BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jongchon Kim (UBC)
DTSTART:20201005T210000Z
DTEND:20201005T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/1
DESCRIPTION:Title: Max
imal functions associated with a set of directions\nby Jongchon Kim (U
BC) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nThere
is a class of geometric problems in harmonic analysis associated with some
curved manifolds such as the sphere or the paraboloid. In the study of th
ese problems\, relevant geometric maximal functions play a central role. I
n this talk\, we consider maximal averaging operators along line segments
oriented in a set of directions and their singular integral counterparts.
How do operator norms of these maximal functions depend on the number and
the distribution of directions? I will discuss some results in this direct
ion and a divide-and-conquer approach for $L^2$ estimates.\n
LOCATION:https://researchseminars.org/talk/OARS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (UW Madison)
DTSTART:20201012T210000Z
DTEND:20201012T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/2
DESCRIPTION:Title: Ort
hogonal systems of spline wavelets as unconditional bases in Sobolev space
s\nby Rajula Srivastava (UW Madison) as part of OARS Online Analysis R
esearch Seminar\n\n\nAbstract\nWe exhibit the necessary range for which fu
nctions in the Sobolev spaces $L^s_p$ can be represented as an uncondition
al sum of orthonormal spline wavelet systems\, such as the Battle-Lemari\\
'e wavelets. We also consider the natural extensions to Triebel-Lizorkin s
paces. This builds upon\, and is a generalization of\, previous work of Se
eger and Ullrich\, where analogous results were established for the Haar w
avelet system.\n
LOCATION:https://researchseminars.org/talk/OARS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bartosz Langowski (IU Bloomington)
DTSTART:20201019T210000Z
DTEND:20201019T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/3
DESCRIPTION:Title: Lat
tice point problems\, equidistribution and ergodic theorems for certain ar
ithmetic spheres\nby Bartosz Langowski (IU Bloomington) as part of OAR
S Online Analysis Research Seminar\n\n\nAbstract\nLet $\\lambda\\in\\Z_+$
be a positive integer and define the set\n$\\mathbf S_{2}^3(\\lambda)$ of
all lattice points on a two-dimensional\nsphere with radius $\\lambda^{1/2
}$ by\n\\[\n\\mathbf S_{2}^3(\\lambda)\n:=\n\\{x \\in \\mathbb Z^3 : x_1^2
+x_2^2 +x_3^2 = \\lambda \\}.\n\\]\nThe study of the behavior of $\\mathb
f S_{2}^3(\\lambda)$ as\n$\\lambda\\to\\infty$ is a central problem in num
ber theory\, which has\ngone through a period of considerable change and d
evelopment in the\nlast three decades.\n\n\nIn the recent work with A. Ios
evich\, M. Mirek and T.Z. Szarek we consider perturbations of\nthe discre
te spheres $\\mathbf S_2^3(\\lambda)$. In particular\, for $c\\in (1\,2)$\
nwe derive an asymptotic formula for the number of lattice points in the
sets\n\\[\n\\mathbf S_{c}^3(\\lambda)\n:=\n\\{x \\in \\mathbb Z^3 : \\lflo
or |x_1|^c \\rfloor + \\lfloor |x_2|^c \\rfloor + \\lfloor |x_3|^c \\rfloo
r= \\lambda \\}\n\\quad \\text{with}\\quad \\lambda\\in\\mathbb Z_+\;\n\\]
\nwhich can be thought of as a perturbation of the classical Waring proble
m in three variables. Then we use the obtained asymptotic formula to stud
y norm and\npointwise convergence of the ergodic averages\n\\[\n\\frac{
1}{\\#\\mathbf S_{c}^3(\\lambda)}\\sum_{n\\in \\mathbf S_{c}^3(\\lambda)}f
(T_1^{n_1}T_2^{n_2}T_3^{n_3}x)\n\\quad \\text{as}\\quad \\lambda\\to\\inft
y\;\n\\]\nwhere $T_1\, T_2\, T_3:X\\to X$ are commuting invertible and\nme
asure-preserving transformations of a $\\sigma$-finite measure space\n$(X\
, \\nu)$ for any function $f\\in L^p(X)$ with $p>\\frac{11-4c}{11-7c}$. F
inally\, we study the equidistribution problem corresponding to the\nspher
es $\\mathbf S_{c}^3(\\lambda)$.\n
LOCATION:https://researchseminars.org/talk/OARS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ntekoume (Rice)
DTSTART:20201026T210000Z
DTEND:20201026T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/4
DESCRIPTION:Title: Hom
ogenization for the cubic nonlinear Schrödinger equation on ℝ²\nby
Maria Ntekoume (Rice) as part of OARS Online Analysis Research Seminar\n\
n\nAbstract\nThe cubic nonlinear Schr\\"odinger equation on $\\mathbb R^2$
is\ngiven by\n$$i \\partial_t u +\\Delta u=\\bar g |u|^2 u\, \\quad u(0
)=u_0 \\in\nL^2(\\mathbb R^2).$$\nThis equation comes in two flavors\, dep
ending on the sign of $\\bar g$:\nWhen $\\bar g<0$\, the self-interaction
described by the nonlinearity is\nattractive. Heuristiaclly\, the nonlinea
r part is working to counteract\nthe dispersive effects of the linear part
\; indeed\, finite time blow-up\nis possible. On the other hand\, the case
$\\bar g>0$ indicates a\nrepulsive self-interaction. In this regime the q
uestion of\nwell-posedness for general initial data in $L^2$ was a long-st
anding\nproblem in the field until its recent resolution by Dodson.\n\nIn
this talk we will look at the corresponding inhomogeneous problem\n$$i \\p
artial_t u +\\Delta u=g(nx) |u|^2 u$$\nwith initial data in $L^2$\, wher
e $g$ does not necessarily have a fixed\nsign. We will discuss how it rela
tes to the homogeneous NLS above and\nderive sufficient conditions on $g$
to ensure existence and uniqueness\nof global solutions for $n$ large\, as
well as homogenization.\n
LOCATION:https://researchseminars.org/talk/OARS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changkeun Oh (UW Madison)
DTSTART:20201102T220000Z
DTEND:20201102T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/5
DESCRIPTION:Title: Res
triction estimates for various surfaces\nby Changkeun Oh (UW Madison)
as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nRestrictio
n problems\, which are introduced by Stein in 1970s\, play key model probl
ems in harmonic analysis. In the first half of the talk\, we will discuss
restriction estimates for hypersurfaces. In the second half of the talk\,
we will talk about restriction estimates for surfaces with codimension lar
ger than one.\n
LOCATION:https://researchseminars.org/talk/OARS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shukun Wu (UIUC)
DTSTART:20201109T220000Z
DTEND:20201109T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/6
DESCRIPTION:Title: On
the Bochner-Riesz operators and the maximal Bochner-Riesz operator\nby
Shukun Wu (UIUC) as part of OARS Online Analysis Research Seminar\n\n\nAb
stract\nThe Bochner-Riesz problem is one of the most important problems in
the field of Fourier analysis. In this talk\, I will present some recent
improvements to the Bochner-Riesz conjecture and the maximal Bochner-Riesz
conjecture. The main methods we use are polynomial partitioning\, and the
Bourgain Demeter l^2 decoupling theorem.\n
LOCATION:https://researchseminars.org/talk/OARS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Neill (UC Davis)
DTSTART:20201116T220000Z
DTEND:20201116T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/7
DESCRIPTION:Title: A N
onnegative Version of Whitney's Extension Problem\nby Kevin O'Neill (U
C Davis) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nW
hitney's Extension Problem asks the following: Given a compact set E⊂
ℝⁿ and a function f:E→ ℝ\, how can we tell if there exists F∈ C
ᵐ(ℝⁿ) such that f is the restriction of F to E? The classical Whitne
y Extension theorem tells us that\, given potential Taylor polynomials Pˣ
at each x∈E\, there is such an extension F if and only if the Pˣ's are
compatible under Taylor's theorem. However\, this leaves open the questio
n of how to tell solely from f. A 2006 paper of Charles Fefferman answers
this question. We explain some of the concepts of that paper\, as well as
recent work of the speaker\, joint with Fushuai Jiang and Garving K. Luli\
, which establishes the analogous result when f≥0 and we require F≥0.\
n
LOCATION:https://researchseminars.org/talk/OARS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Kemp (IU Bloomington)
