
lues at zero may exist\, the eigenspace consisting of L^2-harmonic forms.
The dimension of this space is computable by cohomological methods. I wi
ll present some new results concerning the detailed expansions of generali
sed eigenfunctions\, the scattering matrix\, and the resolvent near zero.
These expansions contain the L^2-harmonic forms so there is no clear sepa
ration between the continuous and the discrete spectrum. This can be used
to obtain more detailed information about the L^2-cohomology as well as t
he spectrum. If I have time I will explain an application of this to phys
ics. (joint work with Alden Waters)\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Logunov (Princeton University)
DTSTART;VALUE=DATE-TIME:20200626T140000Z
DTEND;VALUE=DATE-TIME:20200626T145000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/10
DESCRIPTION:Title: Nodal sets\, Quasiconformal mappings and how to apply them t
o Landis' conjecture\nby Alexander Logunov (Princeton University) as p
art of CRM-Montreal analysis Seminar\n\n\nAbstract\nA while ago Nadirashvi
li proposed a beautiful idea how to attack problems on zero sets of Laplac
e eigenfunctions using quasiconformal mappings\, aiming to estimate the le
ngth of nodal sets (zero sets of eigenfunctions) on closed two-dimensional
surfaces. The idea have not yet worked out as it was planned. However i
t appears to be useful for Landis' Conjecture. We will explain how to app
ly the combination of quasiconformal mappings and zero sets to quantitativ
e properties of solutions to $\\Delta u + V u =0 on the plane\, where $V$
is a real\, bounded function. The method reduces some questions about sol
utions to Shrodinger equation $\\Delta u + V u =0$ on the plane to questio
ns about harmonic functions. Based on a joint work with E.Malinnikova\, N
.Nadirashvili and F. Nazarov.\n\nSPECIAL SEMINAR ON THE OCCASION OF THE 6
5TH BIRTHDAY OF N. NADIRASHVILI\nFRIDAY\, JUNE 26\, STARTS AT 10:00 AM EAS
TERN TIME\, ZOOM SEMINAR\nProgram: 11:00 - 11:50: Vladimir Sverak (Univers
ity of Minnesota)\nZoome banquet Analysis Seminar: 12:15-13:30\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Sverak (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20200626T150000Z
DTEND;VALUE=DATE-TIME:20200626T155000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/11
DESCRIPTION:Title: Liouville theorems for the Navier-Stokes equations\nby V
ladimir Sverak (University of Minnesota) as part of CRM-Montreal analysis
Seminar\n\n\nAbstract\nAssume u is a smooth\, bounded\, and divergence-fre
e field on R^3 satisfying the steady Navier-Stokes equation -\\Delta u +u\
\nabla u + \\nabla p=0 (for a suitable function p). Does u have to be cons
tant? We still don't know. Interesting things are known and Nikolai made i
mportant contributions to our knowledge concerning this question. Similar
problems can also be considered for various model equations. The lecture w
ill concern various aspects of this problem.\n\nSPECIAL SEMINAR ON THE OCC
ASION OF THE 65TH BIRTHDAY OF N. NADIRASHVILI\nFRIDAY\, JUNE 26\, STARTS A
T 10:00 AM EASTERN TIME\, ZOOM SEMINAR\nProgram: 10:00 - 10:50: Alexander
Logunov (Princeton University )\nZoome banquet Analysis Seminar: 12:15-13:
30\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART;VALUE=DATE-TIME:20200715T150000Z
DTEND;VALUE=DATE-TIME:20200715T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/12
DESCRIPTION:Title: The spectral a random hyperbolic surface\nby Michael Mag
ee (Durham University) as part of CRM-Montreal analysis Seminar\n\n\nAbstr
act\nOn a compact hyperbolic surface\, the Laplacian has a spectral gap be
tween 0 and the next smallest eigenvalue if and only if the surface is con
nected. The size of the spectral gap measures both how highly connected th
e surface is\, and the rate of exponential mixing of the geodesic flow on
the surface. There is an analogous concept of spectral gap for graphs\, wi
th analogous connections to connectivity and dynamics. Motivated by theore
ms about the spectral gap of random regular graphs\, we proved that for an
y $\\epsilon > 0$\, a random cover of a fixed compact connected hyperbolic
surface has no new eigenvalues below 3/16 - $\\epsilon$\, with probabilit
y tending to 1 as the covering degree tends to infinity. The number 3/16 i
s\, mysteriously\, the same spectral gap that Selberg obtained for congrue
nce modular curves. The talk is intended to be accessible to graduate stud
ents and is based on joint works with Frédéric Naud and Doron Puder.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Wilson (The University of Vermont)
DTSTART;VALUE=DATE-TIME:20200807T150000Z
DTEND;VALUE=DATE-TIME:20200807T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/13
DESCRIPTION:Title: Perturbed Haar function expansions\nby Mike Wilson (The
University of Vermont) as part of CRM-Montreal analysis Seminar\n\nAbstrac
t: TBA\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malabika Pramanik (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20200828T160000Z
DTEND;VALUE=DATE-TIME:20200828T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/14
DESCRIPTION:Title: Restriction of eigenfunctions to sparse sets on manifolds\nby Malabika Pramanik (University of British Columbia) as part of CRM-Mo
ntreal analysis Seminar\n\n\nAbstract\nGiven a compact Riemannian manifold
$(M\, g)$ without boundary\, we consider the restriction of Laplace-Beltr
ami eigenfunctions to certain subsets $\\Gamma$ of the manifold. How do t
he Lebesgue $L^p$ norms of these restricted eigenfunctions grow? Burq\, Ge
rard\, Szvetkov and independently Hu studied this question when $\\Gamma$
is a submanifold. In ongoing joint work with Suresh Eswarathasan\, we ext
end earlier results to the setting where $\\Gamma$ is an arbitrary Borel s
ubset of $M$. Here differential geometric methods no longer apply. Using
methods from geometric measure theory\, we obtain sharp growth estimates
for the restricted eigenfunctions that rely only on the size of $\\Gamma$.
