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BEGIN:VEVENT
SUMMARY:Jongchon Kim (UBC)
DTSTART:20201005T210000Z
DTEND:20201005T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 1/">Maximal functions associated with a set of directions</a>\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:https://stable.researchseminars.org/talk/OARS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rajula Srivastava (UW Madison)
DTSTART:20201012T210000Z
DTEND:20201012T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 2/">Orthogonal systems of spline wavelets as unconditional bases in Sobole
 v spaces</a>\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:https://stable.researchseminars.org/talk/OARS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bartosz Langowski (IU Bloomington)
DTSTART:20201019T210000Z
DTEND:20201019T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 3/">Lattice point problems\, equidistribution and ergodic theorems for cer
 tain arithmetic spheres</a>\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:https://stable.researchseminars.org/talk/OARS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ntekoume (Rice)
DTSTART:20201026T210000Z
DTEND:20201026T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 4/">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:https://stable.researchseminars.org/talk/OARS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changkeun Oh (UW Madison)
DTSTART:20201102T220000Z
DTEND:20201102T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 5/">Restriction estimates for various surfaces</a>\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:https://stable.researchseminars.org/talk/OARS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shukun Wu (UIUC)
DTSTART:20201109T220000Z
DTEND:20201109T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 6/">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:https://stable.researchseminars.org/talk/OARS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin O'Neill (UC Davis)
DTSTART:20201116T220000Z
DTEND:20201116T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 7/">A Nonnegative Version of Whitney's Extension Problem</a>\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:https://stable.researchseminars.org/talk/OARS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Kemp (IU Bloomington)
DTSTART:20201130T220000Z
DTEND:20201130T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 8/">A weakening of the curvature condition in $\\mathbb{R}^3$ for $\\ell^p
 $ decoupling</a>\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:https://stable.researchseminars.org/talk/OARS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaume de Dios Pont (UCLA)
DTSTART:20201207T220000Z
DTEND:20201207T230000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adi Glücksam (University of Toronto)
DTSTART:20201214T220000Z
DTEND:20201214T230000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Harrop-Griffiths (UCLA)
DTSTART:20210125T220000Z
DTEND:20210125T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/11
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 11/">Sharp well-posedness for the cubic NLS and mKdV on the line</a>\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:https://stable.researchseminars.org/talk/OARS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Bruce (UW Madison)
DTSTART:20210201T220000Z
DTEND:20210201T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/12
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 12/">Fourier restriction to hyperboloids</a>\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:https://stable.researchseminars.org/talk/OARS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Treuer (UC Irvine)
DTSTART:20210208T220000Z
DTEND:20210208T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/13
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 13/">Rigidity theorem of the Bergman kernel and the analytic capacity</a>\
 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:https://stable.researchseminars.org/talk/OARS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gennady Uraltsev (UVA)
DTSTART:20210222T220000Z
DTEND:20210222T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/14
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 14/">Banach-valued time frequency analysis</a>\nby Gennady Uraltsev (UVA) 
 as part of OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Linhan Li (UMN)
DTSTART:20210301T220000Z
DTEND:20210301T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/15
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 15/">Carleson measure estimates for the Green function</a>\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:https://stable.researchseminars.org/talk/OARS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sarah Peluse (Princeton)
DTSTART:20210308T220000Z
DTEND:20210308T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/16
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 16/">On the polynomial Szemerédi theorem and related results</a>\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:https://stable.researchseminars.org/talk/OARS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiumin Du (Northwestern)
DTSTART:20210315T210000Z
DTEND:20210315T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/17
