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BEGIN:VEVENT
SUMMARY:Ryushi GOTO (Osaka University)
DTSTART:20210712T010000Z
DTEND:20210712T015000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/1
DESCRIPTION:Title: Scalar curvature and moment map in Generalized Kähler geometry\nby
Ryushi GOTO (Osaka University) as part of 2021 Pacific Rim Complex & Sympl
ectic Geometry Conference\n\n\nAbstract\nWe introduce a notion of scalar c
urvature of a twisted generalized Kähler manifold in terms of pure spinor
s formalism. A moment map framework on an arbitrary compact twisted genera
lized Kähler manifold is provided and then it turns out that a moment map
is given by the scalar curvature under the certain condition\, which is a
generalization of the result of the scalar curvature as a moment map in t
he ordinary Kähler geometry\, due to Fujiki and Donaldson. A noncommutati
ve compact Lie group G does not have any Kähler structure. However\, we
show that a compact Lie group has a family of generalized Kähler structu
res twisted by the Cartan 3-form\, which is constructed by the action of
the real Pin group of the double of Cartan subalgebra. Then we show that a
n arbitrary compact Lie group admits generalized Kähler structures with c
onstant scalar curvature. In particular\, generalized Kähler structures w
ith constant scalar curvature on the standard Hopf surface are explicitly
given.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byunghee AN (Kyungpook National University)
DTSTART:20210712T021000Z
DTEND:20210712T030000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/2
DESCRIPTION:Title: Augmentations and ruling polynomials for Legendrian graphs\nby Byung
hee AN (Kyungpook National University) as part of 2021 Pacific Rim Complex
& Symplectic Geometry Conference\n\n\nAbstract\nIn this talk\, we will sh
ow the equivalence between two Legendrian isotopy invariants of Legendrian
graphs: (i) augmentation number via point-counting over a finite field fo
r the augmentation variety of the associated Chekanov-Eliashberg DGA\, and
(ii) the ruling polynomial via combinatorics of the decompositions of the
associated front projections. This is a joint work with Youngjin Bae(Inch
eon National University) and Tao Su(Yau Mathematical Sciences Center\, Tsi
nghua University).\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Youngjin Bae (Incheon National University)
DTSTART:20210713T003000Z
DTEND:20210713T012000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/3
DESCRIPTION:Title: Seeds many Lagrangian fillings for Legendrian links\nby Youngjin Bae
(Incheon National University) as part of 2021 Pacific Rim Complex & Sympl
ectic Geometry Conference\n\n\nAbstract\nI will introduce Legendrian links
of finite and affine Dynkin diagrams\, and then argue that there are at l
east as many Lagrangian fillings as seeds in the corresponding cluster str
ucture. The main ingredients are N-graphs developed by Casals-Zaslow\, and
cluster structures by Fomin-Zelevinsky. This is a joint work with Byung H
ee An and Eunjeong Lee.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huai-Liang CHANG (Hong Kong University of Science and Technology)
DTSTART:20210713T013500Z
DTEND:20210713T022500Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/4
DESCRIPTION:Title: Structure of high genus Gromov Witten invariants\nby Huai-Liang CHAN
G (Hong Kong University of Science and Technology) as part of 2021 Pacific
Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nGromov Witten
invariants Fg encodes the numbers of genus g curves in Calabi Yau threefo
lds and play an important role in enumerative geometry. In 1993\, Bershads
ky\, Cecotti\, Ooguri\, Vafa exhibited a hidden ``Feynman structure” gov
erning all Fg’s at once\, using path integral methods. The counterpart i
n mathematics has been missing for many years. After a decades of search\,
in 2018\, a mathematical approach: Mixed Spin P field (MSP) moduli\, is f
inally developed to provide the wanted ``Feynman structure”\, for quinti
c CY 3fold. Instead of enumerating curves in the quintic 3fold\, MSP enume
rate curves in a large N dimensional singular space with quintic-3-fold bo
