BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Gang Tian (Peking University)
DTSTART:20210516T113000Z
DTEND:20210516T122000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/1
DESCRIPTION:Title: Ricci flow on Fano manifolds\nby Gang Tian (Pe
king University) as part of IASM: Geometric PDE and Applications to Proble
ms in Conformal and CR Geometry\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xingwang Xu (Nanjing University)
DTSTART:20210516T123000Z
DTEND:20210516T125500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/2
DESCRIPTION:Title: Gauss curvature flow on 2-sphere\nby Xingwang
Xu (Nanjing University) as part of IASM: Geometric PDE and Applications to
Problems in Conformal and CR Geometry\n\n\nAbstract\nIn this talk\, we sh
ould briefly discuss how we can apply Gauss curvature flow to reprove the
existence for prescribing Gauss curvature problem. The work is joint with
X. Chen \, M. Li and Z. Li.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuxin Ge (Institut de Mathématiques de Toulouse)
DTSTART:20210516T130000Z
DTEND:20210516T132500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/3
DESCRIPTION:Title: On conformally compact Einstein manifolds\nby
Yuxin Ge (Institut de Mathématiques de Toulouse) as part of IASM: Geometr
ic PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbst
ract\nWe discuss some recent progress on compactness result and uniqueness
result of conformally compact Einstein manifolds in all dimensions. This
is a joint work with Alice Chang\, Xiaoshang Jin and Jie Qing.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20210516T133000Z
DTEND:20210516T142000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/4
DESCRIPTION:Title: Singularities formations in some geometric flows\nby Juncheng Wei (University of British Columbia) as part of IASM: Geom
etric PDE and Applications to Problems in Conformal and CR Geometry\n\n\nA
bstract\nIn this talk I will discuss the recently developed inner-outer gl
uing methods in constructing various Type II blow-up for some geometric fl
ows\, including harmonic map flows\, 1/2-harmonic map flows\, harmonic map
flows with free boundary and porous-media flows.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Yang (Princeton University)
DTSTART:20210516T143000Z
DTEND:20210516T145500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/5
DESCRIPTION:Title: Quasiconformal maps on the 4-sphere\nby Paul Y
ang (Princeton University) as part of IASM: Geometric PDE and Applications
to Problems in Conformal and CR Geometry\n\n\nAbstract\nI report on joint
work with Alice Chang and Eden Prywes. A construction of Quasiconformal m
aps between two conformally related metrics in a positive Yamabe class met
ric on S^4. Another construction of a biLipschitz map from such a conforma
l class to the standard conformal class.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Chen (UC Santa Barbara)
DTSTART:20210516T150000Z
DTEND:20210516T152500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/6
DESCRIPTION:Title: The Yamabe flow on asymptotically flat manifolds\nby Eric Chen (UC Santa Barbara) as part of IASM: Geometric PDE and App
lications to Problems in Conformal and CR Geometry\n\n\nAbstract\nI report
on joint work with Alice Chang and Eden Prywes. A construction of Quasico
nformal maps between two conformally related metrics in a positive Yamabe
class metric on S^4. Another construction of a biLipschitz map from such a
conformal class to the standard conformal class.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kengo Hirachi (University of Tokyo)
DTSTART:20210517T113000Z
DTEND:20210517T122000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/7
DESCRIPTION:Title: Normal form for pseudohermitian structures and the
singularity of the Szegö kernel\nby Kengo Hirachi (University of Tok
yo) as part of IASM: Geometric PDE and Applications to Problems in Conform
al and CR Geometry\n\n\nAbstract\nThe Levi forms of a CR structure is defi
ned as a conformal class of hermitian metrics. We give a normal from for t
he Levi froms\, in analogy with the normal form of conformal scale. As an
application\, we give a description of the logarithmic singularity of the
Szegö kernel\, which implies a local characterization of pseudo-Einstein