DTSTART:20201130T220000Z
DTEND:20201130T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/8
DESCRIPTION:Title: A w
eakening of the curvature condition in $\\mathbb{R}^3$ for $\\ell^p$ decou
pling\nby Dominique Kemp (IU Bloomington) as part of OARS Online Analy
sis Research Seminar\n\n\nAbstract\nThe celebrated decoupling theorem of B
ourgain and Demeter allows for a decomposition in the $L^p$ norm of functi
ons Fourier supported near curved hypersurfaces $M \\subset \\mathbb{R}^n$
. In this project\, we find that the condition of non-vanishing principal
curvatures may be weakened. When $M \\subset \\mathbb{R}^3$\, we may allow
one principal curvature at a time to vanish\, and it is assumed additiona
lly that $M$ is foliated by a canonical family of orthogonal curves having
nonzero curvature at every point. We find that $\\ell^p$ decoupling over
nearly flat subsets of $M$ holds within this context.\n
LOCATION:https://researchseminars.org/talk/OARS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume de Dios Pont (UCLA)
DTSTART:20201207T220000Z
DTEND:20201207T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/9
DESCRIPTION:by Jaume de Dios Pont (UCLA) as part of OARS Online Analysis R
esearch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glücksam (University of Toronto)
DTSTART:20201214T220000Z
DTEND:20201214T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/10
DESCRIPTION:by Adi Glücksam (University of Toronto) as part of OARS Onlin
e Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (UCLA)
DTSTART:20210125T220000Z
DTEND:20210125T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/11
DESCRIPTION:Title: Sh
arp well-posedness for the cubic NLS and mKdV on the line\nby Benjamin
Harrop-Griffiths (UCLA) as part of OARS Online Analysis Research Seminar\
n\n\nAbstract\nThe 1d cubic nonlinear Schrödinger equation (NLS) and the
modified Korteweg-de Vries equation (mKdV) are two of the most intensively
studied nonlinear dispersive equations. Not only are they important physi
cal models\, arising\, for example\, from the study of fluid dynamics and
nonlinear optics\, but they also have a rich mathematical structure: they
are both members of the ZS-AKNS hierarchy of integrable equations. In this
talk\, we discuss an optimal well-posedness result for the cubic NLS and
mKdV on the line. An essential ingredient in our arguments is the demonstr
ation of a local smoothing effect for both equations\, which in turn rests
on the discovery of a one-parameter family of microscopic conservation la
ws. This is joint work with Rowan Killip and Monica Vișan.\n
LOCATION:https://researchseminars.org/talk/OARS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bruce (UW Madison)
DTSTART:20210201T220000Z
DTEND:20210201T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/12
DESCRIPTION:Title: Fo
urier restriction to hyperboloids\nby Ben Bruce (UW Madison) as part o
f OARS Online Analysis Research Seminar\n\n\nAbstract\nThe restriction con
jecture is a major open problem in harmonic analysis concerning interactio
ns between the Fourier transform and curved surfaces. While the case of e
lliptic\, or positively curved\, surfaces has been studied most\, this tal
k will describe some recent results from non-elliptic settings. In partic
ular\, global restriction estimates for hyperboloids will be presented.\n
LOCATION:https://researchseminars.org/talk/OARS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Treuer (UC Irvine)
DTSTART:20210208T220000Z
DTEND:20210208T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/13
DESCRIPTION:Title: Ri
gidity theorem of the Bergman kernel and the analytic capacity\nby Joh
n Treuer (UC Irvine) as part of OARS Online Analysis Research Seminar\n\n\
nAbstract\nThe Bergman kernel function of a domain D in the complex plane
is the reproducing integral kernel for the Hilbert space of square integra
ble holomorphic functions on D. It is easily shown that the (on-diagonal)
Bergman kernel is bounded below by the reciprocal of the volume of the do
main D. In this talk\, I geometrically characterize the domains whose Ber
gman kernels achieve the lower bound.\n
LOCATION:https://researchseminars.org/talk/OARS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gennady Uraltsev (UVA)
DTSTART:20210222T220000Z
DTEND:20210222T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/14
DESCRIPTION:Title: Ba
nach-valued time frequency analysis\nby Gennady Uraltsev (UVA) as part
of OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhan Li (UMN)
DTSTART:20210301T220000Z
DTEND:20210301T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/15
DESCRIPTION:Title: Ca
rleson measure estimates for the Green function\nby Linhan Li (UMN) as
part of OARS Online Analysis Research Seminar\n\n\nAbstract\nIt is known
that the oscillation of the Green function for the Laplacian in a domain i
s related to the flatness of the boundary of the domain. In a joint work w
ith Guy David and Svitlana Mayboroda\, we consider the Green function for
a second-order elliptic operator in the half-space. We show that if the co
efficients satisfy a quadratic Carleson condition\, then the Green functio
n is almost affine\, in the sense that the normalized difference between t
he Green function with a sufficiently far away pole and a suitable affine
function at every scale satisfies a Carleson measure estimate. Our results
are optimal\, in the sense that the class of the operators considered can
not be improved.\n\nThis work is motivated mainly by finding PDE character
izations of uniformly rectifiable sets with higher co-dimension\, yet our
result is new of this kind in the co-dimension one setting as well.\n
LOCATION:https://researchseminars.org/talk/OARS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton)
DTSTART:20210308T220000Z
DTEND:20210308T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/16
DESCRIPTION:Title: On
the polynomial Szemerédi theorem and related results\nby Sarah Pelus
e (Princeton) as part of OARS Online Analysis Research Seminar\n\n\nAbstra
ct\nIn this talk\, I'll survey recent progress on problems in additive com
binatorics\, harmonic analysis\, and ergodic theory related to Bergelson a
nd Leibman's polynomial generalization of Szemerédi's theorem.\n
LOCATION:https://researchseminars.org/talk/OARS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern)
DTSTART:20210315T210000Z
DTEND:20210315T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/17
DESCRIPTION:Title: Fa
lconer's distance set problem\nby Xiumin Du (Northwestern) as part of
OARS Online Analysis Research Seminar\n\n\nAbstract\nA classical question
in geometric measure theory\, introduced by Falconer in the 80s is\, how l
arge does the Hausdorff dimension of a compact subset in Euclidean space n
eed to be to ensure that the Lebesgue measure of its set of pairwise Eucli
dean distances is positive. In this talk\, I'll report some recent progres
s on this problem\, which combines several ingredients including Orponen's
radial projection theorem\, Liu's L^2 identity obtained using a group act
ion argument\, and the refined decoupling theory. This is based on joint w
ork with Alex Iosevich\, Yumeng Ou\, Hong Wang\, and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/OARS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Cladek (UCLA)
DTSTART:20210322T210000Z
DTEND:20210322T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/18
DESCRIPTION:Title: Ad
ditive energy of regular measures in one and higher dimensions\, and the f
ractal uncertainty principle\nby Laura Cladek (UCLA) as part of OARS O
nline Analysis Research Seminar\n\n\nAbstract\nWe obtain new bounds on the
additive energy of (Ahlfors-David type) regular measures in both one and
higher dimensions\, which implies expansion results for sums and products
of the associated regular sets\, as well as more general nonlinear functio
ns of these sets. As a corollary of the higher-dimensional results we obta
in some new cases of the fractal uncertainty principle in odd dimensions.
