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BEGIN:VEVENT
SUMMARY:Nicola Arcozzi (University of Bologna)
DTSTART:20200916T160000Z
DTEND:20200916T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/1
DESCRIPTION:Title: The Hardy space from an engineer's perspective\nby Nicola Arcozzi
(University of Bologna) as part of Harmonic analysis e-seminars\n\n\nAbstr
act\nThe Hardy space $H^2$ made its way into signal theory since Wiener's
time\, and it belongs to the standard toolbox of all engineers who deal wi
th signals. We will see how $H^2$ and its related function spaces $H^1$\,
$H^\\infty$\, and $BMOA$ arise from basic practical problems\, and how mul
tiplication\, Toeplitz\, and Hankel operators enter the picture. Feedback
systems will take us at the front step of Pick interpolation. The aim is a
dvertising a possible intuition of a beautiful chapter of pure mathematics
.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Negro (University of Birmingham)
DTSTART:20201021T160000Z
DTEND:20201021T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/2
DESCRIPTION:Title: Sharp estimates for the wave equation via the Penrose transform\nb
y Giuseppe Negro (University of Birmingham) as part of Harmonic analysis e
-seminars\n\n\nAbstract\nIn 2004\, Foschi found the best constant\, and th
e extremizing functions\, for the Strichartz inequality for the wave equa
tion with data in the Sobolev space $\\Hdot^{1/2}\\times\\Hdot^{-1/2}(\\R
^3)$. He also formulated a conjecture\, concerning the extremizers to thi
s Strichartz inequality in all spatial dimensions $d\\ge 2$. We disprove
such conjecture for even $d$\, but we provide evidence to support it for o
dd $d$. The proofs use the conformal compactification of the Minkowski sp
ace-time given by the Penrose transform.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Duoandikoetxea (Euskal Herriko Unibertsitatea)
DTSTART:20200930T160000Z
DTEND:20200930T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/3
DESCRIPTION:Title: Weighted Morrey spaces\nby Javier Duoandikoetxea (Euskal Herriko U
nibertsitatea) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThis
talk is an account of my work on Morrey spaces with Marcel \nRosenthal in
recent years.\n\nThere are several definitions for weighted Morrey spaces
. We obtain \nboundedness results in all of them for operators satisfying
the \nassumptions of the usual extrapolation theorem\, that is\, we get \n
weighted Morrey estimates from weighted Lebesgue estimates with $A_p$ \nw
eights. The results can be applied to a variety of operators and \ntogethe
r with the norm estimates\, our technique also provides the \ndefinition o
f the operator by embedding.\n\nRecently we obtained results for a more ge
neral class of weighted \nMorrey spaces from an extension of the usual Muc
kenhoupt condition to \nthe Morrey setting\, involving the Khöthe dual of
the space. In some \ncases the conditions characterize the weighted inequ
alities of maximal \noperators.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ujué Etayo (TUGraz)
DTSTART:20201111T170000Z
DTEND:20201111T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/4
DESCRIPTION:Title: A Bombieri-type inequality for Weierstrass sigma functions\nby Uju
é Etayo (TUGraz) as part of Harmonic analysis e-seminars\n\n\nAbstract\nT
he Bombieri inequality is a classic inequality in number theory\,see [B. B
eauzamy\, E. Bombieri\, P. Enflo\, and H. L. Montgomery. Products\nof poly
nomials in many variables. Journal of Number Theory\, 36(2):219\n– 245\,
1990)].\nThe original statement says that given two homogeneous polynomia
ls on $N$ variables $P\,Q$ respectively of degree $m$ and $n$\, then\n$$\n
{\\frac {m!n!}{(m+n)!}}\\|P\\|^{2}\\\,\\|Q\\|^{2}\\leq \\|P\\cdot Q\\|^{2}
\\leq \\|P\\|^{2}\\\,\\|Q\\|^{2}\,\n$$\nwhere the norm is the Bombieri-Wey
l norm.\nThis inequality admits a rewriting in terms of integrals on the s
phere\, a property exploited in [U. Etayo. A sharp bombieri inequality\, l
ogarithmic energy and well con-\nditioned polynomials\, 2019].\nIn a joint
work with Joaquim Ortega-Cerd\\`a and Haakan Hedenmalm\, we use this new
definition to generalize the inequality to other Riemannian manifolds\, in
particular the torus $\\mathbb{C}/\\Lambda$\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Decio (Norwegian University of Science and Technology)
DTSTART:20201028T170000Z
DTEND:20201028T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/5
DESCRIPTION:Title: Nodal sets of Steklov eigenfunctions\nby Stefano Decio (Norwegian
University of Science and Technology) as part of Harmonic analysis e-semin
ars\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Bruno (Ghent University)
DTSTART:20201014T160000Z
DTEND:20201014T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/6
DESCRIPTION:Title: Factorization properties of smooth functions and vectors\nby Tomma
so Bruno (Ghent University) as part of Harmonic analysis e-seminars\n\n\nA
bstract\nGiven a module $\\mathcal{M}$ over a non-unital algebra $\\mathca
l{A}$\, we say that $\\mathcal{M}$ has the weak factorization property if
$\\mathcal{M}= \\mathrm{span} \\{\\mathcal{A} \\cdot \\mathcal{M}\\}$\, wh
ile it has the strong factorization property if $\\mathcal{M}= \\mathcal{A
} \\cdot \\mathcal{M}$. In this talk we shall review old and recent result
s about strong and weak factorizations of smooth functions and smooth vect
ors of Lie group representations. We shall also discuss open problems and
current lines of research.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José Luis Romero (University of Vienna)
DTSTART:20201202T174000Z
DTEND:20201202T184000Z
DTSTAMP:20260404T111001Z
UID:HAeS/7
