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BEGIN:VEVENT
SUMMARY:Alessio Martini
DTSTART;VALUE=DATE-TIME:20200428T143000Z
DTEND;VALUE=DATE-TIME:20200428T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/1
DESCRIPTION:Title: A sharp multiplier theorem for degenerate elliptic oper
ators on the plane\nby Alessio Martini as part of Virtual Harmonic Analysi
s Seminars\n\n\nAbstract\nGrushin operators are among the simplest example
s of subelliptic operators. Due to the lack of ellipticity\, standard tech
niques based on heat kernel estimates yield spectral multiplier theorems t
hat are typically not sharp in terms of the smoothness requirement on the
multiplier. We show that\, for a large class of Grushin operators on the p
lane\, a sharp multiplier theorem can be proved\, with the same smoothness
requirement as in the case of the standard Laplacian. Our argument is rob
ust enough to handle nonhomogeneous coefficients vanishing of arbitrarily
high order\, and hinges on the analysis of one-parameter families of Schro
edinger operators. This is based on joint work with Gian Maria Dall'Ara (B
irmingham).\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Bate (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200505T143000Z
DTEND;VALUE=DATE-TIME:20200505T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/2
DESCRIPTION:Title: Cheeger’s differentiation theorem via the multilinear
Kakeya inequality\nby David Bate (University of Warwick) as part of Virtu
al Harmonic Analysis Seminars\n\n\nAbstract\nIn 1999 Cheeger gave a far re
aching generalisation of Rademacher’s differentiation theorem which repl
aces the domain by a metric space equipped with a measure that satisfies a
version of the Poincare inequality. The first half of this talk will cons
ist of a gentle introduction to this result and some of its consequences.
No prior knowledge will be assumed.\n\nThe work of Cheeger inspired a larg
e number of new results in the area of analysis on metric spaces. The seco
nd half of this talk will present a new\, simpler proof of Cheeger’s the
orem based on these developments and the multilinear Kakeya inequality for
rectifiable curves (in Euclidean space). This is based on joint work with
Ilmari Kangasniemi and Tuomas Orponen.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200512T143000Z
DTEND;VALUE=DATE-TIME:20200512T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/3
DESCRIPTION:Title: Bounds in the polynomial Szemerédi theorem\nby Sarah P
eluse (University of Oxford) as part of Virtual Harmonic Analysis Seminars
\n\n\nAbstract\nLet $P_1\,\\ldots\, P_m$ be polynomials with integer coeff
icients and zero constant term. Bergelson and Leibman’s polynomial gener
alization of Szemerédi’s theorem states that any subset $A$ of $\\{1\,\
\ldots\,N\\}$ that contains no nontrivial progressions $x\, x+P_1(y)\, \\l
dots\, x+P_m(y)$ must satisfy $|A|=o(N)$. In contrast to Szemerédi's theo
rem\, quantitative bounds for Bergelson and Leibman's theorem (i.e.\, expl
icit bounds for this $o(N)$ term) are not known except in very few special
cases. In this talk\, I will discuss recent progress on this problem\, fo
cusing on arguments involving Fourier analysis.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:John MacKay (University of Bristol)
DTSTART;VALUE=DATE-TIME:20200519T143000Z
DTEND;VALUE=DATE-TIME:20200519T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/4
DESCRIPTION:Title: Poincaré profiles on graphs and groups\nby John MacKay
(University of Bristol) as part of Virtual Harmonic Analysis Seminars\n\n
\nAbstract\nThe separation profile of an infinite graph was introduced by
Benjamini-Schramm-Timar. It is a function which measures how well-connect
ed the graph is by how hard it is to cut finite subgraphs into small piece
s. In earlier joint work with David Hume and Romain Tessera\, we introduc
ed Poincaré profiles\, generalising this concept by using p-Poincaré ine
qualities to measure the connectedness of subgraphs. I will discuss these
invariants\, their applications to coarse embedding problems\, and work n
earing completion where we find the profiles of all connected unimodular L
ie groups. Joint with Hume and Tessera.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20200526T143000Z
DTEND;VALUE=DATE-TIME:20200526T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/5
DESCRIPTION:Title: Sign uncertainty principles: old and new\nby Diogo Oliv
eira e Silva (University of Birmingham) as part of Virtual Harmonic Analys
is Seminars\n\n\nAbstract\nTen years ago\, Bourgain\, Clozel & Kahane esta
blished a surprising "sign uncertainty principle" (SUP)\, asserting that i
f a function and its Fourier transform are nonpositive at the origin and n
ot identically zero\, then they cannot both be nonnegative outside an arbi
trarily small neighbourhood of the origin. In 2017\, Gonçalves & Cohn sol
ved the 12-dimensional SUP via connections to the sphere packing problem\,
and discovered a complementary SUP. This talk will focus on some new sign
uncertainty principles which generalise the developments of Bourgain\, Cl
ozel & Kahane and Cohn & Gonçalves. In particular\, we will discuss SUPs
for Fourier series\, the Hilbert transform\, spherical harmonics\, and Jac
obi polynomials. As a by-product\, we determine some sharp instances of th
e spherical SUP via connections to tight spherical designs. Time permittin
g\, we will outline a possible path towards the sharp 1-dimensional SUP. T
his talk is based on recent joint work with Felipe Gonçalves and João Pe
dro Ramos.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Brocchi (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20200602T143000Z