Our results are sharp for large $p$\, and are realized for large familie
s of sets $\\Gamma$ that are random and Cantor-like.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Maria Martell (Instituto de Ciencias Matemáticas (ICMAT))
DTSTART;VALUE=DATE-TIME:20200911T130000Z
DTEND;VALUE=DATE-TIME:20200911T140000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/15
DESCRIPTION:Title: Uniform rectifiability and elliptic operators satisfying a C
arleson measure condition\nby Jose Maria Martell (Instituto de Ciencia
s Matemáticas (ICMAT)) as part of CRM-Montreal analysis Seminar\n\n\nAbst
ract\nIn this talk I will study the correspondence between the properties
of the solutions of a class of PDEs and the geometry of sets in Euclidean
space. We settle the question of whether (quantitative) absolute continui
ty of the elliptic measure with respect to the surface measure and uniform
rectifiability of the boundary are equivalent\, in an optimal class of di
vergence form elliptic operators satisfying a suitable Carleson measure co
ndition. Our setting is that of domains having an Ahlfors regular boundar
y and satisfying the so-called interior Corkscrew and Harnack chain condit
ions (these are respectively scale-invariant/quantitative versions of open
ness and path-connectivity) and we show that for the class of Kenig-Pipher
uniformly elliptic operators (operators whose coefficients have controlle
d oscillation in terms of a Carleson measure condition) the solvability of
the $L^p$-Dirichlet problem with some finite $p$ is equivalent to the qua
ntitative openness of the exterior domains or to the uniform rectifiablity
of the boundary. \n\nJoint work with S. Hofmann\, S. Mayboroda\, T.
Toro\, and Z. Zhao.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Wilson (The University of Vermont)
DTSTART;VALUE=DATE-TIME:20200821T150000Z
DTEND;VALUE=DATE-TIME:20200821T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/16
DESCRIPTION:Title: Perturbed Haar function expansions\nby Mike Wilson (The
University of Vermont) as part of CRM-Montreal analysis Seminar\n\nAbstrac
t: TBA\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryan Gibara (Université Laval)
DTSTART;VALUE=DATE-TIME:20201211T143000Z
DTEND;VALUE=DATE-TIME:20201211T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/17
DESCRIPTION:Title: Boundedness and continuity for rearrangements on spaces defi
ned by mean oscillation\nby Ryan Gibara (Université Laval) as part of
CRM-Montreal analysis Seminar\n\n\nAbstract\nIn joint work with Almut Bur
chard and Galia Dafni\, we study the boundedness and continuity of rearran
gement operators on the space BMO of functions of bounded mean oscillation
. Improved bounds are obtained for the BMO-seminorm of the decreasing rear
rangement\, and the symmetric decreasing rearrangement is shown to be boun
ded on BMO. Both of these rearrangements are shown to be discontinuous as
maps on BMO\, but sufficient normalization conditions are established to g
uarantee continuity on the subspace VMO of functions of vanishing mean osc
illation.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renaud Raquepas (McGill University)
DTSTART;VALUE=DATE-TIME:20201211T160000Z
DTEND;VALUE=DATE-TIME:20201211T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/18
DESCRIPTION:Title: Entropy production in nondegenerate diffusions: large times
and small noises\nby Renaud Raquepas (McGill University) as part of CR
M-Montreal analysis Seminar\n\n\nAbstract\nEntropy production (EP) is a ke
y 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. Then\, I
will focus on the context of nondegenerate diffusions and I will describe
the large-deviation properties of EP as time goes to infinity. I will also
explain how the behaviour of the corresponding rate function boils down t
o the study of the smallest eigenvalue for a family of differential operat
ors with a small parameter.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anush Tserunyan (McGill University)
DTSTART;VALUE=DATE-TIME:20210115T190000Z
DTEND;VALUE=DATE-TIME:20210115T200000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
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 th
e classical pointwise ergodic theorem for a probability measure preserving
(pmp) transformation $T$\, one takes averages of a given integrable funct
ion over the intervals $\\{x\, T(x)\, T^2(x)\, \\hdots\, T^n(x)\\}$ in fro
nt of the point $x$. We prove a “backward” ergodic theorem for a count
able-to-one pmp $T$\, where the averages are taken over subtrees of the gr
aph of T that are rooted at $x$ and lie behind $x$ (in the direction of $T
^{-1}$). Surprisingly\, this theorem yields forward ergodic theorems for c
ountable groups\, in particular\, one for pmp actions of free groups of fi
nite rank\, where the averages are taken along subtrees of the standard Ca
yley graph rooted at the identity. This strengthens Bufetov’s theorem fr
om 2000\, which was the most general result in this vein. This is joint wo
rk with Jenna Zomback.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Vig (CRM\, McGill)
DTSTART;VALUE=DATE-TIME:20210212T160000Z
DTEND;VALUE=DATE-TIME:20210212T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/20
DESCRIPTION:Title: Spectral invariants and Birkhoff Billiards\nby Amir Vig
(CRM\, McGill) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nCon
sider a smooth\, bounded\, strictly convex domain in the plane. There are
two games one can play. The classical one is billiards\, in which a billia
rd ball orbits around the domain and reflects elastically at the boundary.
The “quantum” analogue involves the study of wave propagation in the
domain and understanding the frequencies at which such waves oscillate. In
this talk\, we discuss recent progress on the inverse spectral problem of
determining a billiard table from its Laplace spectrum. In particular\, w
e introduce a new class of spectral invariants for a generic class of bill
iard tables obtained from an explicit Hadamard-Riesz type parametrix for t
he wave propagator\, microlocally near geodesic loops of small rotation nu
mber. These same techniques also allow us to prove (infinitesimal) Robin s
pectral rigidity of the ellipse\, when both the boundary and boundary cond
itions are allowed to deform simultaneously. Finally\, we mention ongoing
work together with Vadim Kaloshin to cancel singularities in the wave trac
e for special types of domains.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Jaye (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20210305T160000Z
DTEND;VALUE=DATE-TIME:20210305T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/21
DESCRIPTION:Title: Multi-scale analysis of Jordan curves\nby Benjamin Jaye
(Georgia Tech) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nIn
this talk we will describe how one can detect regularity in Jordan curves
through analysis of associated geometric square functions. We will partic
ularly focus on the resolution of a conjecture of L. Carleson. Joint work
with Xavier Tolsa and Michele Villa (https://arxiv.org/abs/1909.08581).\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Ransford (Université Laval)
DTSTART;VALUE=DATE-TIME:20210319T150000Z
DTEND;VALUE=DATE-TIME:20210319T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/22
DESCRIPTION:Title: Failure of approximation of odd functions by odd polynomials
\nby Thomas Ransford (Université Laval) as part of CRM-Montreal analy
sis Seminar\n\n\nAbstract\nWe construct a Hilbert holomorphic function spa
ce $H$ on the unit disk such that the polynomials are dense in $H$\, but t
he odd polynomials are not dense in the odd functions in $H$. As a consequ
ence\, there exists a function $f$ in $H$ that lies outside the closed lin