This is joint work with Terence Tao.\n
LOCATION:https://researchseminars.org/talk/OARS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (LSU)
DTSTART:20210329T210000Z
DTEND:20210329T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/19
DESCRIPTION:Title: A
polynomial Roth theorem for corners in the finite field setting\nby Ru
i Han (LSU) as part of OARS Online Analysis Research Seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/OARS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Barron (UIUC)
DTSTART:20210405T210000Z
DTEND:20210405T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/20
DESCRIPTION:Title: A
sharp global-in-time Strichartz estimate for the Schrodinger equation on t
he infinite cylinder\nby Alex Barron (UIUC) as part of OARS Online Ana
lysis Research Seminar\n\n\nAbstract\nThe classical Strichartz estimates s
how that a solution to the linear Schrodinger equation on Euclidean space
is in certain Lebesgue spaces globally in time provided the initial data i
s in L^2. On compact manifolds one can no longer have global control\, and
some loss of derivatives is necessary in interesting cases (meaning the i
nitial data needs to be in a Sobolev space rather than L^2). On non-compac
t manifolds it is a challenging problem to understand when one can have go
od space-time estimates with no loss of derivatives. \n\nIn this talk we d
iscuss an endpoint Strichartz-type estimate for the linear Schrodinger equ
ation on the infinite cylinder (or\, equivalently\, with one periodic comp
onent and one Euclidean component). Our estimate is sharp\, scale-invarian
t\, and requires only L^2 data. This contrasts the purely periodic case wh
ere some loss of derivatives is necessary at the endpoint\, as originally
observed by Bourgain.\n\nJoint work with M. Christ and B. Pausader.\n
LOCATION:https://researchseminars.org/talk/OARS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahaf Nitzan (Georgia Tech)
DTSTART:20210412T210000Z
DTEND:20210412T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/21
DESCRIPTION:Title: Wh
at is a good definition of 'uniform completeness'?\nby Shahaf Nitzan (
Georgia Tech) as part of OARS Online Analysis Research Seminar\n\n\nAbstra
ct\nWe discuss possible ways to define a notion of 'uniform completeness'
as a dual notion for uniform minimality. We contrast these definitions wit
h a well known density theorem of Landau\, and a quantified version of thi
s theorem due to Olevskii and Ulanovskii. We show that analogs of these re
sults can be obtained for an appropriate notion of 'uniform completeness'.
\n
LOCATION:https://researchseminars.org/talk/OARS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS)
DTSTART:20210419T210000Z
DTEND:20210419T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/22
DESCRIPTION:Title: St
ationary set method for estimating oscillatory integrals\nby Ruixiang
Zhang (IAS) as part of OARS Online Analysis Research Seminar\n\n\nAbstract
\nGiven a polynomial $P$ of constant degree in $d$ variables and consider
the oscillatory integral $$I_P = \\int_{[0\,1]^d} e(P(\\xi)) \\mathrm{d}\\
xi.$$ Assuming the number $d$ of variables is also fixed\, what is a good
upper bound of $|I_P|$? In this talk\, I will introduce a ``stationary set
'' method that gives an upper bound with simple geometric meaning. The pro
of of this bound mainly relies on the theory of o-minimal structures. As a
n application of our bound\, we obtain the sharp convergence exponent in t
he two dimensional Tarry's problem for every degree via additional analysi
s on stationary sets. Consequently\, we also prove the sharp $L^{\\infty}
\\to L^p$ Fourier extension estimates for every two dimensional Parsell-Vi
nogradov surface whenever the endpoint of the exponent $p$ is even. This i
s joint work with Saugata Basu\, Shaoming Guo and Pavel Zorin-Kranich.\n
LOCATION:https://researchseminars.org/talk/OARS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liding Yao (UW Madison)
DTSTART:20210426T210000Z
DTEND:20210426T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/23
DESCRIPTION:by Liding Yao (UW Madison) as part of OARS Online Analysis Res
earch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itay Londner (UBC)
DTSTART:20210503T170000Z
DTEND:20210503T180000Z
DTSTAMP:20260314T081255Z
UID:OARS/24
DESCRIPTION:Title: Ti
ling the integers with translates of one tile: the Coven-Meyerowitz tiling
conditions for three prime factors\nby Itay Londner (UBC) as part of
OARS Online Analysis Research Seminar\n\n\nAbstract\nIt is well known that
if a finite set of integers A tiles the integers by translations\, then t
he translation set must be periodic\, so that the tiling is equivalent to
a factorization A+B=Z_M of a finite cyclic group. Coven and Meyerowitz (19
98) proved that when the tiling period M has at most two distinct prime fa
ctors\, each of the sets A and B can be replaced by a highly ordered "stan
dard" tiling complement. It is not known whether this behavior persists fo
r all tilings with no restrictions on the number of prime factors of M.\n\
nIn an ongoing collaboration with Izabella Laba\, we proved that this is t
rue when M=(pqr)^2. In my talk I will discuss this problem and introduce t
he main ingredients in the proof.\n
LOCATION:https://researchseminars.org/talk/OARS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART:20210510T210000Z
DTEND:20210510T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/25
DESCRIPTION:Title: In
variant Gibbs measures for the three-dimensional wave equation with a Hart
ree nonlinearity\nby Bjoern Bringmann (UCLA) as part of OARS Online An
alysis Research Seminar\n\n\nAbstract\nIn this talk\, we discuss the const
ruction and invariance of the Gibbs measure for a three-dimensional wave e
quation with a Hartree-nonlinearity.\n\nIn the first part of the talk\, we
construct the Gibbs measure and examine its properties. We discuss the mu
tual singularity of the Gibbs measure and the so-called Gaussian free fiel
d. In contrast\, the Gibbs measure for one or two-dimensional wave equatio
ns is absolutely continuous with respect to the Gaussian free field.\n\nIn
the second part of the talk\, we discuss the probabilistic well-posedness
of the corresponding nonlinear wave equation\, which is needed in the pro
of of invariance. At the moment\, this is the only theorem proving the inv
ariance of any singular Gibbs measure under a dispersive equation.\n
LOCATION:https://researchseminars.org/talk/OARS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART:20211004T210000Z
DTEND:20211004T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/26
DESCRIPTION:Title: Th
e structure of translational tilings\nby Terence Tao (UCLA) as part of
OARS Online Analysis Research Seminar\n\n\nAbstract\nLet $F$ be a finite
subset of an additive group $G$\, and let $E$ be a subset of $G$. A (tran
slational) tiling of $E$ by $F$ is a partition of $E$ into disjoint transl
ates $a+F\, a \\in A$ of $F$. The periodic tiling conjecture asserts that
if a periodic subset $E$ of $G$ can be tiled by $F$\, then it can in fact
be tiled periodically\; among other things\, this implies that the questi
on of whether $E$ is tileable by $F$ at all is logically (or algorithmical
ly) decidable. This conjecture was established in the two-dimensional cas
e $G = {\\bf Z}^2$ by Bhattacharya by ergodic theory methods\; we present
a new and more quantitative proof of this fact\, based on a new structural
theorem for translational tilings. On the other hand\, we show that for
higher dimensional groups the periodic tiling conjecture can fail if one u
ses two tiles $F_1\,F_2$ instead of one\; indeed\, the tiling problem can
now become undecidable. This is established by developing a "tiling langu
age" that can encode arbitrary Turing machines.\n\nThis is joint work with
Rachel Greenfeld.\n
LOCATION:https://researchseminars.org/talk/OARS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (Madison)
DTSTART:20211101T210000Z
DTEND:20211101T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/27