DESCRIPTION:Title: Sampling\, density\, and equidistribution\nby José Luis Romero (U
niversity of Vienna) as part of Harmonic analysis e-seminars\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gennady Uraltsev (Cornell University)
DTSTART:20201209T170000Z
DTEND:20201209T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/8
DESCRIPTION:Title: Some results in Banach space-valued time frequency analysis\nby Ge
nnady Uraltsev (Cornell University) as part of Harmonic analysis e-seminar
s\n\n\nAbstract\nSIO (Singular Integral Operator) theory and\, Calderón-Z
ygmund theory specifically\, developed starting from the '60s\, provides a
vast array of tools for dealing with operators that resemble the Hilbert
transform\n$$\n\\mathrm{H}f(x):= \\int_{\\mathbb R}f(x-y)\\frac{d y}{y}\,\
n$$\n\nan ubiquitous operator in Complex Analysis\, semi-linear PDEs\, and
many other branches of mathematics. Results valid for -valued functions w
ere extended to Banach spaces-valued functions thanks to Bourgain's ground
breaking work on the deep relation between Banach space geometry and bound
edness properties of vector-valued SIOs.\n\nScalar-valued bounds for multi
linear SIOs\, like the bilinear Hilbert transform\n\n$$\n\\mathrm{BHT}[f_{
1}\,f_{2}](x)=\\int_{\\mathbb R} f_{1}(x-t) f_{2}(x+t) \\frac{d t} {t}\,\n
$$\n \nare classic in time-frequency-scale analysis. Banach-space valued r
esults have appeared only in the last couple of years. The well understood
connections with Banach space geometry from linear theory are just starti
ng to be investigated.\n\nOpen questions and generalizations to non-commut
ative analysis abound and would come hand-in-hand with progress in underst
anding SIOs with worse singularities than of Calderón-Zygmund type that c
an often be realized as SIO-valued CZ operators.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Martini (University of Birmingham)
DTSTART:20210113T170000Z
DTEND:20210113T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/9
DESCRIPTION:Title: Spectral multipliers for sub-Laplacians: recent developments and open
problems\nby Alessio Martini (University of Birmingham) as part of Har
monic analysis e-seminars\n\n\nAbstract\nI will present some old and new r
esults about the $L^p$ functional calculus for sub-Laplacians $L$. It has
been known for a long time that\, under quite general assumptions on the s
ub-Laplacian and the underlying sub-Riemannian structure\, an operator of
the form $F(L)$ is bounded on $L^p$\, $1< p<\\infty$\, whenever the multi
plier $F$ satisfies a scale-invariant smoothness condition of sufficiently
larger order.\nThe problem of determining the minimal smoothness assumpti
ons\, however\, remains widely open and will be the focus of our discussio
n.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giona Veronelli (Università di Milano-Bicocca)
DTSTART:20210210T170000Z
DTEND:20210210T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/10
DESCRIPTION:Title: Sobolev spaces on manifolds with lower bounded curvature\nby Gion
a Veronelli (Università di Milano-Bicocca) as part of Harmonic analysis e
-seminars\n\n\nAbstract\nThere are several notions of Sobolev spaces on a
Riemannian manifold: from the operator theory viewpoint it is natural to c
onsider Sobolev functions defined by taking the $L^p$ norms of functions a
nd of powers of their Laplacian. Instead\, the regularity theory of ellipt
ic equations involves Sobolev functions defined via the $L^p$ norm of all
the derivatives up to a certain order. Moreover\, Sobolev spaces can be c
haracterized via compactly supported smooth approximations.\nIn this talk\
, we will focus on non-compact manifolds with lower bounded curvature. We
will discuss some results giving the (non)-equivalence between the differe
nt Sobolev spaces. In particular\, we will highlight the role played in th
e theory by the Calderon-Zygmund inequality and the Bochner formulas\, and
we will sketch how to exploit singular metric spaces (e.g. Alexandrov or
RCD) as a tool to construct smooth counterexamples.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Vallarino (Politecnico di Torino)
DTSTART:20210317T170000Z
DTEND:20210317T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/11
DESCRIPTION:Title: Analysis on trees with nondoubling flows\nby Maria Vallarino (Pol
itecnico di Torino) as part of Harmonic analysis e-seminars\n\n\nAbstract\
nThe classical Calderón–Zygmund theory was developed in the Euclidean s
pace and\,\nmore generally\, on spaces of homogeneous type\, which are mea
sure metric spaces with\nthe doubling property.\nIn this talk we consider
trees endowed with flow measures\, which are nondoubling measures of at le
ast exponential growth. In this setting\, we develop a Calderón–Zygmund
\ntheory and we define $BMO$ and Hardy spaces\, proving a number of desire
d results extending the corresponding theory as known in the classical set
ting.\nThis is a joint work with Matteo Levi\, Federico Santagati and Anit
a Tabacco.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fulvio Ricci (Scuola Normale Superiore)
DTSTART:20210224T170000Z
DTEND:20210224T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/12
DESCRIPTION:Title: Multi-parameter structures\nby Fulvio Ricci (Scuola Normale Super
iore) as part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk
we give a survey on a certain number of multi-parameter structures\, on $\
\mathbb R^n$ and on nilpotent groups\, that have been introduced in the la
st 20 years. They include flag and multi-norm structures.\nThese structure
s are intermediate between the one-parameter dilation structures of standa
rd Calderón-Zygmund theory and the full $n$-parameter product structure.