ear span of its Taylor partial sums $s_n(f)$\, so it cannot be approximate
d by any triangular summability method applied to the $s_n(f)$. We also sh
ow that there exists a function $f$ in $H$ that lies outside the closed li
near span of its radial dilates $f_r\, r < 1$. (Joint work with Javad Mash
reghi and Pierre-Olivier Parise).\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Faifman (Tel Aviv University)
DTSTART;VALUE=DATE-TIME:20210326T180000Z
DTEND;VALUE=DATE-TIME:20210326T190000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
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\nAbstr
act\nThe Funk metric in the interior of a convex set is a lesser-known cou
sin of the Hilbert metric. The latter generalizes the Beltrami-Klein model
of hyperbolic geometry\, and both have straight segments as geodesics\, t
hus constituting solutions of Hilbert's 4th problem alongside normed space
s. Unlike the Hilbert metric\, the Funk metric is not projectively invaria
nt. I will explain how\, nevertheless\, the Funk metric gives rise to many
projective invariants\, which moreover enjoy a duality extending results
of Holmes-Thompson and Alvarez Paiva on spheres of normed spaces and Gutki
n-Tabachnikov on Minkowski billiards. I will also discuss how the maximal
volume problem in Funk geometry yields an extension of the Blaschke-Santal
o inequality.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Khanin (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210409T180000Z
DTEND;VALUE=DATE-TIME:20210409T190000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/24
DESCRIPTION:Title: On Stationary Solutions to the Stochastic Heat Equation\
nby Konstantin Khanin (University of Toronto) as part of CRM-Montreal anal
ysis Seminar\n\n\nAbstract\nI plan to discuss the problem of uniqueness of
global solutions to the random Hamilton-Jacobi equation. I will formulat
e several conjectures and present results supporting them. Then I will di
scuss a new uniqueness result for the Stochastic Heat equation in the regi
me of weak disorder.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolai Krylov (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20210416T140000Z
DTEND;VALUE=DATE-TIME:20210416T150000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/25
DESCRIPTION:Title: A review of some new results in the theory of linear ellipti
c equations with drift in $L_{d}$\nby Nicolai Krylov (University of Mi
nnesota) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nWe presen
t an overview of recent results related to the Aleksandrov type estimates
with power of summability of the free term $d_0 < d$\, the Harnack inequal
ity for $u\\in W^{2}_{d_{0}\,loc}$\, Holder continuity of $L$-harmonic and
$L$-caloric functions. Under the assumption that the main coefficients ar
e almost in VMO (and $b\\in L_{d}$) we also present the results about solv
ability 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 zoom: htt
ps://ulaval.zoom.us/j/62869112863?pwd=dndUME9ORmRVQWxGRklvcmFmL3Fydz09\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitali Vougalter (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210423T180000Z
DTEND;VALUE=DATE-TIME:20210423T190000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/26
DESCRIPTION:Title: Solvability of some integro-differential equations with anom
alous diffusion and transport\nby Vitali Vougalter (University of Toro
nto) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe work deal
s with the existence of solutions of an integro-differential equation in t
he case of the anomalous diffusion with the negative Laplace operator in a
fractional power in the presence of the transport term. The proof of exis
tence of solutions is based on a fixed point technique. Solvability condit
ions for elliptic operators without Fredholm property in unbounded domains
are used. We discuss how the introduction of the transport term impacts t
he regularity of solutions.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nages Shanmugalingam (University of Cincinnati)
DTSTART;VALUE=DATE-TIME:20210507T180000Z
DTEND;VALUE=DATE-TIME:20210507T190000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/27
DESCRIPTION:Title: Prime ends for domains in metric measure spaces and their us
e in potential theory and QC theory\nby Nages Shanmugalingam (Universi
ty of Cincinnati) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\n
Prime ends were first developed by Caratheodory in order to understand the
boundary behavior of conformal mappings from the disk. As such\, the cons
truction of Caratheodory and Ahlfors worked for simply connected planar do
mains\, but had to be modified for more general domains. In this talk we w
ill focus on a construction in the setting of domains in metric spaces\, a
nd describe their use in potential theory (Dirichlet problem for the p-ene
rgy minimizers) and in studying boundary behavior of QC maps.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Germain Gendron (Université de Nantes (1/3))
DTSTART;VALUE=DATE-TIME:20210322T150000Z
DTEND;VALUE=DATE-TIME:20210322T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/28
DESCRIPTION:Title: Uniqueness and stability for an inverse Steklov problem\
nby Germain Gendron (Université de Nantes (1/3)) as part of CRM-Montreal
analysis Seminar\n\n\nAbstract\nIn this talk\, we present results for an i
nverse Steklov problem for a particular class of 2-dimensional manifolds h
aving the topology of a hollow sphere and equipped with a warped product m
etric. We prove that the knowledge of the Steklov spectrum determines uni
quely the associated warping function up to a natural invariance. Then\,
we study the continuous dependence of the warping function defining the wa
rped product with respect to the Steklov spectrum.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Monk (IRMA Strasbourg (2/3))
DTSTART;VALUE=DATE-TIME:20210322T150000Z
DTEND;VALUE=DATE-TIME:20210322T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
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 Semina
r\n\n\nAbstract\nThe main aim of this talk is to present geometric and spe
ctral properties of typical hyperbolic surfaces. More precisely\, I will:
\n• introduce a probabilistic model\, first studied by Mirzakhani\, whi
ch is a natural and convenient way to sample random hyperbolic surfaces \n
• describe the geometric properties of these random surfaces \n• expla
in how one can deduce from this geometric information estimates on the num
ber of eigenvalues of the Laplacian in an interval [a\,b]\, using the Selb
erg trace formula.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhichao Wang (University of Toronto (3/3))
DTSTART;VALUE=DATE-TIME:20210322T150000Z
DTEND;VALUE=DATE-TIME:20210322T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/30
DESCRIPTION:Title: Conformal upper bounds for the volume spectrum\nby Zhich
ao Wang (University of Toronto (3/3)) as part of CRM-Montreal analysis Sem
inar\n\n\nAbstract\nIn this talk\, we prove upper bounds for the volume sp
ectrum of a Riemannian manifold that depend only on the volume\, dimension
\, and a conformal invariant.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Saez (Pontificia Universidad Cat´olica de Chile)
DTSTART;VALUE=DATE-TIME:20210329T160000Z
DTEND;VALUE=DATE-TIME:20210329T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/31
DESCRIPTION:Title: Eigenvalue bounds for the Paneitz operator and its associate
d boundary operator\nby Mariel Saez (Pontificia Universidad Cat´olica
de Chile) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nIn this
talk I will discuss bounds for the first eigenvalue of the Paneitz operat
or P and its associated third-order boundary operator B3 on fourmanifolds.
