BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nicola Arcozzi (University of Bologna) DTSTART:20200916T160000Z DTEND:20200916T170000Z DTSTAMP:20260422T225759Z UID:HAeS/1 DESCRIPTION:Title: The Hardy space from an engineer's perspective\nby Nicola Arcozzi (Univer sity of Bologna) as part of Harmonic analysis e-seminars\n\n\nAbstract\nTh e Hardy space $H^2$ made its way into signal theory since Wiener's time\, and it belongs to the standard toolbox of all engineers who deal with sign als. We will see how $H^2$ and its related function spaces $H^1$\, $H^\\in fty$\, and $BMOA$ arise from basic practical problems\, and how multiplica tion\, Toeplitz\, and Hankel operators enter the picture. Feedback systems will take us at the front step of Pick interpolation. The aim is advertis ing a possible intuition of a beautiful chapter of pure mathematics.\n LOCATION:https://researchseminars.org/talk/HAeS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Giuseppe Negro (University of Birmingham) DTSTART:20201021T160000Z DTEND:20201021T170000Z DTSTAMP:20260422T225759Z UID:HAeS/2 DESCRIPTION:Title: Sha rp estimates for the wave equation via the Penrose transform\nby Giuse ppe Negro (University of Birmingham) as part of Harmonic analysis e-semina rs\n\n\nAbstract\nIn 2004\, Foschi found the best constant\, and the extre mizing functions\, for the Strichartz inequality for the wave equation wi th data in the Sobolev space $\\Hdot^{1/2}\\times\\Hdot^{-1/2}(\\R^3)$. H e also formulated a conjecture\, concerning the extremizers to this Stric hartz inequality in all spatial dimensions $d\\ge 2$. We disprove such co njecture for even $d$\, but we provide evidence to support it for odd $d$. The proofs use the conformal compactification of the Minkowski space-tim e given by the Penrose transform.\n LOCATION:https://researchseminars.org/talk/HAeS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Javier Duoandikoetxea (Euskal Herriko Unibertsitatea) DTSTART:20200930T160000Z DTEND:20200930T170000Z DTSTAMP:20260422T225759Z UID:HAeS/3 DESCRIPTION:Title: Wei ghted Morrey spaces\nby Javier Duoandikoetxea (Euskal Herriko Uniberts itatea) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThis talk i s an account of my work on Morrey spaces with Marcel \nRosenthal in recent years.\n\nThere are several definitions for weighted Morrey spaces. We ob tain \nboundedness results in all of them for operators satisfying the \na ssumptions of the usual extrapolation theorem\, that is\, we get \nweighte d Morrey estimates from weighted Lebesgue estimates with $A_p$ \nweights. The results can be applied to a variety of operators and \ntogether with the norm estimates\, our technique also provides the \ndefinition of the o perator by embedding.\n\nRecently we obtained results for a more general c lass of weighted \nMorrey spaces from an extension of the usual Muckenhoup t condition to \nthe Morrey setting\, involving the Khöthe dual of the sp ace. In some \ncases the conditions characterize the weighted inequalities of maximal \noperators.\n LOCATION:https://researchseminars.org/talk/HAeS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Ujué Etayo (TUGraz) DTSTART:20201111T170000Z DTEND:20201111T180000Z DTSTAMP:20260422T225759Z UID:HAeS/4 DESCRIPTION:Title: A B ombieri-type inequality for Weierstrass sigma functions\nby Ujué Etay o (TUGraz) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe Bomb ieri inequality is a classic inequality in number theory\,see [B. Beauzamy \, E. Bombieri\, P. Enflo\, and H. L. Montgomery. Products\nof polynomials in many variables. Journal of Number Theory\, 36(2):219\n– 245\, 1990)] .\nThe original statement says that given two homogeneous polynomials on $ N$ variables $P\,Q$ respectively of degree $m$ and $n$\, then\n$$\n{\\frac {m!n!}{(m+n)!}}\\|P\\|^{2}\\\,\\|Q\\|^{2}\\leq \\|P\\cdot Q\\|^{2}\\leq \ \|P\\|^{2}\\\,\\|Q\\|^{2}\,\n$$\nwhere the norm is the Bombieri-Weyl norm. \nThis inequality admits a rewriting in terms of integrals on the sphere\, a property exploited in [U. Etayo. A sharp bombieri inequality\, logarith mic energy and well con-\nditioned polynomials\, 2019].\nIn a joint work w ith Joaquim Ortega-Cerd\\`a and Haakan Hedenmalm\, we use this new definit ion to generalize the inequality to other Riemannian manifolds\, in partic ular the torus $\\mathbb{C}/\\Lambda$\n LOCATION:https://researchseminars.org/talk/HAeS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefano Decio (Norwegian University of Science and Technology) DTSTART:20201028T170000Z DTEND:20201028T180000Z DTSTAMP:20260422T225759Z UID:HAeS/5 DESCRIPTION:Title: Nod al sets of Steklov eigenfunctions\nby Stefano Decio (Norwegian Univers ity of Science and Technology) as part of Harmonic analysis e-seminars\n\n Abstract: TBA\n LOCATION:https://researchseminars.org/talk/HAeS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Tommaso Bruno (Ghent University) DTSTART:20201014T160000Z DTEND:20201014T170000Z DTSTAMP:20260422T225759Z UID:HAeS/6 DESCRIPTION:Title: Fac torization properties of smooth functions and vectors\nby Tommaso Brun o (Ghent University) as part of Harmonic analysis e-seminars\n\n\nAbstract \nGiven a module $\\mathcal{M}$ over a non-unital algebra $\\mathcal{A}$\, we say that $\\mathcal{M}$ has the weak factorization property if $\\math cal{M}= \\mathrm{span} \\{\\mathcal{A} \\cdot \\mathcal{M}\\}$\, while it has the strong factorization property if $\\mathcal{M}= \\mathcal{A} \\cdo t \\mathcal{M}$. In this talk we shall review old and recent results about strong and weak factorizations of smooth functions and smooth vectors of Lie group representations. We shall also discuss open problems and current lines of research.