DESCRIPTION:Title: $L
^p$ bounds for the helical maximal function\nby David Beltran (Madison
) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nA natura
l 3-dimensional analogue of Bourgain’s circular maximal function theorem
in the plane is the study of the sharp $L^p$ bounds in $\\mathbb{R}^3$ fo
r the maximal function associated with averages over dilates of the helix
(or\, more generally\, of any curve with non-vanishing curvature and torsi
on). 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://researchseminars.org/talk/OARS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuqiu Fu (MIT)
DTSTART:20211115T220000Z
DTEND:20211115T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/28
DESCRIPTION:Title: De
coupling for short generalized Dirichlet sequences\nby Yuqiu Fu (MIT)
as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe will di
scuss some geometric similarities between the sequence $\\{\\log n\\}_{n=N
+1}^{N+N^{1/2}}$ (and sequences with similar convexity properties) and the
parabola from a decoupling point of view.\nBased on those observations we
present decoupling inequalities for those sequences.\nThe sequence $\\{\\
log n\\}_{n=N+1}^{2N}$ is closely connected to a conjecture of Montgomery
on Dirichlet polynomials but we see some difficulties in studying the sequ
ence $\\{\\log n\\}_{n=N+1}^{N+N^{\\alpha}}$ for $\\alpha > 1/2$. This is
joint work with Larry Guth and Dominique Maldague.\n
LOCATION:https://researchseminars.org/talk/OARS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Jahnke (Federal U. São Carlos)
DTSTART:20210920T210000Z
DTEND:20210920T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/29
DESCRIPTION:by Max Jahnke (Federal U. São Carlos) as part of OARS Online
Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (Wichita)
DTSTART:20211108T220000Z
DTEND:20211108T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/30
DESCRIPTION:Title: Ex
plicit Salem sets in R^n: an application of algebraic number theory to Euc
lidean harmonic analysis\nby Robert Fraser (Wichita) as part of OARS O
nline Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tess Anderson (Purdue)
DTSTART:20210927T210000Z
DTEND:20210927T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/31
DESCRIPTION:Title: Dy
adic analysis meets number theory\nby Tess Anderson (Purdue) as part o
f OARS Online Analysis Research Seminar\n\n\nAbstract\nIn recent work we c
onstruct a measure that is $p$-adic and $q$-adic doubling for any coprime
$p$ and $q$\, yet not doubling overall. The proof involves an intricate i
nterplay of number theory\, geometry and analysis\, and here we give an ov
erview of some of the key features.\n
LOCATION:https://researchseminars.org/talk/OARS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Holmes (Texas A&M)
DTSTART:20211011T210000Z
DTEND:20211011T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/32
DESCRIPTION:Title: A
new proof of a weighted John-Nirenberg Theorem\, via sparse operators\
nby Irina Holmes (Texas A&M) as part of OARS Online Analysis Research Semi
nar\n\n\nAbstract\nIn this talk we revisit a result of Muckenhoupt and Whe
eden\, which gives a weighted version of the classical John-Nirenberg Theo
rem (specifically for Ap weights). We will discuss a modern proof of this
result\, using the recent machinery of sparse operators.\n
LOCATION:https://researchseminars.org/talk/OARS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Mirek (Rutgers)
DTSTART:20211206T220000Z
DTEND:20211206T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/33
DESCRIPTION:by Mariusz Mirek (Rutgers) as part of OARS Online Analysis Res
earch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton)
DTSTART:20211018T210000Z
DTEND:20211018T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/34
DESCRIPTION:Title: Th
e Kakeya needle problem for rectifiable sets\nby Alan Chang (Princeton
) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe show
that the classical results about rotating a line segment in arbitrarily sm
all area\, and the existence of a Besicovitch and a Nikodym set hold if we
replace the line segment by an arbitrary rectifiable set. This is joint w
ork with Marianna Csörnyei.\n
LOCATION:https://researchseminars.org/talk/OARS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (UCLA)
DTSTART:20211025T210000Z
DTEND:20211025T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/35
DESCRIPTION:Title: Pr
ojection theorems and applications\nby Hong Wang (UCLA) as part of OAR
S Online Analysis Research Seminar\n\n\nAbstract\nGiven a fractal set $E$
on the plane and a set $F$ of directions\, can we find one direction $\\th
eta\\in F$ such that the orthogonal projection $\\Pi_{\\theta} E$ is large
?\n\nWe will survey some classical and modern projection theorems and disc
uss their applications.\n
LOCATION:https://researchseminars.org/talk/OARS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Harris (Cornell)
DTSTART:20211129T220000Z
DTEND:20211129T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/36
DESCRIPTION:Title: Th
e behaviour of Hausdorff dimension under curved 1-dimensional families of
projections\nby Terence Harris (Cornell) as part of OARS Online Analys
is Research Seminar\n\n\nAbstract\nGiven a curve C with nonvanishing geode
sic curvature in the unit sphere of R^3\, it is an open problem whether th
e Hausdorff dimension of an arbitrary set A is almost surely preserved und
er projection onto the orthogonal complements of vectors in C. In this tal
k I will outline some recent progress on this problem\, which makes use of
some Fourier restriction tools such as decoupling and wave packet decompo
sitions. Toward the end of the talk I will mention a couple of open probl
ems suggested by the approach.\n
LOCATION:https://researchseminars.org/talk/OARS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingrui Cheng (Stony Brook)
DTSTART:20220131T170000Z
DTEND:20220131T180000Z
DTSTAMP:20260314T081255Z
UID:OARS/37
DESCRIPTION:Title: A
PDE approach to $L^\\infty$ estimate for parabolic complex Monge-Ampere an
d Hessian equations\nby Jingrui Cheng (Stony Brook) as part of OARS On
line Analysis Research Seminar\n\n\nAbstract\nPreviously the $L^{\\infty}$
and Holder estimates for complex Monge-Ampere were obtained using pluri-p
otential theory. We consider a version of the parabolic complex Monge-Ampe
re on compact Kähler manifolds using PDE approach\, generalizing the rece
nt work by Guo\, Phong and Tong in the elliptic case.\n
LOCATION:https://researchseminars.org/talk/OARS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bodan Arsovski (Sheffield)
DTSTART:20220214T170000Z
DTEND:20220214T180000Z
DTSTAMP:20260314T081255Z
UID:OARS/38
DESCRIPTION:Title: Th
e p-adic Kakeya conjecture\nby Bodan Arsovski (Sheffield) as part of O
ARS Online Analysis Research Seminar\n\n\nAbstract\nWe prove that all boun
ded subsets of $\\mathbb{Q}_p^n$ containing a line segment of unit length
in every direction have Hausdorff and Minkowski dimension $n$. This is the
analogue of the classical Kakeya conjecture with $\\mathbb{R}$ replaced b
y $\\mathbb{Q}_p$.\n
LOCATION:https://researchseminars.org/talk/OARS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Prendiville (Lancaster)
DTSTART:20220307T170000Z
DTEND:20220307T180000Z
DTSTAMP:20260314T081255Z
UID:OARS/39
DESCRIPTION:Title: Fo
urier analysis and nonlinear progressions of integers\nby Sean Prendiv
ille (Lancaster) as part of OARS Online Analysis Research Seminar\n\n\nAbs
tract\nFourier analysis has proved a fundamental tool in analytic and comb
inatorial number theory\, usually in the guise of the Hardy-Littlewood cir
cle method. When applicable\, this method allows one to asymptotically est
imate the number of solutions to a given Diophantine equation with variabl
es constrained to a given finite set of integers. I will discuss recent wo
rk\, obtained jointly with Sarah Peluse\, which adapts the circle method t
o count the configuration $x\, x+y\, x+y^2$ in a quantitatively effective
