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BEGIN:VEVENT
SUMMARY:Alessio Martini
DTSTART:20200428T143000Z
DTEND:20200428T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/1
DESCRIPTION:Title: A sharp multiplier theorem for degenerate elliptic operators on t
he plane\nby Alessio Martini as part of Virtual Harmonic Analysis Semi
nar\n\n\nAbstract\nGrushin operators are among the simplest examples of su
belliptic operators. Due to the lack of ellipticity\, standard techniques
based on heat kernel estimates yield spectral multiplier theorems that are
typically not sharp in terms of the smoothness requirement on the multipl
ier. We show that\, for a large class of Grushin operators on the plane\,
a sharp multiplier theorem can be proved\, with the same smoothness requir
ement as in the case of the standard Laplacian. Our argument is robust eno
ugh to handle nonhomogeneous coefficients vanishing of arbitrarily high or
der\, and hinges on the analysis of one-parameter families of Schroedinger
operators. This is based on joint work with Gian Maria Dall'Ara (Birmingh
am).\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Bate (University of Warwick)
DTSTART:20200505T143000Z
DTEND:20200505T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/2
DESCRIPTION:Title: Cheeger’s differentiation theorem via the multilinear Kakeya in
equality\nby David Bate (University of Warwick) as part of Virtual Har
monic Analysis Seminar\n\n\nAbstract\nIn 1999 Cheeger gave a far reaching
generalisation of Rademacher’s differentiation theorem which replaces th
e domain by a metric space equipped with a measure that satisfies a versio
n of the Poincare inequality. The first half of this talk will consist of
a gentle introduction to this result and some of its consequences. No prio
r knowledge will be assumed.\n\nThe work of Cheeger inspired a large numbe
r of new results in the area of analysis on metric spaces. The second half
of this talk will present a new\, simpler proof of Cheeger’s theorem ba
sed on these developments and the multilinear Kakeya inequality for rectif
iable curves (in Euclidean space). This is based on joint work with Ilmari
Kangasniemi and Tuomas Orponen.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (University of Oxford)
DTSTART:20200512T143000Z
DTEND:20200512T153000Z
DTSTAMP:20260422T225722Z
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\nA
bstract\nLet $P_1\,\\ldots\, P_m$ be polynomials with integer coefficients
and zero constant term. Bergelson and Leibman’s polynomial generalizati
on of Szemerédi’s theorem states that any subset $A$ of $\\{1\,\\ldots\
,N\\}$ that contains no nontrivial progressions $x\, x+P_1(y)\, \\ldots\,
x+P_m(y)$ must satisfy $|A|=o(N)$. In contrast to Szemerédi's theorem\, q
uantitative bounds for Bergelson and Leibman's theorem (i.e.\, explicit bo
unds 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\, focusing
on arguments involving Fourier analysis.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John MacKay (University of Bristol)
DTSTART:20200519T143000Z
DTEND:20200519T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/4
DESCRIPTION:Title: Poincaré profiles on graphs and groups\nby John MacKay (Univ
ersity of Bristol) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstr
act\nThe separation profile of an infinite graph was introduced by Benjami
ni-Schramm-Timar. It is a function which measures how well-connected the
graph is by how hard it is to cut finite subgraphs into small pieces. In
earlier joint work with David Hume and Romain Tessera\, we introduced Poin
caré profiles\, generalising this concept by using p-Poincaré inequaliti
es to measure the connectedness of subgraphs. I will discuss these invari
ants\, their applications to coarse embedding problems\, and work nearing
completion where we find the profiles of all connected unimodular Lie grou
ps. Joint with Hume and Tessera.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (University of Birmingham)
DTSTART:20200526T143000Z
DTEND:20200526T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/5
DESCRIPTION:Title: Sign uncertainty principles: old and new\nby Diogo Oliveira e
Silva (University of Birmingham) as part of Virtual Harmonic Analysis Sem
inar\n\n\nAbstract\nTen years ago\, Bourgain\, Clozel & Kahane established
a surprising "sign uncertainty principle" (SUP)\, asserting that if a fun
ction and its Fourier transform are nonpositive at the origin and not iden
tically zero\, then they cannot both be nonnegative outside an arbitrarily
small neighbourhood of the origin. In 2017\, Gonçalves & Cohn solved the
12-dimensional SUP via connections to the sphere packing problem\, and di
