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BEGIN:VEVENT
SUMMARY:Jongchon Kim (UBC)
DTSTART;VALUE=DATE-TIME:20201005T210000Z
DTEND;VALUE=DATE-TIME:20201005T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/1
DESCRIPTION:Title: Maximal functions associated with a set of directions\nby Jongchon
Kim (UBC) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\
nThere is a class of geometric problems in harmonic analysis associated wi
th some curved manifolds such as the sphere or the paraboloid. In the stud
y of these problems\, relevant geometric maximal functions play a central
role. In this talk\, we consider maximal averaging operators along line se
gments oriented in a set of directions and their singular integral counter
parts. How do operator norms of these maximal functions depend on the numb
er and the distribution of directions? I will discuss some results in this
direction and a divide-and-conquer approach for $L^2$ estimates.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (UW Madison)
DTSTART;VALUE=DATE-TIME:20201012T210000Z
DTEND;VALUE=DATE-TIME:20201012T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/2
DESCRIPTION:Title: Orthogonal systems of spline wavelets as unconditional bases in Sobole
v spaces\nby Rajula Srivastava (UW Madison) as part of OARS Online Ana
lysis Research Seminar\n\n\nAbstract\nWe exhibit the necessary range for w
hich functions in the Sobolev spaces $L^s_p$ can be represented as an unco
nditional sum of orthonormal spline wavelet systems\, such as the Battle-L
emari\\'e wavelets. We also consider the natural extensions to Triebel-Liz
orkin spaces. This builds upon\, and is a generalization of\, previous wor
k of Seeger and Ullrich\, where analogous results were established for the
Haar wavelet system.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bartosz Langowski (IU Bloomington)
DTSTART;VALUE=DATE-TIME:20201019T210000Z
DTEND;VALUE=DATE-TIME:20201019T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/3
DESCRIPTION:Title: Lattice point problems\, equidistribution and ergodic theorems for cer
tain arithmetic spheres\nby Bartosz Langowski (IU Bloomington) as part
of OARS Online Analysis Research Seminar\n\n\nAbstract\nLet $\\lambda\\in
\\Z_+$ be a positive integer and define the set\n$\\mathbf S_{2}^3(\\lambd
a)$ of all lattice points on a two-dimensional\nsphere with radius $\\lamb
da^{1/2}$ 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 $
\\mathbf S_{2}^3(\\lambda)$ as\n$\\lambda\\to\\infty$ is a central problem
in number theory\, which has\ngone through a period of considerable chang
e and development in the\nlast three decades.\n\n\nIn the recent work with
A. Iosevich\, M. Mirek and T.Z. Szarek we consider perturbations of\nthe
discrete 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 :
\\lfloor |x_1|^c \\rfloor + \\lfloor |x_2|^c \\rfloor + \\lfloor |x_3|^c
\\rfloor= \\lambda \\}\n\\quad \\text{with}\\quad \\lambda\\in\\mathbb Z_+
\;\n\\]\nwhich can be thought of as a perturbation of the classical Waring
problem in three variables. Then we use the obtained asymptotic formula
to study norm and\npointwise convergence of the ergodic averages\n\\[\n
\\frac{1}{\\#\\mathbf S_{c}^3(\\lambda)}\\sum_{n\\in \\mathbf S_{c}^3(\\la
mbda)}f(T_1^{n_1}T_2^{n_2}T_3^{n_3}x)\n\\quad \\text{as}\\quad \\lambda\\t
o\\infty\;\n\\]\nwhere $T_1\, T_2\, T_3:X\\to X$ are commuting invertible
and\nmeasure-preserving transformations of a $\\sigma$-finite measure spac
e\n$(X\, \\nu)$ for any function $f\\in L^p(X)$ with $p>\\frac{11-4c}{11-
7c}$. Finally\, we study the equidistribution problem corresponding to the
\nspheres $\\mathbf S_{c}^3(\\lambda)$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ntekoume (Rice)
DTSTART;VALUE=DATE-TIME:20201026T210000Z
DTEND;VALUE=DATE-TIME:20201026T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/4
DESCRIPTION:Title: Homogenization for the cubic nonlinear Schrödinger equation on ℝ²<
/a>\nby Maria Ntekoume (Rice) as part of OARS Online Analysis Research Sem
inar\n\n\nAbstract\nThe cubic nonlinear Schr\\"odinger equation on $\\math
bb R^2$ is\ngiven by\n$$i \\partial_t u +\\Delta u=\\bar g |u|^2 u\, \\q
uad u(0)=u_0 \\in\nL^2(\\mathbb R^2).$$\nThis equation comes in two flavor
s\, depending on the sign of $\\bar g$:\nWhen $\\bar g<0$\, the self-inter
action described by the nonlinearity is\nattractive. Heuristiaclly\, the n
onlinear part is working to counteract\nthe dispersive effects of the line
ar part\; indeed\, finite time blow-up\nis possible. On the other hand\, t
he case $\\bar g>0$ indicates a\nrepulsive self-interaction. In this regim
e the question of\nwell-posedness for general initial data in $L^2$ was a
long-standing\nproblem in the field until its recent resolution by Dodson.