structures in 3-dimensions in terms of the vanishing of the log singularit
y to the second order. This result can be seen as an analogy of the descri
ption of the Bergman kernel of Robin Graham for domains in and we explain
the relation between the Bergman and Szegö kernel by using the deformatio
n complex and Rumin complex on CR manifolds.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jih-Hsin Cheng (Academia Sinica Taipei)
DTSTART:20210517T123000Z
DTEND:20210517T125500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/8
DESCRIPTION:Title: Positive mass theorem and the CR Yamabe equation o
n 5-dimensional contact spin manifolds\nby Jih-Hsin Cheng (Academia Si
nica Taipei) as part of IASM: Geometric PDE and Applications to Problems i
n Conformal and CR Geometry\n\n\nAbstract\nWe consider the CR Yamabe equat
ion with critical Sobolev ex-ponent on a closed contact manifold M of dime
nsion 2n + 1. The problem of \nfinding solutions with minimum energy has b
een resolved for all dimensions except for dimension 5 (n = 2). In this pa
per we prove the existence of minimum energy solutions in the 5-dimensiona
l case when M is spin. The proof is based on a positive mass theorem built
up through a spinorial approach. This is joint work with Hung-Lin Chiu.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongbing Zhang (USTC - China)
DTSTART:20210517T130000Z
DTEND:20210517T132500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/9
DESCRIPTION:Title: Free boundary constant p-mean curvature surfaces i
ntersecting the Pansu sphere\nby Yongbing Zhang (USTC - China) as part
of IASM: Geometric PDE and Applications to Problems in Conformal and CR G
eometry\n\n\nAbstract\nWe will introduce the notion of free boundary const
ant p-mean curvature (CPMC) surface in a 3-dimensional pseudohermitian man
ifold with boundary. For the domain bounded by the Pansu sphere in the 3-d
imensional Heisenberg group\, we will talk on examples of free boundary CP
MC surfaces which are rotationally symmetric about the t-axis. This is a j
oint work with Shujing Pan and Jun Sun.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xi Zhang (USTC - China)
DTSTART:20210517T133000Z
DTEND:20210517T135500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/10
DESCRIPTION:Title: The non-abelian Hodge correspondence on some non-
K\\"ahler manifolds\nby Xi Zhang (USTC - China) as part of IASM: Geome
tric PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAb
stract\nThe non-abelian Hodge correspondence was established by Corlette-D
onaldson-Hitchin-Simpson\, it states that\, on a compact K\\"ahler manifol
d \, there is a one-to-one correspondence between the moduli space of semi
simple flat complex vector bundles and the moduli space of poly-stable Hig
gs bundles with vanishing Chern numbers. In this talk\, I will introduce o
ur recent work on extending this correspondence to some \\textcolor{red}{n
on-K\\"ahler} case. This work is joint with Changpeng Pan and Chuanjing Zh
an\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruobing Zhang (Princeton University)
DTSTART:20210517T140000Z
DTEND:20210517T142500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/11
DESCRIPTION:Title: On the structure of collapsing Ricci-flat Kaehler
manifolds in dimension four\nby Ruobing Zhang (Princeton University)
as part of IASM: Geometric PDE and Applications to Problems in Conformal a
nd CR Geometry\n\n\nAbstract\nWe will present recent studies on the Ricci-
flat Kaehler 4-manifolds in the collapsing setting. We will particularly i
ntroduce some structure theorems on their Gromov-Hausdorff limits\, singua
lrity formations\, and rescaling bubbles.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafe Mazzeo (Stanford University)
DTSTART:20210517T143000Z
DTEND:20210517T152200Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/12
DESCRIPTION:Title: ALG spaces and the Hitchin equations\nby Rafe
Mazzeo (Stanford University) as part of IASM: Geometric PDE and Applicati
ons to Problems in Conformal and CR Geometry\n\n\nAbstract\nIn the very si
mplest setting\, the moduli space of all solutions to the Hitchin equation
s on a Riemann surface is a 4-dimensional hyperKaehler space of ALG type.
