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BEGIN:VEVENT
SUMMARY:Pavel Exner (Doppler Institute for Mathematical Physics and Applie
d Mathematics)
DTSTART;VALUE=DATE-TIME:20201103T143000Z
DTEND;VALUE=DATE-TIME:20201103T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/1
DESCRIPTION:Title: Spectral properties of spiral quantum waveguides\nby Pave
l Exner (Doppler Institute for Mathematical Physics and Applied Mathematic
s) as part of Spectral theory and related topics\n\n\nAbstract\nWe discuss
properties of a particle confined to a spiral-shaped region with Dirichle
t boundary. As a case study we analyze in detail the Archimedean spiral fo
r which the spectrum above the continuum threshold is absolutely continuou
s away from the thresholds. The subtle difference between the radial and p
erpendicular width implies\, however\, that in contrast to ‘less curved
’ waveguides\, the discrete spectrum is empty in this case. We also disc
uss modifications such a multi-arm Archimedean spirals and spiral waveguid
es with a central cavity\; in the latter case bound state already exist if
the cavity exceeds a critical size. For more general spiral regions the s
pectral nature depends on whether they are ‘expanding’ or ‘shrinking
’. The most interesting situation occurs in the asymptotically Archimede
an case where the existence of bound states depends on the direction from
which the asymptotics is reached.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denis Borisov (Bashkir State Pedagogical University and Institute
o Mathematics UFRC RAS)
DTSTART;VALUE=DATE-TIME:20201110T133000Z
DTEND;VALUE=DATE-TIME:20201110T143000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/2
DESCRIPTION:Title: Accumulation of resonances and eigenvalues for operators with
distant perturbations\nby Denis Borisov (Bashkir State Pedagogical Un
iversity and Institute o Mathematics UFRC RAS) as part of Spectral theory
and related topics\n\n\nAbstract\nWe consider a model one-dimensional prob
lem with distant perturbations\, for which we study a phenomenon of emergi
ng of infinitely many eigenvalues and resonances near the bottom of the es
sential spectrum. We show that they accumulate to a certain segment of the
essential spectrum. Then we discuss possible generalization of this resul
t to multi-dimensional models and various situations of resonances and eig
envalues distributions.\n\nZoom link: https://zoom.us/j/91097279226 \nFor
password please ask the organizers: fbakharev@yandex.ru\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantin Pankrashkin (Carl von Ossietzky University of Oldenburg
)
DTSTART;VALUE=DATE-TIME:20201117T143000Z
DTEND;VALUE=DATE-TIME:20201117T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/3
DESCRIPTION:Title: Some convergence results for Dirac operators with large param
eters\nby Konstantin Pankrashkin (Carl von Ossietzky University of Old
enburg) as part of Spectral theory and related topics\n\n\nAbstract\nWe co
nsider Euclidean Dirac operators with piecewise constant mass potentials a
nd investigate their spectra in several asymptotic regimes in which the ma
ss becomes large in some regions. If the mass jumps along a smooth interfa
ce\, then it appears that the (low-lying) discrete spectrum of such an ope
rator converges to the (low-lying) discrete spectrum of an effective opera
tor acting either on or in the interior of the interface. The effective op
erators admit a simple geometric interpretation in terms of the spin geome
try\, and the results can be extended to a class of spin manifolds as well
. Most questions remain open if the jump interface is non-smooth. Based on
joint works with Brice Flamencourt\, Markus Holzmann\, Andrei Moroianu\,
and Thomas Ourmieres-Bonafos.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Fedotov (St. Peterburg State University)
DTSTART;VALUE=DATE-TIME:20201124T143000Z
DTEND;VALUE=DATE-TIME:20201124T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/4
DESCRIPTION:Title: On Hierarchical Behavior of Solutions to the Maryland Equatio
n in the Semiclassical Approximation\nby Alexander Fedotov (St. Peterb
urg State University) as part of Spectral theory and related topics\n\n\nA
bstract\nWe describe a multiscale selfsimilar struture of solutions to one
of the most popular models of the almost periodic operator theory\, the d
ifference Schroedinger equation with a potential of the form a $\\ctg(b n+
c)$\, where $a$\, $b$ and $c$ are constants\, and $n$ is an integer variab
le. The talk is based on a joint work with F.Klopp.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anne-Sophie Bonnet-Ben Dhia (Institut Polytechnique de Paris)
