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X-WR-CALNAME:Marker Lecture Series
X-WR-TIMEZONE:America/New_York
BEGIN:VTIMEZONE
TZID:America/New_York
X-LIC-LOCATION:America/New_York
BEGIN:DAYLIGHT
TZOFFSETFROM:-0500
TZOFFSETTO:-0400
TZNAME:EDT
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 - Geometric analysis and topology
DESCRIPTION:Seminar: Marker Lecture Series\nTitle: Geometric analysis and t
opology\nSpeaker: Gang Tian\, (Host: Jinchao Xu)\, Princeton University an
d Peking University\nAbstract: There are strong ties between geometry and
topology. For decades\, geometric\nmethods have been applied to attacking
topological problems. One distinguished example is the solution of the fam
ous Poincare conjecture by using Hamilton’s Ricci flow. The Poincare con
jecture is a famous topological problem which gives a characterization of
the simplest topological 3-space\, while the Ricci flow had been studied i
n geometric analysis for many years before it was used for solving the con
jecture. The other examples include application of the gauge theory to stu
dying differentiable topology of 4-manifolds in 80s and the use of Cauchy-
Riemann equation in constructing the Gromov-Witten invariants in symplecti
c topology in 90s. In this talk aiming at general audience\, I will show h
ow geometric methods can be applied to studying topological spaces. First
I will recall some classical facts on surfaces. Secondly\, I will give a b
rief tour on Perelman’s works on geometrization of 3-manifolds and discu
ss geometric aspects of 4-manifolds. Finally\, I will show some geometric
methods in symplectic topology\, particularly\, constructing the Gromov-Wi
tten invariants related to the \nσ-model in physics.
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150324T153000
DTEND;TZID=America/New_York:20150324T163000
LOCATION:MB114
URL:http://www.math.psu.edu/seminars/meeting.php?id=25364
SUMMARY:Marker Lecture Series - Introduction to gauged Witten equation
DESCRIPTION:Seminar: Marker Lecture Series\nTitle: Introduction to gauged W
itten equation\nSpeaker: Gang Tian\, (Host: Jinchao Xu)\, Princeton Univer
sity and Peking University\nAbstract: In this and subsequent two talks\, I
will discuss my recent program with\nGuangbo Xu on constructing a mathema
tical theory of the gauged linear -\nmodel. First\, I will introduce the
gauged Witten equation\, which also generalizes the symplectic vortex equa
tion studied in the gauged Gromov-Witten theory. I will discuss some of it
s analytical properties\, including the asymptotical behavior of nite ene
rgy solutions and the 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: Gang Tian\, (Host: Jinchao Xu)\, Princeto
n University and Peking University\nAbstract: In this talk\, I will discus
s compactness results for the gauged Witten equation and its perturbation.
The key is to establish a uniform\nC0-bound for solutions. I 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 and Peking University\nAbstract: In this last talk\, I will
give the definition of the correlation function of\nthe gauged linear σ-
model for a fixed smooth r-spin curve. I will first discuss certain cohomo
logy groups which are used as state spaces for the gauged linear σ-model
and which generalize the state spaces in Landau-Ginzburg A-model. The corr
elation function is defined as a family of multi-linear maps on those gene
ralized state spaces by using the moduli for solutions of the gauged Witte
n equation.
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