undary. The “P fields” and “cosections” are used to formulate coun
ting in the singular space via a Landau Ginzburg type construction. In thi
s talk\, I shall focus on geometric ideas behind the MSP moduli. The resul
ts follows from a decade of joint works with Jun Li\, Shuai Guo\, Young Ho
on Kiem\, Weiping Li\, Melissa C.C. Liu\, Jie Zhou\, and Yang Zhou.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hisashi KASUYA (Osaka University)
DTSTART:20210713T024000Z
DTEND:20210713T033000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/5
DESCRIPTION:Title: Non-invariant deformations of left-invariant complex structures on compa
ct Lie groups\nby Hisashi KASUYA (Osaka University) as part of 2021 Pa
cific Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nIt is kn
own that every compact Lie group of even dimension admits left-invariant c
omplex structures. We study deformations of left-invariant complex structu
res on simply connected semisimple compact Lie groups which are non-invari
ant. We compute cohomology of vector bundles for such non-invariant comple
x structures and see the difference between invariant complex structures a
nd non-invariant complex structures. This talk is a joint work with Hiroak
i Ishida (Kagoshima).\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungryul Baik (Korea Advanced Institute of Science and Technology
)
DTSTART:20210714T010000Z
DTEND:20210714T015000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/6
DESCRIPTION:Title: Limits of canonical metrics in low-dimensions\nby Hyungryul Baik (Ko
rea Advanced Institute of Science and Technology) as part of 2021 Pacific
Rim Complex & Symplectic Geometry Conference\n\n\nAbstract\nFor a tower of
finite normal covers of graphs or surfaces\, one can consider a sequence
of metrics on the base given by pull-back of canonical metrc of the covers
. We show that such a sequence has a limit and it depends only on the cove
r approximated by the tower up to scaling. The case of compact Riemann sur
face where the tower approximates the universal cover is due to Kazhdan. I
n this talk\, we will mostly focus on the surface case and explain how the
L^2-theory can be applied. This talk is based on a joint work with Farbod
Shokrieh and Chenxi Wu.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ziyu ZHANG (ShanghaiTech University)
DTSTART:20210714T021000Z
DTEND:20210714T030000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/7
DESCRIPTION:Title: Degenerations of Hilbert schemes of points on K3 surfaces\nby Ziyu Z
HANG (ShanghaiTech University) as part of 2021 Pacific Rim Complex & Sympl
ectic Geometry Conference\n\n\nAbstract\nIt is a widely open problem to un
derstand the degenerations of higher dimensional hyperkähler manifolds. T
he simplest case would be the degenerations of Hilbert schemes of points o
n K3 surfaces. Given a simple degeneration family of K3 surfaces\, there a
re two existing constructions of the degenerations of the Hilbert schemes
of its fibers in the literature\, due to Nagai and Gulbrandsen-Halle-Hulek
respectively. I will compare the two constructions with an emphasis on th
e geometry of the latter. Based on joint work with M.G.Gulbrandsen\, L.H.H
alle and K.Hulek.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ngoc Cuong Nguyen (Korea Advanced Institute of Science and Technol
ogy)
DTSTART:20210715T003000Z
DTEND:20210715T012000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/8
DESCRIPTION:Title: Continuous solutions to Monge-Amp ere equations on Hermitian manifolds f
or measures dominated by capacity\nby Ngoc Cuong Nguyen (Korea Advance
d Institute of Science and Technology) as part of 2021 Pacific Rim Complex
& Symplectic Geometry Conference\n\n\nAbstract\nWe prove the existence of
a continuous quasi-plurisubharmonic solution to the Monge-Amp ere equatio
n on a compact Hermitian manifold for a very general measre on the right h
and side. We admit measures dominated by capacity in a certain manner\, in
particular\, moderate measures studied by Dinh-Nguyen-Sibony. As a conseq
uence\, we give a characterization of measures admitting Holder continuous
quasi-plurisubharmonic potential\, inspired by the work of Dinh-Nguyen. T