DTSTART;VALUE=DATE-TIME:20201201T143000Z
DTEND;VALUE=DATE-TIME:20201201T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/5
DESCRIPTION:Title: A new complex frequency spectrum for the analysis of transmis
sion efficiency in waveguide-like geometries\nby Anne-Sophie Bonnet-Be
n Dhia (Institut Polytechnique de Paris) as part of Spectral theory and re
lated topics\n\n\nAbstract\nWe consider a waveguide\, with one inlet and o
ne outlet\, and some arbitrary perturbation in between. In general\, an in
going wave in the inlet will produce a reflected wave\, due to interaction
with the perturbation. Our objective is to give an answer to the followin
g important questions: what are the frequencies at which the transmission
is the best one? And in particular\, do they exist frequencies for which t
he transmission is perfect\, in the sense that nothing is propagating back
in the inlet?\n\nOur approach relies on a simple idea\, which consists in
using a complex scaling in an original manner: while the same stretching
parameter is classically used in the inlet and the outlet\, here we take
them as two complex conjugated parameters. As a result\, we select ingoing
waves in the inlet and outgoing waves in the outlet\, which is exactly wh
at arises when the transmission is perfect. This simple idea works very we
ll\, and provides useful information on the transmission qualities of the
system\, much faster than any traditional approach. More precisely\, we de
fine a new complex spectrum which contains as real eigenvalues both the fr
equencies where perfect transmission occurs and the frequencies correspond
ing to trapped modes (also known as bound states in the continuum). In add
ition\, we also obtain complex eigenfrequencies which can be exploited to
predict frequency ranges of good transmission. Let us finally mention that
this new spectral problem is PT -symmetric for systems with mirror symmet
ry.\n\nSeveral illustrations performed with finite elements in several si
mple 2D cases will be shown.\n\nIt is a common work with Lucas Chesnel (IN
RIA) and Vincent Pagneux (CNRS).\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrii Khrabustovskyi (University of Hradec Kralove)
DTSTART;VALUE=DATE-TIME:20201208T143000Z
DTEND;VALUE=DATE-TIME:20201208T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/6
DESCRIPTION:Title: Homogenization of the Robin Laplacian in a domain with small
holes: operator estimates\nby Andrii Khrabustovskyi (University of Hra
dec Kralove) as part of Spectral theory and related topics\n\n\nAbstract\n
In the talk we revisit the problem of homogenization of the Robin Laplacia
n in a domain with a lot of tiny holes.\n\nLet $\\varepsilon>0$ be a small
parameter\, $\\Omega$ be an open set in $\\mathbb{R}^n$ with $n\\ge 2$\,
and $\\Omega_\\varepsilon$ be a perforated domain obtained by removing fro
m $\\Omega$ a family of tiny identical balls of the radius $d_\\varepsilon
=o(\\varepsilon)$ $(\\varepsilon\\to 0)$ distributed periodically with a p
eriod \\varepsilon. We denote by $\\Delta_{\\Omega_\\varepsilon\,\\alpha_\
\varepsilon}$ the Laplacian on $\\Omega_\\varepsilon$ subject to the Diric
hlet condition $u=0$ on the external boundary of $\\Omega_\\varepsilon$ an
d the Robin conditions on the boundary of the balls:\n\n \\[{\\partial u\
\over\\partial \\nu}+\\alpha_\\varepsilon u=0\,\\quad \\alpha_\\varepsilon
>0\,\\]\n\nwhere $\\nu$ is an outward-facing unit normal. By $\\Delta_\\Om
ega$ we denote the Dirichlet Laplacian on $\\Omega$. It is known (Kaizu (1
985\, 1989)\, Berlyand & Goncharenko (1990)\, Goncharenko (1997)\, Shaposh
nikova et al. (2018)) that $\\Delta_{\\Omega_\\varepsilon\,\\alpha_\\varep
silon}$ converges in a strong resolvent sense either to zero (solidifying
holes)\, to $\\Delta_\\Omega$ (fading holes) or to the operator $\\Delta_{
\\Omega}-q$ with a constant potential $q>0$ (critical case) as $\\varepsil
on\\to 0$. The form of the limiting operator depends on certain relations
between$ \\varepsilon$\, $d_\\varepsilon$ and $\\alpha_\\varepsilon$.\n\nW
e will discuss our recent improvements of these results. Namely\, for all
three cases we show the norm resolvent convergence of the above operators
and derive estimates in terms of operator norms. As an application we esta
blish the Hausdorff convergence of spectra.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frédéric Klopp (Institut de Mathématiques de Jussieu – Paris
Rive Gauche)
DTSTART;VALUE=DATE-TIME:20201215T143000Z
DTEND;VALUE=DATE-TIME:20201215T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/7
DESCRIPTION:Title: A new look at localization\nby Frédéric Klopp (Institut
