BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Gang Tian (Peking University)
DTSTART:20210516T113000Z
DTEND:20210516T122000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/1
DESCRIPTION:Title: Ricci flow on Fano manifolds\nby Gang T
ian (Peking University) as part of IASM: Geometric PDE and Applications to
Problems in Conformal and CR Geometry\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xingwang Xu (Nanjing University)
DTSTART:20210516T123000Z
DTEND:20210516T125500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/2
DESCRIPTION:Title: Gauss curvature flow on 2-sphere\nby Xi
ngwang Xu (Nanjing University) as part of IASM: Geometric PDE and Applicat
ions to Problems in Conformal and CR Geometry\n\n\nAbstract\nIn this talk\
, we should briefly discuss how we can apply Gauss curvature flow to repro
ve the existence for prescribing Gauss curvature problem. The work is join
t with X. Chen \, M. Li and Z. Li.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuxin Ge (Institut de Mathématiques de Toulouse)
DTSTART:20210516T130000Z
DTEND:20210516T132500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/3
DESCRIPTION:Title: On conformally compact Einstein manifolds\nby Yuxin Ge (Institut de Mathématiques de Toulouse) as part of IASM:
Geometric PDE and Applications to Problems in Conformal and CR Geometry\n\
n\nAbstract\nWe discuss some recent progress on compactness result and uni
queness 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://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juncheng Wei (University of British Columbia)
DTSTART:20210516T133000Z
DTEND:20210516T142000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/4
DESCRIPTION:Title: Singularities formations in some geometric
flows\nby Juncheng Wei (University of British Columbia) as part of IAS
M: Geometric PDE and Applications to Problems in Conformal and CR Geometry
\n\n\nAbstract\nIn this talk I will discuss the recently developed inner-o
uter gluing methods in constructing various Type II blow-up for some geome
tric flows\, including harmonic map flows\, 1/2-harmonic map flows\, harmo
nic map flows with free boundary and porous-media flows.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Yang (Princeton University)
DTSTART:20210516T143000Z
DTEND:20210516T145500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/5
DESCRIPTION:Title: Quasiconformal maps on the 4-sphere\nby
Paul Yang (Princeton University) as part of IASM: Geometric PDE and Appli
cations to Problems in Conformal and CR Geometry\n\n\nAbstract\nI report o
n joint work with Alice Chang and Eden Prywes. A construction of Quasiconf
ormal maps between two conformally related metrics in a positive Yamabe cl
ass metric on S^4. Another construction of a biLipschitz map from such a c
onformal class to the standard conformal class.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Chen (UC Santa Barbara)
DTSTART:20210516T150000Z
DTEND:20210516T152500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/6
DESCRIPTION:Title: The Yamabe flow on asymptotically flat mani
folds\nby Eric Chen (UC Santa Barbara) 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 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://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kengo Hirachi (University of Tokyo)
DTSTART:20210517T113000Z
DTEND:20210517T122000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/7
DESCRIPTION:Title: Normal form for pseudohermitian structures
and the singularity of the Szegö kernel\nby Kengo Hirachi (University
of Tokyo) as part of IASM: Geometric PDE and Applications to Problems in
Conformal and CR Geometry\n\n\nAbstract\nThe Levi forms of a CR structure
is defined as a conformal class of hermitian metrics. We give a normal fro
m for the 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-Ei
nstein structures in 3-dimensions in terms of the vanishing of the log sin
gularity to the second order. This result can be seen as an analogy of the
description of the Bergman kernel of Robin Graham for domains in and we e
xplain the relation between the Bergman and Szegö kernel by using the def
ormation complex and Rumin complex on CR manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jih-Hsin Cheng (Academia Sinica Taipei)
DTSTART:20210517T123000Z
DTEND:20210517T125500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/8
DESCRIPTION:Title: Positive mass theorem and the CR Yamabe equ
ation on 5-dimensional contact spin manifolds\nby Jih-Hsin Cheng (Acad
