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BEGIN:VEVENT
SUMMARY:Ciprian Demeter (Indiana University Bloomington)
DTSTART:20210525T153000Z
DTEND:20210525T163000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/1/">Restriction of exponential sums to hypersurfaces</a>\nby Cipri
 an Demeter (Indiana University Bloomington) as part of HIM Harmonic Analys
 is Seminar\n\n\nAbstract\nWe discuss moment inequalities for exponential s
 ums with respect to singular measures\, whose Fourier decay matches those 
 of curved hypersurfaces. Our emphasis will be on proving estimates that ar
 e sharp with respect to the scale parameter $N$\, apart from $N^ϵ$ losses
 . Joint work with Bartosz Langowski.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruixiang Zhang (IAS)
DTSTART:20210531T153000Z
DTEND:20210531T163000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/2/">A stationary set method for estimating oscillatory integrals</
 a>\nby Ruixiang Zhang (IAS) as part of HIM Harmonic Analysis Seminar\n\n\n
 Abstract\nGiven a polynomial $P$ of constant degree in $d$ variables and c
 onsider the oscillatory integral $$I_P = \\int_{[0\,1]^d} e(P(\\xi)) \\mat
 hrm{d}\\xi.$$ Assuming $d$ is also fixed\, what is a good upper bound of $
 |I_P|$? In this talk\, I will introduce a ``stationary set'' method that g
 ives an upper bound with simple geometric meaning. The proof of this bound
  mainly relies on the theory of o-minimal structures. As an application of
  our bound\, we obtain the sharp convergence exponent in the two dimension
 al Tarry's problem for every degree via additional analysis on stationary 
 sets. Consequently\, we also prove the sharp $L^{\\infty} \\to L^p$ Fourie
 r extension estimates for every two dimensional Parsell-Vinogradov surface
  whenever the endpoint of the exponent $p$ is even. This is joint work wit
 h Saugata Basu\, Shaoming Guo and Pavel Zorin-Kranich.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariusz Mirek
DTSTART:20210621T153000Z
DTEND:20210621T163000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/3/">Pointwise ergodic theorems for bilinear polynomial averages</a
 >\nby Mariusz Mirek as part of HIM Harmonic Analysis Seminar\n\n\nAbstract
 \nWe shall discuss the proof of pointwise almost everywhere convergence fo
 r the non-conventional (in the sense of Furstenberg and Weiss) bilinear po
 lynomial ergodic averages. This is joint work with Ben Krause and Terry Ta
 o: arXiv:2008.00857. We will also talk about recent progress towards estab
 lishing Bergelson's conjecture.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Hickman (University of Edinburgh)
DTSTART:20210628T140000Z
DTEND:20210628T150000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/4/">The helical maximal function</a>\nby Jonathan Hickman (Univers
 ity of Edinburgh) as part of HIM Harmonic Analysis Seminar\n\n\nAbstract\n
 The circular maximal function is a singular variant of the familiar Hardy-
 -Littlewood maximal function. Rather than take maximal averages over conce
 ntric balls\, we take maximal averages over concentric circles in the plan
 e. The study of this operator is closely related to certain GMT packing pr
 oblems for circles\, as well as the theory of the Euclidean wave propagato
 r.  A celebrated result of Bourgain from the mid 80s showed that the circu
 lar maximal function is bounded on $L^p$ if and only if $p > 2$. In this t
 alk I will discuss a higher dimensional variant of Bourgain's theorem\, in
  which the circles are replaced with space curves (such as helices) in $\\
 mathbb{R}^3$. Our main theorem is that the resulting helical maximal opera
 tor is bounded on $L^p$ if and only if $p > 3$. The proof combines a numbe
 r of recently developed Fourier analytic tools\, and in particular a varia
 nt of the Littlewood--Paley theory for functions frequency supported in a 
 neighbourhood of a cone. Joint work with David Beltran\, Shaoming Guo and 
 Andreas Seeger.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Christ (UC Berkeley)
DTSTART:20210705T153000Z
DTEND:20210705T163000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/5/">On quadrilinear implicitly oscillatory integrals</a>\nby Micha