\n\nIn this talk we will look at the corresponding inhomogeneous problem\n
$$i \\partial_t u +\\Delta u=g(nx) |u|^2 u$$\nwith initial data in $L^2$
\, where $g$ does not necessarily have a fixed\nsign. We will discuss how
it relates to the homogeneous NLS above and\nderive sufficient conditions
on $g$ to ensure existence and uniqueness\nof global solutions for $n$ lar
ge\, as well as homogenization.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changkeun Oh (UW Madison)
DTSTART;VALUE=DATE-TIME:20201102T220000Z
DTEND;VALUE=DATE-TIME:20201102T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/5
DESCRIPTION:Title: Restriction estimates for various surfaces\nby Changkeun Oh (UW Ma
dison) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nRes
triction problems\, which are introduced by Stein in 1970s\, play key mode
l problems in harmonic analysis. In the first half of the talk\, we will d
iscuss restriction estimates for hypersurfaces. In the second half of the
talk\, we will talk about restriction estimates for surfaces with codimens
ion larger than one.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shukun Wu (UIUC)
DTSTART;VALUE=DATE-TIME:20201109T220000Z
DTEND;VALUE=DATE-TIME:20201109T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/6
DESCRIPTION:Title: On the Bochner-Riesz operators and the maximal Bochner-Riesz operator<
/a>\nby Shukun Wu (UIUC) as part of OARS Online Analysis Research Seminar\
n\n\nAbstract\nThe Bochner-Riesz problem is one of the most important prob
lems in the field of Fourier analysis. In this talk\, I will present some
recent improvements to the Bochner-Riesz conjecture and the maximal Bochne
r-Riesz conjecture. The main methods we use are polynomial partitioning\,
and the Bourgain Demeter l^2 decoupling theorem.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Neill (UC Davis)
DTSTART;VALUE=DATE-TIME:20201116T220000Z
DTEND;VALUE=DATE-TIME:20201116T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/7
DESCRIPTION:Title: A Nonnegative Version of Whitney's Extension Problem\nby Kevin O'N
eill (UC Davis) as part of OARS Online Analysis Research Seminar\n\n\nAbst
ract\nWhitney'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
∈ Cᵐ(ℝⁿ) such that f is the restriction of F to E? The classical W
hitney Extension theorem tells us that\, given potential Taylor polynomial
s 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 qu
estion of how to tell solely from f. A 2006 paper of Charles Fefferman ans
wers this question. We explain some of the concepts of that paper\, as wel
l 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:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Kemp (IU Bloomington)
DTSTART;VALUE=DATE-TIME:20201130T220000Z
DTEND;VALUE=DATE-TIME:20201130T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/8
DESCRIPTION:Title: A weakening of the curvature condition in $\\mathbb{R}^3$ for $\\ell^p
$ decoupling\nby Dominique Kemp (IU Bloomington) as part of OARS Onlin
e Analysis Research Seminar\n\n\nAbstract\nThe celebrated decoupling theor
em of Bourgain and Demeter allows for a decomposition in the $L^p$ norm of
functions Fourier supported near curved hypersurfaces $M \\subset \\mathb
b{R}^n$. In this project\, we find that the condition of non-vanishing pri
ncipal curvatures may be weakened. When $M \\subset \\mathbb{R}^3$\, we ma
y allow one principal curvature at a time to vanish\, and it is assumed ad
ditionally that $M$ is foliated by a canonical family of orthogonal curves
having nonzero curvature at every point. We find that $\\ell^p$ decouplin
g over nearly flat subsets of $M$ holds within this context.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume de Dios Pont (UCLA)
DTSTART;VALUE=DATE-TIME:20201207T220000Z
DTEND;VALUE=DATE-TIME:20201207T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/9
DESCRIPTION:by Jaume de Dios Pont (UCLA) as part of OARS Online Analysis R
esearch Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glücksam (University of Toronto)
DTSTART;VALUE=DATE-TIME:20201214T220000Z
DTEND;VALUE=DATE-TIME:20201214T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/10
DESCRIPTION:by Adi Glücksam (University of Toronto) as part of OARS Onlin
e Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (UCLA)
DTSTART;VALUE=DATE-TIME:20210125T220000Z
DTEND;VALUE=DATE-TIME:20210125T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/11
DESCRIPTION:Title: Sharp well-posedness for the cubic NLS and mKdV on the line\nby B
enjamin Harrop-Griffiths (UCLA) as part of OARS Online Analysis Research S
eminar\n\n\nAbstract\nThe 1d cubic nonlinear Schrödinger equation (NLS) a
nd the modified Korteweg-de Vries equation (mKdV) are two of the most inte
nsively studied nonlinear dispersive equations. Not only are they importan
t physical models\, arising\, for example\, from the study of fluid dynami
cs 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 N
LS and mKdV on the line. An essential ingredient in our arguments is the d
emonstration of a local smoothing effect for both equations\, which in tur
n rests on the discovery of a one-parameter family of microscopic conserva
tion laws. This is joint work with Rowan Killip and Monica Vișan.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bruce (UW Madison)
DTSTART;VALUE=DATE-TIME:20210201T220000Z
DTEND;VALUE=DATE-TIME:20210201T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/12
DESCRIPTION:Title: Fourier restriction to hyperboloids\nby Ben Bruce (UW Madison) as
part of OARS Online Analysis Research Seminar\n\n\nAbstract\nThe restrict
ion conjecture is a major open problem in harmonic analysis concerning int
eractions between the Fourier transform and curved surfaces. While the ca
se of elliptic\, or positively curved\, surfaces has been studied most\, t
his talk will describe some recent results from non-elliptic settings. In
particular\, global restriction estimates for hyperboloids will be presen
ted.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Treuer (UC Irvine)
DTSTART;VALUE=DATE-TIME:20210208T220000Z
DTEND;VALUE=DATE-TIME:20210208T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/13
DESCRIPTION:Title: Rigidity theorem of the Bergman kernel and the analytic capacity\
nby John Treuer (UC Irvine) as part of OARS Online Analysis Research Semin
ar\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
integrable holomorphic functions on D. It is easily shown that the (on-di
agonal) Bergman kernel is bounded below by the reciprocal of the volume of
the domain D. In this talk\, I geometrically characterize the domains wh
ose Bergman kernels achieve the lower bound.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gennady Uraltsev (UVA)
DTSTART;VALUE=DATE-TIME:20210222T220000Z
DTEND;VALUE=DATE-TIME:20210222T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/14
DESCRIPTION:Title: Banach-valued time frequency analysis\nby Gennady Uraltsev (UVA)
as part of OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhan Li (UMN)
DTSTART;VALUE=DATE-TIME:20210301T220000Z
DTEND;VALUE=DATE-TIME:20210301T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/15
DESCRIPTION:Title: Carleson 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 d
omain is related to the flatness of the boundary of the domain. In a joint
work with Guy David and Svitlana Mayboroda\, we consider the Green functi
on for a second-order elliptic operator in the half-space. We show that if
the coefficients satisfy a quadratic Carleson condition\, then the Green
function is almost affine\, in the sense that the normalized difference be
tween the 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 conside
red cannot be improved.\n\nThis work is motivated mainly by finding PDE ch
aracterizations of uniformly rectifiable sets with higher co-dimension\, y
et our result is new of this kind in the co-dimension one setting as well.