de Mathématiques de Jussieu – Paris Rive Gauche) as part of Spectral t
heory and related topics\n\n\nAbstract\nThe talk is devoted to new\, impro
ved bounds for the eigenfunctions of random operators in the localized re
gime. We prove that\, in the localized regime with good probability\, ea
ch eigenfunction is exponentially decaying outside a ball of a certain ra
dius\, which we call the "localization onset length." We count the number
of eigenfunctions having onset length larger than\, say\, $\\ell>0$ and
find it to be smaller than $\\exp(-c\\ell)$ times the total number of eig
enfunctions in the system (for some positive constant $c$). Thus\, most
eigenfunctions localize on finite size balls independent of the system si
ze.\n\nWe apply our techniques to obtain decay estimates for the $k$-part
icles density matrices of eigenstates of $n$ non interacting fermionic qu
antum particles subjected to the random potential $V_\\omega$ in a large
box.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Logunov (Princeton University)
DTSTART;VALUE=DATE-TIME:20201221T133000Z
DTEND;VALUE=DATE-TIME:20201221T143000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/8
DESCRIPTION:Title: Nodal sets\, quasiconformal mappings and how to apply them to
Landis’ conjecture\nby Alexander Logunov (Princeton University) as
part of Spectral theory and related topics\n\n\nAbstract\nA while ago Nadi
rashvili 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-dimen
sional surfaces. The idea have not yet worked out as it was planned. Howev
er it appears to be useful for Landis' Conjecture. We will explain how to
apply the combination of quasiconformal mappings and zero sets to quantita
tive 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
solutions to Shrodinger equation $\\Delta u + V u =0$ on the plane to ques
tions about harmonic functions. Based on a joint work with E.Malinnikova\,
N.Nadirashvili and F. Nazarov.\n\nThis will be a joint session with Saint
Petersburg V.I. Smirnov seminar on mathematical physics. You could connec
t to the session via the link: https://us02web.zoom.us/j/82147853102?pwd=V
kFVR092dVJKMHk3VWFBU3RXcThjUT09\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Sobolev (University College London)
DTSTART;VALUE=DATE-TIME:20210217T143000Z
DTEND;VALUE=DATE-TIME:20210217T153000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/9
DESCRIPTION:Title: On spectral properties of the one-particle density matrix
\nby Alexander Sobolev (University College London) as part of Spectral the
ory and related topics\n\n\nAbstract\nThe one-particle density matrix $\\g
amma(x\, y)$ is one of the key objects in the quantum-mechanical approxima
tion schemes. The self-adjoint operator $\\Gamma$ with the kernel $\\gamma
(x\, y)$ is trace class but a sharp estimate on the decay of its eigenvalu
es was unknown. In this talk I will present a sharp bound and an asymptoti
c formula for the eigenvalues of $\\Gamma$.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christophe Hazard (Institut Polytechnique de Paris)
DTSTART;VALUE=DATE-TIME:20210303T141500Z
DTEND;VALUE=DATE-TIME:20210303T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/10
DESCRIPTION:Title: Curiosities about the spectrum of a cavity containing a nega
tive material\nby Christophe Hazard (Institut Polytechnique de Paris)
as part of Spectral theory and related topics\n\n\nAbstract\nIn electromag
netism\, a negative material is a dispersive material for which the real p
arts of the electric permittivity and/or the magnetic permeability become
negative in some frequency range(s). In the last decades\, the extraordina
ry properties of these materials have generated a great effervescence amon
g the communities of physicists and mathematicians. The aim of this talk i
s to focus on their spectral properties. Using a simple scalar two-dimensi
onal model\, we will show that negative material are responsible for vario
us unusual resonance phenomena which are related to various components of
an essential spectrum. This is a common work with Sandrine Paolantoni.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wencai Liu (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20210317T141500Z
DTEND;VALUE=DATE-TIME:20210317T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/11
DESCRIPTION:Title: Irreducibility of the Fermi variety for discrete periodic Sc
hr\\"odinger operators\nby Wencai Liu (Texas A&M University) as part o
f Spectral theory and related topics\n\n\nAbstract\nLet $H_0$ be a discret
e periodic Schr\\"odinger operator on $\\Z^d$:\n$$H_0=-\\Delta+V\,$$\nwhe
re $\\Delta$ is the discrete Laplacian and $V:\\Z^d\\to \\R$ is periodic.
