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BEGIN:VEVENT
SUMMARY:Alessio Martini
DTSTART:20200428T143000Z
DTEND:20200428T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/1
DESCRIPTION:Title: A sharp multiplier theorem for degenerate elliptic operato
rs on the plane\nby Alessio Martini as part of Virtual Harmonic Analys
is Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Bate (University of Warwick)
DTSTART:20200505T143000Z
DTEND:20200505T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/2
DESCRIPTION:Title: Cheeger’s differentiation theorem via the multilinear Ka
keya inequality\nby David Bate (University of Warwick) as part of Virt
ual Harmonic Analysis Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (University of Oxford)
DTSTART:20200512T143000Z
DTEND:20200512T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/3
DESCRIPTION:Title: Bounds in the polynomial Szemerédi theorem\nby Sarah
Peluse (University of Oxford) as part of Virtual Harmonic Analysis Seminar
\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John MacKay (University of Bristol)
DTSTART:20200519T143000Z
DTEND:20200519T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/4
DESCRIPTION:Title: Poincaré profiles on graphs and groups\nby John MacKa
y (University of Bristol) as part of Virtual Harmonic Analysis Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (University of Birmingham)
DTSTART:20200526T143000Z
DTEND:20200526T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/5
DESCRIPTION:Title: Sign uncertainty principles: old and new\nby Diogo Oli
veira e Silva (University of Birmingham) as part of Virtual Harmonic Analy
sis Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Brocchi (University of Birmingham)
DTSTART:20200602T143000Z
DTEND:20200602T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/6
DESCRIPTION:Title: Sparse T1 theorems\nby Gianmarco Brocchi (University o
f Birmingham) as part of Virtual Harmonic Analysis Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adolfo Arroyo-Rabasa (University of Warwick)
DTSTART:20200609T143000Z
DTEND:20200609T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/7
DESCRIPTION:Title: Function space questions in CalcVar/GMT that are being sol
ved using Fourier analysis\nby Adolfo Arroyo-Rabasa (University of War
wick) as part of Virtual Harmonic Analysis Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Villa (University of Helsinki)
DTSTART:20200616T143000Z
DTEND:20200616T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/8
DESCRIPTION:Title: A proof the Carleson $\\epsilon^2$-conjecture\nby Mich
ele Villa (University of Helsinki) as part of Virtual Harmonic Analysis Se
minar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Sanders (University of Oxford)
DTSTART:20200623T143000Z
DTEND:20200623T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/9
DESCRIPTION:Title: Approximate homomorphisms and a conjecture of Pełczyński
\nby Tom Sanders (University of Oxford) as part of Virtual Harmonic An
alysis Seminar\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
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (University of Wisconsin-Madison)
DTSTART:20200630T143000Z
DTEND:20200630T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/10
DESCRIPTION:Title: Fourier restriction estimates above rectangles and an app
lication\nby Betsy Stovall (University of Wisconsin-Madison) as part o
f Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe discuss the problem
of obtaining Lebesgue space inequalities for the Fourier restriction opera
tor associated to rectangular pieces of the paraboloid and perturbations t
hereof. 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 restri
ction inequalities on some degenerate hypersurfaces. This is joint work w
ith Jeremy Schwend.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Bennett (University of Birmingham)
DTSTART:20200707T143000Z
DTEND:20200707T153000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/11
DESCRIPTION:Title: Tomography bounds for the Fourier extension operator and
applications\nby Jonathan Bennett (University of Birmingham) as part o
f Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe explore the extent t
o which the Fourier transform of an $L^p$ density supported on the sphere
in $\\mathbb{R}^n$ can have large mass on affine subspaces\, placing parti
cular emphasis on lines and hyperplanes. In the process we identify a con
jectural 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 vi
a Plancherel's theorem on affine subspaces\, avoiding the conventional use
of wave-packet and stationary-phase methods. This is joint work with Shoh
ei Nakamura (Tokyo).\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton University)