Each structure has its own type of maximal functions\, singular integral o
perators\, square functions\, Hardy spaces.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loredana Lanzani (Syracuse University)
DTSTART:20210331T160000Z
DTEND:20210331T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/13
DESCRIPTION:Title: The commutator of the Cauchy-Szegő projection for domains in $C^n$ w
ith minimal smoothness\nby Loredana Lanzani (Syracuse University) as p
art of Harmonic analysis e-seminars\n\n\nAbstract\nLet $D\\subset\\C^n$ be
a bounded\, strongly pseudoconvex domain whose boundary $bD$ satisfies th
e minimal regularity condition of class $C^2$.\nWe characterize boundednes
s and compactness in $L^p(bD\, \\omega)$\,\, for $1< p < \\infty$\,of the
commutator $[b\,S_\\omega]$ where $S_\\omega$ is the Cauchy--Szegő (ortho
gonal) projection of $L^2(bD\, \\omega)$ onto the holomorphic Hardy spac
e $H^2(bD\, \\omega)$\n and the measure $\\omega$ belongs to a family
(the ``Leray Levi-like'' measures)\n that includes induced Lebesgue measur
e $\\sigma$. We next consider a much larger family of measures $\\{\\Omeg
a_p\\}$ modeled after the Muckenhoupt $A_p$-weights for $\\sigma$:\n we de
fine the holomorphic Hardy spaces $H^p(bD\, \\Omega_p)$ and we characteriz
e\n boundedness and compactness of $[b\, S_{\\Omega_2}]$ in $L^2(bD\, \\Om
ega_2)$.\n Earlier closely related results rely upon an asymptotic expansi
on\, and subsequent pointwise estimates\, of the Cauchy--Szegő kernel tha
t are not available in the settings of minimal regularity {of $bD$} and/or
$A_p$-like measures. \n\n\n \n This is joint work with Xuan Thinh Duong
\, Ji Li and Brett D. Wick.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gian Maria Dall'Ara (Indam/Scuola Normale Superiore)
DTSTART:20210324T170000Z
DTEND:20210324T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/14
DESCRIPTION:Title: L^p mapping problems for Bergman projections\nby Gian Maria Dall'
Ara (Indam/Scuola Normale Superiore) as part of Harmonic analysis e-semina
rs\n\n\nAbstract\nThis is for the most part a survey talk. I will discuss
various as-\npects of the following problem: for which values of $p$ is th
e Bergman projection\nof a given domain in $\\mathbb C^n$ bounded on $L^p$
? The answer depends heavily on the\ncomplex geometry of the domain. We wi
ll discuss the problem in one and\nseveral variables\, its connection with
the theory of conformal mappings and\nthat of singular integrals\, highli
ghting many open problems.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan S. Trapasso (Università di Genova)
DTSTART:20210421T160000Z
DTEND:20210421T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/15
DESCRIPTION:Title: Dispersion\, spreading and sparsity of Gabor wave packets\nby Iva
n S. Trapasso (Università di Genova) as part of Harmonic analysis e-semin
ars\n\n\nAbstract\nSparsity properties for phase-space representations of
several types of operators (including pseudodifferential\, metaplectic and
Fourier integral operators) have been extensively studied in recent artic
les\, with applications to the analysis of dispersive evolution equation.
It has been proved that such operators are approximately diagonalized by G
abor wave packets - equivalently\, the corresponding phase-space represent
ations (Gabor matrix/kernel) can be thought of as sparse infinite-dimensio
nal matrices. While wave packets are expected to undergo some spreading an
d dispersion phenomena\, there is no record of these issues in the aforeme
ntioned estimates. We recently proved refined estimates for the Gabor matr
ix of metaplectic operators\, also of generalized type\, where sparsity\,
spreading and dispersive properties are all simultaneously noticeable. We
also provide applications to the propagation of singularities for the Schr
\\"odinger equation\; in this connection\, our results can be regarded as
a microlocal refinement of known estimates. The talk is based on joint wor
k with Elena Cordero and Fabio Nicola.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fraccaroli (Universität Bonn)
DTSTART:20210519T160000Z
DTEND:20210519T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/16
DESCRIPTION:Title: Duality for outer $L^p$ spaces\nby Marco Fraccaroli (Universität
Bonn) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe theory o
f $L^p$ spaces for outer measures\, or outer $L^p$ spaces\, was\ndeveloped
by Do and Thiele to encode the proof of boundedness of certain\nmultiline
ar operators in a streamlined argument. Accordingly to this\npurpose\, the
theory was developed in the direction of the real\ninterpolation features
of these spaces\, while other questions remained\nuntouched.\nFor example
\, the outer $L^p$ spaces are defined by quasi-norms\ngeneralizing the cla
ssical mixed $L^p$ norms on sets with a Cartesian\nproduct structure. Ther
efore\, it is natural to ask whether in arbitrary\nsettings the outer $L^p
$ quasi-norms are equivalent to norms. In this\ntalk\, we will answer this
question\, with a particular focus on certain\nsettings on the upper half
space $\\R^d \\times (0\,\\infty)$ related to the\nwork of Do and Thiele.