We restrict to orientable\, simply connected\, locally confomally flat m
anifolds that have at most two umbilic boundary components. The proof is
based on showing that under the hypotheses of the main theorems\, the cons
idered manifolds are confomally equivalent to canonical models. The 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://researchseminars.org/talk/MathematicalAnalysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hakim Boumaza (Université Paris 13)
DTSTART;VALUE=DATE-TIME:20210402T153000Z
DTEND;VALUE=DATE-TIME:20210402T163000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/32
DESCRIPTION:Title: Integrated density of states of the periodic Airy-Schröding
er operator\nby Hakim Boumaza (Université Paris 13) as part of CRM-Mo
ntreal analysis Seminar\n\n\nAbstract\nIn this talk I present\, in the sem
iclassical regime\, an explicit formula for the integrated density of stat
es of the periodic Airy-Schrodinger operator on the real line. The potent
ial of this Schrödinger operator is periodic\, continuous and piecewise l
inear. For this purpose\, the spectrum of the Schrödinger operator whose
potential is the restriction of the periodic Airy-Schrödinger potential
to a finite number of periods is studied. We prove that all the eigenvalu
es of the operator corresponding to the restricted potential are in the sp
ectral bands of the periodic Airy-Schrodinger operator and none of them ar
e 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 r
esults there are explicit constants which characterize the semiclassical r
egime. This is joint work with Olivier Lafitte (USPN - CRM Montreal).\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederic Naud (Sorbonne Université)
DTSTART;VALUE=DATE-TIME:20210505T173000Z
DTEND;VALUE=DATE-TIME:20210505T183000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/33
DESCRIPTION:Title: The spectral gap of random hyperbolic surfaces\nby Frede
ric Naud (Sorbonne Université) as part of CRM-Montreal analysis Seminar\n
\n\nAbstract\nWe will start with a survey on (some very recent) results on
the low spectrum of random compact hyperbolic surfaces\, for various mode
ls including discrete and continuous Teichmuller spaces. We will then give
some ideas of the proofs by emphasizing the analogy with radom graphs. We
will also dicuss non compact situations where similar results on resonanc
es can be obtained. Joint works with Michael Magee and Doron Puder.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Moonens (Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210519T173000Z
DTEND;VALUE=DATE-TIME:20210519T183000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/34
DESCRIPTION:Title: Solving the divergence equation with measure data in non-reg
ular domains\nby Laurent Moonens (Paris-Saclay) as part of CRM-Montrea
l analysis Seminar\n\n\nAbstract\nIn this talk\, we shall present a recent
joint work with E. Russ (Grenoble) concerning the equation $\\mathrm{div}
\\\,v=\\mu$ in a (rather general) open domain $\\Omega$\, where $\\mu$ is
a (signed) Radon measure in $\\Omega$ satisfying $\\mu(\\Omega)=0$. We sho
w 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 Neumann-
type boundary conditions.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svitlana Mayboroda (University of Minnesota)
DTSTART;VALUE=DATE-TIME:20210412T160000Z
DTEND;VALUE=DATE-TIME:20210412T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/35
DESCRIPTION:Title: The landscape law for the integrated density of states\n
by Svitlana Mayboroda (University of Minnesota) as part of CRM-Montreal an
alysis Seminar\n\n\nAbstract\nWe establish non-asymptotic estimates from a
bove and below on the integrated density of states of the Schr¨odinger op
erator L = −∆ + V \, using a counting function for the minima of the l
ocalization landscape\, a solution to the equation Lu = 1.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Helffer (Université Paris Sud)
DTSTART;VALUE=DATE-TIME:20210419T160000Z
DTEND;VALUE=DATE-TIME:20210419T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/36
DESCRIPTION:Title: Semi-classical edge states for the Robin Laplacian (after He
lffer-Kachmar)\nby Bernard Helffer (Université Paris Sud) as part of
CRM-Montreal analysis Seminar\n\n\nAbstract\nMotivated by the study of hig
h energy Steklov eigenfunctions\, we examine the semi-classical Robin Lapl
acian. In the two dimensional situation\, we determine an effective opera
tor describing the asymptotic distribution of the negative eigenvalues\, a
nd we prove that the corresponding eigenfunctions decay away from the boun
dary\, for all dimensions.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Bogdan (Wroclaw University)
DTSTART;VALUE=DATE-TIME:20210430T180000Z
DTEND;VALUE=DATE-TIME:20210430T190000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/37
DESCRIPTION:Title: Optimal Hardy identities and inequalites for the fractional
Laplacian on $L^p$\nby Krzysztof Bogdan (Wroclaw University) as part o
f CRM-Montreal analysis Seminar\n\n\nAbstract\nWe will present a route fro
m symmetric Markovian semigroups to Hardy inequalities\, to nonexplosion a
nd contractivity results for Feynman-Kac semigroups on $L^p$. We will focu
s on the fractional Laplacian on $\\mathbb{R}^d$\, in which case the const
ants\, estimates of the Feynman-Kac semigroups and tresholds for contracti
vity and explosion are sharp. Namely we will discuss selected results 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://researchseminars.org/talk/MathematicalAnalysis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karl-Mikael Perfekt (University of Reading)
DTSTART;VALUE=DATE-TIME:20210426T160000Z
DTEND;VALUE=DATE-TIME:20210426T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/38
DESCRIPTION:Title: Infinitely many embedded eigenvalues for the Neumann-Poincar
é operator in 3D\nby Karl-Mikael Perfekt (University of Reading) as p
art of CRM-Montreal analysis Seminar\n\n\nAbstract\nI will discuss the spe
ctral theory of the Neumann-Poincar´e operator for 3D domains with rotati
onally symmetric singularities\, which is directly related to the plasmoni
c eigenvalue problem for such domains. I will then describe the construct
ion of some special domains for which the problem features infinitely many
eigenvalues embedded in the essential/continuous spectrum. Several quest
ions and open problems will be stated. \nBased on joint papers with Johan
Helsing and with Wei Li and Stephen Shipman.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lipnowski (McGill University)
DTSTART;VALUE=DATE-TIME:20210514T150000Z
DTEND;VALUE=DATE-TIME:20210514T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/39
DESCRIPTION:Title: Towards optimal spectral gaps in large genus\nby Michael
Lipnowski (McGill University) as part of CRM-Montreal analysis Seminar\n\
n\nAbstract\nI'll discuss recent joint work with Alex Wright (arXiv: 2103.