DTSTART:20200923T150000Z
DTEND:20200923T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/12
DESCRIPTION:Title: The Kakeya needle problem for rectifiable sets\nby Al
an Chang (Princeton University) as part of Virtual Harmonic Analysis Semin
ar\n\n\nAbstract\nWe show that the classical results about rotating a line
segment in arbitrarily small area\, and the existence of a Besicovitch an
d a Nikodym set hold if we replace the line segment by an arbitrary rectif
iable set. This is joint work with Marianna Csörnyei.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Christ (UC Berkeley)
DTSTART:20200930T140000Z
DTEND:20200930T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/13
DESCRIPTION:Title: Oscillation and frustration in multilinear inequalities\nby Michael Christ (UC Berkeley) as part of Virtual Harmonic Analysis S
eminar\n\n\nAbstract\nMultilinear functionals\, and inequalities governing
them\, arise in various contexts in harmonic analysis (in connection with
Fourier restriction)\, in partial differential equations (nonlinear inter
actions) and in additive combinatorics (existence of certain patterns in s
ets of appropriately bounded density). This talk will focus on an inequali
ty that quantifies a weak convergence theorem of Joly\, Metivier\, and Rau
ch (1995) concerning threefold products\, and on related inequalities for
trilinear expressions involving highly oscillatory factors. Sublevel set i
nequalities\, which quantify the impossibility of exactly solving certain
systems of linear functional equations (the frustration of the title)\, ar
e a central element of the analysis.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joris Roos (University of Massachusetts Lowell & University of Edi
nburgh)
DTSTART:20201007T140000Z
DTEND:20201007T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/14
DESCRIPTION:Title: A triangular Hilbert transform with curvature\nby Jor
is Roos (University of Massachusetts Lowell & University of Edinburgh) as
part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nThe talk will be
about a recent joint work with Michael Christ and Polona Durcik on a varia
nt of the triangular Hilbert transform involving curvature. Our results un
ify various previously known results such as bounds for a bilinear Hilbert
transform with curvature and a maximally modulated singular integral of S
tein-Wainger type\, and Bourgain's non-linear Roth theorem in the reals.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Krause (King's College London)
DTSTART:20201014T140000Z
DTEND:20201014T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/15
DESCRIPTION:Title: Pointwise Ergodic Theorems for Non-Conventional Bilinear
Polynomial Averages\nby Ben Krause (King's College London) as part of
Virtual Harmonic Analysis Seminar\n\n\nAbstract\nIn the late 80s and early
90s\, Bourgain proved pointwise convergence results for polynomial ergodi
c averages applied to a single function. In this talk I will discuss joint
work with Mariusz Mirek and Terence Tao on bilinear analogues of Bourgain
's work.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornelia Hera (University of Chicago)
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/16
DESCRIPTION:Title: Hausdorff dimension of Furstenberg-type sets\nby Korn
elia Hera (University of Chicago) as part of Virtual Harmonic Analysis Sem
inar\n\n\nAbstract\nWe say that a planar set F is a (t\,s)-Furstenberg set
\, if there exists an s-dimensional family of lines in the plane such that
each line of this family intersects F in an at least t-dimensional set. W
e present Hausdorff dimension estimates for (t\,s)-Furstenberg sets and fo
r more general Furstenberg type sets in higher dimensions.\nThe talk is ba
sed on joint work with Tamás Keleti and András Máthé\, and with Pablo
Shmerkin and Alexia Yavicoli.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luz Roncal (BCAM)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/17
DESCRIPTION:Title: Directional square functions\nby Luz Roncal (BCAM) as
part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nCharles Fefferma
n's counterexample for the ball multiplier is intimately linked to square
function estimates for directional singular integrals along all possible d
irections. Quantification of such a failure of the boundedness of the ball
multiplier is measured\, for instance\, through $L^p$-bounds for the $N$-
gon multiplier which provide information in terms of $N$.\n\nWe present a
general approach\, based on a directional embedding theorem for Carleson s
equences\, to study time-frequency model square functions associated to co
nical or directional Fourier multipliers. The estimates obtained for these
square functions are applied to obtain sharp or quantified bounds for dir
