BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jiaming Chen (Université Paris 7) DTSTART:20200413T080000Z DTEND:20200413T090000Z DTSTAMP:20260404T110645Z UID:ComplexGeometry/1 DESCRIPTION:Title: O-minimality and its applications (after Pila-Zannier\, Bak ker-Brunebarbe-Klingler-Tsimerman)\nby Jiaming Chen (Université Paris 7) as part of Complex geometry seminar\n\n\nAbstract\nO-minimal structure s\, originally developed by model-theorists\, provide an excellent framewo rk for developing tame topology which was prophesied by Grothendieck in hi s “Esquisse d’un Programme” as a way to amend the inadequacy of the foundations of general topology.\n\nRecent applications of o-minimality ha s revealed its powerful capabilities in understanding some transcendental phenomena appeared in arithmetic and complex algebraic geometry. For examp le\,\n\n (1) it plays a crucial role\, via the celebrated Pila-Wilkie counting theorem\, in the Pila-Zannier’s strategy to attack the Andr ́e - Oort (more general Zilber-Pink) conjecture.\n\n (2) it can be used t o prove some global algebraic results without renouncing the local flexibi lity of analytic varieties\, for instance\, the o-minimal Chow theorem of Peterzil-Starchenko and the very recent applications in classical Hodge th eory (a new proof of a fundamental theorem of Cattani-Deligne- Kaplan on t he algebraicity of Hodge loci by Bakker- Klingler- Tsimerman and a resolut ion of the Griffiths conjecture on the quasiprojectivity of period images by Bakker-Brunebarbe- Tsimerman).\n\nIn the first talk\, I will give a bri ef introduction to o-minimal struc- tures and outline the proof of Manin-M umford conjecture (originally proved by Raynaud using p-adic method) by Pi la-Zannier using o- minimality (after Pila-Zannier).\n\nIn the second talk \, I will discuss the idea of the proof of the above- mentioned Griffiths conjecture (after Bakker\, Brunebarbe\, Klingler and Tsimerman).\n LOCATION:https://stable.researchseminars.org/talk/ComplexGeometry/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Jiaming Chen (Humboldt Universität) DTSTART:20200420T080000Z DTEND:20200420T090000Z DTSTAMP:20260404T110645Z UID:ComplexGeometry/2 DESCRIPTION:Title: O-minimality and its applications Part II\nby Jiaming C hen (Humboldt Universität) as part of Complex geometry seminar\n\nAbstrac t: TBA\n LOCATION:https://stable.researchseminars.org/talk/ComplexGeometry/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Feng Hao (KU Leuven) DTSTART:20200504T073000Z DTEND:20200504T090000Z DTSTAMP:20260404T110645Z UID:ComplexGeometry/3 DESCRIPTION:Title: Limits of Hodge structures Part II (after Steenbrink)\n by Feng Hao (KU Leuven) as part of Complex geometry seminar\n\n\nAbstract\ nFor a family projective varieties degenerating to a singular fiber over a disc\, a limit of pure Hodge structures of general fibers exists as a mix ed Hodge when general fibers approach to the singular fiber. The existence of the limit is first given by Schmid in his celebrated paper “Variatio n of Hodge Structure: The Singularities of the Period Mapping”. There ar e many applications of the existence of limit mixed Hodge structures in th e study of singular fibers of degenerations\, compactification of moduli spaces\, milnor fibers associated to isolated singular points\, cycle theo ry\, etc. In this learning seminar\, I will intoduce the algebraic constr uction of limit mixed Hodge structures given by Steenbrink. The weight fil tration and Hodge filtration are defined over a double complex\, which res olves the cohomology of nearby fiber. Also\, I will cover some basic prop erties of the limit mixed Hodge structure\, and the integral structure via log structures.\n\nReferences: 1. Steenbrink\, Joseph. "Limits of Hodge s tructures." Inventiones mathematicae 31.3 (1976): 229-257. \n\n2. Steenbri nk\, Joseph. "Logarithmic embeddings of varieties with normal crossings an d mixed Hodge structures." Mathematische Annalen 301.1 (1995): 105-118\n\n Zoom conference id: 628 2794 0077\n\nPassword: dim M_{10\,3}\, where M_{10 \,3} denotes the moduli stack of smooth genus 10 algebraic curves with 3 m arked points.\n LOCATION:https://stable.researchseminars.org/talk/ComplexGeometry/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Feng Hao (KU Leuven) DTSTART:20200427T073000Z DTEND:20200427T090000Z DTSTAMP:20260404T110645Z UID:ComplexGeometry/4 DESCRIPTION:Title: Limits of Hodge structures Part I (after Steenbrink)\nb y Feng Hao (KU Leuven) as part of Complex geometry seminar\n\n\nAbstract\n For a family projective varieties degenerating to a singular fiber over a disc\, a limit of pure Hodge structures of general fibers exists as a mixe d Hodge when general fibers approach to the singular fiber. The existence of the limit is first given by Schmid in his celebrated paper “Variation of Hodge Structure: The Singularities of the Period Mapping”. There are many applications of the existence of limit mixed Hodge structures in the study of singular fibers of degenerations\, compactification of moduli s paces\, milnor fibers associated to isolated singular points\, cycle theor y\, etc. In this learning seminar\, I will intoduce the algebraic constru ction of limit mixed Hodge structures given by Steenbrink. The weight filt ration and Hodge filtration are defined over a double complex\, which reso lves the cohomology of nearby fiber. Also\, I will cover some basic prope rties of the limit mixed Hodge structure\, and the integral structure via log structures.\n\nReferences: 1. Steenbrink\, Joseph. "Limits of Hodge st ructures." Inventiones mathematicae 31.3 (1976): 229-257. \n\n2. Steenbrin k\, Joseph. "Logarithmic embeddings of varieties with normal crossings and mixed Hodge structures." Mathematische Annalen 301.1 (1995): 105-118\n LOCATION:https://stable.researchseminars.org/talk/ComplexGeometry/4/ END:VEVENT END:VCALENDAR