scovered a complementary SUP. This talk will focus on some new sign uncert
ainty principles which generalise the developments of Bourgain\, Clozel &
Kahane and Cohn & Gonçalves. In particular\, we will discuss SUPs for Fou
rier series\, the Hilbert transform\, spherical harmonics\, and Jacobi pol
ynomials. As a by-product\, we determine some sharp instances of the spher
ical SUP via connections to tight spherical designs. Time permitting\, we
will outline a possible path towards the sharp 1-dimensional SUP. This tal
k is based on recent joint work with Felipe Gonçalves and João Pedro Ram
os.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gianmarco Brocchi (University of Birmingham)
DTSTART:20200602T143000Z
DTEND:20200602T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/6
DESCRIPTION:Title: Sparse T1 theorems\nby Gianmarco Brocchi (University of Birmi
ngham) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nIn the
last decade a plethora of sharp weighted estimates has been obtained for s
everal different operators. These estimates (sharp in the dependence on th
e characteristic of the weight) follow from a sparse domination of the ope
rator. Roughly speaking\, a sparse domination consists in controlling the
operator with a positive dyadic form. It has been shown that Calderón–Z
ygmund operators and square functions admit such domination even under min
imal T1 hypothesis.\n\nIn this talk we introduce the concept of sparse dom
ination and we present some ideas that allow to upgrade the classical T1 t
heorems by David\, Christ and Journé to sparse ones.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adolfo Arroyo-Rabasa (University of Warwick)
DTSTART:20200609T143000Z
DTEND:20200609T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/7
DESCRIPTION:Title: Function space questions in CalcVar/GMT that are being solved usi
ng Fourier analysis\nby Adolfo Arroyo-Rabasa (University of Warwick) a
s part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nThe space BV of
functions of bounded variation is the space of integrable functions whose
gradient is a Radon measure. Extending this definition to the trendy A-fr
ee measures\, I will define the space BV^A of functions of bounded A-varia
tion: functions such that A(D)u is a measure\, where A(D) is a linear elli
ptic operator with constant coefficients. I will introduce general aspects
of this theory\, share a few recent results\, and some difficult open pro
blems:\n\nL1-estimates -> life without Calderón-Zygmund\n\nSlicing\, geom
etry of A-bounded measures -> life without co-area formula\n\nContinuity p
roperties\, #2ndHardestProblemCalcVar -> life without co-area formula\, a
gain.\n\nInterestingly\, these measure theoretic properties were solved/re
quire Fourier analysis methods.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michele Villa (University of Helsinki)
DTSTART:20200616T143000Z
DTEND:20200616T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/8
DESCRIPTION:Title: A proof the Carleson $\\epsilon^2$-conjecture\nby Michele Vil
la (University of Helsinki) as part of Virtual Harmonic Analysis Seminar\n
\n\nAbstract\nIn this talk we sketch a proof of the Carleson $\\epsilon^2$
-conjecture. This result yields a characterization (up to exceptional sets
of zero length) of the tangent points of a Jordan curve in terms of the f
initeness of the associated Carleson $\\epsilon^2$-square function. This i
s a joint work with Ben Jaye and Xavier Tolsa.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom Sanders (University of Oxford)
DTSTART:20200623T143000Z
DTEND:20200623T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/9
DESCRIPTION:Title: Approximate homomorphisms and a conjecture of Pełczyński\nb
y Tom Sanders (University of Oxford) as part of Virtual Harmonic Analysis
Seminar\n\n\nAbstract\nFollowing the introduction of techniques from addit
ive combinatorics to some problems in Banach spaces by Wojciechowski\, we
discuss the Balog-Szemerédi-Gowers Lemma and how it can be used to tackle
some questions about approximate homomorphisms and a conjecture of Pełcz
yński.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (University of Wisconsin-Madison)
DTSTART:20200630T143000Z
DTEND:20200630T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/10
DESCRIPTION:Title: Fourier restriction estimates above rectangles and an applicatio
n\nby Betsy Stovall (University of Wisconsin-Madison) as part of Virtu
al Harmonic Analysis Seminar\n\n\nAbstract\nWe discuss the problem of obta
ining Lebesgue space inequalities for the Fourier restriction operator ass
ociated to rectangular pieces of the paraboloid and perturbations thereof.