\n LOCATION:https://researchseminars.org/talk/HAeS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:José Luis Romero (University of Vienna) DTSTART:20201202T174000Z DTEND:20201202T184000Z DTSTAMP:20260422T225759Z UID:HAeS/7 DESCRIPTION:Title: Sam pling\, density\, and equidistribution\nby José Luis Romero (Universi ty of Vienna) as part of Harmonic analysis e-seminars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/HAeS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Gennady Uraltsev (Cornell University) DTSTART:20201209T170000Z DTEND:20201209T180000Z DTSTAMP:20260422T225759Z UID:HAeS/8 DESCRIPTION:Title: Som e results in Banach space-valued time frequency analysis\nby Gennady U raltsev (Cornell University) as part of Harmonic analysis e-seminars\n\n\n Abstract\nSIO (Singular Integral Operator) theory and\, Calderón-Zygmund theory specifically\, developed starting from the '60s\, provides a vast a rray of tools for dealing with operators that resemble the Hilbert transfo rm\n$$\n\\mathrm{H}f(x):= \\int_{\\mathbb R}f(x-y)\\frac{d y}{y}\,\n$$\n\n an ubiquitous operator in Complex Analysis\, semi-linear PDEs\, and many o ther branches of mathematics. Results valid for -valued functions were ext ended to Banach spaces-valued functions thanks to Bourgain's groundbreakin g work on the deep relation between Banach space geometry and boundedness properties of vector-valued SIOs.\n\nScalar-valued bounds for multilinear SIOs\, like the bilinear Hilbert transform\n\n$$\n\\mathrm{BHT}[f_{1}\,f_{ 2}](x)=\\int_{\\mathbb R} f_{1}(x-t) f_{2}(x+t) \\frac{d t} {t}\,\n$$\n \n are classic in time-frequency-scale analysis. Banach-space valued results have appeared only in the last couple of years. The well understood connec tions with Banach space geometry from linear theory are just starting to b e investigated.\n\nOpen questions and generalizations to non-commutative a nalysis abound and would come hand-in-hand with progress in understanding SIOs with worse singularities than of Calderón-Zygmund type that can ofte n be realized as SIO-valued CZ operators.\n LOCATION:https://researchseminars.org/talk/HAeS/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessio Martini (University of Birmingham) DTSTART:20210113T170000Z DTEND:20210113T180000Z DTSTAMP:20260422T225759Z UID:HAeS/9 DESCRIPTION:Title: Spe ctral multipliers for sub-Laplacians: recent developments and open problem s\nby Alessio Martini (University of Birmingham) as part of Harmonic a nalysis e-seminars\n\n\nAbstract\nI will present some old and new results about the $L^p$ functional calculus for sub-Laplacians $L$. It has been kn own for a long time that\, under quite general assumptions on the sub-Lapl acian and the underlying sub-Riemannian structure\, an operator of the for m $F(L)$ is bounded on $L^p$\, $1< p<\\infty$\, whenever the multiplier $ F$ satisfies a scale-invariant smoothness condition of sufficiently larger order.\nThe problem of determining the minimal smoothness assumptions\, h owever\, remains widely open and will be the focus of our discussion.\n LOCATION:https://researchseminars.org/talk/HAeS/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Giona Veronelli (Università di Milano-Bicocca) DTSTART:20210210T170000Z DTEND:20210210T180000Z DTSTAMP:20260422T225759Z UID:HAeS/10 DESCRIPTION:Title: So bolev spaces on manifolds with lower bounded curvature\nby Giona Veron elli (Università di Milano-Bicocca) as part of Harmonic analysis e-semina rs\n\n\nAbstract\nThere are several notions of Sobolev spaces on a Riemann ian manifold: from the operator theory viewpoint it is natural to consider Sobolev functions defined by taking the $L^p$ norms of functions and of p owers of their Laplacian. Instead\, the regularity theory of elliptic equa tions involves Sobolev functions defined via the $L^p$ norm of all the de rivatives up to a certain order. Moreover\, Sobolev spaces can be characte rized via compactly supported smooth approximations.\nIn this talk\, we wi ll focus on non-compact manifolds with lower bounded curvature. We will di scuss some results giving the (non)-equivalence between the different Sobo lev spaces. In particular\, we will highlight the role played in the theor y by the Calderon-Zygmund inequality and the Bochner formulas\, and we wil l sketch how to exploit singular metric spaces (e.g. Alexandrov or RCD) as a tool to construct smooth counterexamples.\n LOCATION:https://researchseminars.org/talk/HAeS/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Maria Vallarino (Politecnico di Torino) DTSTART:20210317T170000Z DTEND:20210317T180000Z DTSTAMP:20260422T225759Z UID:HAeS/11 DESCRIPTION:Title: An alysis on trees with nondoubling flows\nby Maria Vallarino (Politecnic o di Torino) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe cl assical Calderón–Zygmund theory was developed in the Euclidean space an d\,\nmore generally\, on spaces of homogeneous type\, which are measure me tric spaces with\nthe doubling property.\nIn this talk we consider trees e ndowed with flow measures\, which are nondoubling measures of at least exp onential growth. In this setting\, we develop a Calderón–Zygmund\ntheor y and we define $BMO$ and Hardy spaces\, proving a number of desired resul ts extending the corresponding theory as known in the classical setting.\n This is a joint work with Matteo Levi\, Federico Santagati and Anita Tabac co.\n LOCATION:https://researchseminars.org/talk/HAeS/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Fulvio Ricci (Scuola Normale Superiore) DTSTART:20210224T170000Z DTEND:20210224T180000Z DTSTAMP:20260422T225759Z UID:HAeS/12 DESCRIPTION:Title: Mu lti-parameter structures\nby Fulvio Ricci (Scuola Normale Superiore) a s part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk we give a survey on a certain number of multi-parameter structures\, on $\\mathbb R^n$ and on nilpotent groups\, that have been introduced in the last 20 y ears. They include flag and multi-norm structures.\nThese structures are i ntermediate between the one-parameter dilation structures of standard Cald erón-Zygmund theory and the full $n$-parameter product structure. Each st ructure has its own type of maximal functions\, singular integral operator s\, square functions\, Hardy spaces.\n LOCATION:https://researchseminars.org/talk/HAeS/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Loredana Lanzani (Syracuse University) DTSTART:20210331T160000Z DTEND:20210331T170000Z DTSTAMP:20260422T225759Z UID:HAeS/13 DESCRIPTION:Title: Th e commutator of the Cauchy-Szegő projection for domains in $C^n$ with min imal smoothness\nby Loredana Lanzani (Syracuse University) as part of Harmonic analysis e-seminars\n\n\nAbstract\nLet $D\\subset\\C^n$ be a boun ded\, strongly pseudoconvex domain whose boundary $bD$ satisfies the minim al regularity condition of class $C^2$.