DTEND;VALUE=DATE-TIME:20200602T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/6
DESCRIPTION:Title: Sparse T1 theorems\nby Gianmarco Brocchi (University of
Birmingham) as part of Virtual Harmonic Analysis Seminars\n\n\nAbstract\n
In the last decade a plethora of sharp weighted estimates has been obtaine
d for several different operators. These estimates (sharp in the dependenc
e on the characteristic of the weight) follow from a sparse domination of
the operator. Roughly speaking\, a sparse domination consists in controlli
ng the operator with a positive dyadic form. It has been shown that Calder
ón–Zygmund operators and square functions admit such domination even un
der minimal T1 hypothesis.\n\nIn this talk we introduce the concept of spa
rse domination and we present some ideas that allow to upgrade the classic
al T1 theorems by David\, Christ and Journé to sparse ones.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adolfo Arroyo-Rabasa (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200609T143000Z
DTEND;VALUE=DATE-TIME:20200609T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/7
DESCRIPTION:Title: Function space questions in CalcVar/GMT that are being
solved using Fourier analysis\nby Adolfo Arroyo-Rabasa (University of Warw
ick) as part of Virtual Harmonic Analysis Seminars\n\n\nAbstract\nThe spac
e BV of functions of bounded variation is the space of integrable function
s whose gradient is a Radon measure. Extending this definition to the tren
dy A-free measures\, I will define the space BV^A of functions of bounded
A-variation: functions such that A(D)u is a measure\, where A(D) is a line
ar elliptic operator with constant coefficients. I will introduce general
aspects of this theory\, share a few recent results\, and some difficult o
pen problems:\n\nL1-estimates -> life without Calderón-Zygmund\n\nSlicing
\, geometry of A-bounded measures -> life without co-area formula\n\nConti
nuity properties\, #2ndHardestProblemCalcVar -> life without co-area form
ula\, again.\n\nInterestingly\, these measure theoretic properties were so
lved/require Fourier analysis methods.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Villa (University of Helsinki)
DTSTART;VALUE=DATE-TIME:20200616T143000Z
DTEND;VALUE=DATE-TIME:20200616T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/8
DESCRIPTION:Title: A proof the Carleson $\\epsilon^2$-conjecture\nby Miche
le Villa (University of Helsinki) as part of Virtual Harmonic Analysis Sem
inars\n\n\nAbstract\nIn this talk we sketch a proof of the Carleson $\\eps
ilon^2$-conjecture. This result yields a characterization (up to exception
al sets of zero length) of the tangent points of a Jordan curve in terms o
f the finiteness of the associated Carleson $\\epsilon^2$-square function.
This is a joint work with Ben Jaye and Xavier Tolsa.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Sanders (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200623T143000Z
DTEND;VALUE=DATE-TIME:20200623T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/9
DESCRIPTION:Title: Approximate homomorphisms and a conjecture of Pełczyń
ski\nby Tom Sanders (University of Oxford) as part of Virtual Harmonic Ana
lysis Seminars\n\n\nAbstract\nFollowing the introduction of techniques fro
m additive combinatorics to some problems in Banach spaces by Wojciechowsk
i\, we discuss the Balog-Szemerédi-Gowers Lemma and how it can be used to
tackle some questions about approximate homomorphisms and a conjecture of
Pełczyński.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20200630T143000Z
DTEND;VALUE=DATE-TIME:20200630T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/10
DESCRIPTION:Title: Fourier restriction estimates above rectangles and an a
pplication\nby Betsy Stovall (University of Wisconsin-Madison) as part of
Virtual Harmonic Analysis Seminars\n\n\nAbstract\nWe discuss the problem o
f obtaining Lebesgue space inequalities for the Fourier restriction operat
or associated to rectangular pieces of the paraboloid and perturbations th
ereof. We state a conjecture for the dependence of the operator norms in
these inequalities on the sidelengths of the rectangles\, outline a proof
of the conjecture (conditional in some cases\, unconditional in others)\,
and demonstrate how these estimates can be applied to obtain sharp restric
tion inequalities on some degenerate hypersurfaces. This is joint work wi
th Jeremy Schwend.\n
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Bennett (University of Birmingham)
DTSTART;VALUE=DATE-TIME:20200707T143000Z
DTEND;VALUE=DATE-TIME:20200707T153000Z
DTSTAMP;VALUE=DATE-TIME:20200812T025718Z
UID:HarmonicAnalysis/11
DESCRIPTION:Title: Tomography bounds for the Fourier extension operator an
d applications\nby Jonathan Bennett (University of Birmingham) as part of
Virtual Harmonic Analysis Seminars\n\n\nAbstract\nWe explore the extent to
which the Fourier transform of an $L^p$ density supported on the sphere i
n $\\mathbb{R}^n$ can have large mass on affine subspaces\, placing partic
ular emphasis on lines and hyperplanes. In the process we identify a conj
ectural statement that sits between the classical Fourier restriction and
Kakeya conjectures\, and provide an application to the theory of weighted
norm inequalities for such Fourier transforms. Our approach\, which takes
its inspiration from work of Planchon and Vega\, exploits cancellation via
Plancherel's theorem on affine subspaces\, avoiding the conventional use
of wave-packet and stationary-phase methods. This is joint work with Shohe
i Nakamura (Tokyo).\n
END:VEVENT
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