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 17/">Falconer's distance set problem</a>\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:https://stable.researchseminars.org/talk/OARS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Cladek (UCLA)
DTSTART:20210322T210000Z
DTEND:20210322T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/18
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 18/">Additive energy of regular measures in one and higher dimensions\, an
 d the fractal uncertainty principle</a>\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:https://stable.researchseminars.org/talk/OARS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rui Han (LSU)
DTSTART:20210329T210000Z
DTEND:20210329T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/19
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 19/">A polynomial Roth theorem for corners in the finite field setting</a>
 \nby Rui Han (LSU) as part of OARS Online Analysis Research Seminar\n\nAbs
 tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Barron (UIUC)
DTSTART:20210405T210000Z
DTEND:20210405T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/20
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 20/">A sharp global-in-time Strichartz estimate for the Schrodinger equati
 on on the infinite cylinder</a>\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:https://stable.researchseminars.org/talk/OARS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahaf Nitzan (Georgia Tech)
DTSTART:20210412T210000Z
DTEND:20210412T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/21
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 21/">What is a good definition of 'uniform completeness'?</a>\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:https://stable.researchseminars.org/talk/OARS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS)
DTSTART:20210419T210000Z
DTEND:20210419T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/22
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 22/">Stationary set method for estimating oscillatory integrals</a>\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:https://stable.researchseminars.org/talk/OARS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liding Yao (UW Madison)
DTSTART:20210426T210000Z
DTEND:20210426T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/23
DESCRIPTION:by Liding Yao (UW Madison) as part of OARS Online Analysis Res
 earch Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itay Londner (UBC)
DTSTART:20210503T170000Z
DTEND:20210503T180000Z
DTSTAMP:20260404T110958Z
UID:OARS/24
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 24/">Tiling the integers with translates of one tile: the Coven-Meyerowitz
  tiling conditions for three prime factors</a>\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:https://stable.researchseminars.org/talk/OARS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bjoern Bringmann (UCLA)
DTSTART:20210510T210000Z
DTEND:20210510T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/25
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 25/">Invariant Gibbs measures for the three-dimensional wave equation with
  a Hartree nonlinearity</a>\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:https://stable.researchseminars.org/talk/OARS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Tao (UCLA)
DTSTART:20211004T210000Z
DTEND:20211004T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/26
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 26/">The structure of translational tilings</a>\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:https://stable.researchseminars.org/talk/OARS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Beltran (Madison)
DTSTART:20211101T210000Z
DTEND:20211101T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/27
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 27/">$L^p$ bounds for the helical maximal function</a>\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:https://stable.researchseminars.org/talk/OARS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuqiu Fu (MIT)
DTSTART:20211115T220000Z
DTEND:20211115T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/28
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 28/">Decoupling for short generalized Dirichlet sequences</a>\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:https://stable.researchseminars.org/talk/OARS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Jahnke (Federal U. São Carlos)
DTSTART:20210920T210000Z
DTEND:20210920T220000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Fraser (Wichita)
DTSTART:20211108T220000Z
DTEND:20211108T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/30
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 30/">Explicit Salem sets in R^n: an application of algebraic number theory
  to Euclidean harmonic analysis</a>\nby Robert Fraser (Wichita) as part of
  OARS Online Analysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tess Anderson (Purdue)
DTSTART:20210927T210000Z
DTEND:20210927T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/31
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 31/">Dyadic analysis meets number theory</a>\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:https://stable.researchseminars.org/talk/OARS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Holmes (Texas A&M)