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 de
monstrate how these estimates can be applied to obtain sharp restriction i
nequalities on some degenerate hypersurfaces. This is joint work with Jer
emy Schwend.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Bennett (University of Birmingham)
DTSTART:20200707T143000Z
DTEND:20200707T153000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/11
DESCRIPTION:Title: Tomography bounds for the Fourier extension operator and applica
tions\nby Jonathan Bennett (University of Birmingham) as part of Virtu
al Harmonic Analysis Seminar\n\n\nAbstract\nWe explore the extent to which
the Fourier transform of an $L^p$ density supported on the sphere in $\\m
athbb{R}^n$ can have large mass on affine subspaces\, placing particular e
mphasis on lines and hyperplanes. In the process we identify a conjectura
l statement that sits between the classical Fourier restriction and Kakeya
conjectures\, and provide an application to the theory of weighted norm i
nequalities for such Fourier transforms. Our approach\, which takes its in
spiration from work of Planchon and Vega\, exploits cancellation via Planc
herel's theorem on affine subspaces\, avoiding the conventional use of wav
e-packet and stationary-phase methods. This is joint work with Shohei Naka
mura (Tokyo).\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton University)
DTSTART:20200923T150000Z
DTEND:20200923T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/12
DESCRIPTION:Title: The Kakeya needle problem for rectifiable sets\nby Alan Chan
g (Princeton University) as part of Virtual Harmonic Analysis Seminar\n\n\
nAbstract\nWe show that the classical results about rotating a line segmen
t in arbitrarily small area\, and the existence of a Besicovitch and a Nik
odym set hold if we replace the line segment by an arbitrary rectifiable s
et. This is joint work with Marianna Csörnyei.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Christ (UC Berkeley)
DTSTART:20200930T140000Z
DTEND:20200930T150000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/13
DESCRIPTION:Title: Oscillation and frustration in multilinear inequalities\nby
Michael Christ (UC Berkeley) as part of Virtual Harmonic Analysis Seminar\
n\n\nAbstract\nMultilinear functionals\, and inequalities governing them\,
arise in various contexts in harmonic analysis (in connection with Fourie
r restriction)\, in partial differential equations (nonlinear interactions
) and in additive combinatorics (existence of certain patterns in sets of
appropriately bounded density). This talk will focus on an inequality that
quantifies a weak convergence theorem of Joly\, Metivier\, and Rauch (199
5) concerning threefold products\, and on related inequalities for triline
ar expressions involving highly oscillatory factors. Sublevel set inequali
ties\, which quantify the impossibility of exactly solving certain systems
of linear functional equations (the frustration of the title)\, are a cen
tral element of the analysis.\n
LOCATION:https://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:20260422T225722Z
UID:HarmonicAnalysis/14
DESCRIPTION:Title: A triangular Hilbert transform with curvature\nby Joris 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 variant of t
he triangular Hilbert transform involving curvature. Our results unify var
ious previously known results such as bounds for a bilinear Hilbert transf
orm with curvature and a maximally modulated singular integral of Stein-Wa
inger type\, and Bourgain's non-linear Roth theorem in the reals.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Krause (King's College London)
DTSTART:20201014T140000Z
DTEND:20201014T150000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/15
DESCRIPTION:Title: Pointwise Ergodic Theorems for Non-Conventional Bilinear Polynom
ial 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 ergodic avera
ges applied to a single function. In this talk I will discuss joint work w
ith Mariusz Mirek and Terence Tao on bilinear analogues of Bourgain's work
.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornelia Hera (University of Chicago)
DTSTART:20201021T140000Z
DTEND:20201021T150000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/16
DESCRIPTION:Title: Hausdorff dimension of Furstenberg-type sets\nby Kornelia He
ra (University of Chicago) as part of Virtual Harmonic Analysis Seminar\n\
n\nAbstract\nWe say that a planar set F is a (t\,s)-Furstenberg set\, if t
here exists an s-dimensional family of lines in the plane such that each l
ine of this family intersects F in an at least t-dimensional set. We prese
nt Hausdorff dimension estimates for (t\,s)-Furstenberg sets and for more
general Furstenberg type sets in higher dimensions.\nThe talk is based on
joint work with Tamás Keleti and András Máthé\, and with Pablo Shmerki
n and Alexia Yavicoli.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luz Roncal (BCAM)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/17
DESCRIPTION:Title: Directional square functions\nby Luz Roncal (BCAM) as part o