manner.\n
LOCATION:https://researchseminars.org/talk/OARS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Denson (Madison)
DTSTART:20220328T160000Z
DTEND:20220328T170000Z
DTSTAMP:20260314T081255Z
UID:OARS/40
DESCRIPTION:Title: La
rge Sets with Fourier Decay avoiding Patterns\nby Jacob Denson (Madiso
n) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe disc
uss the construction of sets with large Fourier dimension avoiding certain
families of linear and non-linear patterns. In other words\, we construct
sets which do not contain a certain subset of points arranged in a partic
ular configuration\, while also supporting probability measures whose Four
ier transforms exhibit polynomial decay. Our analysis involves a discussio
n of the concentration of measure phenomenon in probability\, and some osc
illatory integral estimates. As particular applications of these methods\,
we will construct large sets of $\\mathbf{T}^d$ not containing points $x_
1\,\\dots\,x_n$ solving linear equations of the form $a_1x_1 + ... a_n x_n
= b$\, and large subsets of planar curves with non-vanishing curvature wh
ich do not contain three points forming an isosceles triangle.\n
LOCATION:https://researchseminars.org/talk/OARS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico)
DTSTART:20220404T160000Z
DTEND:20220404T170000Z
DTSTAMP:20260314T081255Z
UID:OARS/41
DESCRIPTION:Title: Sh
arp restriction theory: rigidity\, stability\, and symmetry breaking\n
by Diogo Oliveira e Silva (Instituto Superior Técnico) as part of OARS On
line Analysis Research Seminar\n\n\nAbstract\nWe report on recent progress
concerning two distinct problems in sharp restriction theory to the unit
sphere.\nFirstly\, the classical estimate of Agmon-Hörmander for the adjo
int restriction operator to the sphere is in general not saturated by cons
tants. We describe the surprising intermittent behaviour exhibited by the
optimal constant and the space of maximizers\, both for the inequality its
elf and for a stable form thereof.\nSecondly\, the Stein-Tomas inequality
on the sphere is rigid in the following rather strong sense: constants con
tinue to maximize the weighted inequality as long as the perturbation is s
ufficiently small and regular\, in a precise sense to be discussed. We pre
sent several examples highlighting why such assumptions are natural\, and
describe some consequences to the (mostly unexplored) higher dimensional s
etting.\nThis talk is based on joint work with E. Carneiro and G. Negro.\n
LOCATION:https://researchseminars.org/talk/OARS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galyna Livshyts (Georgia Tech)
DTSTART:20220314T160000Z
DTEND:20220314T170000Z
DTSTAMP:20260314T081255Z
UID:OARS/42
DESCRIPTION:Title: So
me emerging questions about isoperimetric type inequalities under symmetry
assumption\, their connections and partial results\nby Galyna Livshyt
s (Georgia Tech) as part of OARS Online Analysis Research Seminar\n\n\nAbs
tract\nI will talk about the Brunn-Minkowski inequality\, Ehrhard’s ineq
uality\, and some of their conjectured strengthenings — the Log-Brunn-Mi
nkowski conjecture\, the Dimensional Brunn-Minkowski conjecture\, the “s
ymmetric Ehrhard” conjecture\, the B-conjecture\, and all the various re
lations between them. In addition to mentioning many open problems\, I wil
l discuss the state of the art in this area\, and explain some of my resul
ts in it. Finally\, I will talk a bit about a new conjectured strengthenin
g of the Brascamp-Leib inequality\, its potential (significant) implicatio
ns\, and partial progress towards it.\n
LOCATION:https://researchseminars.org/talk/OARS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xueying Yu (U Washington)
DTSTART:20220919T210000Z
DTEND:20220919T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/43
DESCRIPTION:Title: Un
ique continuation properties for generalized fourth-order Schrödinger equ
ations\nby Xueying Yu (U Washington) as part of OARS Online Analysis R
esearch Seminar\n\n\nAbstract\nIn this talk\, we will discuss uniqueness p
roperties of solutions to the linear generalized fourth-order Schrödinger
equations. We show that a solution with fast enough decay in certain Sobo
lev spaces at two different times has to be trivial. This is a joint work
with Zachary Lee.\n
LOCATION:https://researchseminars.org/talk/OARS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (U. Wisconsin-Madison)
DTSTART:20221003T210000Z
DTEND:20221003T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/44
DESCRIPTION:Title: Fa
milies of functionals representing Sobolev norms\nby Andreas Seeger (U
. Wisconsin-Madison) as part of OARS Online Analysis Research Seminar\n\n\
nAbstract\nThis talk is about various families of limit functionals and we
ak type (quasi)-norms which represent the Lp norm of the gradient. This ex
tends and unifies work by Nguyen and by Brezis\, Van Schaftingen and Yung.
We discuss some interesting counterexamples and open problems.\n\nJoint w
ork with Haïm Brezis\, Jean Van Schaftingen and Po Lam Yung.\n
LOCATION:https://researchseminars.org/talk/OARS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Green (Edinburgh/Penn)
DTSTART:20221114T220000Z
DTEND:20221114T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/45
DESCRIPTION:Title: Es
timates for scalar oscillatory integrals: Structure\, stability and method
s that use them\nby John Green (Edinburgh/Penn) as part of OARS Online
Analysis Research Seminar\n\n\nAbstract\nOscillatory integrals are a basi
c object of study in Harmonic Analysis and underpin many important problem
s. The goal of this talk will be to reflect on some elementary yet importa
nt observations on the role of structure in estimating oscillatory integra
ls\, and to discuss some recent works that capture this philosophy.\n
LOCATION:https://researchseminars.org/talk/OARS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Richter (EPFL)
DTSTART:20221205T220000Z
DTEND:20221205T230000Z
DTSTAMP:20260314T081255Z
UID:OARS/46
DESCRIPTION:by Florian Richter (EPFL) as part of OARS Online Analysis Rese
arch Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART:20221017T210000Z
DTEND:20221017T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/47
DESCRIPTION:by Dominique Maldague (MIT) as part of OARS Online Analysis Re
search Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornelia Hera (Alfréd Rényi Institute)
DTSTART:20221031T180000Z
DTEND:20221031T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/48
DESCRIPTION:Title: Ha
usdorff dimension of Besicovitch sets of Cantor graphs\nby Kornelia He
ra (Alfréd Rényi Institute) as part of OARS Online Analysis Research Sem
inar\n\n\nAbstract\nIt is well known that planar Besicovitch sets – sets
\ncontaining a unit line segment in every direction – have Hausdorff\ndi
mension 2. In a joint work with Iqra Altaf and Marianna Csörnyei we\ncons
ider Besicovitch sets of Cantor graphs in the plane– sets\ncontaining a
rotated (and translated) copy of a fixed Cantor graph\n(its line segments
of course removed) in every direction\, and prove\nlower bounds for their
Hausdorff dimension.\n
LOCATION:https://researchseminars.org/talk/OARS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ren (Princeton)
DTSTART:20230919T180000Z
DTEND:20230919T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/49
DESCRIPTION:Title: Sh
arp Furstenberg sets estimate in the plane\nby Kevin Ren (Princeton) a
s part of OARS Online Analysis Research Seminar\n\n\nAbstract\nFix two rea
l numbers $s \\in (0\, 1]$\, $t \\in (0\, 2]$. A set $E \\subset \\mathbb{
R}^2$ is a $(s\, t)$-Furstenberg set if there exists a set of lines $\\mat
hcal{L}$ with Hausdorff dimension $t$ such that for each line $\\ell \\in
\\mathcal{L}$\, we have $\\dim_H (E \\cap \\ell) \\ge s$. (For example\, a
Kakeya set in $\\mathbb{R}^2$ is a special case of a $(1\, 1)$-Furstenber
g set.) The Furstenberg sets problem asks for the minimum possible Hausdor
ff dimension of a $(s\, t)$-Furstenberg set for any given pair of $s\, t$.