We prove that for any $d\\geq3$\, the Fermi variety at every energy level
is irreducible (modulo periodicity). For $d=2$\, we prove that the Fe
rmi variety at every energy level except for the average of the potential
is irreducible (modulo periodicity) and the Fermi variety at the averag
e of the potential has at most two irreducible components (modulo period
icity). This is sharp since for $d=2$ and a constant potential $V$\, the
Fermi variety at $V$-level has exactly two irreducible components (mod
ulo periodicity). In particular\, we show that the Bloch variety is irr
educible \n(modulo periodicity) for any $d\\geq 2$.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Yuditskii (Johannes Kepler Universität Linz)
DTSTART;VALUE=DATE-TIME:20210310T141500Z
DTEND;VALUE=DATE-TIME:20210310T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/12
DESCRIPTION:Title: Reflectionless canonical systems: almost periodicity and cha
racter-automorphic Fourier transforms\nby Peter Yuditskii (Johannes Ke
pler Universität Linz) as part of Spectral theory and related topics\n\n\
nAbstract\nWe develop a comprehensive theory of reflectionless canonical s
ystems with an arbitrary Dirichlet-regular Widom spectrum with the Direct
Cauchy Theorem property. This generalizes\, to an infinite gap setting\, t
he constructions of finite gap quasiperiodic (algebro-geometric) solutions
of stationary integrable hierarchies. Instead of theta functions on a com
pact Riemann surface\, the construction is based on reproducing kernels of
character-automorphic Hardy spaces in Widom domains with respect to Marti
n measure. We also construct unitary character-automorphic Fourier transfo
rms which generalize the Paley-Wiener theorem. Finally\, we find the corre
ct notion of almost periodicity which holds for canonical system parameter
s in Arov gauge\, and we prove generically optimal results for almost peri
odicity for Potapov-de Branges gauge\, and Dirac operators. Based on joint
work with Roman Bessonov and Milivoje Lukic.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Jitomirskaya (University of California)
DTSTART;VALUE=DATE-TIME:20210224T150000Z
DTEND;VALUE=DATE-TIME:20210224T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/13
DESCRIPTION:Title: Spectral properties of the unbounded GPS model\nby Svetl
ana Jitomirskaya (University of California) as part of Spectral theory and
related topics\n\n\nAbstract\nWe discuss spectral properties of the unbou
nded GPS model: a family of discrete 1D Schrodinger operators with unbound
ed potential and exact mobility edge. Based on papers in progress joint wi
th Xu\, You (Nankai) and Zhao (UCI).\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Kuchment (Texas A&M University)
DTSTART;VALUE=DATE-TIME:20210407T141500Z
DTEND;VALUE=DATE-TIME:20210407T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/14
DESCRIPTION:Title: The nodal mysteries\nby Peter Kuchment (Texas A&M Univer
sity) as part of Spectral theory and related topics\n\n\nAbstract\nNodal p
atterns of oscillating membranes have been known for hundreds of years. Le
onardo da Vinci\, Galileo Galilei\, and Robert Hooke have observed them. B
y the nineteenth century they acquired the name of Chladni figures. Mathem
atically\, they represent zero sets of eigenfunctions of the Laplace (or a
more general) operator. In spite of such long history\, many mysteries ab
out these patterns (even in domains of Euclidean spaces\, and even more on
manifolds) still abound and attract recent attention of leading researche
rs working in physics\, mathematics (including PDEs\, math physics\, and n
umber theory) and even medical imaging. The talk will survey these issues\
, with concentration on some recent results. No prior knowledge is assumed