f Virtual Harmonic Analysis Seminar\n\n\nAbstract\nCharles Fefferman's cou
nterexample for the ball multiplier is intimately linked to square functio
n estimates for directional singular integrals along all possible directio
ns. Quantification of such a failure of the boundedness of the ball multip
lier is measured\, for instance\, through $L^p$-bounds for the $N$-gon mul
tiplier which provide information in terms of $N$.\n\nWe present a general
approach\, based on a directional embedding theorem for Carleson sequence
s\, to study time-frequency model square functions associated to conical o
r directional Fourier multipliers. The estimates obtained for these square
functions are applied to obtain sharp or quantified bounds for directiona
l Rubio de Francia type square functions. In particular\, a precise logari
thmic bound for the polygon multiplier is shown\, improving previous resul
ts.\nThis is joint work with Natalia Accomazzo\, Francesco Di Plinio\, Pau
l Hagelstein\, and Ioannis Parissis.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krystal Taylor (Ohio State University)
DTSTART:20201104T150000Z
DTEND:20201104T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/18
DESCRIPTION:Title: Nonlinear projection theory and the Buffon curve problem\nby
Krystal Taylor (Ohio State University) as part of Virtual Harmonic Analys
is Seminar\n\n\nAbstract\nThe Favard length of a subset of the plane is de
fined as the average length of its orthogonal projections. This quantity i
s related to the probabilistic Buffon needle problem\, which considers the
probability that a needle or a line that is dropped at random near a give
n set will intersect the set. We consider the geometric and probabilistic
consequences that arise upon replacing linear projections by more general
families of projection-type mappings. In particular\, we find upper and lo
wer bounds for the rate of decay of the Favard curve length of the four-co
rner Cantor set. Beyond the four-corner set\, we also show that if a subse
t E has finite length in the sense of Hausdorff and is nearly purely unrec
tifiable (so its intersection with any Lipschitz graph has zero length)\,
then its “curve” projections have very small measure.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yufei Zhao (MIT)
DTSTART:20201111T150000Z
DTEND:20201111T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/19
DESCRIPTION:Title: The joints problem for varieties\nby Yufei Zhao (MIT) as par
t of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe generalize the Gu
th-Katz joints theorem from lines to varieties. A special case of our resu
lt 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 thes
e planes not all lying in some hyperplane. Our most general result gives u
pper bounds\, tight up to constant factors\, for joints with multiplicitie
s for several sets of varieties of arbitrary dimensions (known as Carbery'
s conjecture). Our main innovation is a new way to extend the polynomial m
ethod to higher dimensional objects.\n\nJoint work with Jonathan Tidor and
Hung-Hsun Hans Yu\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (IAS)
DTSTART:20201118T150000Z
DTEND:20201118T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/20
DESCRIPTION:Title: Falconer distance set problem using Fourier analysis\nby Hon
g Wang (IAS) as part of Virtual Harmonic Analysis Seminar\n\nAbstract: TBA
\n\nGiven a set $E$ of Hausdorff dimension $s>d/2$ in $\\mathbb{R}^d$ \, F
alconer conjectured that its distance set $\\Delta(E)=\\{ |x-y|: x\, y \\i
n E\\}$ should have positive Lebesgue measure. When $d$ is even\, we show
that $\\dim_H E>d/2+1/4$ implies $|\\Delta(E)|>0$. This improves on the wo
rk of Wolff\, Erdogan\, Du-Zhang\, etc. Our tools include Orponen's radial
projection theorem and refined decoupling estimates. \n\nThis is joint w
ork with Guth\, Iosevich\, and Ou and with Du\, Iosevich\, Ou\, and Zhang.
\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (University of Edinburgh)
DTSTART:20201125T150000Z
DTEND:20201125T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/21
DESCRIPTION:Title: Fourier dimension estimates for exact-order sets\nby Robert
Fraser (University of Edinburgh) as part of Virtual Harmonic Analysis Semi
nar\n\n\nAbstract\nFourier dimension estimates are a growing topic of inte
rest in harmonic analysis\, geometric measure theory\, and metric Diophant
ine approximation. In a joint work with Reuben Wheeler\, we obtain some lo
wer estimates on the Fourier dimension of Bugeaud’s set of numbers appro
ximable to some exact order $\\psi$.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Accomazzo Scotti (BCAM)
DTSTART:20201202T150000Z
DTEND:20201202T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/22
DESCRIPTION:Title: A weighted Carleson embedding and applications\nby Natalia A
ccomazzo Scotti (BCAM) as part of Virtual Harmonic Analysis Seminar\n\n\nA
bstract\nWe will follow up with Luz Roncal's talk\, where she presented a
directional embedding theorem for Carleson sequences which was in turn use
d to obtain bounds for directional Rubio de Francia type square functions.