\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Brocchi
DTSTART:20210616T163000Z
DTEND:20210616T173000Z
DTSTAMP:20260404T111001Z
UID:HAeS/17
DESCRIPTION:Title: Sparse T1 theorems\nby Gianmarco Brocchi as part of Harmonic anal
ysis e-seminars\n\n\nAbstract\nMany operators in analysis are non-local\,
in the sense that a\n perturbation of the input near a point modifies the
output\n everywhere\; consider for example the operator that maps the in
itial\n data to the corresponding solution of the heat equation.\n\n Spa
rse Domination consists in controlling such operators by a sum of\n posit
ive\, local averages. This allows to derive plenty of estimates\,\n which
are often optimal. For example\, it has been shown that Calderón--Zygmun
d operators\n and square functions admit such a domination even under min
imal $T1$ hypotheses.\\newline\n\n In this talk we introduce the concept
of sparse domination\n and present a sparse $T1$ theorem for square funct
ions\,\n discussing the new difficulties and ideas in this case.\n\n Ti
me permitting\, we will see how sparse domination can be applied\n in ver
y different context.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Filippo De Mari (Università di Genova)
DTSTART:20210630T160000Z
DTEND:20210630T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/18
DESCRIPTION:Title: Views on the Radon Transform\nby Filippo De Mari (Università di
Genova) as part of Harmonic analysis e-seminars\n\n\nAbstract\nI will reca
ll and introduce some of the many existing Radon transforms\, focusing in
particular on the setup of $G$-dual pairs $(X\,\\Xi)$ introduced by Helgas
on more than fifty years ago\, where $G$ is a locally compact group that
acts transitively both on $X$ and $\\Xi$. \nI will then present some resul
ts obtained in collaboration with G. S. Alberti\, F. Bartolucci\, E. De Vi
to\, M. Monti and F. Odone which bring into play (square integrable) repr
esentations. If the functions to be analyzed live on $X$ and the quasi re
gular representation of $G$ on $L^2(X)$ and $L^2(\\Xi)$ are square integra
ble\, then it is possible to write a nice inversion formula for the Radon
transform associated to the families of submanifolds of $X$ that are presc
ribed by the object $\\Xi$ which is dual to $X$. This formula hinges on a
unitarization of the Radon transform that may be proved in a rather genera
l setup if the quasi regular representations of $G$ on $L^2(X)$ and $L^2(\
\Xi)$ are irreducible\, and on an intertwining property of the Radon tran
sform. The former result is inspired by work of Helgason. Some examples a
re discussed\, mostly the guiding case related to shearlets that points in
the direction of possible practical inversion techniques.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Iosevich (University of Rochester)
DTSTART:20211006T160000Z
DTEND:20211006T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/19
DESCRIPTION:Title: Finite point configurations and the Vapnik-Chervonenkis dimension
\nby Alex Iosevich (University of Rochester) as part of Harmonic analysis
e-seminars\n\n\nAbstract\nThe Vapnik-Chervonenkis (VC) dimension was inven
ted in 1970 to study learning models. This notion has since become one of
the cornerstones of modern data science. This beautiful idea has also foun
d applications in other areas of mathematics. In this talk we are going to
describe how the study of the VC-dimension in the context of families of
indicator functions of spheres centered at points in sets of a given Hausd
orff dimension (or in sets of a given size inside vector spaces over finit
e fields) gives rise to interesting\, and in some sense extremal\, point c
onfigurations.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karlheinz Gröchenig (University of Vienna)
DTSTART:20211020T160000Z
DTEND:20211020T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/20
DESCRIPTION:Title: Variable bandwidth and sampling theorems\nby Karlheinz Gröcheni
g (University of Vienna) as part of Harmonic analysis e-seminars\n\n\nAbst
ract\nWe study sampling theorems in spectral subspaces of a uniformly elli
ptic differential operator. For constant coefficients\, these are spaces o
f bandlimited functions\, whereas for general elliptic operators\, the res
ulting spaces consist of functions of "variable bandwidth". This is one of
several constructions that gives meaning to the intuitive notion of a loc
al and time-varying bandwidth. The interpretation is supported by the resu
lts on sampling theorems and necessary sampling density.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Steinerberger (University of Washington)
DTSTART:20211110T170000Z
DTEND:20211110T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/21
DESCRIPTION:Title: The Smoothest Average and New Uncertainty Principles for the Fourier
Transform\nby Stefan Steinerberger (University of Washington) as part
of Harmonic analysis e-seminars\n\n\nAbstract\nSuppose you are given a rea
l-valued function f(x) and want to compute a local average at a certain sc
ale. What we usually do is to pick a nice probability measure u\, centered
at 0 and having standard deviation at the desired scale\, and convolve. C
lassical candidates for u are the characteristic function or the Gaussian.
This got me interested in finding the ”best” function u – this prob
lem comes in two parts: (1) describing what one considers to be desirable
properties of the convolution and (2) understanding which functions satisf
y these properties. I tried a basic notion for the first part\, ”the con
volution should be as smooth as the scale allows”\, and ran into fun cla
ssical Fourier Analysis that seems to be new: (a) new uncertainty principl
es for the Fourier transform\, (b) that potentially have the characteristi
c function as an extremizer\, (c) which leads to strange new patterns in h
ypergeometric functions and (d) produces curious local stability inequalit
ies. Noah Kravitz and I managed to solve two specific instances on the dis
crete lattice completely\, this results in some sharp weighted estimates f
or polynomials on the unit interval – both the Dirichlet and the Fejer k
ernel make an appearance. The entire talk will be completely classical Har
monic Analysis\, there are lots and lots of open problems.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Bennett (University of Birmingham)
DTSTART:20211103T170000Z
DTEND:20211103T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/22
DESCRIPTION:Title: The nonlinear Brascamp-Lieb inequality and applications\nby Jonat
han Bennett (University of Birmingham) as part of Harmonic analysis e-semi
nars\n\n\nAbstract\nThe Brascamp-Lieb inequality is a broad generalisation
of many well-known multilinear inequalities in analysis\, including the m
ultilinear Hölder\, Loomis-Whitney and sharp Young convolution inequaliti
es. There is by now a rich theory surrounding this classical inequality\,
along with applications in convex geometry\, harmonic analysis\, partial d