.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jari Taskinen (University of Helsinki)
DTSTART;VALUE=DATE-TIME:20210324T141500Z
DTEND;VALUE=DATE-TIME:20210324T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/15
DESCRIPTION:Title: Spectra of the Robin-Laplace- and Steklov-problems in bounde
d\, cuspidal domains\nby Jari Taskinen (University of Helsinki) as par
t of Spectral theory and related topics\n\n\nAbstract\nIt is well-known by
works of several authors that the spectrum of the Neumann-Laplace operat
or may be non-discrete even in bounded domains\, if the boundary of the
domain has some irregularities. In the same direction\, in a paper in 2008
with S.A. Nazarov we considered the Steklov spectral problem in a bounded
domain $\\Omega \\subset \\mathbb{R}^n$\, $n \\geq 2$\, with a peak and
showed that the spectrum may be discrete or continuous depending on the s
harpness of the peak. Later\, we proved that the spectrum of the Robin Lap
lacian in non-Lipschitz domains may be quite pathological since\, in addit
ion\nto countably many eigenvalues\, the residual spectrum may cover the
whole complex plain. \n\nWe have recently complemented this study in two
papers\, where we consider the spectral Robin-Laplace- and Steklov-proble
ms in a bounded domain $\\Omega$ with a peak and also in\na family $\\Omeg
a_\\varepsilon$ of domains blunted at the small distance $\\varepsilon >0$
from the peak tip. The blunted domains are Lipschitz and the spectra of t
he corresponding problems on\n$\\Omega_\\varepsilon$ are discrete. We st
udy the behaviour of the discrete spectra as $\\varepsilon \\to 0$ an
d their relations with the spectrum of case with $\\Omega$. In particular
we find various subfamilies of eigenvalues which behave in different way
s (e.g. "blinking" and "stable" families") and we describe a mechanism how
the discrete spectra turn into the continuous one in this process. \n\n
The work is a co-operation with Sergei A. Nazarov (St. Petersburg) and
Nicolas Popoff (Bordeaux).\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Gerard (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210414T141500Z
DTEND;VALUE=DATE-TIME:20210414T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/16
DESCRIPTION:Title: Spectral theory of first order operators with Toeplitz coeff
icients on the circle and applications to the Benjamin-Ono equation\nb
y Patrick Gerard (Université Paris-Saclay) as part of Spectral theory and
related topics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Parnovski (University College London)
DTSTART;VALUE=DATE-TIME:20210331T141500Z
DTEND;VALUE=DATE-TIME:20210331T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/17
DESCRIPTION:Title: Floating mats and sloping beaches: spectral asymptotics of t
he Steklov problem on polygons\nby Leonid Parnovski (University Colleg
e London) as part of Spectral theory and related topics\n\n\nAbstract\nI w
ill discuss asymptotic behavior of the eigenvalues of the Steklov problem
(aka Dirichlet-to-Neumann operator) on curvilinear polygons. The answer is
completely unexpected and depends on the arithmetic properties of the ang
les of the polygon.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Khrushchev (Satbayev University)
DTSTART;VALUE=DATE-TIME:20210421T141500Z
DTEND;VALUE=DATE-TIME:20210421T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/18
DESCRIPTION:Title: Uniformly convergent Fourier series with universal power par
ts on closed subsets of measure zero\nby Sergey Khrushchev (Satbayev U
niversity) as part of Spectral theory and related topics\n\n\nAbstract\nGi
ven a closed subset $E$ of Lebesgue measure zero on the unit circle $\\mat
hbb{T}$ there is a function $f$ on $\\mathbb{T}$ with uniformly convergent