07496) showing that typical large genus hyperbolic surfaces have first Lap
lacian eigenvalue at least 3/16−epsilon.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Chen (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20210528T180000Z
DTEND;VALUE=DATE-TIME:20210528T190000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/40
DESCRIPTION:Title: BV functions and some functional inequalities on nested frac
tals\nby Li Chen (Louisiana State University) as part of CRM-Montreal
analysis Seminar\n\n\nAbstract\nIn this talk\, we discuss functions of bou
nded variations (BV) on fractals which satisfy sub-Gaussian heat kernel bo
unds. We also prove isoperimetric inequalities and Poincare inequalities o
n some nested fractals. Our proofs use heat kernel methods and the key ing
redient is a weak Bakry-Emery curvature type condition. The talk are based
on joint works with Patricia Alonso-Ruiz\, Fabrice Baudoin\, Luke Rogers\
, Nageswari Shanmugalingam and Alexander Teplyaev.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jared Wunsch (Northwestern University)
DTSTART;VALUE=DATE-TIME:20210503T160000Z
DTEND;VALUE=DATE-TIME:20210503T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/41
DESCRIPTION:Title: Semiclassical analysis and the convergence of the finite ele
ment method\nby Jared Wunsch (Northwestern University) as part of CRM-
Montreal analysis Seminar\n\n\nAbstract\nAn important problem in numerical
analysis is the solution of the Helmholtz equation in exterior domains\,
in variable media\; this models the scattering of time-harmonic waves. Th
e Finite Element Method (FEM) is a flexible and powerful tool for obtainin
g numerical solutions\, but difficulties are known to arise in obtaining c
onvergence estimates for FEM that are uniform as the frequency of waves te
nds to infinity. I will describe some recent joint work with David Lafont
aine and Euan Spence that yields new convergence results for the FEM which
are uniform in the frequency parameter. The essential new tools come fro
m semiclassical microlocal analysis and the use of the functional calculus
. Another ingredient is a slightly surprising new resolvent estimate.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ram Band (Technion)
DTSTART;VALUE=DATE-TIME:20210510T160000Z
DTEND;VALUE=DATE-TIME:20210510T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/42
DESCRIPTION:Title: Neumann domains on manifolds and graphs\nby Ram Band (Te
chnion) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe nodal
set of a Laplacian eigenfunction forms a partition of the underlying manif
old or graph. Another natural partition is based on the gradient vector f
ield of the eigenfunction (on a manifold) or on the extremal points of the
eigenfunction (on a graph). The submanifolds (or subgraphs) of this part
ition 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 Neu
mann domains on manifolds and on graphs - their count\, geometric properti
es and spectral positions. The Neumann domain results are compared to tho
se of the nodal domain study. \nThe talk is based on joint works with Lio
r Alon\, Michael Bersudsky\, Graham Cox\, Sebastian Egger\, David Fajman a
nd Alexander Taylor.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandre Girouard (Université Laval)
DTSTART;VALUE=DATE-TIME:20210517T160000Z
DTEND;VALUE=DATE-TIME:20210517T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/43
DESCRIPTION:Title: Free boundary minimal surfaces and large Steklov eigenvalues
\nby Alexandre Girouard (Université Laval) as part of CRM-Montreal an
alysis Seminar\n\n\nAbstract\nA free boundary minimal surface (FBMS) in th
e unit ball is a minimal surface Ω ⊂ B ⊂ R 3 which satisfies one of
the two following equivalent conditions: • Ω meets the boundary ∂B o
rthogonally\, • The coordinate functions xi : Ω → R are Steklov eige
nfunctions with eigenvalue σ = 1. The study of FBMS is witnessing a rena
issance thanks to the fundamental work of Fraser and Schoen\, who discover
ed that isoperimetric optimizers for the first nonzero Steklov eigenvalue
σ1(Ω) of surfaces lead to the existence of FBMS with prescribed topolog
y. For surfaces of genus 0\, they proved existence of maximizers for the
perimeter-normalized σ1(Ω) and thereby obtained several new FBMS. In t
his talk I will show how this link can be used to obtain a sequence of FBM
S Ωn ⊂ B such that area(Ωn ) n→∞ −−−→ 4π. This is base
d on a construction of domains in the sphere S 2 with perimeter-normalized
σ1(Ω) converging to 8π. These domains are obtained by removing small
disks from the sphere\, in the spirit of homogenization theory. I will a
lso dicuss a conjecture by Fraser and Li\, stating that σ1(Ω) = 1 for e
ach FBMS Ω ⊂ B. More precisely\, I will show that the conjecture is t
rue for some FBMS which are invariant under the action of the symmetry gro
up of some platonic solids. This talk is based on joint work with Jean La
gac´e (UCL).\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Genqian Liu (Beijing Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210524T160000Z
DTEND;VALUE=DATE-TIME:20210524T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/44
DESCRIPTION:Title: Geometric invariants of spectrum of the Navier-Lame operator
\nby Genqian Liu (Beijing Institute of Technology) as part of CRM-Mont
real analysis Seminar\n\n\nAbstract\nIn this talk\, we review the asymptot
ic expansions of the heat traces for various operators including the Lapla
ce operator\, the poly-Laplace operator\, the Maxwell operator\, the Stoke
s operator\, etc. Then for the elastic Navier-Lame operator (a non-Laplac
e type operator) on a compact connected Riemannian n-manifold M with smoot
h boundary\, we explicitly obtain the first two coefficients of the asympt
otic expansion of the heat trace for NavierLame operator with Dirichlet an
d Neumann boundary conditions. These two coefficients provide precise inf
ormation 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://researchseminars.org/talk/MathematicalAnalysis/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maziej Zworski (Berkeley)
DTSTART;VALUE=DATE-TIME:20210531T160000Z
DTEND;VALUE=DATE-TIME:20210531T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/45
DESCRIPTION:Title: Spectral theory of internal waves in fluids\nby Maziej Z
worski (Berkeley) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\n
The connection between the formation of internal waves in fluids\, spectra
l theory and the dynamics of homeomorphisms of the circle was investigated
by oceanographers in the 90s and resulted in novel experimental observati
ons (Maas et al\, 1997). The specific homeomorphism is given by a chess b
illiard and has been considered by many authors (John 1941\, Arnold 1957\,
Ralston 1973\, ... \, Lenci et al 2021). The relation between the nonli
near dynamics of this homeomorphism and linearized internal waves provides