DTSTART:20211011T210000Z
DTEND:20211011T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/32
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 32/">A new proof of a weighted John-Nirenberg Theorem\, via sparse operato
 rs</a>\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:https://stable.researchseminars.org/talk/OARS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Mirek (Rutgers)
DTSTART:20211206T220000Z
DTEND:20211206T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/33
DESCRIPTION:by Mariusz Mirek (Rutgers) as part of OARS Online Analysis Res
 earch Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Chang (Princeton)
DTSTART:20211018T210000Z
DTEND:20211018T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/34
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 34/">The Kakeya needle problem for rectifiable sets</a>\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:https://stable.researchseminars.org/talk/OARS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hong Wang (UCLA)
DTSTART:20211025T210000Z
DTEND:20211025T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/35
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 35/">Projection theorems and applications</a>\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:https://stable.researchseminars.org/talk/OARS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Terence Harris (Cornell)
DTSTART:20211129T220000Z
DTEND:20211129T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/36
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 36/">The behaviour of Hausdorff dimension under curved 1-dimensional famil
 ies of projections</a>\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:https://stable.researchseminars.org/talk/OARS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingrui Cheng (Stony Brook)
DTSTART:20220131T170000Z
DTEND:20220131T180000Z
DTSTAMP:20260404T110958Z
UID:OARS/37
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 37/">A PDE approach to $L^\\infty$ estimate for parabolic complex Monge-Am
 pere and Hessian equations</a>\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://stable.researchseminars.org/talk/OARS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bodan Arsovski (Sheffield)
DTSTART:20220214T170000Z
DTEND:20220214T180000Z
DTSTAMP:20260404T110958Z
UID:OARS/38
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 38/">The p-adic Kakeya conjecture</a>\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://stable.researchseminars.org/talk/OARS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Prendiville (Lancaster)
DTSTART:20220307T170000Z
DTEND:20220307T180000Z
DTSTAMP:20260404T110958Z
UID:OARS/39
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 39/">Fourier analysis and nonlinear progressions of integers</a>\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://stable.researchseminars.org/talk/OARS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Denson (Madison)
DTSTART:20220328T160000Z
DTEND:20220328T170000Z
DTSTAMP:20260404T110958Z
UID:OARS/40
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 40/">Large Sets with Fourier Decay avoiding Patterns</a>\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://stable.researchseminars.org/talk/OARS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico)
DTSTART:20220404T160000Z
DTEND:20220404T170000Z
DTSTAMP:20260404T110958Z
UID:OARS/41
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 41/">Sharp restriction theory: rigidity\, stability\, and symmetry breakin
 g</a>\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://stable.researchseminars.org/talk/OARS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galyna Livshyts (Georgia Tech)
DTSTART:20220314T160000Z
DTEND:20220314T170000Z
DTSTAMP:20260404T110958Z
UID:OARS/42
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 42/">Some emerging questions about isoperimetric type inequalities under s
 ymmetry assumption\, their connections and partial results</a>\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://stable.researchseminars.org/talk/OARS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xueying Yu (U Washington)
DTSTART:20220919T210000Z
DTEND:20220919T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/43
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 43/">Unique continuation properties for generalized fourth-order Schrödin
 ger equations</a>\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://stable.researchseminars.org/talk/OARS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Seeger (U. Wisconsin-Madison)
DTSTART:20221003T210000Z
DTEND:20221003T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/44
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 44/">Families of functionals representing Sobolev norms</a>\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://stable.researchseminars.org/talk/OARS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Green (Edinburgh/Penn)
DTSTART:20221114T220000Z
DTEND:20221114T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/45
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 45/">Estimates for scalar oscillatory integrals: Structure\, stability and
  methods that use them</a>\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://stable.researchseminars.org/talk/OARS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Richter (EPFL)
