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BEGIN:VEVENT
SUMMARY:Ciprian Demeter (Indiana University Bloomington)
DTSTART:20210525T153000Z
DTEND:20210525T163000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/1/">Restriction of exponential sums to hypersurfaces</a>\nb
 y Ciprian Demeter (Indiana University Bloomington) as part of HIM Harmonic
  Analysis Seminar\n\n\nAbstract\nWe discuss moment inequalities for expone
 ntial sums with respect to singular measures\, whose Fourier decay matches
  those of curved hypersurfaces. Our emphasis will be on proving estimates 
 that are sharp with respect to the scale parameter $N$\, apart from $N^ϵ$
  losses. Joint work with Bartosz Langowski.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS)
DTSTART:20210531T153000Z
DTEND:20210531T163000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/2/">A stationary set method for estimating oscillatory inte
 grals</a>\nby Ruixiang Zhang (IAS) as part of HIM Harmonic Analysis Semina
 r\n\n\nAbstract\nGiven a polynomial $P$ of constant degree in $d$ variable
 s and consider the oscillatory integral $$I_P = \\int_{[0\,1]^d} e(P(\\xi)
 ) \\mathrm{d}\\xi.$$ Assuming $d$ is also fixed\, what is a good upper bou
 nd of $|I_P|$? In this talk\, I will introduce a ``stationary set'' method
  that gives an upper bound with simple geometric meaning. The proof of thi
 s bound mainly relies on the theory of o-minimal structures. As an applica
 tion of our bound\, we obtain the sharp convergence exponent in the two di
 mensional Tarry's problem for every degree via additional analysis on stat
 ionary sets. Consequently\, we also prove the sharp $L^{\\infty} \\to L^p$
  Fourier extension estimates for every two dimensional Parsell-Vinogradov 
 surface whenever the endpoint of the exponent $p$ is even. This is joint w
 ork with Saugata Basu\, Shaoming Guo and Pavel Zorin-Kranich.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Mirek
DTSTART:20210621T153000Z
DTEND:20210621T163000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/3/">Pointwise ergodic theorems for bilinear polynomial aver
 ages</a>\nby Mariusz Mirek as part of HIM Harmonic Analysis Seminar\n\n\nA
 bstract\nWe shall discuss the proof of pointwise almost everywhere converg
 ence for the non-conventional (in the sense of Furstenberg and Weiss) bili
 near polynomial ergodic averages. This is joint work with Ben Krause and T
 erry Tao: arXiv:2008.00857. We will also talk about recent progress toward
 s establishing Bergelson's conjecture.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Hickman (University of Edinburgh)
DTSTART:20210628T140000Z
DTEND:20210628T150000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/4/">The helical maximal function</a>\nby Jonathan Hickman (
 University of Edinburgh) as part of HIM Harmonic Analysis Seminar\n\n\nAbs
 tract\nThe circular maximal function is a singular variant of the familiar
  Hardy--Littlewood maximal function. Rather than take maximal averages ove
 r concentric balls\, we take maximal averages over concentric circles in t
 he plane. The study of this operator is closely related to certain GMT pac
 king problems for circles\, as well as the theory of the Euclidean wave pr
 opagator.  A celebrated result of Bourgain from the mid 80s showed that th
 e circular maximal function is bounded on $L^p$ if and only if $p > 2$. In
  this talk I will discuss a higher dimensional variant of Bourgain's theor
 em\, in which the circles are replaced with space curves (such as helices)
  in $\\mathbb{R}^3$. Our main theorem is that the resulting helical maxima
 l operator is bounded on $L^p$ if and only if $p > 3$. The proof combines 
 a number of recently developed Fourier analytic tools\, and in particular 
 a variant of the Littlewood--Paley theory for functions frequency supporte
 d in a neighbourhood of a cone. Joint work with David Beltran\, Shaoming G
 uo and Andreas Seeger.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Christ (UC Berkeley)
DTSTART:20210705T153000Z
DTEND:20210705T163000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/5/">On quadrilinear implicitly oscillatory integrals</a>\nb
 y Michael Christ (UC Berkeley) as part of HIM Harmonic Analysis Seminar\n\
 n\nAbstract\nThe title refers to multilinear functionals\n\\[ \\int_B \\pr