 el Christ (UC Berkeley) as part of HIM Harmonic Analysis Seminar\n\n\nAbst
 ract\nThe title refers to multilinear functionals\n\\[ \\int_B \\prod_{j\\
 in J} (f_j\\circ\\varphi_j)\\]\nwhere $B\\subset {\\mathbb R}^D$ is a ball
 \, $J$ is a finite index set\, $\\varphi_j:B\\to {\\mathbb R}^d$ are $C^\\
 omega$ submersions\,\n$d$ $<$ $D$\, and $f_j$ are measurable. The goal is 
 majorization by a  product of negative order Sobolev norms of $f_j$\,\nund
 er appropriate hypotheses on the mappings $\\varphi_j$.\n\nInequalities 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)|<\\varepsilo
 n\\big\\}\\big| = O(\\varepsilon^c)\,\\]\nwhere the coefficients satisfy $
 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 $= (3\,2\,1)$\nfor the
  additive inequality\, discuss connections between the two\, and indicate 
 some elements of proofs.\n
LOCATION:https://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:20260422T225927Z
UID:HIMharmonicanalysis/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/6/">A formula for Sobolev seminorms involving weak L^p</a>\nby Po 
 Lam Yung (Australian National University and the Chinese University of Hon
 g Kong) as part of HIM Harmonic Analysis Seminar\n\n\nAbstract\nI will dis
 cuss some joint work with Haim Brezis and Jean Van Schaftingen\, where a n
 ew formula was proved for the $W^{1\,p}$ seminorm of any compactly support
 ed smooth function on $\\mathbb{R}^n$. The formula involves the weak $L^p$
  norm of a modified difference quotient on the product space $\\mathbb{R}^
 n \\times \\mathbb{R}^n$\, and was partly inspired by the BBM formula by B
 ourgain\, Brezis and Mironescu regarding fractional Sobolev seminorms. A s
 imilar formula for the $L^p$ norm of any $L^p$ function on $\\mathbb{R}^n$
  has been obtained in a recent paper with Qingsong Gu. The talk will concl
 ude with some applications of this circle of ideas\, that remedies the fai
 lures of certain critical Gagliardo-Nirenberg type embeddings.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betsy Stovall (UW Madison)
DTSTART:20210726T140000Z
DTEND:20210726T150000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/7/">Fourier restriction to the sphere is extremizable more often t
 han not</a>\nby Betsy Stovall (UW Madison) as part of HIM Harmonic Analysi
 s Seminar\n\n\nAbstract\nWe will sketch a proof that the $L^p \\to L^q$ Fo
 urier extension inequality associated to the $d$-sphere possesses extremiz
 ers whenever $p < q < (d+2)p'/d$.  This is joint work with Taryn Flock.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jim Wright (University of Edinburgh)
DTSTART:20210802T153000Z
DTEND:20210802T163000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/8/">Exponential sums and oscillatory integrals: a unified approach
 </a>\nby Jim Wright (University of Edinburgh) as part of HIM Harmonic Anal
 ysis Seminar\n\n\nAbstract\nIn joint work with Gian Maria Dall'Ara\, we ha
 ve a simple argument which is powerful enough to effectively treat oscilla
 tory integrals defined over general locally compact topological fields who
 se phase is a general polynomial of many variables. Our bounds have an int
 eresting self-improving feature.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shaoming Guo (UW Madison)
DTSTART:20210809T140000Z
DTEND:20210809T150000Z
DTSTAMP:20260422T225927Z
UID:HIMharmonicanalysis/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HIMharmonica
 nalysis/9/">Some recent progress on the Bochner-Riesz problem</a>\nby Shao
 ming Guo (UW Madison) as part of HIM Harmonic Analysis Seminar\n\n\nAbstra
 ct\nI will report some recent progress on the Bochner-Riesz conjecture. We
  observe that recent tools developed to study the Fourier restriction conj
 ecture\, including wave packet decompositions\, broad-narrow analysis\, th
 e polynomial methods\, polynomial Wolff axioms\, etc.\, work equally well 
 for the Bochner-Riesz problem. This is joint work with Changkeun Oh\, Hong
  Wang\, Shukun Wu and Ruixiang Zhang.\n
LOCATION:https://researchseminars.org/talk/HIMharmonicanalysis/9/
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