\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton)
DTSTART;VALUE=DATE-TIME:20210308T220000Z
DTEND;VALUE=DATE-TIME:20210308T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160024Z
UID:OARS/16
DESCRIPTION:Title: On the polynomial Szemerédi theorem and related results\nby Sara
h Peluse (Princeton) as part of OARS Online Analysis Research Seminar\n\n\
nAbstract\nIn this talk\, I'll survey recent progress on problems in addit
ive combinatorics\, harmonic analysis\, and ergodic theory related to Berg
elson and Leibman's polynomial generalization of Szemerédi's theorem.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern)
DTSTART;VALUE=DATE-TIME:20210315T210000Z
DTEND;VALUE=DATE-TIME:20210315T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/17
DESCRIPTION:Title: Falconer's distance set problem\nby Xiumin Du (Northwestern) as p
art of OARS Online Analysis Research Seminar\n\n\nAbstract\nA classical qu
estion in geometric measure theory\, introduced by Falconer in the 80s is\
, how large does the Hausdorff dimension of a compact subset in Euclidean
space need to be to ensure that the Lebesgue measure of its set of pairwis
e Euclidean distances is positive. In this talk\, I'll report some recent
progress on this problem\, which combines several ingredients including Or
ponen's radial projection theorem\, Liu's L^2 identity obtained using a gr
oup action argument\, and the refined decoupling theory. This is based on
joint work with Alex Iosevich\, Yumeng Ou\, Hong Wang\, and Ruixiang Zhang
.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Cladek (UCLA)
DTSTART;VALUE=DATE-TIME:20210322T210000Z
DTEND;VALUE=DATE-TIME:20210322T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/18
DESCRIPTION:Title: Additive energy of regular measures in one and higher dimensions\, an
d the fractal uncertainty principle\nby Laura Cladek (UCLA) as part of
OARS Online Analysis Research Seminar\n\n\nAbstract\nWe obtain new bounds
on the additive energy of (Ahlfors-David type) regular measures in both o
ne and higher dimensions\, which implies expansion results for sums and pr
oducts 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 dimen
sions. This is joint work with Terence Tao.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (LSU)
DTSTART;VALUE=DATE-TIME:20210329T210000Z
DTEND;VALUE=DATE-TIME:20210329T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/19
DESCRIPTION:Title: A polynomial Roth theorem for corners in the finite field setting
\nby Rui Han (LSU) as part of OARS Online Analysis Research Seminar\n\nAbs
tract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Barron (UIUC)
DTSTART;VALUE=DATE-TIME:20210405T210000Z
DTEND;VALUE=DATE-TIME:20210405T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/20
DESCRIPTION:Title: A sharp global-in-time Strichartz estimate for the Schrodinger equati
on on the infinite cylinder\nby Alex Barron (UIUC) as part of OARS Onl
ine Analysis Research Seminar\n\n\nAbstract\nThe classical Strichartz esti
mates show that a solution to the linear Schrodinger equation on Euclidean
space is in certain Lebesgue spaces globally in time provided the initial
data is in L^2. On compact manifolds one can no longer have global contro
l\, and some loss of derivatives is necessary in interesting cases (meanin
g the initial data needs to be in a Sobolev space rather than L^2). On non
-compact manifolds it is a challenging problem to understand when one can
have good space-time estimates with no loss of derivatives. \n\nIn this ta
lk we discuss an endpoint Strichartz-type estimate for the linear Schrodin
ger equation on the infinite cylinder (or\, equivalently\, with one period
ic component and one Euclidean component). Our estimate is sharp\, scale-i
nvariant\, and requires only L^2 data. This contrasts the purely periodic
case where some loss of derivatives is necessary at the endpoint\, as orig
inally observed by Bourgain.\n\nJoint work with M. Christ and B. Pausader.
\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahaf Nitzan (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20210412T210000Z
DTEND;VALUE=DATE-TIME:20210412T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/21
DESCRIPTION:Title: What is a good definition of 'uniform completeness'?\nby Shahaf N
itzan (Georgia Tech) as part of OARS Online Analysis Research Seminar\n\n\
nAbstract\nWe discuss possible ways to define a notion of 'uniform complet
eness' as a dual notion for uniform minimality. We contrast these definiti
ons with a well known density theorem of Landau\, and a quantified version
of this theorem due to Olevskii and Ulanovskii. We show that analogs of t
hese results can be obtained for an appropriate notion of 'uniform complet
eness'.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS)
DTSTART;VALUE=DATE-TIME:20210419T210000Z
DTEND;VALUE=DATE-TIME:20210419T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/22
DESCRIPTION:Title: Stationary set method for estimating oscillatory integrals\nby Ru
ixiang Zhang (IAS) as part of OARS Online Analysis Research Seminar\n\n\nA
bstract\nGiven a polynomial $P$ of constant degree in $d$ variables and co
nsider the oscillatory integral $$I_P = \\int_{[0\,1]^d} e(P(\\xi)) \\math
rm{d}\\xi.$$ 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 ``station
ary set'' method that gives an upper bound with simple geometric meaning.
The proof of this bound mainly relies on the theory of o-minimal structure
s. As an application of our bound\, we obtain the sharp convergence expone
nt in the two dimensional Tarry's problem for every degree via additional
analysis on stationary sets. Consequently\, we also prove the sharp $L^{\\
infty} \\to L^p$ Fourier extension estimates for every two dimensional Par
sell-Vinogradov surface whenever the endpoint of the exponent $p$ is even.