 od_{j\\in J} (f_j\\circ\\varphi_j)\\]\nwhere $B\\subset {\\mathbb R}^D$ is
  a ball\, $J$ is a finite index set\, $\\varphi_j:B\\to {\\mathbb R}^d$ ar
 e $C^\\omega$ submersions\,\n$d$ $<$ $D$\, and $f_j$ are measurable. The g
 oal is majorization by a  product of negative order Sobolev norms of $f_j$
 \,\nunder appropriate hypotheses on the mappings $\\varphi_j$.\n\nInequali
 ties of this type are closely related to sublevel inequalities\n\\[ \\big|
 \\big\\{x\\in B: |\\sum_{j\\in J} a_j(x)\\\,(g_j\\circ\\varphi_j)(x)|<\\va
 repsilon\\big\\}\\big| = O(\\varepsilon^c)\,\\]\nwhere the coefficients sa
 tisfy $a_j\\in C^\\omega$.\n\nI will state results of this type with $(|J|
 \,D\,d) = (4\,2\,1)$ for the multiplicative inequality and $= (3\,2\,1)$\n
 for the additive inequality\, discuss connections between the two\, and in
 dicate some elements of proofs.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Po Lam Yung (Australian National University and the Chinese Univer
 sity of Hong Kong)
DTSTART:20210712T140000Z
DTEND:20210712T150000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/6
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/6/">A formula for Sobolev seminorms involving weak L^p</a>\
 nby Po Lam Yung (Australian National University and the Chinese University
  of Hong Kong) as part of HIM Harmonic Analysis Seminar\n\n\nAbstract\nI w
 ill discuss some joint work with Haim Brezis and Jean Van Schaftingen\, wh
 ere a new formula was proved for the $W^{1\,p}$ seminorm of any compactly 
 supported smooth function on $\\mathbb{R}^n$. The formula involves the wea
 k $L^p$ norm of a modified difference quotient on the product space $\\mat
 hbb{R}^n \\times \\mathbb{R}^n$\, and was partly inspired by the BBM formu
 la by Bourgain\, Brezis and Mironescu regarding fractional Sobolev seminor
 ms. A similar formula for the $L^p$ norm of any $L^p$ function on $\\mathb
 b{R}^n$ has been obtained in a recent paper with Qingsong Gu. The talk wil
 l conclude with some applications of this circle of ideas\, that remedies 
 the failures of certain critical Gagliardo-Nirenberg type embeddings.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (UW Madison)
DTSTART:20210726T140000Z
DTEND:20210726T150000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/7
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/7/">Fourier restriction to the sphere is extremizable more 
 often than not</a>\nby Betsy Stovall (UW Madison) as part of HIM Harmonic 
 Analysis Seminar\n\n\nAbstract\nWe will sketch a proof that the $L^p \\to 
 L^q$ Fourier extension inequality associated to the $d$-sphere possesses e
 xtremizers whenever $p < q < (d+2)p'/d$.  This is joint work with Taryn Fl
 ock.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Wright (University of Edinburgh)
DTSTART:20210802T153000Z
DTEND:20210802T163000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/8
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/8/">Exponential sums and oscillatory integrals: a unified a
 pproach</a>\nby Jim Wright (University of Edinburgh) as part of HIM Harmon
 ic Analysis Seminar\n\n\nAbstract\nIn joint work with Gian Maria Dall'Ara\
 , we have a simple argument which is powerful enough to effectively treat 
 oscillatory integrals defined over general locally compact topological fie
 lds whose phase is a general polynomial of many variables. Our bounds have
  an interesting self-improving feature.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoming Guo (UW Madison)
DTSTART:20210809T140000Z
DTEND:20210809T150000Z
DTSTAMP:20260404T111212Z
UID:HIMharmonicanalysis/9
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/HIMha
 rmonicanalysis/9/">Some recent progress on the Bochner-Riesz problem</a>\n
 by Shaoming Guo (UW Madison) as part of HIM Harmonic Analysis Seminar\n\n\
 nAbstract\nI will report some recent progress on the Bochner-Riesz conject
 ure. We observe that recent tools developed to study the Fourier restricti
 on conjecture\, including wave packet decompositions\, broad-narrow analys
 is\, the polynomial methods\, polynomial Wolff axioms\, etc.\, work equall
 y well for the Bochner-Riesz problem. This is joint work with Changkeun Oh
 \, Hong Wang\, Shukun Wu and Ruixiang Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/HIMharmonicanalysis/9/
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