DTSTART:20221205T220000Z
DTEND:20221205T230000Z
DTSTAMP:20260404T110958Z
UID:OARS/46
DESCRIPTION:by Florian Richter (EPFL) as part of OARS Online Analysis Rese
 arch Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Maldague (MIT)
DTSTART:20221017T210000Z
DTEND:20221017T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/47
DESCRIPTION:by Dominique Maldague (MIT) as part of OARS Online Analysis Re
 search Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kornelia Hera (Alfréd Rényi Institute)
DTSTART:20221031T180000Z
DTEND:20221031T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/48
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 48/">Hausdorff dimension of Besicovitch sets of Cantor graphs</a>\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://stable.researchseminars.org/talk/OARS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Ren (Princeton)
DTSTART:20230919T180000Z
DTEND:20230919T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/49
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 49/">Sharp Furstenberg sets estimate in the plane</a>\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$. In this talk\, I will illustrate the rich theory linking this prob
 lem to the discretized sum-product problem\, orthogonal projections\, and 
 the high-low method in Fourier analysis. Joint works with Yuqiu Fu and Hon
 g Wang.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Becker (Bonn)
DTSTART:20231003T180000Z
DTEND:20231003T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/50
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 50/">Maximal modulations of singular Radon transforms</a>\nby Lars Becker 
 (Bonn) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\nCar
 leson's theorem on the convergence of Fourier series is\nequivalent to the
  weak-$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:https://stable.researchseminars.org/talk/OARS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Rutar (St Andrews)
DTSTART:20231017T180000Z
DTEND:20231017T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/51
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 51/">Assouad-type dimensions: finer information on scaling and homogeneity
 </a>\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:https://stable.researchseminars.org/talk/OARS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bingyuan Liu (U. Texas Rio Grande Valley)
DTSTART:20231114T190000Z
DTEND:20231114T200000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART:20231128T190000Z
DTEND:20231128T200000Z
DTSTAMP:20260404T110958Z
UID:OARS/53
DESCRIPTION:by Cosmin Pohoata (Emory University) as part of OARS Online An
 alysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ravi Shankar (Princeton University)
DTSTART:20240305T190000Z
DTEND:20240305T200000Z
DTSTAMP:20260404T110958Z
UID:OARS/54
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 54/">Doubling inequalities for nonlinear elliptic PDEs</a>\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:https://stable.researchseminars.org/talk/OARS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cosmin Pohoata (Emory University)
DTSTART:20240319T180000Z
DTEND:20240319T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/55
DESCRIPTION:by Cosmin Pohoata (Emory University) as part of OARS Online An
 alysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yen Do (University of Virginia)
DTSTART:20240405T180000Z
DTEND:20240405T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/56
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 56/">Real roots of random algebraic polynomials</a>\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:https://stable.researchseminars.org/talk/OARS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tainara Borges (Brown University)
DTSTART:20240416T180000Z
DTEND:20240416T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/57
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 57/">Sobolev smoothing estimates for bilinear maximal operators with fract
 al dilation sets</a>\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:https://stable.researchseminars.org/talk/OARS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manik Dhar (Massachusetts Institute of Technology)
DTSTART:20240429T180000Z
DTEND:20240429T190000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Camil Muscalu (Cornell University)
DTSTART:20240917T180000Z
DTEND:20240917T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/59
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 59/">A new approach to the Fourier Extension Problem for the paraboloid</a
 >\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:https://stable.researchseminars.org/talk/OARS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roberto Albesiano (University of Waterloo)
DTSTART:20241001T180000Z
DTEND:20241001T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/60
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 60/">A degeneration approach to Skoda’s division theorem</a>\nby Roberto
  Albesiano (University of Waterloo) as part of OARS Online Analysis Resear
 ch Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksandar Bulj (University of Zagreb)
DTSTART:20241015T180000Z
DTEND:20241015T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/61