We will see how we can extend this result to the weighted setting\, from
where we can deduce some weighted estimates for the directional maximal fu
nction and directional singular integrals.\n\nThis is part of joint work w
ith F. Di Plinio\, P. Hagelstein\, I. Parissis and L. Roncal.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lillian Pierce (Duke University)
DTSTART:20201209T150000Z
DTEND:20201209T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/23
DESCRIPTION:Title: Square function inequalities and superorthogonality\nby Lill
ian Pierce (Duke University) as part of Virtual Harmonic Analysis Seminar\
n\n\nAbstract\nWe’ll talk about two notions of square function inequalit
y\, related to a sequence of functions\, which we’ll call direct and con
verse inequalities. In many cases the direct inequality can be proved by v
erifying a type of 2r-superorthogonality\, that is\, proving that the inte
gral of certain 2r-tuples of functions selected from the sequence vanishes
. We will demonstrate a hierarchy of “types” of superorthogonality fo
r which this deduction can be carried out quite formally\, and meanwhile i
llustrate a wide variety of specific settings. In particular\, we will sho
w that two famous results from number theory\, in the setting of bounding
character sums\, fit neatly into this framework.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Wright (University of Edinburgh)
DTSTART:20210113T150000Z
DTEND:20210113T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/24
DESCRIPTION:Title: A theory for oscillatory integrals\nby Jim Wright (Universit
y of Edinburgh) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract
\nWe develop a theory for oscillatory integrals which can be applied in a
variety of settings\, especially settings where scale-invariant bounds do
not hold in the generality we are accustomed to.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Misha Rudnev (University of Bristol)
DTSTART:20210120T150000Z
DTEND:20210120T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/25
DESCRIPTION:Title: Single distance bounds in 3D line complexes\nby Misha Rudnev
(University of Bristol) as part of Virtual Harmonic Analysis Seminar\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 $3$-space ov
er a field $\\mathbb{F}$\, where $-1$ is not a square. In his consideratio
ns he implicitly uses the concept of a line complex\, which has many inter
esting properties. I will present his result in this light and extend it t
o a weaker bound $n^{1.6}$ over $\\mathbb{F}$\, where $-1$ is a square.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Gressman (University of Pennsylvania)
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/26
DESCRIPTION:Title: Radon-like Transforms\, Geometric Measures\, and Invariant Theor
y\nby Philip Gressman (University of Pennsylvania) as part of Virtual
Harmonic Analysis Seminar\n\n\nAbstract\nFourier restriction\, Radon-like
operators\, and decoupling theory are three active areas of harmonic analy
sis which involve submanifolds of Euclidean space in a fundamental way. In
each case\, the mapping properties of the objects of study depend in a fu
ndamental way on the "non-flatness" of the submanifold\, but with the exce
ption of certain extreme cases (primarily curves and hypersurfaces)\, it i
s not clear exactly how to quantify the geometry in an analytically meanin
gful way. In this talk\, I will discuss a series of recent results which s
hed light on this situation using tools from an unusually broad range of m
athematical sources.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Zahl (University of British Columbia)
DTSTART:20210203T150000Z
DTEND:20210203T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/27
DESCRIPTION:Title: Dimension-expanding polynomials and the discretized Elekes-Ronya
i theorem\nby Joshua Zahl (University of British Columbia) as part of
Virtual Harmonic Analysis Seminar\n\n\nAbstract\nI will discuss a discreti
zed version of the Elekes-Ronyai theorem from additive combinatorics\, whi
ch is closely related to the sum-product problem. The Elekes-Ronyai theore
m has recently had applications to combinatorial geometry\, including vari
ants of the Erdos distinct distances problem. The discretized version of t
he Elekes-Ronyai theorem has similar applications\, and in particular I wi
ll discuss some new results on a pinned version of the Falconer distance p
roblem. This is joint work with Orit Raz.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Larry Guth (MIT)
DTSTART:20210210T160000Z
DTEND:20210210T170000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/28
DESCRIPTION:Title: Local smoothing for the wave equation\nby Larry Guth (MIT) a
s part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nThe local smoot
hing problem asks about how much solutions to the wave equation can focus.
It was formulated by Chris Sogge in the early 90s. Hong Wang\, Ruixiang
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 conjec
ture\, and then discuss some of the obstacles and some ideas from the proo
f.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART:20210217T150000Z
DTEND:20210217T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/29
DESCRIPTION:Title: A new proof of decoupling for the parabola\nby Dominique Mal
dague (MIT) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nDe
coupling has to do with measuring the size of functions with specialized F
ourier support (in our case\, in a neighborhood of the truncated parabola)
. Bourgain and Demeter resolved the l^2 decoupling conjecture in 2014\, us
ing ingredients like the multilinear Kakeya inequality\, L^2 orthogonality