ifferential equations\, number theory and beyond. In this talk we present
a certain nonlinear variant of the Brascamp-Lieb inequality\, placing part
icular emphasis on some of its applications. Most of this is joint work wi
th Stefan Buschenhenke\, Neal Bez\, Michael Cowling and Taryn Flock.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anthony Carbery (University of Edinburgh)
DTSTART:20211201T170000Z
DTEND:20211201T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/23
DESCRIPTION:Title: Duality for joints and multijoints - what is it\, what are they\, and
why do we care?\nby Anthony Carbery (University of Edinburgh) as part
of Harmonic analysis e-seminars\n\n\nAbstract\nWe discuss theories of dua
lity which are applicable to the multijoint and joint problems\, which are
themselves discrete formulations of multilinear and linear Kakeya problem
s. This is joint work in part with Timo Hanninen and Stefan Valdimarsson\,
and in part with Michael Tang.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Dragičević (University of Ljubljana)
DTSTART:20211215T170000Z
DTEND:20211215T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/24
DESCRIPTION:Title: $L^p$ asymptotics for powers of the complex Riesz transform\nby O
liver Dragičević (University of Ljubljana) as part of Harmonic analysis
e-seminars\n\n\nAbstract\nWe establish the sharp behaviour of the $L^p$ no
rms of integer powers of the planar Riesz transform $R_2+iR_1$\, and brief
ly discuss the estimates on $L^1$ and $L^\\infty$. This is a joint work wi
th Andrea Carbonaro and Vjekoslav Kovač.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Philippe Anker (Université d’Orléans)
DTSTART:20220112T170000Z
DTEND:20220112T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/25
DESCRIPTION:Title: Dispersive PDE on noncompact symmetric spaces\nby Jean-Philippe A
nker (Université d’Orléans) as part of Harmonic analysis e-seminars\n\
n\nAbstract\nWe consider the wave equation and the Schrödinger equation o
n general symmetric spaces of the noncompact type\, which is an interestin
g class of Riemannian manifolds with nonpositive curvature\, including all
hyperbolic spaces. The standard strategy consists in establishing first p
ointwise kernel estimates for the fundamental solutions\, in deducing next
dispersive and Strichartz inequalities for the linear equations\, and in
applying them finally to semilinearities. This program was successfully ac
hieved for various classes of manifolds over the past 40 years\, in partic
ular for hyperbolic spaces 10-15 years ago. We were recently able to exten
d it to symmetric spaces of higher rank\, in collaboration with V. Pierfel
ice\, S. Meda\, M. Vallarino and H.-W. Zhang. In this talk\, we shall repo
rt on these progresses\, emphasizing on the tools used to tackle the highe
r rank case.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malabika Pramanik (University of British Columbia)
DTSTART:20220126T170000Z
DTEND:20220126T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/26
DESCRIPTION:Title: On projections and circles\nby Malabika Pramanik (University of B
ritish Columbia) as part of Harmonic analysis e-seminars\n\n\nAbstract\nTh
is will be a survey of two classes of problems in analysis: measuring the
size of projections of sets\, and incidences of circles in the plane. I w
ill discuss some landmark results and recently discovered connections betw
een the two.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Hickman (University of Edinburgh)
DTSTART:20220209T170000Z
DTEND:20220209T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/27
DESCRIPTION:Title: Kakeya maximal estimates via real algebraic geometry\nby Jonathan
Hickman (University of Edinburgh) as part of Harmonic analysis e-seminars
\n\n\nAbstract\nThe Kakeya (maximal) conjecture concerns how collections o
f long\, thin tubes which point in different directions can overlap. Such
geometric problems underpin the behaviour of various important oscillatory
integral operators and\, consequently\, understanding the Kakeya conjectu
re is a vital step towards many central problems in harmonic analysis. In
this talk I will discuss work with K. Rogers and R. Zhang which apply tool
s from the theory of semialgebraic sets to yield new partial results on th
e Kakeya conjecture. Also\, more recent work with J. Zahl has used these m
ethods to improve the range of estimates on the Fourier restriction conjec
ture.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Soria (Universidad Autónoma de Madrid)
DTSTART:20220223T170000Z
DTEND:20220223T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/28
DESCRIPTION:Title: Integro-differential operators and nonlocal diffusion\nby Fernand
o Soria (Universidad Autónoma de Madrid) as part of Harmonic analysis e-s
eminars\n\n\nAbstract\nBy a nonlocal diffusion equation we mean an evoluti
on problem where the un-\nknown function is not just reverting to its infi
nitesimal average\, but instead it\n\nis influenced by its values at many
scales. It is still a diffusion\, but trying to\nrevert now to an integral
average of its surrounding values.\nTypical examples in probability arise
when considering jump (Levy) processes\nin optimal control\, game theory
and finance. The quasi-geostrophic equation\nfor ocean-atmosphere interact
ion provides a ’simple’ model in fluid dynamics.\n\nIn this talk we wi
ll present a\, by no means exhaustive\, survey describing how\nthis theory
has evolved in recent years.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Iliopoulou (University of Kent)
DTSTART:20220309T170000Z
DTEND:20220309T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/29
DESCRIPTION:Title: Some remarks on the Mizohata-Takeuchi conjecture\nby Marina Iliop
oulou (University of Kent) as part of Harmonic analysis e-seminars\n\n\nAb
stract\nThis is a conjecture on weighted estimates for the classical Fouri
er extension operators of harmonic analysis. In particular\, let E be the
extension operator associated to some surface\, and f be a function on tha
t surface. If we 'erase' part of Ef\, how well can we control the 2-norm o
f the remaining piece? The Mizohata-Takeuchi conjecture claims some remark
able control on this quantity\, involving the X-ray transform of the part
of the support of Ef that we kept. In this talk we will discuss the histor
y of the problem\, and will describe a new perspective that modestly impro
ves our knowledge (for a certain class of weights). This is joint work wit
h A. Carbery.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Detlef Müller (University of Kiel)
DTSTART:20220323T170000Z
DTEND:20220323T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/30
DESCRIPTION:Title: On Fourier restriction to hyperbolic 2-surfaces: robustness of the po
lynomial compared to the bilinear approach\nby Detlef Müller (Univer
sity of Kiel) as part of Harmonic analysis e-seminars\n\n\nAbstract\nIn th
is talk\, which will be based on joint research with S. Buschenhenke\nand
A.Vargas\, I intend to discuss some of the new challenges that arose in ou
