BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jean-Pierre Demailly (Université Grenoble Alpes/ Institut Fourier ) DTSTART:20210507T140000Z DTEND:20210507T152000Z DTSTAMP:20260422T225848Z UID:Rutgers_Complex/1 DESCRIPTION:Title: Hermitian-Yang-Mills approach to the conjecture of Griffiths on th e positivity of ample vector bundles\nby Jean-Pierre Demailly (Univers ité Grenoble Alpes/ Institut Fourier) as part of Rutgers Seminar on Compl ex Analysis\, Harmonic Analysis and Complex Geometry\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Rutgers_Complex/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yum-Tong Siu (Harvard University) DTSTART:20210514T143000Z DTEND:20210514T153000Z DTSTAMP:20260422T225848Z UID:Rutgers_Complex/2 DESCRIPTION:Title: Global non-deformability\, super rigidity\, and rigidity of vector bundles and CR manifolds\nby Yum-Tong Siu (Harvard University) as par t of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Complex G eometry\n\n\nAbstract\nAbstract: Flat directions are obstacles and at the same time also essential tools for a number of fundamental problems in sev eral complex variables involving rigidity and regularity. Among them are the following examples.\n\n(i) The global non-deformability of irreducibl e compact Hermitian symmetric manifolds.\n\n(ii) The strong rigidity and s uper rigidity problem of holomorphic maps with curvature condition on the target manifold.\n\n(iii) The regularity question of the complex Neumann p roblem for weakly pseudoconvex domains.\n\n(iv) Rigidity and strong rigidi ty problems of holomorphic vector bundles.\n\n(v) Rigidity and strong rigi dity problems of CR manifolds.\n\nFor global nondeformability and regulari ty problems for pseudoconvexity domains flat directions are obstacles. Fo r rigidity of metrics and CR manifolds with the possibility of small pertu rbations\, flat directions are essential tools. The talk starts with the h istoric motivations of the problems and does not assume any background mor e than basic complex analysis. After discussing the general techniques in volving flat directions\, we will focus on the global non-deformability pr oblem and some recent methods in this area.\n LOCATION:https://researchseminars.org/talk/Rutgers_Complex/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Loredana Lanzani (Syracuse University) DTSTART:20210528T143000Z DTEND:20210528T153000Z DTSTAMP:20260422T225848Z UID:Rutgers_Complex/3 DESCRIPTION:Title: The commutator of the Cauchy-Szegö projection for domains in \\C^ n with minimal smoothness\nby Loredana Lanzani (Syracuse University) a s part of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Comp lex Geometry\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/Rutgers_Complex/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Wright (The University of Edinburgh) DTSTART:20210604T143000Z DTEND:20210604T153000Z DTSTAMP:20260422T225848Z UID:Rutgers_Complex/4 DESCRIPTION:Title: A theory for complex oscillatory integrals\nby Jim Wright (The University of Edinburgh) as part of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Complex Geometry\n\n\nAbstract\nHere we develop a t heory for oscillatory integrals with complex phases. Basic scale-invariant bounds for these oscillatory integrals do not hold in the generality that they do in the real setting. In fact they fail in the category of complex analytic phases but we develop a perspective and arguments to establish s cale-invariant bounds for complex polynomial phases.\n LOCATION:https://researchseminars.org/talk/Rutgers_Complex/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Xianghong Gong (University of Wisconsin-Madison) DTSTART:20210611T143000Z DTEND:20210611T153000Z DTSTAMP:20260422T225848Z UID:Rutgers_Complex/5 DESCRIPTION:Title: On regularity of $\\dbar$ solutions on $a_q$ domains with $C^2$ bo undary in complex manifolds\nby Xianghong Gong (University of Wisconsi n-Madison) as part of Rutgers Seminar on Complex Analysis\, Harmonic Analy sis and Complex Geometry\n\n\nAbstract\nWe study regularity of $\\dbar$ so lutions on a relatively compact $C^2$ domain $D$ in a complex manifold. Su ppose that the boundary of the domain has everywhere either $(q+1)$ negati ve or $(n-q)$ positive Levi eigenvalues. Under a necessary condition on th e existence of a locally $L^2$ solution on the domain\, we show the existe nce of the solutions on the closure of the domain that gain $1/2$ derivati ve when $q=1$ and the given $(0\,q)$ form in the $\\dbar$ equation is in t he H\\"older-Zygmund space $\\Lambda^r(\\overline D)$ with $r>1$. For $q>1 $\, the same regularity for the solutions is achieved when the boundary is either sufficiently smooth or of $(n-q)$ positive Levi eigenvalues everyw here.\n LOCATION:https://researchseminars.org/talk/Rutgers_Complex/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Liding Yao (University of Wisconsin-Madison) DTSTART:20220304T153000Z DTEND:20220304T163000Z DTSTAMP:20260422T225848Z UID:Rutgers_Complex/6 DESCRIPTION:Title: An In-depth Look of Rychkov's Universal Extension Operators for Li pschitz Domains\nby Liding Yao (University of Wisconsin-Madison) as pa rt of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Complex Geometry\n\n\nAbstract\nAbstract: Given a bounded Lipschitz domain D in R^ n\, Rychkov showed that there is a linear extension operator E for D which is bounded in Besov and Triebel-Lizorkin spaces. In this talk\, we introd uce several new properties and estimates of the extension operator E and g ive some applications. In particular\, we prove an equivalent norm propert y for general Besov and Triebel-Lizorkin spaces\, which appears to be a we ll-known result but lacks a complete and correct proof to our best knowled ge. We also derive some quantitative smoothing estimates of the extended f unction outside the domain up to boundary. This is joint work with Ziming Shi.\n LOCATION:https://researchseminars.org/talk/Rutgers_Complex/6/ END:VEVENT END:VCALENDAR