a striking example of classical/quantum correspondence (in a classical an
d surprising setting of fluids!). Using a model of tori and of zeroth ord
er pseudodifferential operators\, it has been a subject of recent research
\, first by Colin de Verdi`ere-Saint Raymond 2020 and then by Dyatlov\, Ga
lkowski\, Wang and the speaker. In this talk I will review those results
and present new work\, with Dyatlov and Wang\, on the more physically rele
vant boundary value problem.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kapukhin (California Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210607T160000Z
DTEND;VALUE=DATE-TIME:20210607T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/46
DESCRIPTION:Title: Stability of isoperimetric eigenvalue inequalities\nby M
ikhail Kapukhin (California Institute of Technology) as part of CRM-Montre
al analysis Seminar\n\n\nAbstract\nStability questions for sharp inequalit
ies are important problems in analysis. Recently\, these questions have b
een investigated for the first eigenvalue of the Laplacian on Euclidean do
mains. Optimal stability estimates for Faber-Krahn and Szego-Weinberger i
nequalities were obtained by BrascoDe Philippis-Velichkov and Nadirashvili
\, Brasco-Pratelli respectively. In the present talk we first consider th
e 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 h
armonic maps and minimal surfaces. Finally\, if time permits\, potential
applications to Steklov eigenvalue problem will be discussed. Based on th
e joint work with M. Nahon\, I. Polterovich and D. Stern.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Gomez-Serrano (University of Barcelona)
DTSTART;VALUE=DATE-TIME:20210614T160000Z
DTEND;VALUE=DATE-TIME:20210614T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/47
DESCRIPTION:Title: Computer-assisted proofs and counterexamples in spectral geo
metry\nby Javier Gomez-Serrano (University of Barcelona) as part of CR
M-Montreal analysis Seminar\n\n\nAbstract\nIn this talk I will explain how
to construct counterexamples for two problems in spectral geometry. The
main novelty is that parts of the proofs will be done via a rigorous compu
ter-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 Freitas. In
the second part I will construct a planar domain with 6 holes for which t
he nodal line is closed and does not touch the boundary. In particular\,
this domain does not satisfy Payne’s nodal line conjecture. This gives
a partial answer on a question posed by Hoffmann-Ostenhof\, Hoffmann-Osten
hof and Nadirashvili asking what should be the minimal number of holes of
such domains. The results are joint work with Joel Dahne\, Kimberly Hou a
nd Gerard Orriols.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Luzzini (EPFL)
DTSTART;VALUE=DATE-TIME:20210621T160000Z
DTEND;VALUE=DATE-TIME:20210621T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/48
DESCRIPTION:Title: On the spectral asymptotics for the buckling problem\nby
Paolo Luzzini (EPFL) as part of CRM-Montreal analysis Seminar\n\n\nAbstra
ct\nSince the seminal works of Hermann Weyl at the beginning of the 20th c
entury\, several authors have investigated the spectral asymptotics of par
tial differential operators. Following this tradition\, in this talk I wi
ll first present a recent result on a new proof of Weyl’s law for the bu
ckling eigenvalues requiring minimal assumptions on the domain. The proof
relies on asymptotically sharp lower and upper bounds that we develop for
Riesz means. Moreover\, we compute the second term in Weyl’s law in th
e case of balls and bounded intervals. This\, together with some formal co
nsiderations\, leads us to state a conjecture for the second term in gener
al domains. The talk is based on a joint work with Davide Buoso (UPO)\, L
uigi Provenzano (Sapienza Universit`a di Roma)\, and Joachim Stubbe (EPFL)
.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ari Laptev (Imperial College London)
DTSTART;VALUE=DATE-TIME:20210628T160000Z
DTEND;VALUE=DATE-TIME:20210628T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/49
DESCRIPTION:Title: Spectral inequalities for Jacobi matrices following Hundertm
ark and Simon\nby Ari Laptev (Imperial College London) as part of CRM-
Montreal analysis Seminar\n\n\nAbstract\nWe shall proof of a Lieb-Thirring
type inequality for Jacobi matrices originally conjectured by Hundertmark
and Simon. In particular\, we show that the estimate on the sum of eigen
values does not depend on the off-diagonal terms as long as they are small
er than their asymptotic value. An interesting feature of the proof is th
at it employs a technique originally used by Hundertmark-Laptev-Weidl conc
erning sums of singular values for compact operators. \nThis is a joint w
ork with M.Loss and L.Schimmer.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Ivrii (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210726T160000Z
DTEND;VALUE=DATE-TIME:20210726T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/50
DESCRIPTION:Title: Pointwise Spectral Asymptotics out of the Diagonal\nby V
ictor Ivrii (University of Toronto) as part of CRM-Montreal analysis Semin
ar\n\n\nAbstract\nWe establish semiclassical asymptotics or estimates for
the Schwartz kernel eh(x\, y\; τ ) of spectral projector for a second ord
er elliptic operator on a manifold with a boundary. While such asymptotic
s for its restriction to the diagonal eh(x\, x\, τ ) and\, especially\, f
or its trace Nh(τ ) = R eh(x\, x\, τ ) dx are well-known\, the out-of-di
agonal asymptotics are much less explored. Our main tools: improved succe
ssive 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://researchseminars.org/talk/MathematicalAnalysis/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20210823T160000Z
DTEND;VALUE=DATE-TIME:20210823T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/51
DESCRIPTION:Title: Small denominators and large numerators of quasiperiodic Sch
roedinger operators\nby Wencai Liu (Texas A&M University) as part of C
RM-Montreal analysis Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jürgen Jost (University of Leipzig)
DTSTART;VALUE=DATE-TIME:20210830T160000Z
DTEND;VALUE=DATE-TIME:20210830T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/52
DESCRIPTION:Title: Spectra of graphs and hypergraphs\nby Jürgen Jost (Univ
ersity of Leipzig) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\
nThe spectral theory of the Laplace operator on graphs offers many analogi
es with that of Riemannian manifolds\, like Cheeger type inequalities\, bu
t also shows some different phenomena. For hypergraphs\, a main step cons
ists in the definition of a Laplace operator that can also offer such anal
ogies. Lovasz extensions of Rayleigh quotients can uncover some deeper re
asons behind such analogies.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nalini Anantharaman (IRMA\, Université de Strasbourg)
DTSTART;VALUE=DATE-TIME:20210906T160000Z