The moduli space depends on certain parameters in the original equations\,
and the resulting ALG metric depends on these. A guiding conjecture due t
o Boalch asks whether all gravitational instantons (in particular\, all AL
G metrics) arise as gauge-theoretic moduli spaces.In this talk I will expl
ain the background and explain a proof of this conjecture in this particul
ar case\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuguang Shi (Peking University)
DTSTART:20210518T113000Z
DTEND:20210518T122000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/13
DESCRIPTION:Title: Positive mass theorems of ALF and ALG manifolds\nby Yuguang Shi (Peking University) as part of IASM: Geometric PDE and
Applications to Problems in Conformal and CR Geometry\n\n\nAbstract\nIn th
is talk\, we will prove positive mass theorems for ALF and ALG manifolds w
ith model spaces and respectively in dimensions no greater than 7. Differe
nt from the compatibility condition for spin structure in Theorem 2 of V.
Minerbe’s paper A mass for ALF manifolds\, Comm. Math. Phys. 289 (2009)\
, no. 3\, 925–955 we show that some type of incompressible condition for
and is enough to guarantee the nonnegativity of the mass. As in the asymp
totically flat case\, we reduce the desired positive mass theorems to thos
e ones concerning non-existence of positive scalar curvature metrics on cl
osed manifolds coming from generalize surgery to -torus. Finally\, we inve
stigate certain fill-in problems and obtain an optimal bound for total mea
n curvature of admissible fill-ins for flat product 2-torus . This talk is
based on the paper joint with my Ph.D. students Peng Liu and Jintian Zhu\
, here is the link of the paper :http://arxiv.org/abs/2103.11289.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haizhong Li (Tsinghua University)
DTSTART:20210518T123000Z
DTEND:20210518T125500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/14
DESCRIPTION:Title: Curvature ows for hypersurfaces in hyperbolic spa
ce and their geometric applications\nby Haizhong Li (Tsinghua Universi
ty) as part of IASM: Geometric PDE and Applications to Problems in Conform
al and CR Geometry\n\n\nAbstract\nIn this talk\, we discuss various curvat
ure flows for hypersurfaces in hyperbolic space and their applications to
geometric inequalities.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azahara DelaTorre (University of Granada)
DTSTART:20210518T130000Z
DTEND:20210518T132500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/15
DESCRIPTION:Title: The fractional Yamabe problem with singularities
of maximal dimension\nby Azahara DelaTorre (University of Granada) as
part of IASM: Geometric PDE and Applications to Problems in Conformal and
CR Geometry\n\n\nAbstract\nThe so called Yamabe problem in Conformal Geome
try asks for a metric conformal to a given one and which has constant scal
ar curvature. When we focus on the Euclidean space in the presence of sing
ularities (given by smooth submanifolds)\, the work of Schoen and Yau show
s that to obtain a complete metric\, the singular set must satisfy a dimen
sional restriction. Under this assumption\, singular solutions exist and h
ave been constructed. A quite recent notion of non-local curvature gives r
ise to a parallel study which weakens the geometric assumptions of positiv
e scalar curvature giving rise to a non-local problem. In previous works\,
we covered the construction of solutions which are singular along (zero a
nd positive dimensional) smooth submanifolds in this fractional setting. T
his was done through the development of new methods coming from conformal
geometry and Scattering theory for the study of non-local ODEs. Due to the
limitations of the techniques we used\, the particular case of maximal po
ssible dimension for the singularity was not covered. In this talk\, we wi
ll focus on this specific dimension and we will construct and study singul
ar solutions of critical dimension. This is a joint work with H. Chan.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Gursky (University of Notre Dame)
DTSTART:20210518T133000Z
DTEND:20210518T145500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/16
DESCRIPTION:by Matthew Gursky (University of Notre Dame) as part of IASM:
Geometric PDE and Applications to Problems in Conformal and CR Geometry\n\
nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qing Han (University of Notre Dame)
DTSTART:20210518T143000Z
DTEND:20210518T145500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/17
DESCRIPTION:Title: Geodesics and Isometric Immersions in Kirigami\nby Qing Han (University of Notre Dame) as part of IASM: Geometric PDE a
nd Applications to Problems in Conformal and CR Geometry\n\n\nAbstract\nKi
rigami is the art of cutting paper to make it articulated and deployable\,
allowing for it to be shaped into complex two and three-dimensional geome
tries. The mechanical response of a kirigami sheet when it is pulled at it
s ends is enabled and limited by the presence of cuts that serve to guide
the possible non-planar deformations. Inspired by the geometry of this art
form\, we ask two questions: (i) What is the shortest path between points
at which forces are applied? (ii) What is the nature of the ultimate shap
e of the sheet when it is strongly stretched? Mathematically\, these quest
ions are related to the nature and form of geodesics in the Euclidean plan
e with linear obstructions (cuts)\, and the nature and form of isometric i
mmersions of the sheet with cuts when it can be folded on itself. The talk
is based on joint works with M. Lewicka and L. Mahadevan.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Wang (Johns Hopkins University)
DTSTART:20210518T150000Z
DTEND:20210518T152500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/18
DESCRIPTION:Title: Rigidity of local minimizers of the σk functiona
l\nby Yi Wang (Johns Hopkins University) as part of IASM: Geometric PD
E and Applications to Problems in Conformal and CR Geometry\n\n\nAbstract\
nIn this talk\, I will present a result on the rigidity of local minimizer
s of the functional among all conformally flat metrics in the Euclidean (n
+ 1)-ball. We prove the metric is flat up to a conformal transformation i
n some (noncritical) dimensions. We also prove the analogous result in the
critical dimension n + 1 = 4. The main method is Frank-Lieb’s rearrange
ment-free argument. If minimizers exist\, this implies a fully nonlinear s
harp Sobolev trace inequality. This is joint work with Jeffrey Case.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Musso (University of Bath)
DTSTART:20210519T113000Z
DTEND:20210519T122000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/19
DESCRIPTION:Title: Compactness of the solution set of the boundary Y
amabe problem on smooth compact Riemannian manifolds with boundary in low
dimensions\nby Monica Musso (University of Bath) as part of IASM: Geom
etric PDE and Applications to Problems in Conformal and CR Geometry\n\n\nA
bstract\nThe boundary Yamabe problem consists in establishing if a given s
mooth compact Riemannian manifold with boundary can be conformally deforme
d to a scalar-flat manifold with boundary of constant mean curvature. In t
his talk I will present a recent result on compactness of the solution set
of the boundary Yamabe problem on smooth compact Riemannian manifolds wit
h boundary provided that their dimensions are 4\, 5 or 6. This work is in
collaboration with Seunghyeok Kim and Juncheng Wei.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Carron (Universite de Nantes)
DTSTART:20210519T123000Z
DTEND:20210519T125500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/20
DESCRIPTION:Title: Yamabe flow on singular space\nby Gilles Carr
on (Universite de Nantes) as part of IASM: Geometric PDE and Applications
to Problems in Conformal and CR Geometry\n\n\nAbstract\nIt is joint work w
ith Boris Vertman (Oldenburg) and Jørgen Olsen Lye (Oldenburg). We study
the convergence of the normalized Yamabe flow with positive Yamabe constan
t on a class of pseudo-manifolds that includes stratified spaces with iter
ated cone-edge metrics. We establish convergence under a low-energy condit
ion. We also prove a concentration--compactness dichotomy\, and investigat
e what the alternatives to convergence is.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenlei Zhang (Capital Normal University)
DTSTART:20210519T130000Z
DTEND:20210519T132500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/21
DESCRIPTION:Title: On the Holder estimate of complex Monge-Ampere eq
uation\nby Zhenlei Zhang (Capital Normal University) as part of IASM:
Geometric PDE and Applications to Problems in Conformal and CR Geometry\n\