This is joint work with Saugata Basu\, Shaoming Guo and Pavel Zorin-Krani
ch.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liding Yao (UW Madison)
DTSTART;VALUE=DATE-TIME:20210426T210000Z
DTEND;VALUE=DATE-TIME:20210426T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/23
DESCRIPTION:by Liding Yao (UW Madison) as part of OARS Online Analysis Res
earch Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itay Londner (UBC)
DTSTART;VALUE=DATE-TIME:20210503T170000Z
DTEND;VALUE=DATE-TIME:20210503T180000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/24
DESCRIPTION:Title: Tiling the integers with translates of one tile: the Coven-Meyerowitz
tiling conditions for three prime factors\nby Itay Londner (UBC) as p
art of OARS Online Analysis Research Seminar\n\n\nAbstract\nIt is well kno
wn that if a finite set of integers A tiles the integers by translations\,
then the translation set must be periodic\, so that the tiling is equival
ent to a factorization A+B=Z_M of a finite cyclic group. Coven and Meyerow
itz (1998) proved that when the tiling period M has at most two distinct p
rime factors\, each of the sets A and B can be replaced by a highly ordere
d "standard" tiling complement. It is not known whether this behavior pers
ists for all tilings with no restrictions on the number of prime factors o
f M.\n\nIn an ongoing collaboration with Izabella Laba\, we proved that th
is is true when M=(pqr)^2. In my talk I will discuss this problem and intr
oduce the main ingredients in the proof.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART;VALUE=DATE-TIME:20210510T210000Z
DTEND;VALUE=DATE-TIME:20210510T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/25
DESCRIPTION:Title: Invariant Gibbs measures for the three-dimensional wave equation with
a Hartree nonlinearity\nby Bjoern Bringmann (UCLA) as part of OARS On
line Analysis Research Seminar\n\n\nAbstract\nIn this talk\, we discuss th
e construction and invariance of the Gibbs measure for a three-dimensional
wave equation with a Hartree-nonlinearity.\n\nIn the first part of the ta
lk\, we construct the Gibbs measure and examine its properties. We discuss
the mutual singularity of the Gibbs measure and the so-called Gaussian fr
ee field. In contrast\, the Gibbs measure for one or two-dimensional wave
equations is absolutely continuous with respect to the Gaussian free field
.\n\nIn the second part of the talk\, we discuss the probabilistic well-po
sedness of the corresponding nonlinear wave equation\, which is needed in
the proof of invariance. At the moment\, this is the only theorem proving
the invariance of any singular Gibbs measure under a dispersive equation.\
n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART;VALUE=DATE-TIME:20211004T210000Z
DTEND;VALUE=DATE-TIME:20211004T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/26
DESCRIPTION:Title: The 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 (translational) tiling of $E$ by $F$ is a partition of $E$ into disjoint
translates $a+F\, a \\in A$ of $F$. The periodic tiling conjecture asser
ts 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
question of whether $E$ is tileable by $F$ at all is logically (or algori
thmically) decidable. This conjecture was established in the two-dimensio
nal case $G = {\\bf Z}^2$ by Bhattacharya by ergodic theory methods\; we p
resent a new and more quantitative proof of this fact\, based on a new str
uctural theorem for translational tilings. On the other hand\, we show th
at for higher dimensional groups the periodic tiling conjecture can fail i
f one uses two tiles $F_1\,F_2$ instead of one\; indeed\, the tiling probl
em can now become undecidable. This is established by developing a "tilin
g language" that can encode arbitrary Turing machines.\n\nThis is joint wo
rk with Rachel Greenfeld.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (Madison)
DTSTART;VALUE=DATE-TIME:20211101T210000Z
DTEND;VALUE=DATE-TIME:20211101T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
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
natural 3-dimensional analogue of Bourgain’s circular maximal function
theorem in the plane is the study of the sharp $L^p$ bounds in $\\mathbb{R
}^3$ for the maximal function associated with averages over dilates of the
helix (or\, more generally\, of any curve with non-vanishing curvature an
d torsion). In this talk\, we present a sharp result\, which establishes t
hat $L^p$ bounds hold if and only if $p>3$. This is joint work with Shaomi
ng Guo\, Jonathan Hickman and Andreas Seeger.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuqiu Fu (MIT)
DTSTART;VALUE=DATE-TIME:20211115T220000Z
DTEND;VALUE=DATE-TIME:20211115T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/28
DESCRIPTION:Title: Decoupling for short generalized Dirichlet sequences\nby Yuqiu Fu
(MIT) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe
will discuss 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 observat
ions we present decoupling inequalities for those sequences.\nThe sequence
$\\{\\log n\\}_{n=N+1}^{2N}$ is closely connected to a conjecture of Mont
gomery on Dirichlet polynomials but we see some difficulties in studying t
he sequence $\\{\\log n\\}_{n=N+1}^{N+N^{\\alpha}}$ for $\\alpha > 1/2$. T
his is joint work with Larry Guth and Dominique Maldague.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Jahnke (Federal U. São Carlos)
DTSTART;VALUE=DATE-TIME:20210920T210000Z
DTEND;VALUE=DATE-TIME:20210920T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/29
DESCRIPTION:by Max Jahnke (Federal U. São Carlos) as part of OARS Online
Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (Wichita)
DTSTART;VALUE=DATE-TIME:20211108T220000Z
DTEND;VALUE=DATE-TIME:20211108T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/30
DESCRIPTION:Title: Explicit Salem sets in R^n: an application of algebraic number theory
to Euclidean harmonic analysis\nby Robert Fraser (Wichita) as part of
OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tess Anderson (Purdue)
DTSTART;VALUE=DATE-TIME:20210927T210000Z
DTEND;VALUE=DATE-TIME:20210927T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/31
DESCRIPTION:Title: Dyadic analysis meets number theory\nby Tess Anderson (Purdue) as
part of OARS Online Analysis Research Seminar\n\n\nAbstract\nIn recent wo
rk we construct a measure that is $p$-adic and $q$-adic doubling for any c
oprime $p$ and $q$\, yet not doubling overall. The proof involves an intr