emia Sinica Taipei) as part of IASM: Geometric PDE and Applications to Pro
blems in Conformal and CR Geometry\n\n\nAbstract\nWe consider the CR Yamab
e equation with critical Sobolev ex-ponent on a closed contact manifold M
of dimension 2n + 1. The problem of \nfinding solutions with minimum energ
y has been resolved for all dimensions except for dimension 5 (n = 2). In
this paper we prove the existence of minimum energy solutions in the 5-dim
ensional case when M is spin. The proof is based on a positive mass theore
m built up through a spinorial approach. This is joint work with Hung-Lin
Chiu.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yongbing Zhang (USTC - China)
DTSTART:20210517T130000Z
DTEND:20210517T132500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/9
DESCRIPTION:Title: Free boundary constant p-mean curvature sur
faces intersecting the Pansu sphere\nby Yongbing Zhang (USTC - China)
as part of IASM: Geometric PDE and Applications to Problems in Conformal a
nd CR Geometry\n\n\nAbstract\nWe will introduce the notion of free boundar
y constant p-mean curvature (CPMC) surface in a 3-dimensional pseudohermit
ian manifold with boundary. For the domain bounded by the Pansu sphere in
the 3-dimensional Heisenberg group\, we will talk on examples of free boun
dary CPMC surfaces which are rotationally symmetric about the t-axis. This
is a joint work with Shujing Pan and Jun Sun.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xi Zhang (USTC - China)
DTSTART:20210517T133000Z
DTEND:20210517T135500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/10
DESCRIPTION:Title: The non-abelian Hodge correspondence on so
me non-K\\"ahler manifolds\nby Xi Zhang (USTC - China) as part of IASM
: Geometric PDE and Applications to Problems in Conformal and CR Geometry\
n\n\nAbstract\nThe non-abelian Hodge correspondence was established by Cor
lette-Donaldson-Hitchin-Simpson\, it states that\, on a compact K\\"ahler
manifold \, there is a one-to-one correspondence between the moduli space
of semisimple flat complex vector bundles and the moduli space of poly-sta
ble Higgs bundles with vanishing Chern numbers. In this talk\, I will intr
oduce our recent work on extending this correspondence to some \\textcolor
{red}{non-K\\"ahler} case. This work is joint with Changpeng Pan and Chuan
jing Zhan\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruobing Zhang (Princeton University)
DTSTART:20210517T140000Z
DTEND:20210517T142500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/11
DESCRIPTION:Title: On the structure of collapsing Ricci-flat
Kaehler manifolds in dimension four\nby Ruobing Zhang (Princeton Unive
rsity) as part of IASM: Geometric PDE and Applications to Problems in Conf
ormal and CR Geometry\n\n\nAbstract\nWe will present recent studies on the
Ricci-flat Kaehler 4-manifolds in the collapsing setting. We will particu
larly introduce some structure theorems on their Gromov-Hausdorff limits\,
singualrity formations\, and rescaling bubbles.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafe Mazzeo (Stanford University)
DTSTART:20210517T143000Z
DTEND:20210517T152200Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/12
DESCRIPTION:Title: ALG spaces and the Hitchin equations\n
by Rafe Mazzeo (Stanford University) as part of IASM: Geometric PDE and Ap
plications to Problems in Conformal and CR Geometry\n\n\nAbstract\nIn the
very simplest setting\, the moduli space of all solutions to the Hitchin e
quations on a Riemann surface is a 4-dimensional hyperKaehler space of ALG
type. The moduli space depends on certain parameters in the original equa
tions\, and the resulting ALG metric depends on these. A guiding conjectur
e due to Boalch asks whether all gravitational instantons (in particular\,
all ALG metrics) arise as gauge-theoretic moduli spaces.In this talk I wi
ll explain the background and explain a proof of this conjecture in this p
articular case\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuguang Shi (Peking University)
DTSTART:20210518T113000Z
DTEND:20210518T122000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/13
DESCRIPTION:Title: Positive mass theorems of ALF and ALG mani
folds\nby Yuguang Shi (Peking University) as part of IASM: Geometric P
DE and Applications to Problems in Conformal and CR Geometry\n\n\nAbstract
\nIn this talk\, we will prove positive mass theorems for ALF and ALG mani
folds with model spaces and respectively in dimensions no greater than 7.