n\nAbstract\nI the talk we present a Holder estimate of complex Monge-Ampe
re equation on manifolds. The estimate follows from Kolodziej approach to
solve complex Monge-Ampere with L^p bounded measure.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaodong Wang (Michigan State University)
DTSTART:20210519T133000Z
DTEND:20210519T135500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/22
DESCRIPTION:Title: Improved Sobolev inequality under constraints on
the sphere\nby Xiaodong Wang (Michigan State University) as part of IA
SM: Geometric PDE and Applications to Problems in Conformal and CR Geometr
y\n\n\nAbstract\nI will discuss a recent joint work with Fengbo Hang on im
proved Sobolev inequality on the sphere when certain moments vanish up to
a given order. The 1st oder case was proved by Aubin’ about 40 years ago
. Our new approach yields a characterization of the best constant for any
order. It leads to an interesting extremal problem on the sphere. We are a
ble to determine the constant explicitly in the second order case.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyi Zhang (University of Notre Dame)
DTSTART:20210519T140000Z
DTEND:20210519T142500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/23
DESCRIPTION:Title: Conformally invariant rigidity theorems on four-m
anifolds with boundary\nby Siyi Zhang (University of Notre Dame) as pa
rt of IASM: Geometric PDE and Applications to Problems in Conformal and CR
Geometry\n\n\nAbstract\nWe introduce conformal and smooth invariants on o
riented\, compact four-manifolds with boundary and show that "positivity"
conditions on these invariants will impose topological restrictions on und
erlying manifolds with boundary. We also establish conformally invariant r
igidity theorems for Bach-flat four-manifolds with boundary under the assu
mptions on these invariants. It is noteworthy to point out that we rule ou
t some examples arising from the study of closed manifolds in the setting
of manifolds with umbilic boundary.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (Caltech / University of Munich)
DTSTART:20210519T143000Z
DTEND:20210519T152000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/24
DESCRIPTION:Title: Which magnetic fields support a zero mode?\nb
y Rupert Frank (Caltech / University of Munich) as part of IASM: Geometric
PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbstra
ct\nMotivated by the question from mathematical physics about the size of
magnetic fields that support zero modes for the three dimensional Dirac eq
uation\, we study a certain conformally invariant spinor equation. We stat
e some conjectures and present results in their support. Those concern\, i
n particular\, two novel Sobolev inequalities for spinors and vector field
s. The talk is based on joint work with Michael Loss.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fang Wang (Shanghai Jiao Tong University)
DTSTART:20210520T113000Z
DTEND:20210520T142000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/25
DESCRIPTION:Title: A new lower bound for the relative volume inequal
ity for CCE\nby Fang Wang (Shanghai Jiao Tong University) as part of I
ASM: Geometric PDE and Applications to Problems in Conformal and CR Geomet
ry\n\n\nAbstract\nIn this talk\, I will provide a new lower bound for the
relative volume inequality for conformally compact Einstein manifolds\, as
well as its applications in the rigidity theorem for CCE.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuxin Dong (Fudan University)
DTSTART:20210520T123000Z
DTEND:20210520T125500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/26
DESCRIPTION:Title: Prescribed Webster scalar curvatures on compact p
seudo-Hermitian manifolds\nby Yuxin Dong (Fudan University) as part of
IASM: Geometric PDE and Applications to Problems in Conformal and CR Geom
etry\n\n\nAbstract\nIn this talk\, we will discuss the problem of prescrib
ing Webster scalar curvatures on compact strictly pseudo convex CR manifol
ds. In terms of the upper and lower solutions method and the perturbation
theory of self-adjoint operators\, we try to describe some sets of Webster
scalar curvature functions which can be realized through pointwise CR con
formal deformations and CR conformally equivalent deformations respectivel