r\nstudies of Fourier restriction estimates for hyperbolic surfaces\, comp
ared to\nthe case of elliptic surfaces. Given the complexity of the biline
ar\, and even\nmore so of the polynomial partitioning approach\, I shall m
ainly focus on\nthose parts of these methods which required new ideas\, so
that a familiarity\nwith these methods will not be expected from the audi
ence.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carmelo Puliatti (Euskal Herriko Unibertsitatea)
DTSTART:20220413T160000Z
DTEND:20220413T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/31
DESCRIPTION:Title: Gradients of single layer potentials for elliptic operators with coef
ficients of Dini mean oscillation-type\nby Carmelo Puliatti (Euskal He
rriko Unibertsitatea) as part of Harmonic analysis e-seminars\n\n\nAbstrac
t\nWe consider a uniformly elliptic operator $L_A$ in divergence form \nas
sociated with a matrix $A$ with real\, bounded\, and possibly \nnon-symmet
ric coefficients. If a proper $L^1$-mean oscillation of the \ncoefficients
of $A$ satisfies suitable Dini-type assumptions\, we prove \nthe followin
g: if $\\mu$ is a compactly supported Radon measure in \n$R^{n+1}\, n\\geq
2\,$ the $L^2(\\mu)$-operator norm of the gradient of the \nsingle layer
potential $T_\\mu$ associated with $L_A$ is comparable to the \n$L^2$-nor
m of the $n$-dimensional Riesz transform $R_\\mu$\, modulo an \nadditive c
onstant.\nThis makes possible to obtain direct generalizations of some dee
p \ngeometric results\, initially proved for the Riesz transform\, which \
nwere recently extended to $T_\\mu$ under a H\\"older continuity assumptio
n \non the coefficients of the matrix $A$.\n\nThis is a joint work with Al
ejandro Molero\, Mihalis Mourgoglou\, and \nXavier Tolsa.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandra Saliani (Università degli Studi della Basilicata)
DTSTART:20220420T160000Z
DTEND:20220420T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/32
DESCRIPTION:Title: Spectral graph transforms: wavelets\, frames\, and open problems\
nby Sandra Saliani (Università degli Studi della Basilicata) as part of H
armonic analysis e-seminars\n\n\nAbstract\nClassical transforms\, as Fouri
er\, wavelet\, wavelet packets and time-frequency dictionaries have been
generalized to functions defined on finite\, undirected graphs\, where the
connections between vertices are encoded by the Laplacian matrix.\n\nDesp
ite working in a finite and discrete environment\, many problems arise in
applications where the graph is very large\, as it is not possible to dete
rmine all the eigenvectors of the Laplacian explicitly. For example\, in t
he case of our interest: a voxel-wise brain graph $\\mathcal{G}$ with $900
760$ nodes (representing the brain voxels)\, and signals given by the fRMI
(functional magnetic resonance imaging).\n\nAfter an overview of the meth
ods and of the open problems\, we present a new method to generate frames
of wavelet packets defined in the graph spectral domain to represent sign
als on finite graphs.\n\n\nJoint work with Iulia Martina Bulai.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Bramati (Ghent University)
DTSTART:20220518T160000Z
DTEND:20220518T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/33
DESCRIPTION:Title: Resonances of invariant differential operators\nby Roberto Bramat
i (Ghent University) as part of Harmonic analysis e-seminars\n\n\nAbstract
\nGiven a self-adjoint differential operator with continuous spectrum acti
ng on a Hilbert space H\, its resonances are the poles of a meromorphic ex
tension across the spectrum of its resolvent acting on a dense subspace of
H in which the operator is no longer self-adjoint. They can be thought of
as replacements of eigenvalues for problems on noncompact domains. In thi
s talk we will first explore two well-understood cases: the Laplacian on E
uclidean spaces and the Laplace-Beltrami operator on rank one Riemannian s
ymmetric spaces of the noncompact type\, two settings where a notion of Fo
urier analysis is available. In both cases\, the Laplacian comes from the
action of the Casimir operator through the left regular representation of
the underlying group\, and the Plancherel formula provides a direct integr
al decomposition of such representation. Elaborating from this point of vi
ew\, in collaboration with A. Pasquale and T. Przebinda we started to deve
lop methods to study resonances in more general settings. As an example of
such methods\, in the talk we will consider some instances of Capelli ope
rators and see how one can exploit Howe’s theory for reductive dual pair
s. We will also consider the problem of identifying the representations th
at are naturally attached to the resonances in these settings.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Vitturi (University College Cork)
DTSTART:20220615T160000Z
DTEND:20220615T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/34
DESCRIPTION:Title: A restricted 2-plane transform related to Fourier Restriction in codi
mension 2\nby Marco Vitturi (University College Cork) as part of Harmo
nic analysis e-seminars\n\n\nAbstract\nThe $2-$plane transform is the oper
ator that maps a function to its averages along affine $2-$planes. We cons
ider the operator obtained by restricting the allowed directions of the $2
-$planes to those normal to a fixed surface $S$ (quadratic\, for simplicit
y) of codimension $2$. By duality and discretisation\, $L^p\\to L^q$ estim
ates for such an operator imply Kakeya-type estimates for the supports of
Fourier-transformed wave-packets adapted to the surface $S$ (wave-packet d
ecompositions being a powerful tool in proving Fourier Restriction results
). We connect this operator to Gressman's theory of affine invariant measu
res by showing that if the surface is well-curved à la Gressman (meaning\
, the affine invariant surface measure on S is non-vanishing) then the res
tricted $2-$plane transform is $L^p\\to L^q$ bounded in the maximal range
of $(p\,q)$ exponents allowed. The proof relies on a characterisation of w
ell-curvedness in Geometric Invariant Theory terms\, which will be discuss
ed.\nJoint work with S. Dendrinos and A. Mustata.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sinai Robins (Universidade de São Paulo)
DTSTART:20220629T160000Z
DTEND:20220629T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/35
DESCRIPTION:Title: The covariogram and extensions of the Bombieri-Siegel formula\nby
Sinai Robins (Universidade de São Paulo) as part of Harmonic analysis e
-seminars\n\n\nAbstract\nWe extend a formula of C. L. Siegel in the geomet
ry of numbers\, allowing the body to contain an arbitrary number of interi
or lattice points. Our extension involves a lattice sum of the cross covar
iogram for any two bounded sets $A\, B\\subseteq \\mathbb R^d$\, and turns
out to also extend a\nresult of E. Bombieri. We begin with a new variatio
n of the Poisson summation formula\, which may be of independent interest.