ectional Rubio de Francia type square functions. In particular\, a precise
logarithmic bound for the polygon multiplier is shown\, improving previou
s results.\nThis is joint work with Natalia Accomazzo\, Francesco Di Plini
o\, Paul Hagelstein\, and Ioannis Parissis.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krystal Taylor (Ohio State University)
DTSTART:20201104T150000Z
DTEND:20201104T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/18
DESCRIPTION:Title: Nonlinear projection theory and the Buffon curve problem<
/a>\nby Krystal Taylor (Ohio State University) as part of Virtual Harmonic
Analysis Seminar\n\n\nAbstract\nThe Favard length of a subset of the plan
e is defined as the average length of its orthogonal projections. This qua
ntity is related to the probabilistic Buffon needle problem\, which consid
ers the probability that a needle or a line that is dropped at random near
a given set will intersect the set. We consider the geometric and probabi
listic consequences that arise upon replacing linear projections by more g
eneral families of projection-type mappings. In particular\, we find upper
and lower bounds for the rate of decay of the Favard curve length of the
four-corner Cantor set. Beyond the four-corner set\, we also show that if
a subset E has finite length in the sense of Hausdorff and is nearly purel
y unrectifiable (so its intersection with any Lipschitz graph has zero len
gth)\, then its “curve” projections have very small measure.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yufei Zhao (MIT)
DTSTART:20201111T150000Z
DTEND:20201111T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/19
DESCRIPTION:Title: The joints problem for varieties\nby Yufei Zhao (MIT)
as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe generalize
the Guth-Katz joints theorem from lines to varieties. A special case of o
ur result says that $N$ planes (2-flats) in 6 dimensions (over any field)
have $O(N^{3/2})$ joints\, where a joint is a point contained in a triple
of these planes not all lying in some hyperplane. Our most general result
gives upper bounds\, tight up to constant factors\, for joints with multip
licities for several sets of varieties of arbitrary dimensions (known as C
arbery's conjecture). Our main innovation is a new way to extend the polyn
omial method to higher dimensional objects.\n\nJoint work with Jonathan Ti
dor and Hung-Hsun Hans Yu\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (IAS)
DTSTART:20201118T150000Z
DTEND:20201118T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/20
DESCRIPTION:Title: Falconer distance set problem using Fourier analysis\
nby Hong Wang (IAS) as part of Virtual Harmonic Analysis Seminar\n\nAbstra
ct: TBA\n\nGiven a set $E$ of Hausdorff dimension $s>d/2$ in $\\mathbb{R}^
d$ \, Falconer conjectured that its distance set $\\Delta(E)=\\{ |x-y|: x\
, y \\in E\\}$ should have positive Lebesgue measure. When $d$ is even\, w
e show that $\\dim_H E>d/2+1/4$ implies $|\\Delta(E)|>0$. This improves on
the work of Wolff\, Erdogan\, Du-Zhang\, etc. Our tools include Orponen's
radial projection theorem and refined decoupling estimates. \n\nThis is
joint work with Guth\, Iosevich\, and Ou and with Du\, Iosevich\, Ou\, and
Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (University of Edinburgh)
DTSTART:20201125T150000Z
DTEND:20201125T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/21
DESCRIPTION:Title: Fourier dimension estimates for exact-order sets\nby
Robert Fraser (University of Edinburgh) as part of Virtual Harmonic Analys
is Seminar\n\n\nAbstract\nFourier dimension estimates are a growing topic
of interest in harmonic analysis\, geometric measure theory\, and metric D
iophantine approximation. In a joint work with Reuben Wheeler\, we obtain
some lower estimates on the Fourier dimension of Bugeaud’s set of number
s approximable to some exact order $\\psi$.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Accomazzo Scotti (BCAM)
DTSTART:20201202T150000Z
DTEND:20201202T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/22
DESCRIPTION:Title: A weighted Carleson embedding and applications\nby Na
talia Accomazzo Scotti (BCAM) as part of Virtual Harmonic Analysis Seminar
\n\n\nAbstract\nWe will follow up with Luz Roncal's talk\, where she prese
nted a directional embedding theorem for Carleson sequences which was in t
urn used to obtain bounds for directional Rubio de Francia type square fun
ctions. We will see how we can extend this result to the weighted setting\
, from where we can deduce some weighted estimates for the directional max
imal function and directional singular integrals.\n\nThis is part of joint