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 61/">Powers of unimodular homogeneous multipliers</a>\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:https://stable.researchseminars.org/talk/OARS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (University of South Carolina)
DTSTART:20241029T180000Z
DTEND:20241029T190000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phil Gressman (University of Pennsylvania)
DTSTART:20241112T190000Z
DTEND:20241112T200000Z
DTSTAMP:20260404T110958Z
UID:OARS/63
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 63/">Understanding affine symmetry in geometric harmonic analysis</a>\nby 
 Phil Gressman (University of Pennsylvania) as part of OARS Online Analysis
  Research Seminar\n\n\nAbstract\nMany geometrically-inspired problems of i
 nterest in harmonic analysis\, including $L^p$-improving properties of Rad
 on-like transforms and appropriate formulations of the Fourier restriction
  problem\, exhibit natural affine invariance. In some cases\, this can mea
 n that the geometry of submanifolds viewed as subsets of Euclidean space f
 ails to capture important subtleties in much the same way that understandi
 ng the size of the entries of a matrix fails to capture its nondegeneracy 
 properties. In this talk\, I will discuss how these ideas relate to recent
  work on characterizing the $L^p-L^q$ norm of Radon-like transforms for pa
 irs $(1/p\,1/q)$ on a natural scaling line. Along the way\, natural connec
 tions to Geometric Invariant Theory will be described. This work is part o
 f a broader project to understand other geometrically-flavored nonnegative
  operators related to fractional integration\; some initial work on this b
 roader project will be presented as time permits.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lars Niedorf (University of Wisconsin-Madison)
DTSTART:20241126T190000Z
DTEND:20241126T200000Z
DTSTAMP:20260404T110958Z
UID:OARS/64
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 64/">Restriction type estimates and spectral multipliers on Métivier grou
 ps</a>\nby Lars Niedorf (University of Wisconsin-Madison) as part of OARS 
 Online Analysis Research Seminar\n\n\nAbstract\nWe present a restriction t
 ype estimate for sub-Laplacians on arbitrary two-step stratified Lie group
 s. Although weaker than previously known estimates for the subclass of Hei
 senberg type groups\, these estimates turn out to be sufficient to prove a
 n $L^p$-spectral multiplier theorem with sharp regularity condition $s > d
 |1/p-1/2|$ for sub-Laplacians on Métivier groups.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Karam (University of Oxford)
DTSTART:20241210T190000Z
DTEND:20241210T200000Z
DTSTAMP:20260404T110958Z
UID:OARS/65
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 65/">The structure of a function and small images</a>\nby Thomas Karam (Un
 iversity of Oxford) as part of OARS Online Analysis Research Seminar\n\n\n
 Abstract\nIt is well known that if $G$ is an abelian group and $A$ is a fi
 nite subset of $G$ which minimises the size of $A+A$ for a fixed size of $
 A$\, then $A$ must essentially be as close as possible to being a coset of
  some subgroup of $G$: for instance\, if $G$ is finite then the set $A$ mu
 st be a coset in $G$ (provided that $G$ has subgroups with size $|A|$)\, a
 nd 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
  functions than addition on abelian groups: if $X$ is a set and $F: X \\ti
 mes X \\rightarrow X$ is a function\, then can the structure of $F$ (to th
 e extent that there is some) be read from the structure of the sets $A$ mi
 nimising the size of the image $F(A\,A)$ for a fixed size of $A$ ? We will
  discuss the progress that has been made in this direction and what remain
 s to be understood.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paata Ivanisvili (University of California Irvine)
DTSTART:20250211T210000Z
DTEND:20250211T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/66
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 66/">Jackson's inequality on the hypercube</a>\nby Paata Ivanisvili (Unive
 rsity of California Irvine) as part of OARS Online Analysis Research Semin
 ar\n\n\nAbstract\nI will talk about the uniform polynomial approximation p
 roblem on the hypercube of dimension $n$. I will present two results\, fir
 st indicating that there is a threshold power $n/2$\, i.e.\, polynomials o
 f degree at most $0.4999n$ will not always approximate well enough functio
 ns of constant sensitivity. The second result\, on the opposite side\, giv
 es quantitative estimates on the error of approximation when  degree is cl
 ose to $n$. There will be two applications presented: one showing that sen
 sitivity theorem does not hold for bounded real valued functions when degr
 ee is replaced by approximate degree. The second application will be a cou
 nterexample to reverse Markov-Bernstein inequality  for functions in $L^1$
  tail space having frequencies at least $0.4999n$. This is joint work with
  Roman Vershynin and Xinyuan Xie.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingfeng Chen (University of Wisconsin-Madison)
DTSTART:20250225T210000Z
DTEND:20250225T220000Z
DTSTAMP:20260404T110958Z
UID:OARS/67
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 67/">The dichotomy of Nikodym sets and local smoothing estimates for wave 
 equations</a>\nby Mingfeng Chen (University of Wisconsin-Madison) as part 