One of the consequences of these results is a new characterization of mul
titilings of Euclidean space by translations\, which is an application of
Bombieri’s identity and of our extension of it. Some classical results\,
such as Van der Corput’s inequality\, and Hardy’s identity for the Ga
uss circle problem\, also follow as corollaries. This is joint work with M
ichel Faleiros Martins.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Izabella Łaba (University of British Columbia)
DTSTART:20221005T160000Z
DTEND:20221005T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/36
DESCRIPTION:Title: Favard length estimates via cyclotomic divisibility\nby Izabella
Łaba (University of British Columbia) as part of Harmonic analysis e-semi
nars\n\n\nAbstract\nThe Favard length of a planar set $E$ is the average l
ength of its one-dimensional projections. It is well known (due to Besicov
itch) that if $E$ is a purely unrectifiable planar self-similar set of Hau
sdorff dimension 1\, then its Favard length is 0. Consequently\, if $E_\\d
elta$ is the $\\delta$-neighbourhood of $E$\, then the Favard length of $E
_\\delta$ goes to 0 as $\\delta\\to 0$. A question of interest in geometri
c measure theory\, ergodic theory and analytic function theory is to estim
ate the rate of decay\, both from above and below. Partial results in this
direction have been proved by many authors\, including Mattila\, Nazarov\
, Perez\, Volberg\, Bond\, Bateman\, and myself. In addition to geometric
measure theory\, this work has involved methods from harmonic analysis\, a
dditive combinatorics\, and algebraic number theory. I will review the rel
evant background\, and then discuss my recent work with Caleb Marshall on
upper bounds on the Favard length for 1-dimensional planar Cantor sets wit
h a rational product structure. This improves on my earlier work with Bond
and Volberg\, and incorporates new methods introduced in my work with Ita
y Londner on integer tilings.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenia Malinnikova (Stanford University - NTNU)
DTSTART:20221019T160000Z
DTEND:20221019T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/37
DESCRIPTION:Title: Some inequalities for Laplace eigenfunctions and their gradients\
nby Eugenia Malinnikova (Stanford University - NTNU) as part of Harmonic
analysis e-seminars\n\n\nAbstract\nWe will survey some recent results on r
estrictions of Laplace eigenfunctions\nand present new norm inequalities f
or the eigenfunctions and their gradients\nobtained in a joint work with S
tefano Decio. The guiding principle\, which\ngoes back to the works of Don
nelly and Fefferman\, is that eigenfunctions with\neigenvalue $\\textrm{E}
^2$ behave like (harmonic) polynomials of degree $\\textrm{E}$.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giancarlo Travaglini (University of Milano-Bicocca)
DTSTART:20221116T170000Z
DTEND:20221116T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/38
DESCRIPTION:Title: Irregularities of distribution\nby Giancarlo Travaglini (Universi
ty of Milano-Bicocca) as part of Harmonic analysis e-seminars\n\n\nAbstrac
t\nThe term “Irregularities of distribution” appeared for the first ti
me in the title of 1954 K. Roth’s seminal paper and referred to a conjec
ture of J. van der Corput on the non-existence of a “good” way to cho
ose an infinite sequence in the unit interval. Roth approached van der Cor
put’s conjecture by checking the quality of any choice of N points in th
e 2-dimensional torus with respect to arbitrary squares therein\, and prov
ing a logarithmic lower bound for the discrepancy. Later W. Schmidt\, H. M
ontgomery and J. Beck independently proved that the discrepancy is at leas
t a power of N when squares are replaced with disks. \n\nWe construct a fa
mily of intermediate cases and we show that positive curvature plays no ro
le in this problem which reduces to a careful study of the decay of certai
n Fourier transforms.\n\nWe shall also describe two related d-dimensional
problems. \n\n(from joint works with Luca Brandolini and Leonardo Colzani)
\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (University of Bonn - Max Planck Institute for M
athematics)
DTSTART:20230111T170000Z
DTEND:20230111T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/39
DESCRIPTION:Title: The Korányi Spherical Maximal Function on Heisenberg groups\nby
Rajula Srivastava (University of Bonn - Max Planck Institute for Mathemati
cs) as part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk\,
we discuss the problem of obtaining sharp $L^p \\to L^q$ estimates for the
local maximal operator associated with averaging over dilates of the Kor
ányi sphere on Heisenberg groups. This is a codimension one surface compa
tible with the non-isotropic Heisenberg dilation structure. I will describ
e the main features of the problem\, some of which are helpful while other
s are obstructive. These include the non-Euclidean group structure (the ex
tra “twist” due to the Heisenberg group law)\, the geometry of the Kor
ányi sphere (in particular\, the flatness at the poles) and an “imbalan
ced” scaling argument encapsulated by a new type of Knapp example\, whic
h we shall describe in detail.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (University of Valencia)
DTSTART:20230125T170000Z
DTEND:20230125T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/40
DESCRIPTION:Title: Endpoint sparse domination for oscillatory Fourier multipliers\nb