work with F. Di Plinio\, P. Hagelstein\, I. Parissis and L. Roncal.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART:20201209T150000Z
DTEND:20201209T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/23
DESCRIPTION:Title: Square function inequalities and superorthogonality\n
by Lillian Pierce (Duke University) as part of Virtual Harmonic Analysis S
eminar\n\n\nAbstract\nWe’ll talk about two notions of square function in
equality\, related to a sequence of functions\, which we’ll call direct
and converse inequalities. In many cases the direct inequality can be prov
ed by verifying a type of 2r-superorthogonality\, that is\, proving that t
he integral of certain 2r-tuples of functions selected from the sequence v
anishes. We will demonstrate a hierarchy of “types” of superorthogona
lity for which this deduction can be carried out quite formally\, and mean
while illustrate a wide variety of specific settings. In particular\, we w
ill show that two famous results from number theory\, in the setting of bo
unding character sums\, fit neatly into this framework.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Wright (University of Edinburgh)
DTSTART:20210113T150000Z
DTEND:20210113T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/24
DESCRIPTION:Title: A theory for oscillatory integrals\nby Jim Wright (Un
iversity of Edinburgh) as part of Virtual Harmonic Analysis Seminar\n\n\nA
bstract\nWe develop a theory for oscillatory integrals which can be applie
d in a variety of settings\, especially settings where scale-invariant bou
nds do not hold in the generality we are accustomed to.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Rudnev (University of Bristol)
DTSTART:20210120T150000Z
DTEND:20210120T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/25
DESCRIPTION:Title: Single distance bounds in 3D line complexes\nby Misha
Rudnev (University of Bristol) as part of Virtual Harmonic Analysis Semin
ar\n\n\nAbstract\nIn his recent paper Josh Zahl proves (among other things
) a new single distance bound $n^{3/2}$ for a set of $n$ points in a $3$-s
pace over a field $\\mathbb{F}$\, where $-1$ is not a square. In his consi
derations he implicitly uses the concept of a line complex\, which has man
y interesting properties. I will present his result in this light and exte
nd it to a weaker bound $n^{1.6}$ over $\\mathbb{F}$\, where $-1$ is a squ
are.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Gressman (University of Pennsylvania)
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/26
DESCRIPTION:Title: Radon-like Transforms\, Geometric Measures\, and Invarian
t Theory\nby Philip Gressman (University of Pennsylvania) as part of V
irtual Harmonic Analysis Seminar\n\n\nAbstract\nFourier restriction\, Rado
n-like operators\, and decoupling theory are three active areas of harmoni
c analysis which involve submanifolds of Euclidean space in a fundamental
way. In each case\, the mapping properties of the objects of study depend
in a fundamental way on the "non-flatness" of the submanifold\, but with t
he exception of certain extreme cases (primarily curves and hypersurfaces)
\, it is not clear exactly how to quantify the geometry in an analytically
meaningful way. In this talk\, I will discuss a series of recent results
which shed light on this situation using tools from an unusually broad ran
ge of mathematical sources.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Zahl (University of British Columbia)
DTSTART:20210203T150000Z
DTEND:20210203T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/27
DESCRIPTION:Title: Dimension-expanding polynomials and the discretized Eleke
s-Ronyai theorem\nby Joshua Zahl (University of British Columbia) as p
art of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nI will discuss a d
iscretized version of the Elekes-Ronyai theorem from additive combinatoric
s\, which is closely related to the sum-product problem. The Elekes-Ronyai
theorem has recently had applications to combinatorial geometry\, includi
ng variants of the Erdos distinct distances problem. The discretized versi
on of the Elekes-Ronyai theorem has similar applications\, and in particul
ar I will discuss some new results on a pinned version of the Falconer dis
tance problem. This is joint work with Orit Raz.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Larry Guth (MIT)
DTSTART:20210210T160000Z
DTEND:20210210T170000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/28
DESCRIPTION:Title: Local smoothing for the wave equation\nby Larry Guth
(MIT) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nThe loca
l smoothing problem asks about how much solutions to the wave equation can
focus. It was formulated by Chris Sogge in the early 90s. Hong Wang\, R