In this talk\, I will illustrate the rich theory linking this problem to
the discretized sum-product problem\, orthogonal projections\, and the hig
h-low method in Fourier analysis. Joint works with Yuqiu Fu and Hong Wang.
\n
LOCATION:https://researchseminars.org/talk/OARS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Becker (Bonn)
DTSTART:20231003T180000Z
DTEND:20231003T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/50
DESCRIPTION:Title: Ma
ximal modulations of singular Radon transforms\nby Lars Becker (Bonn)
as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nCarleson's
theorem on the convergence of Fourier series is\nequivalent to the weak-$
L^2$-boundedness of the maximally modulated\nHilbert transform\, and adapt
ions of the proof show more generally\nweak-$L^2$-boundedness of maximally
modulated Calderón-Zygmund operators.\nThis talk is about the open probl
em of whether this result can be extended\nto singular Radon transforms\,
such as the Hilbert transform along the\nparabola $H_P$. I will discuss th
e main ingredients used in the proof of\nCarleson's theorem\, and to what
extent they can be adapted for $H_P$. A\ncorollary are improved quantitati
ve estimates for maximal modulations of\noperators approximating $H_P$.\n
LOCATION:https://researchseminars.org/talk/OARS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Rutar (St Andrews)
DTSTART:20231017T180000Z
DTEND:20231017T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/51
DESCRIPTION:Title: As
souad-type dimensions: finer information on scaling and homogeneity\nb
y Alex Rutar (St Andrews) as part of OARS Online Analysis Research Seminar
\n\n\nAbstract\nThe Assouad dimension is a notion of dimension which captu
res the worst-case scaling of a set at all locations and all scales. Howev
er\, in many situations the Assouad dimension measures scaling in a way wh
ich is too coarse\, and quantifying the precise resolution at which larger
-than-average scaling occurs has been important in applications. In this t
alk\, I will give an introduction and overview of recent work on variation
s of the Assouad dimension. I will also touch on some recent applications
in the literature including: large deviations of branching processes\, smo
othness of iterated function system attractors\, quasi-conformal distortio
n of sets\, and $L^p$-improving properties of maximal operators with restr
icted dilation sets.\n
LOCATION:https://researchseminars.org/talk/OARS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingyuan Liu (U. Texas Rio Grande Valley)
DTSTART:20231114T190000Z
DTEND:20231114T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/52
DESCRIPTION:by Bingyuan Liu (U. Texas Rio Grande Valley) as part of OARS O
nline Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART:20231128T190000Z
DTEND:20231128T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/53
DESCRIPTION:by Cosmin Pohoata (Emory University) as part of OARS Online An
alysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ravi Shankar (Princeton University)
DTSTART:20240305T190000Z
DTEND:20240305T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/54
DESCRIPTION:Title: Do
ubling inequalities for nonlinear elliptic PDEs\nby Ravi Shankar (Prin
ceton University) as part of OARS Online Analysis Research Seminar\n\n\nAb
stract\nFully nonlinear elliptic PDEs include the Monge-Ampere equation fr
om optimal transport and the PDEs for constructing minimal surfaces of hig
h codimension. Such PDEs can be solved in the weak\, viscosity sense\, so
the question is whether such solutions are smooth\, or what kinds of sing
ularities are possible. In the past\, these questions were solved for eac
h equation using very different approaches. In this talk\, we indicate a
unified approach to these questions and equations\, based on the idea of a
doubling inequality.\n
LOCATION:https://researchseminars.org/talk/OARS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART:20240319T180000Z
DTEND:20240319T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/55
DESCRIPTION:by Cosmin Pohoata (Emory University) as part of OARS Online An
alysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen Do (University of Virginia)
DTSTART:20240405T180000Z
DTEND:20240405T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/56
DESCRIPTION:Title: Re
al roots of random algebraic polynomials\nby Yen Do (University of Vir
ginia) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nThe
number of real roots for random algebraic polynomials is a topic with a l
ong history and contributions of many authors. In this talk\, I will discu
ss a brief history of the topic and some recent developments.\n
LOCATION:https://researchseminars.org/talk/OARS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tainara Borges (Brown University)
DTSTART:20240416T180000Z
DTEND:20240416T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/57
DESCRIPTION:Title: So
bolev smoothing estimates for bilinear maximal operators with fractal dila
tion sets\nby Tainara Borges (Brown University) as part of OARS Online
Analysis Research Seminar\n\n\nAbstract\nGiven a hypersurface $S\\subset
\\mathbb{R}^{2d}$\, we study the bilinear averaging operator that averages
a pair of functions over S\, as well as more general bilinear multipliers
of limited decay and various maximal analogs. Of particular interest are
bilinear maximal operators associated to a fractal dilation set $E\\subset
[1\,2]$\; in this case\, the boundedness region of the maximal operator i
s associated to the geometry of the hypersurface and various notions of th
e dimension of the dilation set. In particular\, we determine Sobolev smoo
thing estimates at the exponent $L^{2}\\times L^{2}\\rightarrow L^2$ using
Fourier-analytic methods\, which allow us to deduce additional $L^{p}$ im
proving bounds for the operators and sparse bounds and their weighted coro
llaries for the associated multi-scale maximal functions. We also extend t
he method to study analogues of these questions for the triangle averaging
operator and biparameter averaging operators. In addition\, some necessar
y conditions for boundedness of these operators are obtained.\n
LOCATION:https://researchseminars.org/talk/OARS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manik Dhar (Massachusetts Institute of Technology)
DTSTART:20240429T180000Z
DTEND:20240429T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/58
DESCRIPTION:by Manik Dhar (Massachusetts Institute of Technology) as part
of OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camil Muscalu (Cornell University)
DTSTART:20240917T180000Z
DTEND:20240917T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/59
DESCRIPTION:Title: A
new approach to the Fourier Extension Problem for the paraboloid\nby C
amil Muscalu (Cornell University) as part of OARS Online Analysis Research
Seminar\n\n\nAbstract\nThe plan of the talk is to describe a new approach
to the so-called Restriction Conjectures\, that Itamar Oliveira and I hav
e developed recently. Without entering into details\, this new point of vi
ew allows one to prove that (essentially) all the relevant conjectures (li
near or multi-linear) are true\, provided that one of the functions involv
ed has a tensor structure.\n
LOCATION:https://researchseminars.org/talk/OARS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Albesiano (University of Waterloo)
DTSTART:20241001T180000Z
DTEND:20241001T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/60
DESCRIPTION:Title: A
degeneration approach to Skoda’s division theorem\nby Roberto Albesi
ano (University of Waterloo) as part of OARS Online Analysis Research Semi
nar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandar Bulj (University of Zagreb)
DTSTART:20241015T180000Z
DTEND:20241015T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/61
DESCRIPTION:Title: Po