\nWe characterize boundedness and c ompactness in $L^p(bD\, \\omega)$\,\, for $1< p < \\infty$\,of the commuta tor $[b\,S_\\omega]$ where $S_\\omega$ is the Cauchy--Szegő (orthogonal) projection of $L^2(bD\, \\omega)$ onto the holomorphic Hardy space $H^2( bD\, \\omega)$\n and the measure $\\omega$ belongs to a family (the `` Leray Levi-like'' measures)\n that includes induced Lebesgue measure $\\si gma$. We next consider a much larger family of measures $\\{\\Omega_p\\}$ modeled after the Muckenhoupt $A_p$-weights for $\\sigma$:\n we define th e holomorphic Hardy spaces $H^p(bD\, \\Omega_p)$ and we characterize\n bou ndedness and compactness of $[b\, S_{\\Omega_2}]$ in $L^2(bD\, \\Omega_2)$ .\n Earlier closely related results rely upon an asymptotic expansion\, an d subsequent pointwise estimates\, of the Cauchy--Szegő kernel that are n ot available in the settings of minimal regularity {of $bD$} and/or $A_p$- like measures. \n\n\n \n This is joint work with Xuan Thinh Duong\, Ji L i and Brett D. Wick.\n LOCATION:https://researchseminars.org/talk/HAeS/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Gian Maria Dall'Ara (Indam/Scuola Normale Superiore) DTSTART:20210324T170000Z DTEND:20210324T180000Z DTSTAMP:20260422T225759Z UID:HAeS/14 DESCRIPTION:Title: L^ p mapping problems for Bergman projections\nby Gian Maria Dall'Ara (In dam/Scuola Normale Superiore) as part of Harmonic analysis e-seminars\n\n\ nAbstract\nThis is for the most part a survey talk. I will discuss various as-\npects of the following problem: for which values of $p$ is the Bergm an projection\nof a given domain in $\\mathbb C^n$ bounded on $L^p$? The a nswer depends heavily on the\ncomplex geometry of the domain. We will disc uss the problem in one and\nseveral variables\, its connection with the th eory of conformal mappings and\nthat of singular integrals\, highlighting many open problems.\n LOCATION:https://researchseminars.org/talk/HAeS/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan S. Trapasso (Università di Genova) DTSTART:20210421T160000Z DTEND:20210421T170000Z DTSTAMP:20260422T225759Z UID:HAeS/15 DESCRIPTION:Title: Di spersion\, spreading and sparsity of Gabor wave packets\nby Ivan S. Tr apasso (Università di Genova) as part of Harmonic analysis e-seminars\n\n \nAbstract\nSparsity properties for phase-space representations of several types of operators (including pseudodifferential\, metaplectic and Fourie r integral operators) have been extensively studied in recent articles\, w ith applications to the analysis of dispersive evolution equation. It has been proved that such operators are approximately diagonalized by Gabor wa ve packets - equivalently\, the corresponding phase-space representations (Gabor matrix/kernel) can be thought of as sparse infinite-dimensional mat rices. While wave packets are expected to undergo some spreading and dispe rsion phenomena\, there is no record of these issues in the aforementioned estimates. We recently proved refined estimates for the Gabor matrix of m etaplectic operators\, also of generalized type\, where sparsity\, spreadi ng and dispersive properties are all simultaneously noticeable. We also pr ovide applications to the propagation of singularities for the Schr\\"odin ger equation\; in this connection\, our results can be regarded as a micro local refinement of known estimates. The talk is based on joint work with Elena Cordero and Fabio Nicola.\n LOCATION:https://researchseminars.org/talk/HAeS/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Fraccaroli (Universität Bonn) DTSTART:20210519T160000Z DTEND:20210519T170000Z DTSTAMP:20260422T225759Z UID:HAeS/16 DESCRIPTION:Title: Du ality for outer $L^p$ spaces\nby Marco Fraccaroli (Universität Bonn) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe theory of $L^p$ spaces for outer measures\, or outer $L^p$ spaces\, was\ndeveloped by Do and Thiele to encode the proof of boundedness of certain\nmultilinear oper ators in a streamlined argument. Accordingly to this\npurpose\, the theory was developed in the direction of the real\ninterpolation features of the se spaces\, while other questions remained\nuntouched.\nFor example\, the outer $L^p$ spaces are defined by quasi-norms\ngeneralizing the classical mixed $L^p$ norms on sets with a Cartesian\nproduct structure. Therefore\, it is natural to ask whether in arbitrary\nsettings the outer $L^p$ quasi -norms are equivalent to norms. In this\ntalk\, we will answer this questi on\, with a particular focus on certain\nsettings on the upper half space $\\R^d \\times (0\,\\infty)$ related to the\nwork of Do and Thiele.\n LOCATION:https://researchseminars.org/talk/HAeS/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Gianmarco Brocchi DTSTART:20210616T163000Z DTEND:20210616T173000Z DTSTAMP:20260422T225759Z UID:HAeS/17 DESCRIPTION:Title: Sp arse T1 theorems\nby Gianmarco Brocchi as part of Harmonic analysis e- seminars\n\n\nAbstract\nMany operators in analysis are non-local\, in the sense that a\n perturbation of the input near a point modifies the output \n everywhere\; consider for example the operator that maps the initial\n data to the corresponding solution of the heat equation.\n\n Sparse Dom ination consists in controlling such operators by a sum of\n positive\, l ocal averages. This allows to derive plenty of estimates\,\n which are of ten optimal. For example\, it has been shown that Calderón--Zygmund opera tors\n and square functions admit such a domination even under minimal $T 1$ hypotheses.\\newline\n\n In this talk we introduce the concept of spar se domination\n and present a sparse $T1$ theorem for square functions\,\ n discussing the new difficulties and ideas in this case.\n\n Time perm itting\, we will see how sparse domination can be applied\n in very diffe rent context.