Different 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 condit
ion for and is enough to guarantee the nonnegativity of the mass. As in th
e asymptotically flat case\, we reduce the desired positive mass theorems
to those ones concerning non-existence of positive scalar curvature metric
s on closed manifolds coming from generalize surgery to -torus. Finally\,
we investigate certain fill-in problems and obtain an optimal bound for to
tal mean 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 Jinti
an Zhu\, here is the link of the paper :http://arxiv.org/abs/2103.11289.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haizhong Li (Tsinghua University)
DTSTART:20210518T123000Z
DTEND:20210518T125500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/14
DESCRIPTION:Title: Curvature ows for hypersurfaces in hyperbo
lic space and their geometric applications\nby Haizhong Li (Tsinghua U
niversity) as part of IASM: Geometric PDE and Applications to Problems in
Conformal and CR Geometry\n\n\nAbstract\nIn this talk\, we discuss various
curvature flows for hypersurfaces in hyperbolic space and their applicati
ons to geometric inequalities.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azahara DelaTorre (University of Granada)
DTSTART:20210518T130000Z
DTEND:20210518T132500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/15
DESCRIPTION:Title: The fractional Yamabe problem with singula
rities of maximal dimension\nby Azahara DelaTorre (University of Grana
da) as part of IASM: Geometric PDE and Applications to Problems in Conform
al and CR Geometry\n\n\nAbstract\nThe so called Yamabe problem in Conforma
l Geometry asks for a metric conformal to a given one and which has consta
nt scalar curvature. When we focus on the Euclidean space in the presence
of singularities (given by smooth submanifolds)\, the work of Schoen and Y
au shows that to obtain a complete metric\, the singular set must satisfy
a dimensional restriction. Under this assumption\, singular solutions exis
t and have been constructed. A quite recent notion of non-local curvature
gives rise to a parallel study which weakens the geometric assumptions of
positive scalar curvature giving rise to a non-local problem. In previous
works\, we covered the construction of solutions which are singular along
(zero and positive dimensional) smooth submanifolds in this fractional set
ting. This was done through the development of new methods coming from con
formal geometry and Scattering theory for the study of non-local ODEs. Due
to the limitations of the techniques we used\, the particular case of max
imal possible dimension for the singularity was not covered. In this talk\
, we will focus on this specific dimension and we will construct and study
singular solutions of critical dimension. This is a joint work with H. Ch
an.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Gursky (University of Notre Dame)
DTSTART:20210518T133000Z
DTEND:20210518T145500Z
DTSTAMP:20260404T041134Z
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://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qing Han (University of Notre Dame)
DTSTART:20210518T143000Z
DTEND:20210518T145500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/17
DESCRIPTION:Title: Geodesics and Isometric Immersions in Kiri
gami\nby Qing Han (University of Notre Dame) as part of IASM: Geometri
c PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbstr
act\nKirigami is the art of cutting paper to make it articulated and deplo
yable\, allowing for it to be shaped into complex two and three-dimensiona
l geometries. The mechanical response of a kirigami sheet when it is pulle
d at its ends is enabled and limited by the presence of cuts that serve to
guide the possible non-planar deformations. Inspired by the geometry of t
his 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 ultima
te shape of the sheet when it is strongly stretched? Mathematically\, thes
e questions are related to the nature and form of geodesics in the Euclide
an plane with linear obstructions (cuts)\, and the nature and form of isom
etric immersions of the sheet with cuts when it can be folded on itself. T
he talk is based on joint works with M. Lewicka and L. Mahadevan.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Wang (Johns Hopkins University)
DTSTART:20210518T150000Z
DTEND:20210518T152500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/18
DESCRIPTION:Title: Rigidity of local minimizers of the σk fu
nctional\nby Yi Wang (Johns Hopkins University) as part of IASM: Geome
tric PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAb
stract\nIn this talk\, I will present a result on the rigidity of local mi
nimizers of the functional among all conformally flat metrics in the Eucli
dean (n + 1)-ball. We prove the metric is flat up to a conformal transform
ation in some (noncritical) dimensions. We also prove the analogous result
in the critical dimension n + 1 = 4. The main method is Frank-Lieb’s re