y from a given pseudo-Hermitian structure. This is a joint work with Yibin
Ren and Weike Yu.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoli Han (Tsinghua University)
DTSTART:20210520T130000Z
DTEND:20210520T132500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/27
DESCRIPTION:Title: Existence of deformed Hermitian-Yang Mills metric
\nby Xiaoli Han (Tsinghua University) as part of IASM: Geometric PDE a
nd Applications to Problems in Conformal and CR Geometry\n\n\nAbstract\nFi
rst I will introduce the equation of the deformed Hermitian-Yang Mills met
ric on the holomorphic line bundle of the Kahler manifold. Then I will int
roduce some existence results of this equation under some assumptions. I w
ill also introduce the corresponding heat equation and some long time exis
tence and convergence of the heat flow.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiping Zhang (Nankai University)
DTSTART:20210520T133000Z
DTEND:20210520T142000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/28
DESCRIPTION:Title: Positive scalar curvature on manifolds and foliat
ions\nby Weiping Zhang (Nankai University) as part of IASM: Geometric
PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbstrac
t\nA famous vanishing theorem of due to Lichnerowicz states that if a clos
ed spin manifold admits a Riemannian metric with positive scalar curvature
\, then it's a-hat genus equals to zero. In this talk we will describe som
e recent advanced generalizing this kind of results to other manifolds as
well as foliations.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKeown (University of Texas - Dallas)
DTSTART:20210520T142000Z
DTEND:20210520T145500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/29
DESCRIPTION:Title: Renormalized volume of partially bounded subregio
ns of asymptotically hyperbolic Einstein spaces\nby Stephen McKeown (U
niversity of Texas - Dallas) as part of IASM: Geometric PDE and Applicatio
ns to Problems in Conformal and CR Geometry\n\n\nAbstract\nThe renormalize
d volume of an asymptotically hyperbolic Einstein four-manifold is among i
ts most important global invariants. We define renormalized volume for min
imally bounded half-spaces\, then prove a Gauss-Bonnet formula for the vol
ume and compute its variation under variations of the minimal boundary. Th
is is joint work with Matthew J. Gursky and Aaron J. Tyrrell.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Martinazzi (University of Padova)
DTSTART:20210520T150000Z
DTEND:20210520T152500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/30
DESCRIPTION:Title: Local and non-local singular Liouville equations
in Euclidean spaces\nby Luca Martinazzi (University of Padova) as part
of IASM: Geometric PDE and Applications to Problems in Conformal and CR G
eometry\n\n\nAbstract\nWe show some recent existence and classification re
sults for conformal metrics in Euclidean spaces having prescribed constant
Q-curvature and a singularity at the origin. While in dimension 2 this pr
oblem was studied and fully understood by Prajapat-Tarantello\, in higher
dimension new phenomena arise and several questions remain open. This is a
joint work with A. Hyder and G. Mancini.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rod Gover (University of Auckland)
DTSTART:20210521T113000Z
DTEND:20210521T115500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/31
DESCRIPTION:Title: A conformally invariant Yang-Mills energy and equ
ation on 6-manifolds.\nby Rod Gover (University of Auckland) as part o
f IASM: Geometric PDE and Applications to Problems in Conformal and CR Geo
metry\n\n\nAbstract\nThe gauge field equations known as the Yang-Mills equ
ations are extremely important in both mathematics and physics\, and their
conformal invariance in dimension 4 is a critical feature for many applic
ations. We show that there is a simple and elegant route to higher order e
quations in dimension 6 that are analogous and arise as the Euler-Lagrange
equations of a conformally invariant action. The functional gradient of t
his action recovers the conformal Fefferman-Graham obstruction tensor when
the gauge connection is taken to be the conformal Cartan (or tractor) con
nection. This also has importance for CR geometry through the Fefferman am
bient metric. This is joint work with Larry Peterson and Callum Sleigh.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria del Mar Gonzalez (UniversidadAutonoma de Madrid)