\n LOCATION:https://researchseminars.org/talk/HAeS/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Filippo De Mari (Università di Genova) DTSTART:20210630T160000Z DTEND:20210630T170000Z DTSTAMP:20260422T225759Z UID:HAeS/18 DESCRIPTION:Title: Vi ews on the Radon Transform\nby Filippo De Mari (Università di Genova) as part of Harmonic analysis e-seminars\n\n\nAbstract\nI will recall and introduce some of the many existing Radon transforms\, focusing in particu lar on the setup of $G$-dual pairs $(X\,\\Xi)$ introduced by Helgason more than fifty years ago\, where $G$ is a locally compact group that acts tr ansitively both on $X$ and $\\Xi$. \nI will then present some results obta ined in collaboration with G. S. Alberti\, F. Bartolucci\, E. De Vito\, M . Monti and F. Odone which bring into play (square integrable) representat ions. If the functions to be analyzed live on $X$ and the quasi regular r epresentation of $G$ on $L^2(X)$ and $L^2(\\Xi)$ are square integrable\, t hen it is possible to write a nice inversion formula for the Radon transfo rm associated to the families of submanifolds of $X$ that are prescribed b y the object $\\Xi$ which is dual to $X$. This formula hinges on a unitari zation of the Radon transform that may be proved in a rather general setup if the quasi regular representations of $G$ on $L^2(X)$ and $L^2(\\Xi)$ are irreducible\, and on an intertwining property of the Radon transform. The former result is inspired by work of Helgason. Some examples are disc ussed\, mostly the guiding case related to shearlets that points in the di rection of possible practical inversion techniques.\n LOCATION:https://researchseminars.org/talk/HAeS/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Alex Iosevich (University of Rochester) DTSTART:20211006T160000Z DTEND:20211006T170000Z DTSTAMP:20260422T225759Z UID:HAeS/19 DESCRIPTION:Title: Fi nite point configurations and the Vapnik-Chervonenkis dimension\nby Al ex Iosevich (University of Rochester) as part of Harmonic analysis e-semin ars\n\n\nAbstract\nThe Vapnik-Chervonenkis (VC) dimension was invented in 1970 to study learning models. This notion has since become one of the cor nerstones of modern data science. This beautiful idea has also found appli cations in other areas of mathematics. In this talk we are going to descri be how the study of the VC-dimension in the context of families of indicat or functions of spheres centered at points in sets of a given Hausdorff di mension (or in sets of a given size inside vector spaces over finite field s) gives rise to interesting\, and in some sense extremal\, point configur ations.\n LOCATION:https://researchseminars.org/talk/HAeS/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Karlheinz Gröchenig (University of Vienna) DTSTART:20211020T160000Z DTEND:20211020T170000Z DTSTAMP:20260422T225759Z UID:HAeS/20 DESCRIPTION:Title: Va riable bandwidth and sampling theorems\nby Karlheinz Gröchenig (Univ ersity of Vienna) as part of Harmonic analysis e-seminars\n\n\nAbstract\nW e study sampling theorems in spectral subspaces of a uniformly elliptic di fferential operator. For constant coefficients\, these are spaces of bandl imited functions\, whereas for general elliptic operators\, the resulting spaces consist of functions of "variable bandwidth". This is one of severa l constructions that gives meaning to the intuitive notion of a local and time-varying bandwidth. The interpretation is supported by the results on sampling theorems and necessary sampling density.\n LOCATION:https://researchseminars.org/talk/HAeS/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefan Steinerberger (University of Washington) DTSTART:20211110T170000Z DTEND:20211110T180000Z DTSTAMP:20260422T225759Z UID:HAeS/21 DESCRIPTION:Title: Th e Smoothest Average and New Uncertainty Principles for the Fourier Transfo rm\nby Stefan Steinerberger (University of Washington) as part of Harm onic analysis e-seminars\n\n\nAbstract\nSuppose you are given a real-value d function f(x) and want to compute a local average at a certain scale. Wh at we usually do is to pick a nice probability measure u\, centered at 0 a nd having standard deviation at the desired scale\, and convolve. Classica l candidates for u are the characteristic function or the Gaussian. This g ot me interested in finding the ”best” function u – this problem com es in two parts: (1) describing what one considers to be desirable propert ies of the convolution and (2) understanding which functions satisfy these properties. I tried a basic notion for the first part\, ”the convolutio n should be as smooth as the scale allows”\, and ran into fun classical Fourier Analysis that seems to be new: (a) new uncertainty principles for the Fourier transform\, (b) that potentially have the characteristic funct ion as an extremizer\, (c) which leads to strange new patterns in hypergeo metric functions and (d) produces curious local stability inequalities. No ah Kravitz and I managed to solve two specific instances on the discrete l attice completely\, this results in some sharp weighted estimates for poly nomials on the unit interval – both the Dirichlet and the Fejer kernel m ake an appearance. The entire talk will be completely classical Harmonic A nalysis\, there are lots and lots of open problems.\n LOCATION:https://researchseminars.org/talk/HAeS/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Bennett (University of Birmingham) DTSTART:20211103T170000Z DTEND:20211103T180000Z DTSTAMP:20260422T225759Z UID:HAeS/22 DESCRIPTION:Title: Th e nonlinear Brascamp-Lieb inequality and applications\nby Jonathan Ben nett (University of Birmingham) as part of Harmonic analysis e-seminars\n\ n\nAbstract\nThe Brascamp-Lieb inequality is a broad generalisation of man y well-known multilinear inequalities in analysis\, including the multilin ear Hölder\, Loomis-Whitney and sharp Young convolution inequalities. The re is by now a rich theory surrounding this classical inequality\, along w ith applications in convex geometry\, harmonic analysis\, partial differen tial equations\, number theory and beyond. In this talk we present a certa in nonlinear variant of the Brascamp-Lieb inequality\, placing particular emphasis on some of its applications. Most of this is joint work with Stef an Buschenhenke\, Neal Bez\, Michael Cowling and Taryn Flock.\n LOCATION:https://researchseminars.org/talk/HAeS/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Anthony Carbery (University of Edinburgh) DTSTART:20211201T170000Z DTEND:20211201T180000Z DTSTAMP:20260422T225759Z UID:HAeS/23 DESCRIPTION:Title: Du ality for joints and multijoints - what is it\, what are they\, and why do we care?