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X-WR-CALNAME:Marker Lecture Series
X-WR-TIMEZONE:America/New_York
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TZOFFSETFROM:-0500
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DTSTART:19700308T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
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DTSTART:19701101T020000
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150323T200000
DTEND;TZID=America/New_York:20150323T210000
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=25513
SUMMARY:Marker Lecture Series - Mathematical Aspects of gauged linear σ-mo
del
DESCRIPTION:Seminar: Marker Lecture Series\nTitle: Mathematical Aspects of
gauged linear σ-model\nSpeaker: Professor Gang Tian\, Princeton Universit
y\nAbstract: In 90s\, the Gromov-Witten invariants were constructed rigoro
usly by using\nJ-holomorphic curves and have become a fundamental tool in
symplectic\ntopology as well as in algebraic geometry. On the other hand\,
since early 80s\,\nthe gauge theory has played a very important role in d
ifferential topology and\nalgebraic geometry\, in particular\, in the stud
y of differentiable 4-manifolds.\nThe coupling of gauge theory and σ-mode
l is fundamental in physics\, which\nhas also been pursued by mathematicia
ns. In 1993\, Witten proposed an elliptic\nequation associated to a quasi-
homogeneous polynomial W. This equation\nwas used to construct a quantum t
heory\, i.e.\, the FJRW theory\, about singularities.\nCoupling gauge fiel
ds with the Witten equation leads to the gauged\nlinear σ-model. It was o
bserved by Witten that a correspondence between the\n“Landau-Ginzburg mo
del” and the “Gromov-Witten” theory of Calabi-Yau hypersurfaces\ncan
be established through the gauged linear σ-model. In last few\nyears\, G
uangbo Xu and I have had a program on constructing a mathematical\ntheory
of the gauged linear σ-model. In this talk aiming at general audience\, I
\nwill give a brief tour on constructing Gromov-Witten invariants and our
recent\nworks on mathematical aspects of gauged linear σ-model.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150324T153500
DTEND;TZID=America/New_York:20150324T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=25777
SUMMARY:Marker Lecture Series - Introduction to gauged Witten equation
DESCRIPTION:Seminar: Marker Lecture Series\nTitle: Introduction to gauged W
itten equation\nSpeaker: Professor Gang Tian\, Princeton University\nAbstr
act: In this talk\, I will start with the Witten equation and then introdu
ce the\ngauged Witten equation\, which also generalizes the symplectic vor
tex equation\nstudied in the gauged Gromov-Witten theory. I will discuss s
ome of its analytical\nproperties\, including the asymptotical behavior of
finite energy solutions and\nthe linear Fredholm property.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150325T153500
DTEND;TZID=America/New_York:20150325T163500
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=25380
SUMMARY:Marker Lecture Series - Compactness theorem for gauged Witten equat
ion
DESCRIPTION:Seminar: Marker Lecture Series\nTitle: Compactness theorem for
gauged Witten equation\nSpeaker: Professor Gang Tian\, Princeton Universit
y\nAbstract: In this talk\, I will discuss compactness results for the gau
ged Witten equation\nand its perturbation. The key is to establish a unifo
rm C0-bound for solutions.\nI will explain how this can be done.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150326T100000
DTEND;TZID=America/New_York:20150326T110000
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=26701
SUMMARY:Marker Lecture Series - Correlation functions for gauged linear σ-
model
DESCRIPTION:Seminar: Marker Lecture Series\nTitle: Correlation functions fo
r gauged linear σ-model\nSpeaker: Gang Tian\, (Host: Jinchao Xu)\, Prince
ton University\nAbstract: In this last talk\, I will give the definition o
f the correlation function of\nthe gauged linear σ-model for a fixed smoo
th r-spin curve. I will first discuss\ncertain cohomology groups which are
used as state spaces for the gauged linear\nσ-model and which generalize
the state spaces in Landau-Ginzburg A-model.\nThe correlation function is
defined as a family of multi-linear maps on those\ngeneralized state spac
es by using the moduli for solutions of the gauged Witten\nequation.
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