his is joint work with S lawomir Ko lodziej.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peng WU (Fudan University)
DTSTART:20210715T013500Z
DTEND:20210715T022500Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/9
DESCRIPTION:Title: Complex structures on Einstein four-manifolds of positive scalar curvatu
re\nby Peng WU (Fudan University) as part of 2021 Pacific Rim Complex
& Symplectic Geometry Conference\n\n\nAbstract\nThe question that when a f
our-manifold with a complex structure admits a compatible Einstein metric
of positive scalar curvature has been answered by Tian\, LeBrun\, respecti
vely. Tian classified Kahler-Einstein four-manifolds with positive scalar
curvature\, LeBrun classified Hermitian\, Einstein four-manifolds of posit
ive scalar curvature. In this talk we consider the inverse problem\, that
is\, when a simply connected four-manifold with an Einstein metric of posi
tive scalar curvature admits a compatible complex structure. We will show
that if the determinant of the self-dual Weyl curvature is positive then t
he manifold admits a compatible complex structure.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ryosuke TAKAHASHI (Kyushu University)
DTSTART:20210716T010000Z
DTEND:20210716T015000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/10
DESCRIPTION:Title: Some geometric flow approaches for deformed Hermitian-Yang-Mills equati
on\nby Ryosuke TAKAHASHI (Kyushu University) as part of 2021 Pacific R
im Complex & Symplectic Geometry Conference\n\n\nAbstract\nOn SYZ mirror s
ymmetry\, a deformed Hermitian-Yang-Mills (dHYM) metric is a fiber metric
on a holomorphic line bundle\, which is the mirror object to a special Lag
rangian section of the dual torus fibration. As a parabolic analogue\, Jac
ob-Yau introduced the Line Bundle Mean Curvature Flow (LBMCF) as the mirro
r of the Lagrangian Mean Curvature Flow. In this talk\, we explore some ge
ometric flow approaches for dHYM metrics: (A) On K\\”ahler surfaces\, it
is known that the existence of dHYM metrics is equivalent to a K\\”ahle
r condition for a certain cohomology class. We relax this condition and st
udy how the LBMCF blows up. (B) Recently\, Collins-Yau discovered a new va
riational characterization for dHYM metrics. Motivated by this\, we introd
uce a new geometric flow which is designed to deform a given metric to a d
HYM one. Then we show that this new flow potentially has more global exist
ence and convergence properties than the LBMCF.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyeongsu CHOI (Korea Institute for Advanced Study)
DTSTART:20210716T021000Z
DTEND:20210716T030000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/11
DESCRIPTION:Title: Translators of the Gauss curvature flow\nby Kyeongsu CHOI (Korea In
stitute for Advanced Study) as part of 2021 Pacific Rim Complex & Symplect
ic Geometry Conference\n\n\nAbstract\nWe begin by reviewing the blow-up an
alysis for the minimal surfaces at isolated singularities\, and will quick
ly discuss about some related recent developments in the singularity analy
sis for the mean curvature flow. Then\, we will classify the translating s
urfaces under the flows by sub-affine-critical powers of the Gauss curvatu
re\, which is a Liouville theorem for a class of Monge-Ampere equations. W
e will put an emphasis on the divergence free property of the linearized o
perator of the Monge-Ampere equation. This is a joint work with Beomjun Ch
oi and Soojung Kim.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Genki HOSONO (Tohoku University)
DTSTART:20210715T024000Z
DTEND:20210715T033000Z
DTSTAMP:20260422T212704Z
UID:2021PRCSG/12
DESCRIPTION:Title: On Berndtsson-Lempert's proof of optimal $L^2$ extension theorem and ex
tension from non-reduced varieties\nby Genki HOSONO (Tohoku University
) as part of 2021 Pacific Rim Complex & Symplectic Geometry Conference\n\n
\nAbstract\nI'd like to talk about the proof of an optimal version of the
Ohsawa-Takegoshi $L^2$ extension theorem and its application to an extensi
on theorem from non-reduced varieties.\n
LOCATION:https://researchseminars.org/talk/2021PRCSG/12/
END:VEVENT
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