\nby Anthony Carbery (University of Edinburgh) as part of Har monic analysis e-seminars\n\n\nAbstract\nWe discuss theories of duality wh ich are applicable to the multijoint and joint problems\, which are themse lves discrete formulations of multilinear and linear Kakeya problems. This is joint work in part with Timo Hanninen and Stefan Valdimarsson\, and in part with Michael Tang.\n LOCATION:https://researchseminars.org/talk/HAeS/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Oliver Dragičević (University of Ljubljana) DTSTART:20211215T170000Z DTEND:20211215T180000Z DTSTAMP:20260422T225759Z UID:HAeS/24 DESCRIPTION:Title: $L ^p$ asymptotics for powers of the complex Riesz transform\nby Oliver D ragičević (University of Ljubljana) as part of Harmonic analysis e-semin ars\n\n\nAbstract\nWe establish the sharp behaviour of the $L^p$ norms of integer powers of the planar Riesz transform $R_2+iR_1$\, and briefly disc uss the estimates on $L^1$ and $L^\\infty$. This is a joint work with Andr ea Carbonaro and Vjekoslav Kovač.\n LOCATION:https://researchseminars.org/talk/HAeS/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philippe Anker (Université d’Orléans) DTSTART:20220112T170000Z DTEND:20220112T180000Z DTSTAMP:20260422T225759Z UID:HAeS/25 DESCRIPTION:Title: Di spersive PDE on noncompact symmetric spaces\nby Jean-Philippe Anker (U niversité d’Orléans) as part of Harmonic analysis e-seminars\n\n\nAbst ract\nWe consider the wave equation and the Schrödinger equation on gener al symmetric spaces of the noncompact type\, which is an interesting class of Riemannian manifolds with nonpositive curvature\, including all hyperb olic spaces. The standard strategy consists in establishing first pointwis e kernel estimates for the fundamental solutions\, in deducing next disper sive and Strichartz inequalities for the linear equations\, and in applyin g them finally to semilinearities. This program was successfully achieved for various classes of manifolds over the past 40 years\, in particular fo r hyperbolic spaces 10-15 years ago. We were recently able to extend it to symmetric spaces of higher rank\, in collaboration with V. Pierfelice\, S . Meda\, M. Vallarino and H.-W. Zhang. In this talk\, we shall report on t hese progresses\, emphasizing on the tools used to tackle the higher rank case.\n LOCATION:https://researchseminars.org/talk/HAeS/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Malabika Pramanik (University of British Columbia) DTSTART:20220126T170000Z DTEND:20220126T180000Z DTSTAMP:20260422T225759Z UID:HAeS/26 DESCRIPTION:Title: On projections and circles\nby Malabika Pramanik (University of British Columbia) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThis will be a survey of two classes of problems in analysis: measuring the size o f projections of sets\, and incidences of circles in the plane. I will dis cuss some landmark results and recently discovered connections between the two.\n LOCATION:https://researchseminars.org/talk/HAeS/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Jonathan Hickman (University of Edinburgh) DTSTART:20220209T170000Z DTEND:20220209T180000Z DTSTAMP:20260422T225759Z UID:HAeS/27 DESCRIPTION:Title: Ka keya maximal estimates via real algebraic geometry\nby Jonathan Hickma n (University of Edinburgh) as part of Harmonic analysis e-seminars\n\n\nA bstract\nThe Kakeya (maximal) conjecture concerns how collections of long\ , thin tubes which point in different directions can overlap. Such geometr ic problems underpin the behaviour of various important oscillatory integr al operators and\, consequently\, understanding the Kakeya conjecture is a vital step towards many central problems in harmonic analysis. In this ta lk I will discuss work with K. Rogers and R. Zhang which apply tools from the theory of semialgebraic sets to yield new partial results on the Kakey a conjecture. Also\, more recent work with J. Zahl has used these methods to improve the range of estimates on the Fourier restriction conjecture.\n LOCATION:https://researchseminars.org/talk/HAeS/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Fernando Soria (Universidad Autónoma de Madrid) DTSTART:20220223T170000Z DTEND:20220223T180000Z DTSTAMP:20260422T225759Z UID:HAeS/28 DESCRIPTION:Title: In tegro-differential operators and nonlocal diffusion\nby Fernando Soria (Universidad Autónoma de Madrid) as part of Harmonic analysis e-seminars \n\n\nAbstract\nBy a nonlocal diffusion equation we mean an evolution prob lem where the un-\nknown function is not just reverting to its infinitesim al average\, but instead it\n\nis influenced by its values at many scales. It is still a diffusion\, but trying to\nrevert now to an integral averag e of its surrounding values.\nTypical examples in probability arise when c onsidering jump (Levy) processes\nin optimal control\, game theory and fin ance. The quasi-geostrophic equation\nfor ocean-atmosphere interaction pro vides a ’simple’ model in fluid dynamics.\n\nIn this talk we will pres ent a\, by no means exhaustive\, survey describing how\nthis theory has ev olved in recent years.\n LOCATION:https://researchseminars.org/talk/HAeS/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Marina Iliopoulou (University of Kent) DTSTART:20220309T170000Z DTEND:20220309T180000Z DTSTAMP:20260422T225759Z UID:HAeS/29 DESCRIPTION:Title: So me remarks on the Mizohata-Takeuchi conjecture\nby Marina Iliopoulou ( University of Kent) as part of Harmonic analysis e-seminars\n\n\nAbstract\ nThis is a conjecture on weighted estimates for the classical Fourier exte nsion operators of harmonic analysis. In particular\, let E be the extensi on operator associated to some surface\, and f be a function on that surfa ce. If we 'erase' part of Ef\, how well can we control the 2-norm of the r emaining piece? The Mizohata-Takeuchi conjecture claims some remarkable co ntrol on this quantity\, involving the X-ray transform of the part of the support of Ef that we kept. In this talk we will discuss the history of th e problem\, and will describe a new perspective that modestly improves our knowledge (for a certain class of weights). This is joint work with A. Ca rbery.