DTEND;VALUE=DATE-TIME:20210906T170000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
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://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;VALUE=DATE-TIME:20210913T123000Z
DTEND;VALUE=DATE-TIME:20210913T165000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/54
DESCRIPTION:Title: Young researchers in spectral geometry III - 3 short talks\nby Vladimir Medvedev\; Marco Michetti\; William Hide (Higher School of
Economics (HSE University) (1/3)\; Université de Lorraine (2/3)\; Durham
University (3/3)) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\
n(1/3) On the index of the critical Moebius band in the 4-ball \n\nIn thi
s talk I will show that the Morse index of the critical Moebius band in th
e 4-dimensional Euclidean ball equals 5. This result makes use of the qua
rtic Hopf differential technique and a comparison theorem between the inde
x of a free boundary minimal surface in the Euclidean ball and its spectra
l index. The latter also enables us to reprove a well-known result that t
he index of the critical catenoid in the 3-ball equals 4. These results a
re obtained in my paper in progress. \n\n(2/3) A comparison between Neu
mann and Steklov eigenvalues \n\nIn this talk we present a comparison bet
ween the normalized first (non-trivial) Neumann eigenvalue |Ω|µ1(Ω) f
or a Lipschitz open set Ω in the plane\, and the normalized first (non-t
rivial) Steklov eigenvalue P(Ω)σ1(Ω). More precisely\, we study the
ratio F(Ω) := |Ω|µ1(Ω)/P(Ω)σ1(Ω). We prove that this ratio ca
n take arbitrarily small or large values if we do not put any restriction
on the class of sets Ω. Then we restrict ourselves to the class of plan
e convex domains for which we get explicit bounds. We also study the case
of thin convex domains for which we give more precise bounds. In the las
t part of the talk we present the corresponding Blaschke-Santal´o diagram
s (x\, y) = (|Ω|µ1(Ω)\, P(Ω)σ1(Ω)) and we state some open proble
ms. This talk is based on a joint work with Antoine Henrot. \n\n(3/3) Sp
ectral gaps for random hyperbolic surfaces with cusps \n\nWe shall study t
he discrete spectrum of the Laplacian on random non-compact finite-area hy
perbolic surfaces\, focusing on the size of the first non-zero eigenvalue
i.e. the spectral gap. We shall introduce a model for random surfaces\,
arising from the Weil-Petersson metric on moduli space. Then we shall dis
cuss some recent results in this model for compact surfaces and their exte
nsion to the non-compact case. In particular\, we prove the existence of
a positive uniform spectral gap of explicit size for random large genus no
n-compact surfaces.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannick Sire (Johns Hopkins)
DTSTART;VALUE=DATE-TIME:20211022T183000Z
DTEND;VALUE=DATE-TIME:20211022T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/55
DESCRIPTION:Title: Some results on harmonic maps with free boundary and beyond<
/a>\nby Yannick Sire (Johns Hopkins) as part of CRM-Montreal analysis Semi
nar\n\n\nAbstract\nThe theory of harmonic maps with free boundary is an ol
d topic in geometric analysis. I will report on recent results on their G
inzburg-Landau approximation\, regularity theory\, and their heat flow. I
will also describe several models in the theory of liquid crystals where
the heat flow of those maps appears\, emphasizing on some well-posedness i
ssues and some hints on the construction of blow-up solutions. Several im
portant results in geometric analysis such as extremal metrics for the Ste
klov eigenvalues for instance make a crucial use of such maps. I’ll giv
e some open problems and will try to explain how to attack few open questi
ons in the field using tools recently developed.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Roysdon (Tel Aviv)
DTSTART;VALUE=DATE-TIME:20211029T183000Z
DTEND;VALUE=DATE-TIME:20211029T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/56
DESCRIPTION:Title: On measure theoretic projection bodies\nby Michael Roysd
on (Tel Aviv) as part of CRM-Montreal analysis Seminar\n\n\nAbstract\nThe
inequalities of Petty and Zhang are affine isoperimetric-type inequalities
providing sharp bounds for voln−1 n (K)voln(Π◦K)\, where ΠK is a pr
ojection body of a convex body K is the convex body with support function
given by hΠK(θ) = voln−1(K|θ ⊥)\, θ ∈ S n−1 \, where θ ⊥ de
notes the hyperplane orthogonal to the direction θ. The upper bound\, du
e to Petty\, and referred to as Petty’s projection inequality attains eq
uality only when K is an ellipsoid\, and the lower bound is due to Zhang a
nd equality occurs only when K is a simplex. In this talk\, we present a
number of generalizations of Zhang’s inequality to the setting of measur
es. In addition\, we introduce extensions of the projection body operator
Π to the setting of arbitrary measures\, that is\, given a measure 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\, wher
e ∂K denotes the boundary of K and nK(y) denotes the outer unit normal o
f ∂K at y. We remark that the support function hπµK has been deeply s
tudied in the literature\, and is an example of a generalized zoniod when
ϕ is taken to be even. Authors: Dylan Langharst\; Kent State University
Michael Roysdon\; Tel Aviv University Artem Zvavitch\; Kent State Universi
ty\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fortier Bourque (Universite de Montreal)
DTSTART;VALUE=DATE-TIME:20211112T193000Z
DTEND;VALUE=DATE-TIME:20211112T203000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/57
DESCRIPTION:Title: The extremal length systole of the Bolza surface\nby Max
ime Fortier Bourque (Universite de Montreal) as part of CRM-Montreal analy
sis Seminar\n\n\nAbstract\nThe extremal length of a curve on a Riemann sur
face is a conformal invariant that has a nice geometric description but is
not so simple to compute in practice. The extremal length systole is def
ined 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 Bol
za surface\, the most symmetric surface of genus two. The calculation inv
olves certain identities for elliptic integrals called the Landen transfor
mations. We also prove that the Bolza surface is a local maximizer for th
e extremal length systole and conjecture that it is the unique global maxi
mizer.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrios Ntalampekos (Stony Brook)
DTSTART;VALUE=DATE-TIME:20211119T193000Z
DTEND;VALUE=DATE-TIME:20211119T203000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/58
DESCRIPTION:Title: Rigidity theorems for circle domains\nby Dimitrios Ntala
mpekos (Stony Brook) as part of CRM-Montreal analysis Seminar\n\n\nAbstrac
t\nA circle domain $\\Omega$ in the Riemann sphere is a domain each of who
se boundary components is either a circle or a point. A circle domain $\\
Omega$ is called conformally rigid if every conformal map from $\\Omega$ o
nto another circle domain is the restriction of a Mobius transformation.