icate interplay of number theory\, geometry and analysis\, and here we giv
e an overview of some of the key features.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Holmes (Texas A&M)
DTSTART;VALUE=DATE-TIME:20211011T210000Z
DTEND;VALUE=DATE-TIME:20211011T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/32
DESCRIPTION:Title: A new proof of a weighted John-Nirenberg Theorem\, via sparse operato
rs\nby Irina Holmes (Texas A&M) as part of OARS Online Analysis Resear
ch Seminar\n\n\nAbstract\nIn this talk we revisit a result of Muckenhoupt
and Wheeden\, which gives a weighted version of the classical John-Nirenbe
rg Theorem (specifically for Ap weights). We will discuss a modern proof o
f this result\, using the recent machinery of sparse operators.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Mirek (Rutgers)
DTSTART;VALUE=DATE-TIME:20211206T220000Z
DTEND;VALUE=DATE-TIME:20211206T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/33
DESCRIPTION:by Mariusz Mirek (Rutgers) as part of OARS Online Analysis Res
earch Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton)
DTSTART;VALUE=DATE-TIME:20211018T210000Z
DTEND;VALUE=DATE-TIME:20211018T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/34
DESCRIPTION:Title: The Kakeya needle problem for rectifiable sets\nby Alan Chang (Pr
inceton) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nW
e show that the classical results about rotating a line segment in arbitra
rily small area\, and the existence of a Besicovitch and a Nikodym set hol
d if we replace the line segment by an arbitrary rectifiable set. This is
joint work with Marianna Csörnyei.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (UCLA)
DTSTART;VALUE=DATE-TIME:20211025T210000Z
DTEND;VALUE=DATE-TIME:20211025T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/35
DESCRIPTION:Title: Projection theorems and applications\nby Hong Wang (UCLA) as part
of OARS Online Analysis Research Seminar\n\n\nAbstract\nGiven a fractal s
et $E$ on the plane and a set $F$ of directions\, can we find one directio
n $\\theta\\in F$ such that the orthogonal projection $\\Pi_{\\theta} E$ i
s large?\n\nWe will survey some classical and modern projection theorems a
nd discuss their applications.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Harris (Cornell)
DTSTART;VALUE=DATE-TIME:20211129T220000Z
DTEND;VALUE=DATE-TIME:20211129T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/36
DESCRIPTION:Title: The behaviour of Hausdorff dimension under curved 1-dimensional famil
ies of projections\nby Terence Harris (Cornell) as part of OARS Online
Analysis Research Seminar\n\n\nAbstract\nGiven a curve C with nonvanishin
g geodesic curvature in the unit sphere of R^3\, it is an open problem whe
ther the Hausdorff dimension of an arbitrary set A is almost surely preser
ved under projection onto the orthogonal complements of vectors in C. In t
his talk I will outline some recent progress on this problem\, which makes
use of some Fourier restriction tools such as decoupling and wave packet
decompositions. Toward the end of the talk I will mention a couple of ope
n problems suggested by the approach.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingrui Cheng (Stony Brook)
DTSTART;VALUE=DATE-TIME:20220131T170000Z
DTEND;VALUE=DATE-TIME:20220131T180000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/37
DESCRIPTION:Title: A PDE approach to $L^\\infty$ estimate for parabolic complex Monge-Am
pere and Hessian equations\nby Jingrui Cheng (Stony Brook) as part of
OARS Online Analysis Research Seminar\n\n\nAbstract\nPreviously the $L^{\\
infty}$ and Holder estimates for complex Monge-Ampere were obtained using
pluri-potential theory. We consider a version of the parabolic complex Mon
ge-Ampere on compact Kähler manifolds using PDE approach\, generalizing t
he recent work by Guo\, Phong and Tong in the elliptic case.\n
LOCATION:https://master.researchseminars.org/talk/OARS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bodan Arsovski (Sheffield)
DTSTART;VALUE=DATE-TIME:20220214T170000Z
DTEND;VALUE=DATE-TIME:20220214T180000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/38
DESCRIPTION:Title: The p-adic Kakeya conjecture\nby Bodan Arsovski (Sheffield) as pa
rt of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe prove that a
ll bounded 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 $\\mathbb{R}$ rep
laced by $\\mathbb{Q}_p$.\n
LOCATION:https://master.researchseminars.org/talk/OARS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Prendiville (Lancaster)
DTSTART;VALUE=DATE-TIME:20220307T170000Z
DTEND;VALUE=DATE-TIME:20220307T180000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/39
DESCRIPTION:Title: Fourier analysis and nonlinear progressions of integers\nby Sean
Prendiville (Lancaster) as part of OARS Online Analysis Research Seminar\n
\n\nAbstract\nFourier analysis has proved a fundamental tool in analytic a
nd combinatorial number theory\, usually in the guise of the Hardy-Littlew
ood circle method. When applicable\, this method allows one to asymptotica
lly estimate the number of solutions to a given Diophantine equation with
variables constrained to a given finite set of integers. I will discuss re
cent work\, obtained jointly with Sarah Peluse\, which adapts the circle m
ethod to count the configuration $x\, x+y\, x+y^2$ in a quantitatively eff
ective manner.\n
LOCATION:https://master.researchseminars.org/talk/OARS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Denson (Madison)
DTSTART;VALUE=DATE-TIME:20220328T160000Z
DTEND;VALUE=DATE-TIME:20220328T170000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/40
DESCRIPTION:Title: Large Sets with Fourier Decay avoiding Patterns\nby Jacob Denson
(Madison) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\n
We discuss the construction of sets with large Fourier dimension avoiding
certain families of linear and non-linear patterns. In other words\, we co
nstruct sets which do not contain a certain subset of points arranged in a
particular configuration\, while also supporting probability measures who
se Fourier transforms exhibit polynomial decay. Our analysis involves a di
scussion of the concentration of measure phenomenon in probability\, and s
ome oscillatory integral estimates. As particular applications of these me
thods\, we will construct large sets of $\\mathbf{T}^d$ not containing poi
nts $x_1\,\\dots\,x_n$ solving linear equations of the form $a_1x_1 + ...