uixiang Zhang\, and I recently proved the conjecture in two dimensions.\n\
nIn the talk\, we will build up some intuition about waves to motivate the
conjecture\, and then discuss some of the obstacles and some ideas from t
he proof.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART:20210217T150000Z
DTEND:20210217T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/29
DESCRIPTION:Title: A new proof of decoupling for the parabola\nby Domini
que Maldague (MIT) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstr
act\nDecoupling has to do with measuring the size of functions with specia
lized Fourier support (in our case\, in a neighborhood of the truncated pa
rabola). Bourgain and Demeter resolved the l^2 decoupling conjecture in 20
14\, using ingredients like the multilinear Kakeya inequality\, L^2 orthog
onality\, and induction-on-scales. I will present the ideas that go into a
new proof of decoupling and make some comparison between the two approach
es. This is related to recent joint work with Larry Guth and Hong Wang\, a
s well as forthcoming joint work with Yuqiu Fu and Larry Guth.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeev Dvir (Princeton University)
DTSTART:20210224T150000Z
DTEND:20210224T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/30
DESCRIPTION:Title: The Kakeya set conjecture over rings of integers modulo s
quare free m\nby Zeev Dvir (Princeton University) as part of Virtual H
armonic Analysis Seminar\n\n\nAbstract\nWe show that\, when $N$ is any squ
are-free integer\, the size of the smallest Kakeya set in $(\\mathbb{Z}/N\
\mathbb{Z})^n$ is at least $C_{\\epsilon\,n}N^{n-\\epsilon}$ for any $\\ep
silon>0$ -- resolving a special case of a conjecture of Hickman and Wright
. Previously\, such bounds were only known for the case of prime $N$. We a
lso show that the case of general $N$ can be reduced to lower bounding the
$p$-rank of the incidence matrix of points and hyperplanes over $(\\mathb
b{Z}/p^k\\mathbb{Z})^n$. Joint work with Manik Dhar\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akshat Mudgal (University of Bristol)
DTSTART:20210303T150000Z
DTEND:20210303T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/31
DESCRIPTION:Title: Diameter free estimates and Incidence geometry\nby Ak
shat Mudgal (University of Bristol) as part of Virtual Harmonic Analysis S
eminar\n\n\nAbstract\nVarious problems in harmonic analysis are intimately
connected with studying solutions to additive equations over subsets of c
urves and surfaces. The latter is amenable to techniques from incidence ge
ometry since we can count such solutions by interpreting them as incidence
s between points and curves/surfaces. In this talk\, we study additive ene
rgies of arbitrary subsets of parabolas/convex curves\, and their connecti
ons to a problem of Bourgain and Demeter regarding a diameter-free version
of the quadratic Vinogradov mean value theorem. We also mention some new
results associated with additive energies on higher dimensional surfaces w
hich are related to restriction type problems on spheres.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern University)
DTSTART:20210310T150000Z
DTEND:20210310T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/32
DESCRIPTION:Title: Falconer's distance set problem\nby Xiumin Du (Northw
estern University) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstr
act\nA classical question in geometric measure theory\, introduced by Falc
oner in the 80s is\, how large does the Hausdorff dimension of a compact s
ubset in Euclidean space need to be to ensure that the Lebesgue measure of
its set of pairwise Euclidean distances is positive. In this talk\, I'll
report some recent progress on this problem\, which combines several ingre
dients including Orponen's radial projection theorem\, Liu's L^2 identity
obtained using a group action argument\, and the refined decoupling theory
. This is based on joint work with Alex Iosevich\, Yumeng Ou\, Hong Wang\,
and Ruixiang Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Cladek (UCLA)
DTSTART:20210317T150000Z
DTEND:20210317T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/33
DESCRIPTION:Title: Additive energy of regular measures in one and higher dim
ensions\, and the fractal uncertainty principle\nby Laura Cladek (UCLA
) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe obtain ne
w bounds on the additive energy of (Ahlfors-David type) regular measures i
n both one and higher dimensions\, which implies expansion results for sum
s and products of the associated regular sets\, as well as more general no
nlinear functions of these sets. As a corollary of the higher-dimensional
results we obtain some new cases of the fractal uncertainty principle in o