 of OARS Online Analysis Research Seminar\n\n\nAbstract\nWe show that Nikod
 ym sets and local smoothing estimates for linear wave equations form a dic
 hotomy: If Nikodym sets for a family of curves exist\, then the related ma
 ximal operator is not bounded on $L^p(\\mathbb{R}^2)$ for any $p<\\infty$\
 ; if Nikodym sets do not exist\, then local smoothing estimates hold\, and
  the related maximal operator is bounded on $L^p(\\mathbb{R}^2)$ for some 
 $p<\\infty$. We also determine the sharp exponent for $L^p$ bounds. This i
 s joint work with Shaoming Guo.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20250311T200000Z
DTEND:20250311T210000Z
DTSTAMP:20260404T110958Z
UID:OARS/68
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 68/">Rectifiability in Carnot groups</a>\nby Daniela Di Donato (University
  of Pavia) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\
 nIntrinsic regular surfaces in Carnot groups play the same role as $C^1$ s
 urfaces in Euclidean spaces. As in Euclidean spaces\, intrinsic regular su
 rfaces can be locally defined in different ways: e.g. as non critical leve
 l sets or as continuously intrinsic differentiable graphs. The equivalence
  of these natural definitions is the problem that we are studying. Precise
 ly our aim is to generalize some results proved by Ambrosio\, Serra Cassan
 o\, Vittone valid in Heisenberg groups to the more general setting of Carn
 ot groups. This is joint work with Antonelli\, Don and Le Donne\n
LOCATION:https://stable.researchseminars.org/talk/OARS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis White (University of California Irvine)
DTSTART:20250325T200000Z
DTEND:20250325T210000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Bedert (University of Oxford)
DTSTART:20250429T200000Z
DTEND:20250429T210000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Cairo (University of California\, Berkeley)
DTSTART:20250408T200000Z
DTEND:20250408T210000Z
DTSTAMP:20260404T110958Z
UID:OARS/71
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 71/">A counterexample to the Mizohata-Takeuchi Conjecture</a>\nby Hannah C
 airo (University of California\, Berkeley) as part of OARS Online Analysis
  Research Seminar\n\nAbstract: TBA\n\nWe derive a family of $L^p$ estimate
 s of the X-Ray transform of positive measures in $\\mathbb{R}^d$\, which w
 e use to construct a log $R$-loss counterexample to the Mizohata-Takeuchi 
 conjecture for every $C^2$ hypersurface in $\\mathbb{R}^d$ that does not l
 ie in a hyperplane. In particular\, multilinear restriction estimates at t
 he endpoint cannot be sharpened directly by the Mizohata-Takeuchi conjectu
 re.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehtaab Sawhney (Columbia University)
DTSTART:20251007T180000Z
DTEND:20251007T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/72
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 72/">Quasipolynomial bounds for the corners theorem</a>\nby Mehtaab Sawhne
 y (Columbia University) as part of OARS Online Analysis Research Seminar\n
 \n\nAbstract\nWe discuss recent quasipolynomial bounds for the corners the
 orem. We will zoom in on the application of graph counting lemmas in this 
 arithmetic problem and explain how variations of densification (as develop
 ed by Conlon\, Fox and Zhao) appear in our work.\nBased on joint work with
  Michael Jaber\, Yang P Liu\, Shachar Lovett and Anthony Ostuni.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Fraccaroli (University of Massachusetts Lowell)
DTSTART:20251021T180000Z
DTEND:20251021T190000Z
DTSTAMP:20260404T110958Z
UID:OARS/73
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 73/">Endpoint estimates for Fourier multipliers with Zygmund singularities
 </a>\nby Marco Fraccaroli (University of Massachusetts Lowell) as part of 
 OARS Online Analysis Research Seminar\n\n\nAbstract\nThe Hilbert transform
  maps $L^1$ functions into $L^{1\,\\infty}$ ones. In fact\, this estimate 
 holds true for any operator $T_m$ defined by a bounded Fourier multiplier 
 $m$ with singularity only in the origin. Tao and Wright identified the spa
 ce replacing $L^1$ in the endpoint estimate for $T_m$ when $m$ has singula
 rities in a lacunary set of frequencies\, in the sense of the Hörmander-M
 ihlin condition.\n\nIn this talk we will quantify how the endpoint estimat
 e for $T_m$ for any arbitrary $m$ is characterized by the lack of additivi
 ty of its set of singularities $\\Xi(m)$ . This property of $\\Xi(m)$ is e
 xpressed in terms of a Zygmund-type inequality. The main ingredient in the
  proof of the estimate is a multi-frequency projection lemma based on Gabo
 r expansion playing the role of Calderón-Zygmund decomposition.\n\nThe ta
 lk is based on joint work with Bakas\, Ciccone\, Di Plinio\, Parissis\, an
 d Vitturi.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arian Nadjimzadah (University of California Los Angeles)
DTSTART:20251104T190000Z
DTEND:20251104T200000Z
DTSTAMP:20260404T110958Z
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://stable.researchseminars.org/talk/OARS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nathan Wagner (George Mason University)
DTSTART:20251118T190000Z
DTEND:20251118T200000Z
DTSTAMP:20260404T110958Z
UID:OARS/75
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 75/">Optimal Sparse Bounds and Commutator Characterizations Without Doubli