a_n x_n = b$\, and large subsets of planar curves with non-vanishing curva
ture which do not contain three points forming an isosceles triangle.\n
LOCATION:https://master.researchseminars.org/talk/OARS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico)
DTSTART;VALUE=DATE-TIME:20220404T160000Z
DTEND;VALUE=DATE-TIME:20220404T170000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/41
DESCRIPTION:Title: Sharp restriction theory: rigidity\, stability\, and symmetry breakin
g\nby Diogo Oliveira e Silva (Instituto Superior Técnico) as part of
OARS Online Analysis Research Seminar\n\n\nAbstract\nWe report on recent p
rogress concerning two distinct problems in sharp restriction theory to th
e unit sphere.\nFirstly\, the classical estimate of Agmon-Hörmander for t
he adjoint restriction operator to the sphere is in general not saturated
by constants. We describe the surprising intermittent behaviour exhibited
by the optimal constant and the space of maximizers\, both for the inequal
ity itself and for a stable form thereof.\nSecondly\, the Stein-Tomas ineq
uality on the sphere is rigid in the following rather strong sense: consta
nts continue to maximize the weighted inequality as long as the perturbati
on is sufficiently small and regular\, in a precise sense to be discussed.
We present several examples highlighting why such assumptions are natural
\, and describe some consequences to the (mostly unexplored) higher dimens
ional setting.\nThis talk is based on joint work with E. Carneiro and G. N
egro.\n
LOCATION:https://master.researchseminars.org/talk/OARS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galyna Livshyts (Georgia Tech)
DTSTART;VALUE=DATE-TIME:20220314T160000Z
DTEND;VALUE=DATE-TIME:20220314T170000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/42
DESCRIPTION:Title: Some emerging questions about isoperimetric type inequalities under s
ymmetry assumption\, their connections and partial results\nby Galyna
Livshyts (Georgia Tech) as part of OARS Online Analysis Research Seminar\n
\n\nAbstract\nI will talk about the Brunn-Minkowski inequality\, Ehrhard
’s inequality\, and some of their conjectured strengthenings — the Log
-Brunn-Minkowski conjecture\, the Dimensional Brunn-Minkowski conjecture\,
the “symmetric Ehrhard” conjecture\, the B-conjecture\, and all the v
arious relations between them. In addition to mentioning many open problem
s\, I will discuss the state of the art in this area\, and explain some of
my results in it. Finally\, I will talk a bit about a new conjectured str
engthening of the Brascamp-Leib inequality\, its potential (significant) i
mplications\, and partial progress towards it.\n
LOCATION:https://master.researchseminars.org/talk/OARS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xueying Yu (U Washington)
DTSTART;VALUE=DATE-TIME:20220919T210000Z
DTEND;VALUE=DATE-TIME:20220919T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/43
DESCRIPTION:Title: Unique continuation properties for generalized fourth-order Schrödin
ger equations\nby Xueying Yu (U Washington) as part of OARS Online Ana
lysis Research Seminar\n\n\nAbstract\nIn this talk\, we will discuss uniqu
eness properties of solutions to the linear generalized fourth-order Schr
ödinger equations. We show that a solution with fast enough decay in cert
ain Sobolev spaces at two different times has to be trivial. This is a joi
nt work with Zachary Lee.\n
LOCATION:https://master.researchseminars.org/talk/OARS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (U. Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20221003T210000Z
DTEND;VALUE=DATE-TIME:20221003T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/44
DESCRIPTION:Title: Families of functionals representing Sobolev norms\nby Andreas Se
eger (U. Wisconsin-Madison) as part of OARS Online Analysis Research Semin
ar\n\n\nAbstract\nThis talk is about various families of limit functionals
and weak type (quasi)-norms which represent the Lp norm of the gradient.
This extends and unifies work by Nguyen and by Brezis\, Van Schaftingen an
d Yung. We discuss some interesting counterexamples and open problems.\n\n
Joint work with Haïm Brezis\, Jean Van Schaftingen and Po Lam Yung.\n
LOCATION:https://master.researchseminars.org/talk/OARS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Green (Edinburgh/Penn)
DTSTART;VALUE=DATE-TIME:20221114T220000Z
DTEND;VALUE=DATE-TIME:20221114T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/45
DESCRIPTION:Title: Estimates for scalar oscillatory integrals: Structure\, stability and
methods that use them\nby John Green (Edinburgh/Penn) as part of OARS
Online Analysis Research Seminar\n\n\nAbstract\nOscillatory integrals are
a basic object of study in Harmonic Analysis and underpin many important
problems. The goal of this talk will be to reflect on some elementary yet
important observations on the role of structure in estimating oscillatory
integrals\, and to discuss some recent works that capture this philosophy.