dd dimensions. This is joint work with Terence Tao.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (UW Madison)
DTSTART:20210324T150000Z
DTEND:20210324T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/34
DESCRIPTION:Title: L^p bounds for the helical maximal function\nby David
Beltran (UW Madison) as part of Virtual Harmonic Analysis Seminar\n\n\nAb
stract\nA natural 3-dimensional analogue of Bourgain’s circular maximal
function theorem in the plane is the study of the sharp L^p bounds in R^3
for the maximal function associated with averages over dilates of the heli
x (or\, more generally\, of any curve with non-vanishing curvature and tor
sion). In this talk\, we present a sharp result\, which establishes that L
^p bounds hold if and only if p>3. This is joint work with Shaoming Guo\,
Jonathan Hickman and Andreas Seeger.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Vitturi (University College Cork)
DTSTART:20210331T140000Z
DTEND:20210331T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/35
DESCRIPTION:Title: Two surface weights of Gressman\nby Marco Vitturi (Un
iversity College Cork) as part of Virtual Harmonic Analysis Seminar\n\n\nA
bstract\nIn recent years P. Gressman\, in the context of the L^p-improving
problem for Radon averages\, has introduced two types of weighted surface
measures. One is an affine-invariant surface measure (of "best-possible"
type) for surfaces of arbitrary codimension\, obtained by a clever constru
ction related to Geometric Invariant Theory (GIT). The other arises via a
non-degeneracy condition that enables an inflation method devised to prove
L^p-improving inequalities (this is the antecedent of the work that P. Gr
essman presented in his talk on 27/1/2021).\n\nWe pose the question of wha
t the relationship between the two weights is and provide some partial ans
wers. It is a matter of a simple calculation to verify that in codimension
1 the weights are comparable\, but the situation in higher codimensions i
s much less clear - sometimes the comparability fails. Using GIT technique
s\, we are able to show the weights continue to be comparable in codimensi
on 2 (in even ambient dimension). (Joint work with S. Dendrinos and A. Mus
tata)\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Orponen (University of Jyväskylä)
DTSTART:20210407T140000Z
DTEND:20210407T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/36
DESCRIPTION:Title: Quantifying the Besicovitch projection theorem\nby Tu
omas Orponen (University of Jyväskylä) as part of Virtual Harmonic Analy
sis Seminar\n\n\nAbstract\nA theorem of Besicovitch from the 30s states th
at a planar set with finite length and “many” projections of positive
measure has a rectifiable piece. How big is this piece\, relative to the m
easure of the projections? In general\, quantifying Besicovitch’s theore
m remains an open problem\, but I will discuss a recent partial result: n-
regular sets in Rd with “plenty of big projections”\, in the sense of
David and Semmes\, contain big pieces of Lipschitz graphs.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume de Dios Pont (UCLA)
DTSTART:20211020T140000Z
DTEND:20211020T150000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/37
DESCRIPTION:Title: Decoupling\, Cantor sets\, and additive combinatorics
\nby Jaume de Dios Pont (UCLA) as part of Virtual Harmonic Analysis Semina
r\n\n\nAbstract\nDecoupling and discrete restriction inequalities have bee
n very fruitful in recent years to solve problems in additive combinatoric
s and analytic number theory. In this talk I will present some work in dec
oupling for Cantor sets\, including Cantor sets on a parabola\, decoupling
for product sets\, and give applications of these results to additive com
binatorics. Time permitting\, I will present some open problems.\n\nContai
ns joint work with Alan Chang (Princeton)\,\nRachel Greenfeld (UCLA)\, Asg
ar Jamneshan (Koç University)\, Zane Li (IU Bloomington)\, José Ramón M
adrid Padilla (UCLA).\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Thiele (University of Bonn)
DTSTART:20211103T150000Z
DTEND:20211103T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/38
DESCRIPTION:Title: Bilinear multipliers associated with convex sets\nby
Christoph Thiele (University of Bonn) as part of Virtual Harmonic Analysis
Seminar\n\n\nAbstract\nThis is joint work with Olli Saari. We will review
some highlights of the theory of Fourier multipliers in one dimension\, s
uch as Coifman-Rubio-de-Francia Semmes theory\, and variational Carleson e
stimates. We will then discuss two dimensional multiplier theorems\, in pa
rticular multipliers which are characteristic functions of convex sets. We
present some new results and some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (UCLA)