wers of unimodular homogeneous multipliers\nby Aleksandar Bulj (Univer
sity of Zagreb) as part of OARS Online Analysis Research Seminar\n\n\nAbst
ract\nWe study asymptotically sharp estimates for the $L^p\\to L^p$ norms
of multipliers associated with unimodular homogeneous symbols of degree 0\
, i.e. multipliers associated with symbols $\\xi\\mapsto \\exp(i\\lambda\\
Phi(\\xi/|\\xi|))$\, where $\\lambda$ is a real number and $\\Phi \\in C^{
\\infty}(S^{n-1})$.\nWe show that that the powers of a generic multiplier
in that class exhibit asymptotically maximal order of growth. As a consequ
ence\, we disprove Maz'ya's conjecture regarding the asymptotically sharp
estimates of such multipliers in all dimensions and solve the problem pose
d by Dragicevic\, Petermichl\, and Volberg concerning the sharp lower esti
mate of a certain multiplier falling within the mentioned class.\n
LOCATION:https://researchseminars.org/talk/OARS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (University of South Carolina)
DTSTART:20241029T180000Z
DTEND:20241029T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/62
DESCRIPTION:by Haonan Zhang (University of South Carolina) as part of OARS
Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Gressman (University of Pennsylvania)
DTSTART:20241112T190000Z
DTEND:20241112T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/63
DESCRIPTION:Title: Un
derstanding affine symmetry in geometric harmonic analysis\nby Phil Gr
essman (University of Pennsylvania) as part of OARS Online Analysis Resear
ch Seminar\n\n\nAbstract\nMany geometrically-inspired problems of interest
in harmonic analysis\, including $L^p$-improving properties of Radon-like
transforms and appropriate formulations of the Fourier restriction proble
m\, exhibit natural affine invariance. In some cases\, this can mean that
the geometry of submanifolds viewed as subsets of Euclidean space fails to
capture important subtleties in much the same way that understanding the
size of the entries of a matrix fails to capture its nondegeneracy propert
ies. In this talk\, I will discuss how these ideas relate to recent work o
n characterizing the $L^p-L^q$ norm of Radon-like transforms for pairs $(1
/p\,1/q)$ on a natural scaling line. Along the way\, natural connections t
o Geometric Invariant Theory will be described. This work is part of a bro
ader project to understand other geometrically-flavored nonnegative operat
ors related to fractional integration\; some initial work on this broader
project will be presented as time permits.\n
LOCATION:https://researchseminars.org/talk/OARS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Niedorf (University of Wisconsin-Madison)
DTSTART:20241126T190000Z
DTEND:20241126T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/64
DESCRIPTION:Title: Re
striction type estimates and spectral multipliers on Métivier groups\
nby Lars Niedorf (University of Wisconsin-Madison) as part of OARS Online
Analysis Research Seminar\n\n\nAbstract\nWe present a restriction type est
imate for sub-Laplacians on arbitrary two-step stratified Lie groups. Alth
ough weaker than previously known estimates for the subclass of Heisenberg
type groups\, these estimates turn out to be sufficient to prove an $L^p$
-spectral multiplier theorem with sharp regularity condition $s > d|1/p-1/
2|$ for sub-Laplacians on Métivier groups.\n
LOCATION:https://researchseminars.org/talk/OARS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Karam (University of Oxford)
DTSTART:20241210T190000Z
DTEND:20241210T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/65
DESCRIPTION:Title: Th
e structure of a function and small images\nby Thomas Karam (Universit
y of Oxford) as part of OARS Online Analysis Research Seminar\n\n\nAbstrac
t\nIt is well known that if $G$ is an abelian group and $A$ is a finite su
bset of $G$ which minimises the size of $A+A$ for a fixed size of $A$\, th
en $A$ must essentially be as close as possible to being a coset of some s
ubgroup of $G$: for instance\, if $G$ is finite then the set $A$ must be a
coset in $G$ (provided that $G$ has subgroups with size $|A|$)\, and if $
G=\\mathbb{Z}$ then the set $A$ must be an arithmetic progression. One may
wish to describe an extension of this phenomenon to more arbitrary functi
ons than addition on abelian groups: if $X$ is a set and $F: X \\times X \
\rightarrow X$ is a function\, then can the structure of $F$ (to the exten
t that there is some) be read from the structure of the sets $A$ minimisin
g the size of the image $F(A\,A)$ for a fixed size of $A$ ? We will discus
s the progress that has been made in this direction and what remains to be
understood.\n
LOCATION:https://researchseminars.org/talk/OARS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paata Ivanisvili (University of California Irvine)
DTSTART:20250211T210000Z
DTEND:20250211T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/66
DESCRIPTION:Title: Ja
ckson's inequality on the hypercube\nby Paata Ivanisvili (University o
f California Irvine) as part of OARS Online Analysis Research Seminar\n\n\
nAbstract\nI will talk about the uniform polynomial approximation problem
on the hypercube of dimension $n$. I will present two results\, first indi
cating that there is a threshold power $n/2$\, i.e.\, polynomials of degre
e at most $0.4999n$ will not always approximate well enough functions of c
onstant sensitivity. The second result\, on the opposite side\, gives quan
titative estimates on the error of approximation when degree is close to
$n$. There will be two applications presented: one showing that sensitivit
y theorem does not hold for bounded real valued functions when degree is r
eplaced by approximate degree. The second application will be a counterexa
mple to reverse Markov-Bernstein inequality for functions in $L^1$ tail s
pace having frequencies at least $0.4999n$. This is joint work with Roman
Vershynin and Xinyuan Xie.\n
LOCATION:https://researchseminars.org/talk/OARS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingfeng Chen (University of Wisconsin-Madison)
DTSTART:20250225T210000Z
DTEND:20250225T220000Z
DTSTAMP:20260314T081255Z
UID:OARS/67
DESCRIPTION:Title: Th
e dichotomy of Nikodym sets and local smoothing estimates for wave equatio
ns\nby Mingfeng Chen (University of Wisconsin-Madison) as part of OARS
Online Analysis Research Seminar\n\n\nAbstract\nWe show that Nikodym sets
and local smoothing estimates for linear wave equations form a dichotomy:
If Nikodym sets for a family of curves exist\, then the related maximal o
perator is not bounded on $L^p(\\mathbb{R}^2)$ for any $p<\\infty$\; if Ni
kodym sets do not exist\, then local smoothing estimates hold\, and the re
lated maximal operator is bounded on $L^p(\\mathbb{R}^2)$ for some $p<\\in
fty$. We also determine the sharp exponent for $L^p$ bounds. This is joint
work with Shaoming Guo.\n
LOCATION:https://researchseminars.org/talk/OARS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20250311T200000Z
DTEND:20250311T210000Z
DTSTAMP:20260314T081255Z
UID:OARS/68
DESCRIPTION:Title: Re
ctifiability in Carnot groups\nby Daniela Di Donato (University of Pav
ia) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nIntrin
sic regular surfaces in Carnot groups play the same role as $C^1$ surfaces
in Euclidean spaces. As in Euclidean spaces\, intrinsic regular surfaces
can be locally defined in different ways: e.g. as non critical level sets
or as continuously intrinsic differentiable graphs. The equivalence of the
se natural definitions is the problem that we are studying. Precisely our
aim is to generalize some results proved by Ambrosio\, Serra Cassano\, Vit
tone valid in Heisenberg groups to the more general setting of Carnot grou
ps. This is joint work with Antonelli\, Don and Le Donne\n