\, and induction-on-scales. I will present the ideas that go into a new pr
oof of decoupling and make some comparison between the two approaches. Thi
s is related to recent joint work with Larry Guth and Hong Wang\, as well
as forthcoming joint work with Yuqiu Fu and Larry Guth.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeev Dvir (Princeton University)
DTSTART:20210224T150000Z
DTEND:20210224T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/30
DESCRIPTION:Title: The Kakeya set conjecture over rings of integers modulo square f
ree m\nby Zeev Dvir (Princeton University) as part of Virtual Harmonic
Analysis Seminar\n\n\nAbstract\nWe show that\, when $N$ is any square-fre
e 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 $\\epsilon>0
$ -- resolving a special case of a conjecture of Hickman and Wright. Previ
ously\, such bounds were only known for the case of prime $N$. We also sho
w that the case of general $N$ can be reduced to lower bounding the $p$-ra
nk of the incidence matrix of points and hyperplanes over $(\\mathbb{Z}/p^
k\\mathbb{Z})^n$. Joint work with Manik Dhar\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akshat Mudgal (University of Bristol)
DTSTART:20210303T150000Z
DTEND:20210303T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/31
DESCRIPTION:Title: Diameter free estimates and Incidence geometry\nby Akshat Mu
dgal (University of Bristol) as part of Virtual Harmonic Analysis Seminar\
n\n\nAbstract\nVarious problems in harmonic analysis are intimately connec
ted with studying solutions to additive equations over subsets of curves a
nd surfaces. The latter is amenable to techniques from incidence geometry
since we can count such solutions by interpreting them as incidences betwe
en points and curves/surfaces. In this talk\, we study additive energies o
f arbitrary subsets of parabolas/convex curves\, and their connections 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 which ar
e related to restriction type problems on spheres.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern University)
DTSTART:20210310T150000Z
DTEND:20210310T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/32
DESCRIPTION:Title: Falconer's distance set problem\nby Xiumin Du (Northwestern
University) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nA
classical question in geometric measure theory\, introduced by Falconer in
the 80s is\, how large does the Hausdorff dimension of a compact subset i
n Euclidean space need to be to ensure that the Lebesgue measure of its se
t of pairwise Euclidean distances is positive. In this talk\, I'll report
some recent progress on this problem\, which combines several ingredients
including Orponen's radial projection theorem\, Liu's L^2 identity obtaine
d using a group action argument\, and the refined decoupling theory. This
is based on joint work with Alex Iosevich\, Yumeng Ou\, Hong Wang\, and Ru
ixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Cladek (UCLA)
DTSTART:20210317T150000Z
DTEND:20210317T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/33
DESCRIPTION:Title: Additive energy of regular measures in one and higher dimensions
\, and the fractal uncertainty principle\nby Laura Cladek (UCLA) as pa
rt of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe obtain new bound
s on the additive energy of (Ahlfors-David type) regular measures in both
one and higher dimensions\, which implies expansion results for sums and p
roducts of the associated regular sets\, as well as more general nonlinear
functions of these sets. As a corollary of the higher-dimensional results
we obtain some new cases of the fractal uncertainty principle in odd dime
nsions. This is joint work with Terence Tao.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (UW Madison)
DTSTART:20210324T150000Z
DTEND:20210324T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/34
DESCRIPTION:Title: L^p bounds for the helical maximal function\nby David Beltra
n (UW Madison) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\
nA natural 3-dimensional analogue of Bourgain’s circular maximal functio
n 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 helix (or\,
more generally\, of any curve with non-vanishing curvature and torsion).
In this talk\, we present a sharp result\, which establishes that L^p boun
ds hold if and only if p>3. This is joint work with Shaoming Guo\, Jonatha
n Hickman and Andreas Seeger.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Vitturi (University College Cork)
DTSTART:20210331T140000Z
DTEND:20210331T150000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/35
DESCRIPTION:Title: Two surface weights of Gressman\nby Marco Vitturi (Universit
y College Cork) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract
\nIn recent years P. Gressman\, in the context of the L^p-improving proble
m for Radon averages\, has introduced two types of weighted surface measur
es. One is an affine-invariant surface measure (of "best-possible" type) f
or surfaces of arbitrary codimension\, obtained by a clever construction r
elated to Geometric Invariant Theory (GIT). The other arises via a non-deg
eneracy condition that enables an inflation method devised to prove L^p-im
proving inequalities (this is the antecedent of the work that P. Gressman
presented in his talk on 27/1/2021).\n\nWe pose the question of what the r
elationship between the two weights is and provide some partial answers. I
t is a matter of a simple calculation to verify that in codimension 1 the
weights are comparable\, but the situation in higher codimensions is much
less clear - sometimes the comparability fails. Using GIT techniques\, we
are able to show the weights continue to be comparable in codimension 2 (i