\n
LOCATION:https://master.researchseminars.org/talk/OARS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Richter (EPFL)
DTSTART;VALUE=DATE-TIME:20221205T220000Z
DTEND;VALUE=DATE-TIME:20221205T230000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/46
DESCRIPTION:by Florian Richter (EPFL) as part of OARS Online Analysis Rese
arch Seminar\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/OARS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART;VALUE=DATE-TIME:20221017T210000Z
DTEND;VALUE=DATE-TIME:20221017T220000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/47
DESCRIPTION:by Dominique Maldague (MIT) as part of OARS Online Analysis Re
search Seminar\n\nAbstract: TBA\n
LOCATION:https://master.researchseminars.org/talk/OARS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornelia Hera (Alfréd Rényi Institute)
DTSTART;VALUE=DATE-TIME:20221031T180000Z
DTEND;VALUE=DATE-TIME:20221031T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/48
DESCRIPTION:Title: Hausdorff dimension of Besicovitch sets of Cantor graphs\nby Korn
elia Hera (Alfréd Rényi Institute) as part of OARS Online Analysis Resea
rch Seminar\n\n\nAbstract\nIt is well known that planar Besicovitch sets
– sets\ncontaining a unit line segment in every direction – have Hausd
orff\ndimension 2. In a joint work with Iqra Altaf and Marianna Csörnyei
we\nconsider Besicovitch sets of Cantor graphs in the plane– sets\nconta
ining a rotated (and translated) copy of a fixed Cantor graph\n(its line s
egments of course removed) in every direction\, and prove\nlower bounds fo
r their Hausdorff dimension.\n
LOCATION:https://master.researchseminars.org/talk/OARS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ren (Princeton)
DTSTART;VALUE=DATE-TIME:20230919T180000Z
DTEND;VALUE=DATE-TIME:20230919T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/49
DESCRIPTION:Title: Sharp Furstenberg sets estimate in the plane\nby Kevin Ren (Princ
eton) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nFix
two real 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
$\\mathcal{L}$ with Hausdorff dimension $t$ such that for each line $\\el
l \\in \\mathcal{L}$\, we have $\\dim_H (E \\cap \\ell) \\ge s$. (For exam
ple\, a Kakeya set in $\\mathbb{R}^2$ is a special case of a $(1\, 1)$-Fur
stenberg set.) The Furstenberg sets problem asks for the minimum possible
Hausdorff dimension of a $(s\, t)$-Furstenberg set for any given pair of $
s\, t$. In this talk\, I will illustrate the rich theory linking this prob
lem to the discretized sum-product problem\, orthogonal projections\, and
the high-low method in Fourier analysis. Joint works with Yuqiu Fu and Hon
g Wang.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Becker (Bonn)
DTSTART;VALUE=DATE-TIME:20231003T180000Z
DTEND;VALUE=DATE-TIME:20231003T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/50
DESCRIPTION:Title: Maximal modulations of singular Radon transforms\nby Lars Becker
(Bonn) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nCar
leson's theorem on the convergence of Fourier series is\nequivalent to the
weak-$L^2$-boundedness of the maximally modulated\nHilbert transform\, an
d adaptions of the proof show more generally\nweak-$L^2$-boundedness of ma
ximally modulated Calderón-Zygmund operators.\nThis talk is about the ope
n problem of whether this result can be extended\nto singular Radon transf
orms\, such as the Hilbert transform along the\nparabola $H_P$. I will dis
cuss the main ingredients used in the proof of\nCarleson's theorem\, and t
o what extent they can be adapted for $H_P$. A\ncorollary are improved qua
ntitative estimates for maximal modulations of\noperators approximating $H
_P$.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Rutar (St Andrews)
DTSTART;VALUE=DATE-TIME:20231017T180000Z
DTEND;VALUE=DATE-TIME:20231017T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/51
DESCRIPTION:Title: Assouad-type dimensions: finer information on scaling and homogeneity
\nby Alex Rutar (St Andrews) as part of OARS Online Analysis Research
Seminar\n\n\nAbstract\nThe Assouad dimension is a notion of dimension whic
h captures the worst-case scaling of a set at all locations and all scales
. However\, in many situations the Assouad dimension measures scaling in a
way which is too coarse\, and quantifying the precise resolution at which
larger-than-average scaling occurs has been important in applications. In
this talk\, I will give an introduction and overview of recent work on va
riations of the Assouad dimension. I will also touch on some recent applic
ations in the literature including: large deviations of branching processe
s\, smoothness of iterated function system attractors\, quasi-conformal di
stortion of sets\, and $L^p$-improving properties of maximal operators wit
h restricted dilation sets.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingyuan Liu (U. Texas Rio Grande Valley)
DTSTART;VALUE=DATE-TIME:20231114T190000Z
DTEND;VALUE=DATE-TIME:20231114T200000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
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:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART;VALUE=DATE-TIME:20231128T190000Z
DTEND;VALUE=DATE-TIME:20231128T200000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/53
DESCRIPTION:by Cosmin Pohoata (Emory University) as part of OARS Online An
alysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ravi Shankar (Princeton University)
DTSTART;VALUE=DATE-TIME:20240305T190000Z
DTEND;VALUE=DATE-TIME:20240305T200000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/54
DESCRIPTION:Title: Doubling inequalities for nonlinear elliptic PDEs\nby Ravi Shanka
r (Princeton University) as part of OARS Online Analysis Research Seminar\
n\n\nAbstract\nFully nonlinear elliptic PDEs include the Monge-Ampere equa
tion from optimal transport and the PDEs for constructing minimal surfaces
of high codimension. Such PDEs can be solved in the weak\, viscosity sen
se\, so the question is whether such solutions are smooth\, or what kinds
of singularities are possible. In the past\, these questions were solved
for each equation using very different approaches. In this talk\, we indi
cate a unified approach to these questions and equations\, based on the id
ea of a doubling inequality.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART;VALUE=DATE-TIME:20240319T180000Z
DTEND;VALUE=DATE-TIME:20240319T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/55
DESCRIPTION:by Cosmin Pohoata (Emory University) as part of OARS Online An
alysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen Do (University of Virginia)
DTSTART;VALUE=DATE-TIME:20240405T180000Z