\n LOCATION:https://researchseminars.org/talk/HAeS/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Detlef Müller (University of Kiel) DTSTART:20220323T170000Z DTEND:20220323T180000Z DTSTAMP:20260422T225759Z UID:HAeS/30 DESCRIPTION:Title: On Fourier restriction to hyperbolic 2-surfaces: robustness of the polynomia l compared to the bilinear approach\nby Detlef Müller (University of Kiel) as part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk \, which will be based on joint research with S. Buschenhenke\nand A.Varga s\, I intend to discuss some of the new challenges that arose in our\nstud ies of Fourier restriction estimates for hyperbolic surfaces\, compared to \nthe case of elliptic surfaces. Given the complexity of the bilinear\, an d even\nmore so of the polynomial partitioning approach\, I shall mainly f ocus on\nthose parts of these methods which required new ideas\, so that a familiarity\nwith these methods will not be expected from the audience.\n LOCATION:https://researchseminars.org/talk/HAeS/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Carmelo Puliatti (Euskal Herriko Unibertsitatea) DTSTART:20220413T160000Z DTEND:20220413T170000Z DTSTAMP:20260422T225759Z UID:HAeS/31 DESCRIPTION:Title: Gr adients of single layer potentials for elliptic operators with coefficient s of Dini mean oscillation-type\nby Carmelo Puliatti (Euskal Herriko U nibertsitatea) as part of Harmonic analysis e-seminars\n\n\nAbstract\nWe c onsider a uniformly elliptic operator $L_A$ in divergence form \nassociate d with a matrix $A$ with real\, bounded\, and possibly \nnon-symmetric coe fficients. If a proper $L^1$-mean oscillation of the \ncoefficients of $A$ satisfies suitable Dini-type assumptions\, we prove \nthe following: if $ \\mu$ is a compactly supported Radon measure in \n$R^{n+1}\, n\\geq 2\,$ the $L^2(\\mu)$-operator norm of the gradient of the \nsingle layer potent ial $T_\\mu$ associated with $L_A$ is comparable to the \n$L^2$-norm of th e $n$-dimensional Riesz transform $R_\\mu$\, modulo an \nadditive constant .\nThis makes possible to obtain direct generalizations of some deep \ngeo metric results\, initially proved for the Riesz transform\, which \nwere r ecently extended to $T_\\mu$ under a H\\"older continuity assumption \non the coefficients of the matrix $A$.\n\nThis is a joint work with Alejandro Molero\, Mihalis Mourgoglou\, and \nXavier Tolsa.\n LOCATION:https://researchseminars.org/talk/HAeS/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Sandra Saliani (Università degli Studi della Basilicata) DTSTART:20220420T160000Z DTEND:20220420T170000Z DTSTAMP:20260422T225759Z UID:HAeS/32 DESCRIPTION:Title: Sp ectral graph transforms: wavelets\, frames\, and open problems\nby San dra Saliani (Università degli Studi della Basilicata) as part of Harmonic analysis e-seminars\n\n\nAbstract\nClassical transforms\, as Fourier\, wa velet\, wavelet packets and time-frequency dictionaries have been general ized to functions defined on finite\, undirected graphs\, where the connec tions between vertices are encoded by the Laplacian matrix.\n\nDespite wor king in a finite and discrete environment\, many problems arise in applica tions where the graph is very large\, as it is not possible to determine a ll the eigenvectors of the Laplacian explicitly. For example\, in the case of our interest: a voxel-wise brain graph $\\mathcal{G}$ with $900760$ no des (representing the brain voxels)\, and signals given by the fRMI (funct ional magnetic resonance imaging).\n\nAfter an overview of the methods and of the open problems\, we present a new method to generate frames of wav elet packets defined in the graph spectral domain to represent signals on finite graphs.\n\n\nJoint work with Iulia Martina Bulai.\n LOCATION:https://researchseminars.org/talk/HAeS/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Roberto Bramati (Ghent University) DTSTART:20220518T160000Z DTEND:20220518T170000Z DTSTAMP:20260422T225759Z UID:HAeS/33 DESCRIPTION:Title: Re sonances of invariant differential operators\nby Roberto Bramati (Ghen t University) as part of Harmonic analysis e-seminars\n\n\nAbstract\nGiven a self-adjoint differential operator with continuous spectrum acting on a Hilbert space H\, its resonances are the poles of a meromorphic extension across the spectrum of its resolvent acting on a dense subspace of H in w hich the operator is no longer self-adjoint. They can be thought of as rep lacements of eigenvalues for problems on noncompact domains. In this talk we will first explore two well-understood cases: the Laplacian on Euclidea n spaces and the Laplace-Beltrami operator on rank one Riemannian symmetri c spaces of the noncompact type\, two settings where a notion of Fourier a nalysis is available. In both cases\, the Laplacian comes from the action of the Casimir operator through the left regular representation of the und erlying group\, and the Plancherel formula provides a direct integral deco mposition of such representation. Elaborating from this point of view\, in collaboration with A. Pasquale and T. Przebinda we started to develop met hods to study resonances in more general settings. As an example of such m ethods\, in the talk we will consider some instances of Capelli operators and see how one can exploit Howe’s theory for reductive dual pairs. We w ill also consider the problem of identifying the representations that are naturally attached to the resonances in these settings.\n LOCATION:https://researchseminars.org/talk/HAeS/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Vitturi (University College Cork) DTSTART:20220615T160000Z DTEND:20220615T170000Z DTSTAMP:20260422T225759Z UID:HAeS/34 DESCRIPTION:Title: A restricted 2-plane transform related to Fourier Restriction in codimension 2\nby Marco Vitturi (University College Cork) as part of Harmonic ana lysis e-seminars\n\n\nAbstract\nThe $2-$plane transform is the operator th at maps a function to its averages along affine $2-$planes. We consider th e operator obtained by restricting the allowed directions of the $2-$plane s to those normal to a fixed surface $S$ (quadratic\, for simplicity) of c odimension $2$. By duality and discretisation\, $L^p\\to L^q$ estimates fo r such an operator imply Kakeya-type estimates for the supports of Fourier -transformed wave-packets adapted to the surface $S$ (wave-packet decompos itions being a powerful tool in proving Fourier Restriction results). We c onnect this operator to Gressman's theory of affine invariant measures by showing that if the surface is well-curved à la Gressman (meaning\, the a ffine invariant surface measure on S is non-vanishing) then the restricted $2-$plane transform is $L^p\\to L^q$ bounded in the maximal range of $(p\ ,q)$ exponents allowed. The proof relies on a characterisation of well-cur vedness in Geometric Invariant Theory terms\, which will be discussed.