n even ambient dimension). (Joint work with S. Dendrinos and A. Mustata)\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuomas Orponen (University of Jyväskylä)
DTSTART:20210407T140000Z
DTEND:20210407T150000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/36
DESCRIPTION:Title: Quantifying the Besicovitch projection theorem\nby Tuomas Or
ponen (University of Jyväskylä) as part of Virtual Harmonic Analysis Sem
inar\n\n\nAbstract\nA theorem of Besicovitch from the 30s states that a pl
anar set with finite length and “many” projections of positive measure
has a rectifiable piece. How big is this piece\, relative to the measure
of the projections? In general\, quantifying Besicovitch’s theorem remai
ns 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 a
nd Semmes\, contain big pieces of Lipschitz graphs.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume de Dios Pont (UCLA)
DTSTART:20211020T140000Z
DTEND:20211020T150000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/37
DESCRIPTION:Title: Decoupling\, Cantor sets\, and additive combinatorics\nby Ja
ume de Dios Pont (UCLA) as part of Virtual Harmonic Analysis Seminar\n\n\n
Abstract\nDecoupling and discrete restriction inequalities have been very
fruitful in recent years to solve problems in additive combinatorics and a
nalytic number theory. In this talk I will present some work in decoupling
for Cantor sets\, including Cantor sets on a parabola\, decoupling for pr
oduct sets\, and give applications of these results to additive combinator
ics. Time permitting\, I will present some open problems.\n\nContains join
t work with Alan Chang (Princeton)\,\nRachel Greenfeld (UCLA)\, Asgar Jamn
eshan (Koç University)\, Zane Li (IU Bloomington)\, José Ramón Madrid P
adilla (UCLA).\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Thiele (University of Bonn)
DTSTART:20211103T150000Z
DTEND:20211103T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/38
DESCRIPTION:Title: Bilinear multipliers associated with convex sets\nby Christo
ph Thiele (University of Bonn) as part of Virtual Harmonic Analysis Semina
r\n\n\nAbstract\nThis is joint work with Olli Saari. We will review some h
ighlights of the theory of Fourier multipliers in one dimension\, such as
Coifman-Rubio-de-Francia Semmes theory\, and variational Carleson estimate
s. We will then discuss two dimensional multiplier theorems\, in particula
r multipliers which are characteristic functions of convex sets. We presen
t some new results and some open problems.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Greenfeld (UCLA)
DTSTART:20211117T150000Z
DTEND:20211117T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/39
DESCRIPTION:Title: Translational tilings in lattices\nby Rachel Greenfeld (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 o
f $\\mathbb{Z}^d$ if it is possible to cover $\\mathbb{Z}^d$ by translates
of $F$ without any overlap. \nThe periodic tiling conjecture\, which is p
erhaps the most well-known conjecture in the area\, asserts that any trans
lational tile admits at least one periodic tiling. In the talk\, we will
motivate and discuss the study of this conjecture. We will also present so
me recent results\, joint with Terence Tao\, on the structure of translati
onal tilings in lattices and introduce some applications.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Detlef Müller (University of Kiel)
DTSTART:20211201T150000Z
DTEND:20211201T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/40
DESCRIPTION:Title: Fourier restriction to hyperbolic 2-surfaces: robustness of the
polynomial compared to the bilinear approach\nby Detlef Müller (Unive
rsity of Kiel) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\
nIn this talk\, which will be based on joint research with S. Buschenhenk
e and A. Vargas\, I intend to discuss some of the new challenges that ar
ose in our studies of Fourier restriction estimates for hyperbolic surface
s\, compared to the case of elliptic surfaces. \n\nGiven the complexity of
the bilinear\, and even more so of the polynomial partitioning approach\,
I shall mainly focus on those parts of these methods which required new i
deas\, so that a familiarity with these methods will not be expected from
the audience.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Carbery (University of Edinburgh)
DTSTART:20211215T150000Z
DTEND:20211215T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/41
DESCRIPTION:Title: Joints\, multijoints and duality\nby Tony Carbery (Universit
y of Edinburgh) as part of Virtual Harmonic Analysis Seminar\n\n\nAbstract
\nJoints and multijoints provide discrete analogues of the Kakeya maximal
function and multilinear Kakeya respectively. While Guth's sharp endpoint
multilinear Kakeya theorem in Euclidean space is established "on the side
of the maximal function"\, Zhang's joint and multijoint theorems are estab
lished "on the side of the covering lemma". We explore the dualities betwe
en these alternative approaches\, both in the context of joints/multijoint
s and also more abstractly. This is joint work with Michael Tang.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polona Durcik (Chapman University)
DTSTART:20220112T150000Z
DTEND:20220112T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/42
DESCRIPTION:Title: Local bounds for singular Brascamp-Lieb forms with cubical struc
ture\nby Polona Durcik (Chapman University) as part of Virtual Harmoni
c Analysis Seminar\n\n\nAbstract\nWe discuss a range of $L^p$ bounds for s
ingular Brascamp-Lieb forms with cubical structure. This extends an earlie
r result which only allowed for a single tuple of the Lebesgue exponents.
