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SUMMARY:Jiaming Chen (Université Paris 7)
DTSTART;VALUE=DATE-TIME:20200413T080000Z
DTEND;VALUE=DATE-TIME:20200413T090000Z
DTSTAMP;VALUE=DATE-TIME:20230926T000708Z
UID:ComplexGeometry/1
DESCRIPTION:Title: O-minimality and its applications (after Pila-Zannier\, Bakker-Bru
nebarbe-Klingler-Tsimerman)\nby Jiaming Chen (Université Paris 7) as
part of Complex geometry seminar\n\n\nAbstract\nO-minimal structures\, ori
ginally developed by model-theorists\, provide an excellent framework for
developing tame topology which was prophesied by Grothendieck in his “Es
quisse d’un Programme” as a way to amend the inadequacy of the foundat
ions of general topology.\n\nRecent applications of o-minimality has revea
led its powerful capabilities in understanding some transcendental phenome
na appeared in arithmetic and complex algebraic geometry. For example\,\n\
n (1) it plays a crucial role\, via the celebrated Pila-Wilkie countin
g 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 to prove
some global algebraic results without renouncing the local flexibility of
analytic varieties\, for instance\, the o-minimal Chow theorem of Peterzi
l-Starchenko and the very recent applications in classical Hodge theory (a
new proof of a fundamental theorem of Cattani-Deligne- Kaplan on the alge
braicity of Hodge loci by Bakker- Klingler- Tsimerman and a resolution of
the Griffiths conjecture on the quasiprojectivity of period images by Bakk
er-Brunebarbe- Tsimerman).\n\nIn the first talk\, I will give a brief intr
oduction to o-minimal struc- tures and outline the proof of Manin-Mumford
conjecture (originally proved by Raynaud using p-adic method) by Pila-Zann
ier using o- minimality (after Pila-Zannier).\n\nIn the second talk\, I wi
ll discuss the idea of the proof of the above- mentioned Griffiths conject
ure (after Bakker\, Brunebarbe\, Klingler and Tsimerman).\n
LOCATION:https://researchseminars.org/talk/ComplexGeometry/1/
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BEGIN:VEVENT
SUMMARY:Jiaming Chen (Humboldt Universität)
DTSTART;VALUE=DATE-TIME:20200420T080000Z
DTEND;VALUE=DATE-TIME:20200420T090000Z
DTSTAMP;VALUE=DATE-TIME:20230926T000708Z
UID:ComplexGeometry/2
DESCRIPTION:Title: O-minimality and its applications Part II\nby Jiaming Chen (Hu
mboldt Universität) as part of Complex geometry seminar\n\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/ComplexGeometry/2/
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SUMMARY:Feng Hao (KU Leuven)
DTSTART;VALUE=DATE-TIME:20200504T073000Z
DTEND;VALUE=DATE-TIME:20200504T090000Z
DTSTAMP;VALUE=DATE-TIME:20230926T000708Z
UID:ComplexGeometry/3
DESCRIPTION:Title: Limits of Hodge structures Part II (after Steenbrink)\nby 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 mixed Hodg
e when general fibers approach to the singular fiber. The existence of the
limit is first given by Schmid in his celebrated paper “Variation of Ho
dge 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 spaces\
, milnor fibers associated to isolated singular points\, cycle theory\, et
c. In this learning seminar\, I will intoduce the algebraic construction
of limit mixed Hodge structures given by Steenbrink. The weight filtration
and Hodge filtration are defined over a double complex\, which resolves t
he cohomology of nearby fiber. Also\, I will cover some basic properties
of the limit mixed Hodge structure\, and the integral structure via log st
ructures.\n\nReferences: 1. Steenbrink\, Joseph. "Limits of Hodge structur
es." Inventiones mathematicae 31.3 (1976): 229-257. \n\n2. Steenbrink\, Jo
seph. "Logarithmic embeddings of varieties with normal crossings and mixed
Hodge structures." Mathematische Annalen 301.1 (1995): 105-118\n\nZoom co
nference id: 628 2794 0077\n\nPassword: dim M_{10\,3}\, where M_{10\,3} de
notes the moduli stack of smooth genus 10 algebraic curves with 3 marked p
oints.\n
LOCATION:https://researchseminars.org/talk/ComplexGeometry/3/
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SUMMARY:Feng Hao (KU Leuven)
DTSTART;VALUE=DATE-TIME:20200427T073000Z
DTEND;VALUE=DATE-TIME:20200427T090000Z
DTSTAMP;VALUE=DATE-TIME:20230926T000708Z
UID:ComplexGeometry/4
DESCRIPTION:Title: Limits of Hodge structures Part I (after Steenbrink)\nby Feng
Hao (KU Leuven) as part of Complex geometry seminar\n\n\nAbstract\nFor a f
amily projective varieties degenerating to a singular fiber over a disc\,
a limit of pure Hodge structures of general fibers exists as a mixed 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 Hod
ge Structure: The Singularities of the Period Mapping”. There are many a
pplications of the existence of limit mixed Hodge structures in the study
of singular fibers of degenerations\, compactification of moduli spaces\,
milnor fibers associated to isolated singular points\, cycle theory\, etc
. In this learning seminar\, I will intoduce the algebraic construction o
f limit mixed Hodge structures given by Steenbrink. The weight filtration
and Hodge filtration are defined over a double complex\, which resolves th
e cohomology of nearby fiber. Also\, I will cover some basic properties o
f the limit mixed Hodge structure\, and the integral structure via log str
uctures.\n\nReferences: 1. Steenbrink\, Joseph. "Limits of Hodge structure
s." Inventiones mathematicae 31.3 (1976): 229-257. \n\n2. Steenbrink\, Jos
eph. "Logarithmic embeddings of varieties with normal crossings and mixed
Hodge structures." Mathematische Annalen 301.1 (1995): 105-118\n
LOCATION:https://researchseminars.org/talk/ComplexGeometry/4/
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