\nJo int work with S. Dendrinos and A. Mustata.\n LOCATION:https://researchseminars.org/talk/HAeS/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Sinai Robins (Universidade de São Paulo) DTSTART:20220629T160000Z DTEND:20220629T170000Z DTSTAMP:20260422T225759Z UID:HAeS/35 DESCRIPTION:Title: Th e covariogram and extensions of the Bombieri-Siegel formula\nby Sinai Robins (Universidade de São Paulo) as part of Harmonic analysis e-semina rs\n\n\nAbstract\nWe extend a formula of C. L. Siegel in the geometry of n umbers\, allowing the body to contain an arbitrary number of interior latt ice points. Our extension involves a lattice sum of the cross covariogram for any two bounded sets $A\, B\\subseteq \\mathbb R^d$\, and turns out to also extend a\nresult of E. Bombieri. We begin with a new variation of th e Poisson summation formula\, which may be of independent interest. One of the consequences of these results is a new characterization of multitilin gs of Euclidean space by translations\, which is an application of Bombier i’s identity and of our extension of it. Some classical results\, such a s Van der Corput’s inequality\, and Hardy’s identity for the Gauss cir cle problem\, also follow as corollaries. This is joint work with Michel F aleiros Martins.\n LOCATION:https://researchseminars.org/talk/HAeS/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Izabella Łaba (University of British Columbia) DTSTART:20221005T160000Z DTEND:20221005T170000Z DTSTAMP:20260422T225759Z UID:HAeS/36 DESCRIPTION:Title: Fa vard length estimates via cyclotomic divisibility\nby Izabella Łaba ( University of British Columbia) as part of Harmonic analysis e-seminars\n\ n\nAbstract\nThe Favard length of a planar set $E$ is the average length o f its one-dimensional projections. It is well known (due to Besicovitch) t hat if $E$ is a purely unrectifiable planar self-similar set of Hausdorff dimension 1\, then its Favard length is 0. Consequently\, if $E_\\delta$ i s the $\\delta$-neighbourhood of $E$\, then the Favard length of $E_\\delt a$ goes to 0 as $\\delta\\to 0$. A question of interest in geometric measu re theory\, ergodic theory and analytic function theory is to estimate the rate of decay\, both from above and below. Partial results in this direct ion have been proved by many authors\, including Mattila\, Nazarov\, Perez \, Volberg\, Bond\, Bateman\, and myself. In addition to geometric measure theory\, this work has involved methods from harmonic analysis\, additive combinatorics\, and algebraic number theory. I will review the relevant b ackground\, and then discuss my recent work with Caleb Marshall on upper b ounds on the Favard length for 1-dimensional planar Cantor sets with a rat ional product structure. This improves on my earlier work with Bond and Vo lberg\, and incorporates new methods introduced in my work with Itay Londn er on integer tilings.\n LOCATION:https://researchseminars.org/talk/HAeS/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Eugenia Malinnikova (Stanford University - NTNU) DTSTART:20221019T160000Z DTEND:20221019T170000Z DTSTAMP:20260422T225759Z UID:HAeS/37 DESCRIPTION:Title: So me inequalities for Laplace eigenfunctions and their gradients\nby Eug enia Malinnikova (Stanford University - NTNU) as part of Harmonic analysi s e-seminars\n\n\nAbstract\nWe will survey some recent results on restrict ions of Laplace eigenfunctions\nand present new norm inequalities for the eigenfunctions and their gradients\nobtained in a joint work with Stefano Decio. The guiding principle\, which\ngoes back to the works of Donnelly a nd Fefferman\, is that eigenfunctions with\neigenvalue $\\textrm{E}^2$ beh ave like (harmonic) polynomials of degree $\\textrm{E}$.\n LOCATION:https://researchseminars.org/talk/HAeS/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Giancarlo Travaglini (University of Milano-Bicocca) DTSTART:20221116T170000Z DTEND:20221116T180000Z DTSTAMP:20260422T225759Z UID:HAeS/38 DESCRIPTION:Title: Ir regularities of distribution\nby Giancarlo Travaglini (University of M ilano-Bicocca) as part of Harmonic analysis e-seminars\n\n\nAbstract\nThe term “Irregularities of distribution” appeared for the first time in t he title of 1954 K. Roth’s seminal paper and referred to a conjecture of J. van der Corput on the non-existence of a “good” way to choose an infinite sequence in the unit interval. Roth approached van der Corput’s conjecture by checking the quality of any choice of N points in the 2-dim ensional torus with respect to arbitrary squares therein\, and proving a l ogarithmic lower bound for the discrepancy. Later W. Schmidt\, H. Montgome ry and J. Beck independently proved that the discrepancy is at least a pow er of N when squares are replaced with disks. \n\nWe construct a family of intermediate cases and we show that positive curvature plays no role in t his problem which reduces to a careful study of the decay of certain Fouri er transforms.\n\nWe shall also describe two related d-dimensional problem s. \n\n(from joint works with Luca Brandolini and Leonardo Colzani)\n LOCATION:https://researchseminars.org/talk/HAeS/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Rajula Srivastava (University of Bonn - Max Planck Institute for M athematics) DTSTART:20230111T170000Z DTEND:20230111T180000Z DTSTAMP:20260422T225759Z UID:HAeS/39 DESCRIPTION:Title: Th e Korányi Spherical Maximal Function on Heisenberg groups\nby Rajula Srivastava (University of Bonn - Max Planck Institute for Mathematics) as part of Harmonic analysis e-seminars\n\n\nAbstract\nIn this talk\, we disc uss the problem of obtaining sharp $L^p \\to L^q$ estimates for the local maximal operator associated with averaging over dilates of the Korányi sp here on Heisenberg groups. This is a codimension one surface compatible wi th the non-isotropic Heisenberg dilation structure. I will describe the ma in features of the problem\, some of which are helpful while others are ob structive. These include the non-Euclidean group structure (the extra “t wist” due to the Heisenberg group law)\, the geometry of the Korányi sp here (in particular\, the flatness at the poles) and an “imbalanced” s caling argument encapsulated by a new type of Knapp example\, which we sha ll describe in detail.