DTEND;VALUE=DATE-TIME:20240405T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/56
DESCRIPTION:Title: Real roots of random algebraic polynomials\nby Yen Do (University
of Virginia) as part of OARS Online Analysis Research Seminar\n\n\nAbstra
ct\nThe number of real roots for random algebraic polynomials is a topic w
ith a long history and contributions of many authors. In this talk\, I wil
l discuss a brief history of the topic and some recent developments.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tainara Borges (Brown University)
DTSTART;VALUE=DATE-TIME:20240416T180000Z
DTEND;VALUE=DATE-TIME:20240416T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/57
DESCRIPTION:Title: Sobolev smoothing estimates for bilinear maximal operators with fract
al dilation 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 a
verages a pair of functions over S\, as well as more general bilinear mult
ipliers of limited decay and various maximal analogs. Of particular intere
st are bilinear maximal operators associated to a fractal dilation set $E\
\subset [1\,2]$\; in this case\, the boundedness region of the maximal ope
rator is associated to the geometry of the hypersurface and various notion
s of the dimension of the dilation set. In particular\, we determine Sobol
ev smoothing estimates at the exponent $L^{2}\\times L^{2}\\rightarrow L^2
$ using Fourier-analytic methods\, which allow us to deduce additional $L^
{p}$ improving bounds for the operators and sparse bounds and their weight
ed corollaries for the associated multi-scale maximal functions. We also e
xtend the method to study analogues of these questions for the triangle av
eraging operator and biparameter averaging operators. In addition\, some n
ecessary conditions for boundedness of these operators are obtained.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manik Dhar (Massachusetts Institute of Technology)
DTSTART;VALUE=DATE-TIME:20240429T180000Z
DTEND;VALUE=DATE-TIME:20240429T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/58
DESCRIPTION:by Manik Dhar (Massachusetts Institute of Technology) as part
of OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camil Muscalu (Cornell University)
DTSTART;VALUE=DATE-TIME:20240917T180000Z
DTEND;VALUE=DATE-TIME:20240917T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/59
DESCRIPTION:Title: A new approach to the Fourier Extension Problem for the paraboloid\nby Camil Muscalu (Cornell University) as part of OARS Online Analysis R
esearch Seminar\n\n\nAbstract\nThe plan of the talk is to describe a new a
pproach to the so-called Restriction Conjectures\, that Itamar Oliveira an
d I have developed recently. Without entering into details\, this new poin
t of view allows one to prove that (essentially) all the relevant conjectu
res (linear or multi-linear) are true\, provided that one of the functions
involved has a tensor structure.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Albesiano (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20241001T180000Z
DTEND;VALUE=DATE-TIME:20241001T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/60
DESCRIPTION:Title: A degeneration approach to Skoda’s division theorem\nby Roberto
Albesiano (University of Waterloo) as part of OARS Online Analysis Resear
ch Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandar Bulj (University of Zagreb)
DTSTART;VALUE=DATE-TIME:20241015T180000Z
DTEND;VALUE=DATE-TIME:20241015T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/61
DESCRIPTION:Title: Powers of unimodular homogeneous multipliers\nby Aleksandar Bulj
(University of Zagreb) as part of OARS Online Analysis Research Seminar\n\
n\nAbstract\nWe study asymptotically sharp estimates for the $L^p\\to L^p$
norms of multipliers associated with unimodular homogeneous symbols of de
gree 0\, i.e. multipliers associated with symbols $\\xi\\mapsto \\exp(i\\l
ambda\\Phi(\\xi/|\\xi|))$\, where $\\lambda$ is a real number and $\\Phi \
\in C^{\\infty}(S^{n-1})$.\nWe show that that the powers of a generic mult
iplier in that class exhibit asymptotically maximal order of growth. As a
consequence\, we disprove Maz'ya's conjecture regarding the asymptotically
sharp estimates of such multipliers in all dimensions and solve the probl
em posed by Dragicevic\, Petermichl\, and Volberg concerning the sharp low
er estimate of a certain multiplier falling within the mentioned class.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (University of South Carolina)
DTSTART;VALUE=DATE-TIME:20241029T180000Z
DTEND;VALUE=DATE-TIME:20241029T190000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/62
DESCRIPTION:by Haonan Zhang (University of South Carolina) as part of OARS
Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Gressman (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20241112T190000Z
DTEND;VALUE=DATE-TIME:20241112T200000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/63
DESCRIPTION:by Phil Gressman (University of Pennsylvania) as part of OARS
Online Analysis Research Seminar\n\nInteractive livestream: https://uml.zo
om.us/j/93784530288\nAbstract: TBA\n
LOCATION:https://uml.zoom.us/j/93784530288
URL:https://uml.zoom.us/j/93784530288
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Niedorf (University of Wisconsin-Madison)
DTSTART;VALUE=DATE-TIME:20241126T190000Z
DTEND;VALUE=DATE-TIME:20241126T200000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/64
DESCRIPTION:Title: Restriction type estimates and spectral multipliers on Métivier grou
ps\nby Lars Niedorf (University of Wisconsin-Madison) as part of OARS
Online Analysis Research Seminar\n\nInteractive livestream: https://uml.zo
om.us/j/93784530288\n\nAbstract\nWe present a restriction type estimate fo
r sub-Laplacians on arbitrary two-step stratified Lie groups. Although wea
ker than previously known estimates for the subclass of Heisenberg type gr
oups\, these estimates turn out to be sufficient to prove an $L^p$-spectra
l multiplier theorem with sharp regularity condition $s > d|1/p-1/2|$ for
sub-Laplacians on Métivier groups.\n
LOCATION:https://uml.zoom.us/j/93784530288
URL:https://uml.zoom.us/j/93784530288
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Karam (University of Oxford)
DTSTART;VALUE=DATE-TIME:20241210T190000Z
DTEND;VALUE=DATE-TIME:20241210T200000Z
DTSTAMP;VALUE=DATE-TIME:20241107T160025Z
UID:OARS/65
DESCRIPTION:by Thomas Karam (University of Oxford) as part of OARS Online
Analysis Research Seminar\n\nInteractive livestream: https://uml.zoom.us/j
/93784530288\nAbstract: TBA\n
LOCATION:https://uml.zoom.us/j/93784530288
URL:https://uml.zoom.us/j/93784530288
END:VEVENT
END:VCALENDAR