symmetric Fourier series\n\n \\[ S_n(f\,\\zeta)=\\sum_{k=-n}^n\\hat{f}(k
)\\zeta^k\\underset{\\mathbb{T}}{\\rightrightarrows} f(\\zeta)\,\\]\n\nsuc
h that for every continuous function $g$ on $E$\, there is a subsequence o
f partial power sums\n\n \\[ S^+_n(f\,\\zeta)=\\sum_{k=0}^n\\hat{f}(k)\\z
eta^k\\]\n\nof $f$\, which converges to $g$ uniformly on $E$. Here\n\n \\
[ \\hat{f}(k)=\\int_{\\mathbb{T}}\\bar{\\zeta}^kf(\\zeta)\\\, dm(\\zeta)\,
\\]\n\nand $m$ is the normalized Lebesgue measure on $\\mathbb{T}$.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Poltoratski (University of Wisconsin)
DTSTART;VALUE=DATE-TIME:20210428T161500Z
DTEND;VALUE=DATE-TIME:20210428T171500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/19
DESCRIPTION:Title: Pointwise convergence of scattering data\nby Alexei Polt
oratski (University of Wisconsin) as part of Spectral theory and related t
opics\n\n\nAbstract\nt is widely understood that the scattering transform
can be viewed as an analog of the Fourier transform in non-linear settings
. This connection brings up numerous questions on finding non-linear analo
gs of classical results of Fourier analysis. One of the fundamental result
s of classical harmonic analysis is a theorem by L. Carleson on pointwise
convergence of the Fourier series. In this talk I will discuss convergence
for the scattering data of a real Dirac system on the half-line and prese
nt an analog of Carleson's theorem for the non-linear Fourier transform.\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Silva (Universidad Nacional Autónoma de México)
DTSTART;VALUE=DATE-TIME:20210505T141500Z
DTEND;VALUE=DATE-TIME:20210505T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/20
DESCRIPTION:by Luis Silva (Universidad Nacional Autónoma de México) as p
art of Spectral theory and related topics\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxim Zinchenko (University of New Mexico)
DTSTART;VALUE=DATE-TIME:20210519T161500Z
DTEND;VALUE=DATE-TIME:20210519T171500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/21
DESCRIPTION:by Maxim Zinchenko (University of New Mexico) as part of Spect
ral theory and related topics\n\nInteractive livestream: https://us02web.z
oom.us/j/812916426\nPassword hint: please contact Fedor Bakharev (fbakhare
v@yandex.ru)\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/21/
URL:https://us02web.zoom.us/j/812916426
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Comech (Texas A&M University and IITP RAS)
DTSTART;VALUE=DATE-TIME:20210512T141500Z
DTEND;VALUE=DATE-TIME:20210512T151500Z
DTSTAMP;VALUE=DATE-TIME:20210514T203951Z
UID:eimi_spectral_theory/22
DESCRIPTION:Title: Virtual levels and virtual states of Schrodinger operators\nby Andrew Comech (Texas A&M University and IITP RAS) as part of Spectr
al theory and related topics\n\n\nAbstract\nVirtual levels admit several e
quivalent characterizations:\n\n(1) there are corresponding eigenstates fr
om $L^2$ or a space “slightly weaker” than $L^2$\;\n\n(2) there is no
limiting absorption principle in the vicinity of a virtual level (e.g. no
weights such that the “sandwiched” resolvent remains uniformly bounded
)\;\n\n(3) an arbitrarily small perturbation can produce an eigenvalue.\n\
nWe study virtual levels in the context of Schrodinger operators\, with no
nselfadjoint potentials and in all dimensions. In particular\, we derive t
he “missing” limiting absorption principle — the estimates on the re
solvent — near the threshold in two dimensions in the case when the thre
shold is not a virtual level.\n\nThis is a joint work with Nabile Boussaid
based on the preprint arXiv:2101.11979\n
LOCATION:https://researchseminars.org/talk/eimi_spectral_theory/22/
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