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:20260404T100033Z UID:Rutgers_Complex/1 DESCRIPTION:Title: Hermitian-Yang-Mills approach to the conjecture of Griffith s on the positivity of ample vector bundles\nby Jean-Pierre Demailly ( Université Grenoble Alpes/ Institut Fourier) as part of Rutgers Seminar o n Complex Analysis\, Harmonic Analysis and Complex Geometry\n\nAbstract: T BA\n LOCATION:https://stable.researchseminars.org/talk/Rutgers_Complex/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yum-Tong Siu (Harvard University) DTSTART:20210514T143000Z DTEND:20210514T153000Z DTSTAMP:20260404T100033Z 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 part of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and Co mplex Geometry\n\n\nAbstract\nAbstract: Flat directions are obstacles and at the same time also essential tools for a number of fundamental problems in several complex variables involving rigidity and regularity. Among th em are the following examples.\n\n(i) The global non-deformability of irr educible compact Hermitian symmetric manifolds.\n\n(ii) The strong rigidit y and super rigidity problem of holomorphic maps with curvature condition on the target manifold.\n\n(iii) The regularity question of the complex Ne umann problem for weakly pseudoconvex domains.\n\n(iv) Rigidity and strong rigidity problems of holomorphic vector bundles.\n\n(v) Rigidity and stro ng rigidity problems of CR manifolds.\n\nFor global nondeformability and r egularity problems for pseudoconvexity domains flat directions are obstacl es. For rigidity of metrics and CR manifolds with the possibility of smal l perturbations\, flat directions are essential tools. The talk starts wit h the historic motivations of the problems and does not assume any backgro und more than basic complex analysis. After discussing the general techni ques involving flat directions\, we will focus on the global non-deformabi lity problem and some recent methods in this area.\n LOCATION:https://stable.researchseminars.org/talk/Rutgers_Complex/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Loredana Lanzani (Syracuse University) DTSTART:20210528T143000Z DTEND:20210528T153000Z DTSTAMP:20260404T100033Z 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 Univer sity) as part of Rutgers Seminar on Complex Analysis\, Harmonic Analysis a nd Complex Geometry\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/Rutgers_Complex/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jim Wright (The University of Edinburgh) DTSTART:20210604T143000Z DTEND:20210604T153000Z DTSTAMP:20260404T100033Z UID:Rutgers_Complex/4 DESCRIPTION:Title: A theory for complex oscillatory integrals\nby Jim Wrig ht (The University of Edinburgh) as part of Rutgers Seminar on Complex Ana lysis\, Harmonic Analysis and Complex Geometry\n\n\nAbstract\nHere we deve lop a theory for oscillatory integrals with complex phases. Basic scale-in variant bounds for these oscillatory integrals do not hold in the generali ty 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 esta blish scale-invariant bounds for complex polynomial phases.\n LOCATION:https://stable.researchseminars.org/talk/Rutgers_Complex/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Xianghong Gong (University of Wisconsin-Madison) DTSTART:20210611T143000Z DTEND:20210611T153000Z DTSTAMP:20260404T100033Z UID:Rutgers_Complex/5 DESCRIPTION:Title: On regularity of $\\dbar$ solutions on $a_q$ domains with $ C^2$ boundary in complex manifolds\nby Xianghong Gong (University of W isconsin-Madison) as part of Rutgers Seminar on Complex Analysis\, Harmoni c Analysis and Complex Geometry\n\n\nAbstract\nWe study regularity of $\\d bar$ solutions on a relatively compact $C^2$ domain $D$ in a complex manif old. Suppose that the boundary of the domain has everywhere either $(q+1)$ negative or $(n-q)$ positive Levi eigenvalues. Under a necessary conditio n on the existence of a locally $L^2$ solution on the domain\, we show the existence of the solutions on the closure of the domain that gain $1/2$ d erivative when $q=1$ and the given $(0\,q)$ form in the $\\dbar$ equation is in the H\\"older-Zygmund space $\\Lambda^r(\\overline D)$ with $r>1$. F or $q>1$\, the same regularity for the solutions is achieved when the boun dary is either sufficiently smooth or of $(n-q)$ positive Levi eigenvalues everywhere.\n LOCATION:https://stable.researchseminars.org/talk/Rutgers_Complex/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Liding Yao (University of Wisconsin-Madison) DTSTART:20220304T153000Z DTEND:20220304T163000Z DTSTAMP:20260404T100033Z UID:Rutgers_Complex/6 DESCRIPTION:Title: An In-depth Look of Rychkov's Universal Extension Operators for Lipschitz Domains\nby Liding Yao (University of Wisconsin-Madison ) as part of Rutgers Seminar on Complex Analysis\, Harmonic Analysis and C omplex 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 introduce several new properties and estimates of the extension operator E and give some applications. In particular\, we prove an equivalent norm property for general Besov and Triebel-Lizorkin spaces\, which appears to be a well-known result but lacks a complete and correct proof to our best knowledge. We also derive some quantitative smoothing estimates of the ext ended function outside the domain up to boundary. This is joint work with Ziming Shi.\n LOCATION:https://stable.researchseminars.org/talk/Rutgers_Complex/6/ END:VEVENT END:VCALENDAR