 ng</a>\nby Nathan Wagner (George Mason University) as part of OARS Online 
 Analysis Research Seminar\n\n\nAbstract\nWe examine dyadic paraproducts an
 d commutators in the non-homogeneous setting\, where the underlying Borel 
 measure $\\mu$ is not assumed doubling. We first establish a pointwise spa
 rse domination for dyadic paraproducts and related operators with symbols 
 $b \\in BMO(\\mu)$\, improving upon a result of Lacey\, where $b$ satisfie
 d a stronger Carleson-type condition coinciding with BMO only in the doubl
 ing case. As an application\, we derive sharpened weighted inequalities fo
 r the commutator of a dyadic Hilbert transform H previously studied by Bor
 ges\, Conde Alonso\, Pipher\, and Wagner. We also characterize the symbols
  for which $[H\,b]$ is bounded on $L^p$ for $1<p<\\infty$\, and provide ex
 amples showing that this symbol class lies strictly between those satisfyi
 ng the $p$-Carleson packing condition and those belonging to martingale BM
 O. This talk is based on joint work with Francesco D'Emilio\, Yongxi Lin\,
  and Brett D. Wick.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Ortiz (Rice University)
DTSTART:20260203T160000Z
DTEND:20260203T170000Z
DTSTAMP:20260404T110958Z
UID:OARS/76
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 76/">Tangency counting for well-spaced circles</a>\nby Alex Ortiz (Rice Un
 iversity) as part of OARS Online Analysis Research Seminar\n\n\nAbstract\n
 In the late 1990s\, Wolff introduced the circle tangency problem: among $N
 $ circles\, with no three tangent at a point\, how many pairs can be inter
 nally tangent? 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 polynom
 ial method. The conjectured sharp bound $N^{4/3+ε}$ is achieved by a grid
  of circles. In recent joint work with Dominique Maldague\, we show that f
 or approximately gridlike families of circles\, the $N^{3/2}$ barrier can 
 be broken: we obtain an upper bound of $N^{25/18+ε}$\, coming close to th
 e conjectured $4/3$ exponent. I will outline the background and the connec
 tion of the circle tangency problem with restriction theory\, and then des
 cribe our stopping-time framework\, which uses a new square-function inter
 pretation of refined decoupling for the truncated cone in $\\mathbb{R}^3$.
 \n
LOCATION:https://stable.researchseminars.org/talk/OARS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donggeun Ryou (Indiana University)
DTSTART:20260303T160000Z
DTEND:20260303T170000Z
DTSTAMP:20260404T110958Z
UID:OARS/77
DESCRIPTION:by Donggeun Ryou (Indiana University) as part of OARS Online A
 nalysis Research Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/OARS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dor Minzer (Massachusetts Institute of Technology)
DTSTART:20260317T150000Z
DTEND:20260317T160000Z
DTSTAMP:20260404T110958Z
UID:OARS/78
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 78/">On inverse theorems\, constraint satisfaction problems and combinator
 ial lines</a>\nby Dor Minzer (Massachusetts Institute of Technology) as pa
 rt of OARS Online Analysis Research Seminar\n\n\nAbstract\nSuppose $f_1\, 
 ...\, f_k$ are functions that have a non-negligible correlation over a pro
 duct distribution $\\mu^n$\; what structure can be deduced about the funct
 ions $f_1\, ...\, f_k$? \nWhile our initial motivation to study this probl
 em stems from theoretical computer science\, it turns out to appear in man
 y different settings. In this talk\, we will discuss some preliminary resu
 lts and their applications. \nBased on joint works with Amey Bhangale\, Su
 bhash Khot and Yang P. Liu\n
LOCATION:https://stable.researchseminars.org/talk/OARS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernie Croot (Georgia Tech)
DTSTART:20260331T150000Z
DTEND:20260331T160000Z
DTSTAMP:20260404T110958Z
UID:OARS/79
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 79/">Results on digits of numbers in different bases and a problem of R. L
 . Graham.</a>\nby Ernie Croot (Georgia Tech) as part of OARS Online Analys
 is Research Seminar\n\n\nAbstract\nIn this talk I'll discuss two works I'v
 e been involved in (one with former students Hamed Mousavi and Maxie Schmi
 dt\, and the other with Thomas Bloom) and producing integers n most of who
 se digits are small in several bases simultaneously.  This turned out to b
 e related to a conjecture of R. L. Graham on p-divisibility of central bin
 omial coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/OARS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eyvindur Palsson (Virginia Tech)
DTSTART:20260217T160000Z
DTEND:20260217T170000Z
DTSTAMP:20260404T110958Z
UID:OARS/80
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/OARS/
 80/">The Falconer distance problem and its many variants</a>\nby Eyvindur 
 Palsson (Virginia Tech) as part of OARS Online Analysis Research Seminar\n
 \n\nAbstract\nThe Falconer distance problem\, a major open problem on the 
 interface of geometric measure theory and harmonic analysis\, has seen muc
 h progress in the last decade. There are many variants of it\, including p
 inned and non-empty interior ones\, as well as multipoint configuration an
 alogues. 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://stable.researchseminars.org/talk/OARS/80/
END:VEVENT
END:VCALENDAR