DTSTART:20211117T150000Z
DTEND:20211117T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/39
DESCRIPTION:Title: Translational tilings in lattices\nby Rachel Greenfel
d (UCLA) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nLet $
F$ be a finite subset of $\\mathbb{Z}^d$. We say that F is a translational
tile of $\\mathbb{Z}^d$ if it is possible to cover $\\mathbb{Z}^d$ by tra
nslates of $F$ without any overlap. \nThe periodic tiling conjecture\, whi
ch is perhaps the most well-known conjecture in the area\, asserts that an
y translational tile admits at least one periodic tiling. In the talk\, w
e will motivate and discuss the study of this conjecture. We will also pre
sent some recent results\, joint with Terence Tao\, on the structure of tr
anslational tilings in lattices and introduce some applications.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Detlef Müller (University of Kiel)
DTSTART:20211201T150000Z
DTEND:20211201T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/40
DESCRIPTION:Title: Fourier restriction to hyperbolic 2-surfaces: robustness
of the polynomial compared to the bilinear approach\nby Detlef Müller
(University of Kiel) as part of Virtual Harmonic Analysis Seminar\n\n\nAb
stract\nIn this talk\, which will be based on joint research with S. Busc
henhenke and A. Vargas\, I intend to discuss some of the new challenges
that arose in our studies of Fourier restriction estimates for hyperbolic
surfaces\, compared to the case of elliptic surfaces. \n\nGiven the comple
xity of the bilinear\, and even more so of the polynomial partitioning app
roach\, I shall mainly focus on those parts of these methods which require
d new ideas\, so that a familiarity with these methods will not be expecte
d from the audience.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Carbery (University of Edinburgh)
DTSTART:20211215T150000Z
DTEND:20211215T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/41
DESCRIPTION:Title: Joints\, multijoints and duality\nby Tony Carbery (Un
iversity of Edinburgh) as part of Virtual Harmonic Analysis Seminar\n\n\nA
bstract\nJoints and multijoints provide discrete analogues of the Kakeya m
aximal function and multilinear Kakeya respectively. While Guth's sharp en
dpoint multilinear Kakeya theorem in Euclidean space is established "on th
e side of the maximal function"\, Zhang's joint and multijoint theorems ar
e established "on the side of the covering lemma". We explore the dualitie
s between these alternative approaches\, both in the context of joints/mul
tijoints and also more abstractly. This is joint work with Michael Tang.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20220112T150000Z
DTEND:20220112T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/42
DESCRIPTION:Title: Local bounds for singular Brascamp-Lieb forms with cubica
l structure\nby Polona Durcik (Chapman University) as part of Virtual
Harmonic Analysis Seminar\n\n\nAbstract\nWe discuss a range of $L^p$ bound
s for singular Brascamp-Lieb forms with cubical structure. This extends an
earlier result which only allowed for a single tuple of the Lebesgue expo
nents. We pass through local and sparse bounds. This is a joint work with
L. Slavíková and C. Thiele.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Wolf (University of Cambridge)
DTSTART:20220126T150000Z
DTEND:20220126T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/43
DESCRIPTION:Title: Higher-order generalisations of stability and arithmetic
regularity\nby Julia Wolf (University of Cambridge) as part of Virtual
Harmonic Analysis Seminar\n\n\nAbstract\nSince Szemerédi's seminal work
in the 70s\, regularity lemmas have proven to be of fundamental importance
in many areas of discrete mathematics. This talk will survey recent work
on regularity decompositions of subsets of finite groups under additional
assumptions such as stability or bounded VC-dimension\, which turn out to
have particularly desirable properties. In the second half of the talk\, w
e will describe very recent joint work with Caroline Terry (Ohio State Uni
versity) which extends these ideas to the realm of higher-order Fourier an
alysis.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vjekoslav Kovač (University of Zagreb)
DTSTART:20220209T150000Z
DTEND:20220209T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/44
DESCRIPTION:Title: Bilinear and trilinear estimates for semigroups generated
by complex elliptic operators\nby Vjekoslav Kovač (University of Zag
reb) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe will d
iscuss bi(sub)linear and tri(sub)linear embeddings for semigroups generate
d by non-smooth complex-coefficient elliptic operators in divergence form.