arrangement-free argument. If minimizers exist\, this implies a fully nonl
inear sharp Sobolev trace inequality. This is joint work with Jeffrey Case
.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica Musso (University of Bath)
DTSTART:20210519T113000Z
DTEND:20210519T122000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/19
DESCRIPTION:Title: Compactness of the solution set of the bou
ndary Yamabe problem on smooth compact Riemannian manifolds with boundary
in low dimensions\nby Monica Musso (University of Bath) as part of IAS
M: Geometric PDE and Applications to Problems in Conformal and CR Geometry
\n\n\nAbstract\nThe boundary Yamabe problem consists in establishing if a
given smooth compact Riemannian manifold with boundary can be conformally
deformed to a scalar-flat manifold with boundary of constant mean curvatur
e. In this talk I will present a recent result on compactness of the solut
ion set of the boundary Yamabe problem on smooth compact Riemannian manifo
lds with boundary provided that their dimensions are 4\, 5 or 6. This work
is in collaboration with Seunghyeok Kim and Juncheng Wei.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gilles Carron (Universite de Nantes)
DTSTART:20210519T123000Z
DTEND:20210519T125500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/20
DESCRIPTION:Title: Yamabe flow on singular space\nby Gill
es Carron (Universite de Nantes) as part of IASM: Geometric PDE and Applic
ations to Problems in Conformal and CR Geometry\n\n\nAbstract\nIt is joint
work with Boris Vertman (Oldenburg) and Jørgen Olsen Lye (Oldenburg). We
study the convergence of the normalized Yamabe flow with positive Yamabe
constant on a class of pseudo-manifolds that includes stratified spaces wi
th iterated cone-edge metrics. We establish convergence under a low-energy
condition. We also prove a concentration--compactness dichotomy\, and inv
estigate what the alternatives to convergence is.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhenlei Zhang (Capital Normal University)
DTSTART:20210519T130000Z
DTEND:20210519T132500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/21
DESCRIPTION:Title: On the Holder estimate of complex Monge-Am
pere equation\nby Zhenlei Zhang (Capital Normal University) as part of
IASM: Geometric PDE and Applications to Problems in Conformal and CR Geom
etry\n\n\nAbstract\nI the talk we present a Holder estimate of complex Mon
ge-Ampere equation on manifolds. The estimate follows from Kolodziej appro
ach to solve complex Monge-Ampere with L^p bounded measure.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaodong Wang (Michigan State University)
DTSTART:20210519T133000Z
DTEND:20210519T135500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/22
DESCRIPTION:Title: Improved Sobolev inequality under constrai
nts on the sphere\nby Xiaodong Wang (Michigan State University) as par
t of IASM: Geometric PDE and Applications to Problems in Conformal and CR
Geometry\n\n\nAbstract\nI will discuss a recent joint work with Fengbo Han
g on improved Sobolev inequality on the sphere when certain moments vanish
up to a given order. The 1st oder case was proved by Aubin’ about 40 ye
ars ago. Our new approach yields a characterization of the best constant f
or any order. It leads to an interesting extremal problem on the sphere. W
e are able to determine the constant explicitly in the second order case.\
n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Siyi Zhang (University of Notre Dame)
DTSTART:20210519T140000Z
DTEND:20210519T142500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/23
DESCRIPTION:Title: Conformally invariant rigidity theorems on
four-manifolds with boundary\nby Siyi Zhang (University of Notre Dame
) as part of IASM: Geometric PDE and Applications to Problems in Conformal
and CR Geometry\n\n\nAbstract\nWe introduce conformal and smooth invarian
ts on oriented\, compact four-manifolds with boundary and show that "posit
ivity" conditions on these invariants will impose topological restrictions
on underlying manifolds with boundary. We also establish conformally inva
riant rigidity theorems for Bach-flat four-manifolds with boundary under t
he assumptions on these invariants. It is noteworthy to point out that we
rule out some examples arising from the study of closed manifolds in the s
etting of manifolds with umbilic boundary.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rupert Frank (Caltech / University of Munich)
DTSTART:20210519T143000Z
DTEND:20210519T152000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/24
DESCRIPTION:Title: Which magnetic fields support a zero mode?
\nby Rupert Frank (Caltech / University of Munich) as part of IASM: Ge
ometric PDE and Applications to Problems in Conformal and CR Geometry\n\n\
nAbstract\nMotivated by the question from mathematical physics about the s
ize of magnetic fields that support zero modes for the three dimensional D
irac equation\, we study a certain conformally invariant spinor equation.