In this talk I will present some new rigidity theorems for circle domains
satisfying a certain quasihyperbolic condition. As a corollary\, John and
Holder circle domains are rigid. This provides new evidence for a conjec
ture of He and Schramm\, relating rigidity and conformal removability. Th
is talk is based on joint work with Malik Younsi.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suresh Eswarathasan (Dalhousie)
DTSTART;VALUE=DATE-TIME:20211126T193000Z
DTEND;VALUE=DATE-TIME:20211126T203000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/59
DESCRIPTION:Title: Fractal uncertainty principle for discrete Cantor sets for r
andom alphabets\nby Suresh Eswarathasan (Dalhousie) as part of CRM-Mon
treal analysis Seminar\n\n\nAbstract\nThe fractal uncertainty principle (F
UP) introduced by Dyatlov-Zahl’16 has seen some powerful applications in
the last few years and become a hot topic in harmonic analysis. In this
talk\, we study the FUP for discrete Cantor sets from a probabilistic pers
pective. We show that randomizing our alphabets gives a quantifiable impr
ovement 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 join
t work with Xiaolong Han (Cal. State Northridge)\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Bishop (Stony Brook)
DTSTART;VALUE=DATE-TIME:20220211T193000Z
DTEND;VALUE=DATE-TIME:20220211T203000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/60
DESCRIPTION:Title: Dessins and Dynamics\nby Chris Bishop (Stony Brook) as p
art of CRM-Montreal analysis Seminar\n\n\nAbstract\nAfter defining harmoni
c 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 and so th
at 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\, where a
graph on a topological surface induces a conformal structure on that surfa
ce. I will recall the connection between dessins\, equilateral triangulat
ions and branched coverings (Belyi's theorem). I will also describe some
recent applications of these ideas to holomorphic dynamics: approximating
sets by polynomial Julia sets\, finding meromorphic functions with prescri
bed postcritical orbits\, constructing finite type dynamical systems on hy
perbolic Riemann surfaces\, building wandering domains for entire function
s\, and estimating the fractal dimensions of transcendental Julia sets. T
here will be many pictures and few proofs.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jane Wang (Indiana University)
DTSTART;VALUE=DATE-TIME:20220225T193000Z
DTEND;VALUE=DATE-TIME:20220225T203000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/61
DESCRIPTION:Title: Slope Gap Distributions of Veech Translation Surfaces
\nby Jane Wang (Indiana University) as part of CRM-Montreal analysis Semin
ar\n\n\nAbstract\nTranslation surfaces are surfaces that are locally Eucli
dean except at finitely many points called cone points\, an example being
the regular octagon with opposite sides identified (the vertices are ident
ified and become a single cone point). A saddle connection is then a stra
ight trajectory that begins and ends at a cone point. It is known that on
almost every translation surface\, the set of angles of saddle connection
s on the surface is equidistributed in the circle. A finer notion of how
random the saddle connection directions are is given by something called t
he gap distribution of the surface. In this talk\, we will explain wha
t the slope gap distribution of a translation surface is and survey so
me known results about slope gap distributions\, including how one can
use properties of the horocycle flow to compute the slope gap distribut
ions of special translation surfaces called Veech surfaces. We'll then d
iscuss recent results showing that the slope gap distributions of Veec
h surfaces have to satisfy some nice analytic properties. This project is
joint work with Luis Kumanduri and Anthony Sanchez.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Pilgrim (Indiana University)
DTSTART;VALUE=DATE-TIME:20220325T183000Z
DTEND;VALUE=DATE-TIME:20220325T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/62
DESCRIPTION:Title: Conformal surface embeddings and extremal length\nby Kev
in Pilgrim (Indiana University) as part of CRM-Montreal analysis Seminar\n
\n\nAbstract\nGiven two Riemann surfaces with boundary and a homotopy clas
s of topological embeddings between them\, we show there is a conformal em
bedding in the homotopy class if and only if the extremal length of every
simple multi-curve is decreased under the embedding. For applications to d
ynamical systems\, we need an additional fact: if the ratio is bounded abo
ve away from one\, then it remains so under passing to any finite cover. I
will also briefly mention how under natural conditions the technique of q
uasiconformal 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. Thurst
on\; https://arxiv.org/abs/1507.05294 .\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norm Levenberg (Indiana University)
DTSTART;VALUE=DATE-TIME:20220415T183000Z
DTEND;VALUE=DATE-TIME:20220415T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/63
DESCRIPTION:Title: Zeros of Random Polynomial Mappings in Several Complex Varia
bles\nby Norm Levenberg (Indiana University) as part of CRM-Montreal a
nalysis Seminar\n\n\nAbstract\nWe discuss some results on random polynomia
ls with an eye towards obtaining universality results under the most gener
al assumptions on the random coefficients. In particular\, we generalize a
nd strengthen some previous results on asymptotic distribution of normaliz
ed zero measures and currents associated to random polynomials and random
polynomial mappings in several complex variables. The talk is based on joi
nt work with Turgay Bayraktar and Tom Bloom.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro Romaniega (ICMAT)
DTSTART;VALUE=DATE-TIME:20220520T183000Z
DTEND;VALUE=DATE-TIME:20220520T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/64
DESCRIPTION:Title: Nodal sets of monochromatic waves from a deterministic and r
andom point of view\nby Álvaro Romaniega (ICMAT) as part of CRM-Montr
eal analysis Seminar\n\n\nAbstract\nIn this talk we present recent results
on the nodal set (i.e.\, the zero level set) of monochromatic waves (i.e.
\, solutions of the Helmholtz equation) on the Euclidean space. Following
the breakthrough work of F. Nazarov and M. Sodin\, a growing literature gi
ves us powerful probabilistic results for the number of connected componen
ts of the nodal set of random monochromatic waves. The aim of this talk is
to explore the properties of these standard random monochromatic waves an
d\, consequently\, define a more general class of random monochromatic wav
es depending on a parameter \, which includes the standard definition as a
particular case. This parameter controls some regularity (of the Fourier
transform) and decay properties of these waves. Given that\, we study the
structure of the nodal set depending on that parameter from a deterministi
c and from a random point of view. Finally\, we show how to construct dete
rministic realizations or examples of monochromatic waves satisfying the p
robabilistic Nazarov-Sodin volumetric growth for the number of connected c
omponents of the nodal set and similarly for the volume of the nodal set.
This is a joint work with A. Enciso\, D. Peralta-Salas and A. Sartori.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norm Levenberg (Indiana University)
DTSTART;VALUE=DATE-TIME:20220422T183000Z
DTEND;VALUE=DATE-TIME:20220422T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
UID:MathematicalAnalysis/65
DESCRIPTION:Title: Zeros of Random Polynomial Mappings in Several Complex Varia
bles\nby Norm Levenberg (Indiana University) as part of CRM-Montreal a
nalysis Seminar\n\n\nAbstract\nWe discuss some results on random polynomia
ls with an eye towards obtaining universality results under the most gener
al assumptions on the random coefficients. In particular\, we generalize
and strengthen some previous results on asymptotic distribution of normali
zed zero measures and currents associated to random polynomials and random
polynomial mappings in several complex variables. The talk is based on j
oint work with Turgay Bayraktar and Tom Bloom.\n
LOCATION:https://researchseminars.org/talk/MathematicalAnalysis/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Decio (Norwegian University of Science and Technology)
DTSTART;VALUE=DATE-TIME:20220506T183000Z
DTEND;VALUE=DATE-TIME:20220506T193000Z
DTSTAMP;VALUE=DATE-TIME:20240222T173247Z
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://researchseminars.org/talk/MathematicalAnalysis/66/
END:VEVENT
END:VCALENDAR