Bilinear embeddings can be thought of as sharpenings and generalizations
of estimates for second-order singular integrals. In the context of comple
x elliptic operators such $L^p$ bounds were shown by Carbonaro and Dragič
ević\, who emphasized and crucially used certain generalized convexity pr
operties of powers. We remove this obstruction and generalize their approa
ch to the level of Orlicz-space norms that only “behave like powers”.
Next\, what we call a trilinear embedding is a paraproduct-type estimate.
It incorporates bounds for the conical square function and finds an applic
ation to fractional Leibniz-type rules. In the proofs we use two carefully
constructed auxiliary functions that generalize a classic Bellman functio
n constructed by Nazarov and Treil in two different ways. The talk is base
d on joint work with Andrea Carbonaro\, Oliver Dragičević\, and Kristina
Škreb.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zihui Zhao (University of Chicago)
DTSTART:20220223T160000Z
DTEND:20220223T170000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/45
DESCRIPTION:Title: Boundary unique continuation and the estimate of the sing
ular set\nby Zihui Zhao (University of Chicago) as part of Virtual Har
monic Analysis Seminar\n\n\nAbstract\nUnique continuation property is a fu
ndamental property of harmonic functions\, as well as solutions to a large
class of elliptic and parabolic PDEs. It says that if a harmonic function
vanishes to infinite order at a point\, it must be zero everywhere. In th
e same spirit\, we can use the local growth rate of harmonic functions to
deduce global information\, such as estimating the size of the singular se
t for elliptic PDEs. This is joint work with Carlos Kenig.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (UW Madison)
DTSTART:20220309T160000Z
DTEND:20220309T170000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/46
DESCRIPTION:Title: Families of functionals representing Sobolev norms\nb
y Andreas Seeger (UW Madison) as part of Virtual Harmonic Analysis Seminar
\n\n\nAbstract\nWe discuss families of limit functionals and weak type (qu
asi)- norms which represent the standard Sobolev norms\, extending and uni
fying work by Nguyen and by Brezis\, Van Schaftingen and Yung. We also con
sider versions with fractional smoothness and applications\, including a c
haracterization of approximation spaces for nonlinear wavelet approximatio
n. \n\nJoint works with H. Brezis\, J. Van Schaftingen and P. Yung\, and w
ith Ó. Domínguez\, B. Street\, J. Van Schaftingen and P. Yung.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zane Li (Indiana University Bloomington)
DTSTART:20220323T150000Z
DTEND:20220323T160000Z
DTSTAMP:20260404T111005Z
UID:HarmonicAnalysis/47
DESCRIPTION:Title: A decoupling interpretation of an old argument for Vinogr
adov's Mean Value Theorem\nby Zane Li (Indiana University Bloomington)
as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nThere are two
proofs of Vinogradov's Mean Value Theorem (VMVT)\, the harmonic analysis
decoupling proof by Bourgain\, Demeter\, and Guth from 2015 and the number
theoretic efficient congruencing proof by Wooley from 2017. While there h
as been recent work illustrating the relation between these two methods\,
VMVT has been around since 1935. It is then natural to ask: What does old
partial progress on VMVT look like in harmonic analysis language? How simi
lar or different does it look from current decoupling proofs? We talk abou
t an old argument that shows VMVT "asymptotically" due to Karatsuba and in
terpret this in decoupling language. This is joint work with Brian Cook\,
Kevin Hughes\, Olivier Robert\, Akshat Mudgal\, and Po-Lam Yung.\n
LOCATION:https://stable.researchseminars.org/talk/HarmonicAnalysis/47/
END:VEVENT
END:VCALENDAR