y David Beltran (University of Valencia) as part of Harmonic analysis e-se
minars\n\n\nAbstract\nSparse domination was first introduced in the contex
t of Calderón--Zygmund theory. Shortly after\, the concept was successful
ly extended to many other operators in Harmonic Analysis\, although many e
ndpoint situations have remained unknown. In this talk\, we will present n
ew endpoint sparse bounds for oscillatory and Miyachi-type Fourier multipl
iers using Littlewood--Paley theory. Furthermore\, the results can be exte
nded to more general dilation-invariant classes of multiplier transformati
ons via Hardy space techniques\, yielding results\, for instance\, for mul
ti-scale sums of radial bump multipliers.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesca Bartolucci (ETH - Zurich)
DTSTART:20230208T170000Z
DTEND:20230208T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/41
DESCRIPTION:Title: What's new in wavelet phase retrieval?\nby Francesca Bartolucci (
ETH - Zurich) as part of Harmonic analysis e-seminars\n\n\nAbstract\nWavel
et phase retrieval consists of the inverse problem of reconstructing a squ
are-integrable function $f$ from its scalogram\, that is from the absolute
value of its wavelet transform\n\\[\n \\mathcal{W}_{\\phi}f(b\,a) = a^
{-\\frac{1}{2}} \\int_{\\R} f(x) \\overline{\\phi\\left(\\frac{x-b}{a}\\ri
ght)} \\\,\\mathrm{d} x\, \\qquad b \\in \\R\,~a \\in \\R_+. \n\\]\nThe wa
velet transform emerged from the research activities aimed to develop new
analysis and processing tools to enhance signal theory\, and has proved to
be extremely efficient in various applications such as denoising and comp
ression. However\, there is still limited knowledge of the problem of reco
nstructing a function from the absolute value of its wavelet transform. Mo
re precisely\, wavelet phase retrieval aims to determine for which analyzi
ng wavelets $\\phi$ and which choices of $\\Lambda \\subseteq \\R \\times
\\R_+$ as well as $\\mathcal{M} \\subseteq L^2(\\R)$ the forward operator
\n\\[\nF_\\phi : \\mathcal{M} /\\!\\sim \\\, \\to\\\, [0\,+\\infty)^\\Lamb
da\,\\qquad F_\\phi f(b\,a) = \\lvert \\mathcal{W}_\\phi f (b\,a) \\rvert\
, \\quad (b\,a) \\in \\Lambda\,\n\\]\nis injective\, where $f\\sim g$ if a
nd only if $f=\\text{e}^{i\\alpha}g$ for some $\\alpha\\in\\R$. In this ta
lk\, we present old and new results on this question and conclude by discu
ssing some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico Lisboa)
DTSTART:20230308T170000Z
DTEND:20230308T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/42
DESCRIPTION:Title: Exponentials rarely maximize Fourier extension inequalities for cones
\nby Diogo Oliveira e Silva (Instituto Superior Técnico Lisboa) as pa
rt of Harmonic analysis e-seminars\n\n\nAbstract\nThis talk is based on re
cent joint work with G. Negro\, B. Stovall and J. Tautges.\nGlobal maximiz
ers for the $L^2$ Fourier extension inequality on the cone in $\\mathbb R^
{1+d}$ have been characterized in the lowest-dimensional cases $d\\in\\{2\
,3\\}$. We prove that these functions are critical points for the $L^p$ to
$L^q$ Fourier extension inequality if and only if $p=2$. We also establis
h the existence of maximizers and the precompactness of $L^p$-normalized m
aximizing sequences modulo symmetries for all valid scale-invariant Fourie
r extension inequalities on the cone in $\\mathbb R^{1+d}$. In the range f
or which such inequalities are conjectural\, our result is conditional on
the boundedness of the extension operator. The proof uses tools from the c
alculus of variations\, bilinear restriction theory\, conformal geometry a
nd the theory of special functions.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nir Lev (Bar-Ilan University)
DTSTART:20230322T170000Z
DTEND:20230322T180000Z
DTSTAMP:20260404T111001Z
UID:HAeS/43
DESCRIPTION:Title: Tiling by translates of a function\nby Nir Lev (Bar-Ilan Universi
ty) as part of Harmonic analysis e-seminars\n\n\nAbstract\nI will discuss
tilings of the real line by translates of a function $f$\, that is\, syste
ms $\\{f(x - \\lambda)\, \\lambda \\in \\Lambda\\}$ of translates of $f$ t
hat form a partition of unity. Which functions $f$ can tile by translation
s\, and what can be the structure of the translation set $\\Lambda$? I wil
l survey the subject and present some recent results.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Bilyk (University of Minnesota)
DTSTART:20230419T160000Z
DTEND:20230419T170000Z
DTSTAMP:20260404T111001Z
UID:HAeS/44
DESCRIPTION:Title: Minimizers of discrete measures and energy integrals.\nby Dmitri
y Bilyk (University of Minnesota) as part of Harmonic analysis e-seminars\
n\n\nAbstract\nWe shall survey various results and conjectures about ener
gy minimization problems that arise in different fields: electrostatics\,
discrete and metric geometry\, discrepancy theory and uniform distribution
\, signal processing etc. While in many natural examples optimizing the e
nergy imposes uniform distribution\, we shall pay special attention to the
opposite effect -- when minimizers exhibit clustering or discretization\,
or are supported on small or lower dimensional subsets. We shall also tou
ch upon energies that depend on interactions of three or more particles\,
rather than just pairwise interactions\, and describe difficulties that ar
ise in this setting.\n
LOCATION:https://stable.researchseminars.org/talk/HAeS/44/
END:VEVENT
END:VCALENDAR