We pass through local and sparse bounds. This is a joint work with L. Sla
víková and C. Thiele.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julia Wolf (University of Cambridge)
DTSTART:20220126T150000Z
DTEND:20220126T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/43
DESCRIPTION:Title: Higher-order generalisations of stability and arithmetic regular
ity\nby Julia Wolf (University of Cambridge) as part of Virtual Harmon
ic Analysis Seminar\n\n\nAbstract\nSince Szemerédi's seminal work in the
70s\, regularity lemmas have proven to be of fundamental importance in man
y areas of discrete mathematics. This talk will survey recent work on regu
larity decompositions of subsets of finite groups under additional assumpt
ions such as stability or bounded VC-dimension\, which turn out to have pa
rticularly desirable properties. In the second half of the talk\, we will
describe very recent joint work with Caroline Terry (Ohio State University
) which extends these ideas to the realm of higher-order Fourier analysis.
\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vjekoslav Kovač (University of Zagreb)
DTSTART:20220209T150000Z
DTEND:20220209T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/44
DESCRIPTION:Title: Bilinear and trilinear estimates for semigroups generated by com
plex elliptic operators\nby Vjekoslav Kovač (University of Zagreb) as
part of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nWe will discuss
bi(sub)linear and tri(sub)linear embeddings for semigroups generated by no
n-smooth complex-coefficient elliptic operators in divergence form. Biline
ar embeddings can be thought of as sharpenings and generalizations of esti
mates for second-order singular integrals. In the context of complex ellip
tic operators such $L^p$ bounds were shown by Carbonaro and Dragičević\,
who emphasized and crucially used certain generalized convexity propertie
s of powers. We remove this obstruction and generalize their approach to t
he level of Orlicz-space norms that only “behave like powers”. Next\,
what we call a trilinear embedding is a paraproduct-type estimate. It inco
rporates bounds for the conical square function and finds an application t
o fractional Leibniz-type rules. In the proofs we use two carefully constr
ucted auxiliary functions that generalize a classic Bellman function const
ructed by Nazarov and Treil in two different ways. The talk is based on jo
int work with Andrea Carbonaro\, Oliver Dragičević\, and Kristina Škreb
.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zihui Zhao (University of Chicago)
DTSTART:20220223T160000Z
DTEND:20220223T170000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/45
DESCRIPTION:Title: Boundary unique continuation and the estimate of the singular se
t\nby Zihui Zhao (University of Chicago) as part of Virtual Harmonic A
nalysis Seminar\n\n\nAbstract\nUnique continuation property is a fundament
al property of harmonic functions\, as well as solutions to a large class
of elliptic and parabolic PDEs. It says that if a harmonic function vanish
es to infinite order at a point\, it must be zero everywhere. In the same
spirit\, we can use the local growth rate of harmonic functions to deduce
global information\, such as estimating the size of the singular set for e
lliptic PDEs. This is joint work with Carlos Kenig.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (UW Madison)
DTSTART:20220309T160000Z
DTEND:20220309T170000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/46
DESCRIPTION:Title: Families of functionals representing Sobolev norms\nby Andre
as Seeger (UW Madison) as part of Virtual Harmonic Analysis Seminar\n\n\nA
bstract\nWe discuss families of limit functionals and weak type (quasi)- n
orms which represent the standard Sobolev norms\, extending and unifying w
ork by Nguyen and by Brezis\, Van Schaftingen and Yung. We also consider v
ersions with fractional smoothness and applications\, including a characte
rization of approximation spaces for nonlinear wavelet approximation. \n\n
Joint works with H. Brezis\, J. Van Schaftingen and P. Yung\, and with Ó.
Domínguez\, B. Street\, J. Van Schaftingen and P. Yung.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zane Li (Indiana University Bloomington)
DTSTART:20220323T150000Z
DTEND:20220323T160000Z
DTSTAMP:20260422T225722Z
UID:HarmonicAnalysis/47
DESCRIPTION:Title: A decoupling interpretation of an old argument for Vinogradov's
Mean Value Theorem\nby Zane Li (Indiana University Bloomington) as par
t of Virtual Harmonic Analysis Seminar\n\n\nAbstract\nThere are two proofs
of Vinogradov's Mean Value Theorem (VMVT)\, the harmonic analysis decoupl
ing proof by Bourgain\, Demeter\, and Guth from 2015 and the number theore
tic efficient congruencing proof by Wooley from 2017. While there has been
recent work illustrating the relation between these two methods\, VMVT ha
s been around since 1935. It is then natural to ask: What does old partial
progress on VMVT look like in harmonic analysis language? How similar or
different does it look from current decoupling proofs? We talk about an ol
d argument that shows VMVT "asymptotically" due to Karatsuba and interpret
this in decoupling language. This is joint work with Brian Cook\, Kevin H
ughes\, Olivier Robert\, Akshat Mudgal\, and Po-Lam Yung.\n
LOCATION:https://researchseminars.org/talk/HarmonicAnalysis/47/
END:VEVENT
END:VCALENDAR