\n LOCATION:https://researchseminars.org/talk/HAeS/39/ END:VEVENT BEGIN:VEVENT SUMMARY:David Beltran (University of Valencia) DTSTART:20230125T170000Z DTEND:20230125T180000Z DTSTAMP:20260422T225759Z UID:HAeS/40 DESCRIPTION:Title: En dpoint sparse domination for oscillatory Fourier multipliers\nby David Beltran (University of Valencia) as part of Harmonic analysis e-seminars\ n\n\nAbstract\nSparse domination was first introduced in the context of Ca lderón--Zygmund theory. Shortly after\, the concept was successfully exte nded to many other operators in Harmonic Analysis\, although many endpoint situations have remained unknown. In this talk\, we will present new endp oint sparse bounds for oscillatory and Miyachi-type Fourier multipliers us ing Littlewood--Paley theory. Furthermore\, the results can be extended to more general dilation-invariant classes of multiplier transformations via Hardy space techniques\, yielding results\, for instance\, for multi-scal e sums of radial bump multipliers.\n LOCATION:https://researchseminars.org/talk/HAeS/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesca Bartolucci (ETH - Zurich) DTSTART:20230208T170000Z DTEND:20230208T180000Z DTSTAMP:20260422T225759Z UID:HAeS/41 DESCRIPTION:Title: Wh at's new in wavelet phase retrieval?\nby Francesca Bartolucci (ETH - Z urich) as part of Harmonic analysis e-seminars\n\n\nAbstract\nWavelet phas e retrieval consists of the inverse problem of reconstructing a square-int egrable function $f$ from its scalogram\, that is from the absolute value of its wavelet transform\n\\[\n \\mathcal{W}_{\\phi}f(b\,a) = a^{-\\fra c{1}{2}} \\int_{\\R} f(x) \\overline{\\phi\\left(\\frac{x-b}{a}\\right)} \ \\,\\mathrm{d} x\, \\qquad b \\in \\R\,~a \\in \\R_+. \n\\]\nThe wavelet t ransform emerged from the research activities aimed to develop new analysi s and processing tools to enhance signal theory\, and has proved to be ext remely efficient in various applications such as denoising and compression . However\, there is still limited knowledge of the problem of reconstruct ing a function from the absolute value of its wavelet transform. More prec isely\, wavelet phase retrieval aims to determine for which analyzing wave lets $\\phi$ and which choices of $\\Lambda \\subseteq \\R \\times \\R_+$ as well as $\\mathcal{M} \\subseteq L^2(\\R)$ the forward operator \n\\[\n F_\\phi : \\mathcal{M} /\\!\\sim \\\, \\to\\\, [0\,+\\infty)^\\Lambda\,\\q quad F_\\phi f(b\,a) = \\lvert \\mathcal{W}_\\phi f (b\,a) \\rvert\, \\qua d (b\,a) \\in \\Lambda\,\n\\]\nis injective\, where $f\\sim g$ if and only if $f=\\text{e}^{i\\alpha}g$ for some $\\alpha\\in\\R$. In this talk\, we present old and new results on this question and conclude by discussing s ome open problems.\n LOCATION:https://researchseminars.org/talk/HAeS/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Diogo Oliveira e Silva (Instituto Superior Técnico Lisboa) DTSTART:20230308T170000Z DTEND:20230308T180000Z DTSTAMP:20260422T225759Z UID:HAeS/42 DESCRIPTION:Title: Ex ponentials rarely maximize Fourier extension inequalities for cones\nb y Diogo Oliveira e Silva (Instituto Superior Técnico Lisboa) as part of H armonic analysis e-seminars\n\n\nAbstract\nThis talk is based on recent jo int work with G. Negro\, B. Stovall and J. Tautges.\nGlobal maximizers for the $L^2$ Fourier extension inequality on the cone in $\\mathbb R^{1+d}$ have been characterized in the lowest-dimensional cases $d\\in\\{2\,3\\}$. We prove that these functions are critical points for the $L^p$ to $L^q$ Fourier extension inequality if and only if $p=2$. We also establish the e xistence of maximizers and the precompactness of $L^p$-normalized maximizi ng sequences modulo symmetries for all valid scale-invariant Fourier exten sion inequalities on the cone in $\\mathbb R^{1+d}$. In the range for whic h such inequalities are conjectural\, our result is conditional on the bou ndedness of the extension operator. The proof uses tools from the calculus of variations\, bilinear restriction theory\, conformal geometry and the theory of special functions.\n LOCATION:https://researchseminars.org/talk/HAeS/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Nir Lev (Bar-Ilan University) DTSTART:20230322T170000Z DTEND:20230322T180000Z DTSTAMP:20260422T225759Z UID:HAeS/43 DESCRIPTION:Title: Ti ling by translates of a function\nby Nir Lev (Bar-Ilan University) as part of Harmonic analysis e-seminars\n\n\nAbstract\nI will discuss tilings of the real line by translates of a function $f$\, that is\, systems $\\{ f(x - \\lambda)\, \\lambda \\in \\Lambda\\}$ of translates of $f$ that for m a partition of unity. Which functions $f$ can tile by translations\, and what can be the structure of the translation set $\\Lambda$? I will surve y the subject and present some recent results.\n LOCATION:https://researchseminars.org/talk/HAeS/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Dmitriy Bilyk (University of Minnesota) DTSTART:20230419T160000Z DTEND:20230419T170000Z DTSTAMP:20260422T225759Z UID:HAeS/44 DESCRIPTION:Title: Mi nimizers of discrete measures and energy integrals.\nby Dmitriy Bilyk (University of Minnesota) as part of Harmonic analysis e-seminars\n\n\nAb stract\nWe shall survey various results and conjectures about energy mini mization problems that arise in different fields: electrostatics\, discret e and metric geometry\, discrepancy theory and uniform distribution\, sign al processing etc. While in many natural examples optimizing the energy i mposes uniform distribution\, we shall pay special attention to the opposi te effect -- when minimizers exhibit clustering or discretization\, or are supported on small or lower dimensional subsets. We shall also touch upon energies that depend on interactions of three or more particles\, rather than just pairwise interactions\, and describe difficulties that arise in this setting.\n LOCATION:https://researchseminars.org/talk/HAeS/44/ END:VEVENT END:VCALENDAR