LOCATION:https://researchseminars.org/talk/OARS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis White (University of California Irvine)
DTSTART:20250325T200000Z
DTEND:20250325T210000Z
DTSTAMP:20260314T081255Z
UID:OARS/69
DESCRIPTION:by Francis White (University of California Irvine) as part of
OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Bedert (University of Oxford)
DTSTART:20250429T200000Z
DTEND:20250429T210000Z
DTSTAMP:20260314T081255Z
UID:OARS/70
DESCRIPTION:by Benjamin Bedert (University of Oxford) as part of OARS Onli
ne Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Cairo (University of California\, Berkeley)
DTSTART:20250408T200000Z
DTEND:20250408T210000Z
DTSTAMP:20260314T081255Z
UID:OARS/71
DESCRIPTION:Title: A
counterexample to the Mizohata-Takeuchi Conjecture\nby Hannah Cairo (U
niversity of California\, Berkeley) as part of OARS Online Analysis Resear
ch Seminar\n\nAbstract: TBA\n\nWe derive a family of $L^p$ estimates of th
e X-Ray transform of positive measures in $\\mathbb{R}^d$\, which we use t
o construct a log $R$-loss counterexample to the Mizohata-Takeuchi conject
ure for every $C^2$ hypersurface in $\\mathbb{R}^d$ that does not lie in a
hyperplane. In particular\, multilinear restriction estimates at the endp
oint cannot be sharpened directly by the Mizohata-Takeuchi conjecture.\n
LOCATION:https://researchseminars.org/talk/OARS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehtaab Sawhney (Columbia University)
DTSTART:20251007T180000Z
DTEND:20251007T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/72
DESCRIPTION:Title: Qu
asipolynomial bounds for the corners theorem\nby Mehtaab Sawhney (Colu
mbia University) as part of OARS Online Analysis Research Seminar\n\n\nAbs
tract\nWe discuss recent quasipolynomial bounds for the corners theorem. W
e will zoom in on the application of graph counting lemmas in this arithme
tic problem and explain how variations of densification (as developed by C
onlon\, Fox and Zhao) appear in our work.\nBased on joint work with Michae
l Jaber\, Yang P Liu\, Shachar Lovett and Anthony Ostuni.\n
LOCATION:https://researchseminars.org/talk/OARS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fraccaroli (University of Massachusetts Lowell)
DTSTART:20251021T180000Z
DTEND:20251021T190000Z
DTSTAMP:20260314T081255Z
UID:OARS/73
DESCRIPTION:Title: En
dpoint estimates for Fourier multipliers with Zygmund singularities\nb
y Marco Fraccaroli (University of Massachusetts Lowell) as part of OARS On
line Analysis Research Seminar\n\n\nAbstract\nThe Hilbert transform maps $
L^1$ functions into $L^{1\,\\infty}$ ones. In fact\, this estimate holds t
rue for any operator $T_m$ defined by a bounded Fourier multiplier $m$ wit
h singularity only in the origin. Tao and Wright identified the space repl
acing $L^1$ in the endpoint estimate for $T_m$ when $m$ has singularities
in a lacunary set of frequencies\, in the sense of the Hörmander-Mihlin c
ondition.\n\nIn this talk we will quantify how the endpoint estimate for $
T_m$ for any arbitrary $m$ is characterized by the lack of additivity of i
ts set of singularities $\\Xi(m)$ . This property of $\\Xi(m)$ is expresse
d in terms of a Zygmund-type inequality. The main ingredient in the proof
of the estimate is a multi-frequency projection lemma based on Gabor expan
sion playing the role of Calderón-Zygmund decomposition.\n\nThe talk is b
ased on joint work with Bakas\, Ciccone\, Di Plinio\, Parissis\, and Vittu
ri.\n
LOCATION:https://researchseminars.org/talk/OARS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arian Nadjimzadah (University of California Los Angeles)
DTSTART:20251104T190000Z
DTEND:20251104T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/74
DESCRIPTION:by Arian Nadjimzadah (University of California Los Angeles) as
part of OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Wagner (George Mason University)
DTSTART:20251118T190000Z
DTEND:20251118T200000Z
DTSTAMP:20260314T081255Z
UID:OARS/75
DESCRIPTION:Title: Op
timal Sparse Bounds and Commutator Characterizations Without Doubling\
nby Nathan Wagner (George Mason University) as part of OARS Online Analysi
s Research Seminar\n\n\nAbstract\nWe examine dyadic paraproducts and commu
tators in the non-homogeneous setting\, where the underlying Borel measure
$\\mu$ is not assumed doubling. We first establish a pointwise sparse dom
ination for dyadic paraproducts and related operators with symbols $b \\in
BMO(\\mu)$\, improving upon a result of Lacey\, where $b$ satisfied a str
onger Carleson-type condition coinciding with BMO only in the doubling cas
e. As an application\, we derive sharpened weighted inequalities for the c
ommutator of a dyadic Hilbert transform H previously studied by Borges\, C
onde Alonso\, Pipher\, and Wagner. We also characterize the symbols for wh
ich $[H\,b]$ is bounded on $L^p$ for $1Ta
ngency counting for well-spaced circles\nby Alex Ortiz (Rice Universit
y) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nIn the
late 1990s\, Wolff introduced the circle tangency problem: among $N$ circl
es\, with no three tangent at a point\, how many pairs can be internally t
angent? He proved an $N^{3/2+ε}$ upper bound\, which was sharpened to $N^
{3/2}$ by Ellenberg\, Solymosi\, and Zahl in 2016 using the polynomial met
hod. The conjectured sharp bound $N^{4/3+ε}$ is achieved by a grid of cir
cles. In recent joint work with Dominique Maldague\, we show that for appr
oximately gridlike families of circles\, the $N^{3/2}$ barrier can be brok
en: we obtain an upper bound of $N^{25/18+ε}$\, coming close to the conje
ctured $4/3$ exponent. I will outline the background and the connection of
the circle tangency problem with restriction theory\, and then describe o
ur stopping-time framework\, which uses a new square-function interpretati
on of refined decoupling for the truncated cone in $\\mathbb{R}^3$.\n
LOCATION:https://researchseminars.org/talk/OARS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donggeun Ryou (Indiana University)
DTSTART:20260303T160000Z
DTEND:20260303T170000Z
DTSTAMP:20260314T081255Z
UID:OARS/77
DESCRIPTION:by Donggeun Ryou (Indiana University) as part of OARS Online A
nalysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dor Minzer (Massachusetts Institute of Technology)
DTSTART:20260317T150000Z
DTEND:20260317T160000Z
DTSTAMP:20260314T081255Z
UID:OARS/78
DESCRIPTION:by Dor Minzer (Massachusetts Institute of Technology) as part
of OARS Online Analysis Research Seminar\n\nInteractive livestream: https:
//uml.zoom.us/j/93784530288\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/78/
URL:https://uml.zoom.us/j/93784530288
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernie Croot (Georgia Tech)
DTSTART:20260331T150000Z
DTEND:20260331T160000Z
DTSTAMP:20260314T081255Z
UID:OARS/79
DESCRIPTION:by Ernie Croot (Georgia Tech) as part of OARS Online Analysis
Research Seminar\n\nInteractive livestream: https://uml.zoom.us/j/93784530
288\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/OARS/79/
URL:https://uml.zoom.us/j/93784530288
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eyvindur Palsson (Virginia Tech)
DTSTART:20260217T160000Z
DTEND:20260217T170000Z
DTSTAMP:20260314T081255Z
UID:OARS/80
DESCRIPTION:Title: Th
e Falconer distance problem and its many variants\nby Eyvindur Palsson
(Virginia Tech) as part of OARS Online Analysis Research Seminar\n\n\nAbs
tract\nThe Falconer distance problem\, a major open problem on the interfa
ce of geometric measure theory and harmonic analysis\, has seen much progr
ess in the last decade. There are many variants of it\, including pinned a
nd non-empty interior ones\, as well as multipoint configuration analogues
. In this talk I will give a brief introduction and report on some recent
results on general distance graph variants of this classic question.\n
LOCATION:https://researchseminars.org/talk/OARS/80/
END:VEVENT
END:VCALENDAR