We state some conjectures and present results in their support. Those conc
ern\, in particular\, two novel Sobolev inequalities for spinors and vecto
r fields. The talk is based on joint work with Michael Loss.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fang Wang (Shanghai Jiao Tong University)
DTSTART:20210520T113000Z
DTEND:20210520T142000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/25
DESCRIPTION:Title: A new lower bound for the relative volume
inequality for CCE\nby Fang Wang (Shanghai Jiao Tong University) as pa
rt of IASM: Geometric PDE and Applications to Problems in Conformal and CR
Geometry\n\n\nAbstract\nIn this talk\, I will provide a new lower bound f
or the relative volume inequality for conformally compact Einstein manifol
ds\, as well as its applications in the rigidity theorem for CCE.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuxin Dong (Fudan University)
DTSTART:20210520T123000Z
DTEND:20210520T125500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/26
DESCRIPTION:Title: Prescribed Webster scalar curvatures on co
mpact pseudo-Hermitian manifolds\nby Yuxin Dong (Fudan University) as
part of IASM: Geometric PDE and Applications to Problems in Conformal and
CR Geometry\n\n\nAbstract\nIn this talk\, we will discuss the problem of p
rescribing Webster scalar curvatures on compact strictly pseudo convex CR
manifolds. In terms of the upper and lower solutions method and the pertur
bation theory of self-adjoint operators\, we try to describe some sets of
Webster scalar curvature functions which can be realized through pointwise
CR conformal deformations and CR conformally equivalent deformations resp
ectively from a given pseudo-Hermitian structure. This is a joint work wit
h Yibin Ren and Weike Yu.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaoli Han (Tsinghua University)
DTSTART:20210520T130000Z
DTEND:20210520T132500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/27
DESCRIPTION:Title: Existence of deformed Hermitian-Yang Mills
metric\nby Xiaoli Han (Tsinghua University) as part of IASM: Geometri
c PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbstr
act\nFirst I will introduce the equation of the deformed Hermitian-Yang Mi
lls metric on the holomorphic line bundle of the Kahler manifold. Then I w
ill introduce some existence results of this equation under some assumptio
ns. I will also introduce the corresponding heat equation and some long ti
me existence and convergence of the heat flow.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weiping Zhang (Nankai University)
DTSTART:20210520T133000Z
DTEND:20210520T142000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/28
DESCRIPTION:Title: Positive scalar curvature on manifolds and
foliations\nby Weiping Zhang (Nankai University) as part of IASM: Geo
metric PDE and Applications to Problems in Conformal and CR Geometry\n\n\n
Abstract\nA famous vanishing theorem of due to Lichnerowicz states that if
a closed spin manifold admits a Riemannian metric with positive scalar cu
rvature\, then it's a-hat genus equals to zero. In this talk we will descr
ibe some recent advanced generalizing this kind of results to other manifo
lds as well as foliations.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen McKeown (University of Texas - Dallas)
DTSTART:20210520T142000Z
DTEND:20210520T145500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/29
DESCRIPTION:Title: Renormalized volume of partially bounded s
ubregions of asymptotically hyperbolic Einstein spaces\nby Stephen McK
eown (University of Texas - Dallas) as part of IASM: Geometric PDE and App
lications to Problems in Conformal and CR Geometry\n\n\nAbstract\nThe reno
rmalized volume of an asymptotically hyperbolic Einstein four-manifold is
among its most important global invariants. We define renormalized volume
for minimally bounded half-spaces\, then prove a Gauss-Bonnet formula for
the volume and compute its variation under variations of the minimal bound
ary. This is joint work with Matthew J. Gursky and Aaron J. Tyrrell.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luca Martinazzi (University of Padova)
DTSTART:20210520T150000Z
DTEND:20210520T152500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/30
DESCRIPTION:Title: Local and non-local singular Liouville equ
ations in Euclidean spaces\nby Luca Martinazzi (University of Padova)
as part of IASM: Geometric PDE and Applications to Problems in Conformal a
nd CR Geometry\n\n\nAbstract\nWe show some recent existence and classifica
tion results for conformal metrics in Euclidean spaces having prescribed c
onstant Q-curvature and a singularity at the origin. While in dimension 2
this problem was studied and fully understood by Prajapat-Tarantello\, in
higher dimension new phenomena arise and several questions remain open. Th
is is a joint work with A. Hyder and G. Mancini.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rod Gover (University of Auckland)
DTSTART:20210521T113000Z
DTEND:20210521T115500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/31
DESCRIPTION:Title: A conformally invariant Yang-Mills energy