DTSTART:20210521T120000Z
DTEND:20210521T122500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/32
DESCRIPTION:Title: Non-local ODE in conformal geometry\nby Maria
del Mar Gonzalez (UniversidadAutonoma de Madrid) as part of IASM: Geometr
ic PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbst
ract\nWhen one looks for radial solutions of an equation with fractional L
aplacian\, it is not generally possible to use usual ODE methods. If such
equation has some conformal invariances\, then one may rewrite it in Emden
-Fowler (cylindrical) coordinates and to use the properties of the conform
al fractional Laplacian on the cylinder\, which is a fractional order Pane
itz operator. After giving the necessary background\, we will briefly cons
ider two particular applications of this technique: 1. Symmetry breaking\,
non-degeneracy and uniqueness for the fractional Caffarelli-Kohn-Nirenber
g inequality (joint work with W. Ao and A. DelaTorre). 2. Existence and re
gularity for fractional Laplacian equations with drift and a critical Hard
y potential (joint with H. Chan\, M. Fontelos and J. Wei).\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Biquard (Sorbonne Université)
DTSTART:20210521T123000Z
DTEND:20210521T132000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/33
DESCRIPTION:Title: Curved discrete series\nby Olivier Biquard (S
orbonne Université) as part of IASM: Geometric PDE and Applications to Pr
oblems in Conformal and CR Geometry\n\n\nAbstract\nIt is well-known that c
onformally compact Einstein metrics give a tool to understand the conforma
l geometry of the boundary in terms of the Riemannian geometry of the inte
rior. Using this philosophy we relate Dirac operators in the interior with
the BGG operators of the boundary. In the flat case\, this relates discre
te series for the orthogonal group with the BGG operators of the boundary
sphere.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sagun Chanillo (Rutgers University)
DTSTART:20210521T133000Z
DTEND:20210521T142000Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/34
DESCRIPTION:Title: Local Version of Courant's Nodal Domain theorem\nby Sagun Chanillo (Rutgers University) as part of IASM: Geometric PDE
and Applications to Problems in Conformal and CR Geometry\n\n\nAbstract\nG
iven a compact Riemannian manifold with no boundary endowed with a smooth
metric g\, one of the important objects of study is the Laplace-Beltrami o
perator and its eigenfunctions. That is The Courant nodal domain theorem a
sserts that the k-th eigenfunction has at most k nodal domains\, where a n
odal domain is a connected component of the set . Harold Donnelly and C. F
efferman initiated the study of local versions of this result with a goal
to show that nodal domains cannot be long and narrow. This was related to
a conjecture of S.-T. Yau on the length of the nodal set. The nodal set is
the set . In this joint work with A. Logunov\, E. Mallinikova and D. Mang
oubi\, we obtain an optimal bound for results of this type.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Case (The Pennsylvania State University)
DTSTART:20210521T143000Z
DTEND:20210521T145500Z
DTSTAMP:20260422T184929Z
UID:GeometricPDEConformalCRGeometry/35
DESCRIPTION:Title: The I-prime curvature in CR geometry\nby Jeff
rey Case (The Pennsylvania State University) as part of IASM: Geometric PD
E and Applications to Problems in Conformal and CR Geometry\n\n\nAbstract\
nIn this talk we discuss aspects of the CR analogue of the Deser—Schwimm
er conjecture. One possible formulation is that any pseudohermitian scalar
invariant whose integral is independent of the choice of pseudo-Einstein
contact form is a linear combination of the Q-prime curvature\, a local CR
invariant\, and a divergence. In dimension three\, this statement was pro
ved in the affirmative by Hirachi. In higher dimensions\, the I-prime curv
atures give counterexamples to this statement. We will describe the I-prim
e curvatures and some of their properties\, including the proposal of a ne
w CR analogue of the Deser—Schwimmer conjecture. This is based on joint
works with Rod Gover and Yuya Takeuchi.\n
LOCATION:https://researchseminars.org/talk/GeometricPDEConformalCRGeometry
/35/
END:VEVENT
END:VCALENDAR