and equation on 6-manifolds.\nby Rod Gover (University of Auckland) as
part of IASM: Geometric PDE and Applications to Problems in Conformal and
CR Geometry\n\n\nAbstract\nThe gauge field equations known as the Yang-Mi
lls equations are extremely important in both mathematics and physics\, an
d their conformal invariance in dimension 4 is a critical feature for many
applications. We show that there is a simple and elegant route to higher
order equations in dimension 6 that are analogous and arise as the Euler-L
agrange equations of a conformally invariant action. The functional gradie
nt of this action recovers the conformal Fefferman-Graham obstruction tens
or when the gauge connection is taken to be the conformal Cartan (or tract
or) connection. This also has importance for CR geometry through the Feffe
rman ambient metric. This is joint work with Larry Peterson and Callum Sle
igh.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria del Mar Gonzalez (UniversidadAutonoma de Madrid)
DTSTART:20210521T120000Z
DTEND:20210521T122500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/32
DESCRIPTION:Title: Non-local ODE in conformal geometry\nb
y Maria del Mar Gonzalez (UniversidadAutonoma de Madrid) as part of IASM:
Geometric PDE and Applications to Problems in Conformal and CR Geometry\n\
n\nAbstract\nWhen one looks for radial solutions of an equation with fract
ional Laplacian\, it is not generally possible to use usual ODE methods. I
f such equation has some conformal invariances\, then one may rewrite it i
n Emden-Fowler (cylindrical) coordinates and to use the properties of the
conformal fractional Laplacian on the cylinder\, which is a fractional ord
er Paneitz operator. After giving the necessary background\, we will brief
ly consider two particular applications of this technique: 1. Symmetry bre
aking\, non-degeneracy and uniqueness for the fractional Caffarelli-Kohn-N
irenberg inequality (joint work with W. Ao and A. DelaTorre). 2. Existence
and regularity for fractional Laplacian equations with drift and a critic
al Hardy potential (joint with H. Chan\, M. Fontelos and J. Wei).\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Biquard (Sorbonne Université)
DTSTART:20210521T123000Z
DTEND:20210521T132000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/33
DESCRIPTION:Title: Curved discrete series\nby Olivier Biq
uard (Sorbonne Université) as part of IASM: Geometric PDE and Application
s to Problems in Conformal and CR Geometry\n\n\nAbstract\nIt is well-known
that conformally compact Einstein metrics give a tool to understand the c
onformal geometry of the boundary in terms of the Riemannian geometry of t
he interior. Using this philosophy we relate Dirac operators in the interi
or with the BGG operators of the boundary. In the flat case\, this relates
discrete series for the orthogonal group with the BGG operators of the bo
undary sphere.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sagun Chanillo (Rutgers University)
DTSTART:20210521T133000Z
DTEND:20210521T142000Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/34
DESCRIPTION:Title: Local Version of Courant's Nodal Domain th
eorem\nby Sagun Chanillo (Rutgers University) as part of IASM: Geometr
ic PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAbst
ract\nGiven a compact Riemannian manifold with no boundary endowed with a
smooth metric g\, one of the important objects of study is the Laplace-Bel
trami operator and its eigenfunctions. That is The Courant nodal domain th
eorem asserts that the k-th eigenfunction has at most k nodal domains\, wh
ere a nodal domain is a connected component of the set . Harold Donnelly a
nd C. Fefferman initiated the study of local versions of this result with
a goal to show that nodal domains cannot be long and narrow. This was rela
ted 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. Mangoubi\, we obtain an optimal bound for results of this type.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Case (The Pennsylvania State University)
DTSTART:20210521T143000Z
DTEND:20210521T145500Z
DTSTAMP:20260404T041134Z
UID:GeometricPDEConformalCRGeometry/35
DESCRIPTION:Title: The I-prime curvature in CR geometry\n
by Jeffrey Case (The Pennsylvania State University) as part of IASM: Geome
tric PDE and Applications to Problems in Conformal and CR Geometry\n\n\nAb
stract\nIn this talk we discuss aspects of the CR analogue of the Deser—
Schwimmer conjecture. One possible formulation is that any pseudohermitian
scalar invariant whose integral is independent of the choice of pseudo-Ei
nstein contact form is a linear combination of the Q-prime curvature\, a l
ocal CR invariant\, and a divergence. In dimension three\, this statement
was proved in the affirmative by Hirachi. In higher dimensions\, the I-pri
me curvatures give counterexamples to this statement. We will describe the
I-prime curvatures and some of their properties\, including the proposal
of a new CR analogue of the Deser—Schwimmer conjecture. This is based on
joint works with Rod Gover and Yuya Takeuchi.\n
LOCATION:https://stable.researchseminars.org/talk/GeometricPDEConformalCRG
eometry/35/
END:VEVENT
END:VCALENDAR