BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Anusha Krishnan (Syracuse University)
DTSTART:20200430T190000Z
DTEND:20200430T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/1
DESCRIPTION:Title: Diagonalizing the Ricci tensor\nby Anusha Krishn
an (Syracuse University) as part of CUNY Geometric Analysis Seminar\n\n\nA
bstract\nWe will discuss some recent work on diagonalizing the Ricci tenso
r of invariant metrics on compact Lie groups\, homogeneous spaces and coho
mogeneity one manifolds\, and connections to the Ricci flow.\n\nZoom Meeti
ng ID: 961-8801-7284. The password to join will be sent to the seminar's m
ailing list\; if you are not on the mailing list\, please email NKatz(NoSp
amPlease)citytech.cuny.edu or R.Bettiol(NoSpamPlease)lehman.cuny.edu to re
ceive the password directly.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Buttsworth (Cornell University)
DTSTART:20200507T200000Z
DTEND:20200507T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/2
DESCRIPTION:Title: The prescribed Ricci curvature problem on manifolds
with large symmetry groups\nby Timothy Buttsworth (Cornell University)
as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nThe prescribed
Ricci curvature problem continues to be of fundamental interest in Riemann
ian geometry. In this talk\, I will describe some classical results on thi
s topic\, as well as some more recent results that have been achieved with
homogeneous and cohomogeneity-one assumptions.\n\nZoom Meeting ID: TBA (w
ill be posted here and in the seminar's website). The password to join wil
l be sent to the seminar's mailing list\; if you are not on the mailing li
st\, please email NKatz(NoSpamPlease)citytech.cuny.edu or R.Bettiol(NoSpam
Please)lehman.cuny.edu to receive the password directly.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronan Conlon (Florida International University)
DTSTART:20200514T200000Z
DTEND:20200514T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/3
DESCRIPTION:Title: Classification results for expanding and shrinking g
radient Kahler-Ricci solitons\nby Ronan Conlon (Florida International
University) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nA co
mplete Kahler metric g on a Kahler manifold $M$ is a "gradient Kahler-Ricc
i soliton" if there exists a smooth real-valued function $f\\colon M\\to R
$ with $\\nabla f$ holomorphic such that $Ric(g)-Hess(f)+\\lambda g=0$ fo
r $\\lambda$ a real number. I will present some classification results for
such manifolds. This is joint work with Alix Deruelle (Université Paris-
Sud) and Song Sun (UC Berkeley).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Longa (University of Sao Paulo (Brazil))
DTSTART:20200528T190000Z
DTEND:20200528T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/4
DESCRIPTION:Title: Sharp systolic inequalities for 3-manifolds with bou
ndary\nby Eduardo Longa (University of Sao Paulo (Brazil)) as part of
CUNY Geometric Analysis Seminar\n\n\nAbstract\nSystolic Geometry dates bac
k to the late 1940s\, with the work of Loewner and his doctoral student Pu
. This branch of differential geometry received more attention after the s
eminal work of Gromov\, where he proved his famous systolic inequality and
introduced many important concepts. In this talk I will recall the notion
of systole and present some sharp systolic inequalities for free boundary
surfaces in 3-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Kröncke (Universität Hamburg)
DTSTART:20200604T180000Z
DTEND:20200604T190000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/5
DESCRIPTION:Title: L^p-stability and positive scalar curvature rigidity
of Ricci-flat ALE manifolds\nby Klaus Kröncke (Universität Hamburg)
as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nWe will establi
sh long-time and derivative estimates for the heat semigroup of various na
tural Schrödinger operators on asymptotically locally Euclidean (ALE) man
ifolds. These include the Lichnerowicz Laplacian of a Ricci-flat ALE manif
old\, provided that it is spin and admits a parallel spinor. The estimates
will be used to prove its L^p-stability under the Ricci flow for pThe isometry group of spherical quotients\nby Ri
cardo A. E. Mendes (University of Oklahoma) as part of CUNY Geometric Anal
ysis Seminar\n\n\nAbstract\nA special class of Alexandrov metric spaces ar
e the quotients $X=S^n/G$ of the round spheres by isometric actions of com
pact subgroups $G$ of $O(n+1)$. We will consider the question of how to co
mpute the isometry group of such $X$\, the main result being that every el
ement in the identity component of $Isom(X)$ lifts to a $G$-equivariant is
ometry of the sphere. The proof relies on a pair of important results abou
t the "smooth structure" of $X$.\n\nPlease contact organizers for Zoom mee
ting details.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shih-Kai Chiu (University of Notre Dame)
DTSTART:20200618T190000Z
DTEND:20200618T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/7
DESCRIPTION:Title: A Liouville type theorem for harmonic 1-forms\nb
y Shih-Kai Chiu (University of Notre Dame) as part of CUNY Geometric Analy
sis Seminar\n\n\nAbstract\nThe famous Cheng-Yau gradient estimate implies
that on a\ncomplete Riemannian manifold with nonnegative Ricci curvature\,
any\nharmonic function that grows sublinearly must be a constant. This is
\nthe same as saying the function is closed as a 0-form. We prove an\nanal
ogous result for harmonic 1-forms. Namely\, on a complete\nRicci-flat mani
fold with Euclidean volume growth\, any harmonic 1-form\nwith polynomial s
ublinear growth must be the differential of a\nharmonic function. We prove
this by proving an $L^2$ version of the\n"gradient estimate" for harmonic
1-forms. As a corollary\, we show that\nwhen the manifold is Ricci-flat K
ähler with Euclidean volume growth\,\nthen any subquadratic harmonic func
tion must be pluriharmonic. This\ngeneralizes the result of Conlon-Hein.\n
\nContact organizers for Zoom meeting details.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Aldana (Universidad del Norte (Colombia))
DTSTART:20200625T190000Z
DTEND:20200625T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/8
DESCRIPTION:Title: Strong $A_\\infty$ weights and compactness of confor
mal metrics\nby Clara Aldana (Universidad del Norte (Colombia)) as par
t of CUNY Geometric Analysis Seminar\n\n\nAbstract\nIn the talk I will int
roduce $A_\\infty$-weights and strong $A_\\infty$-weights and present some
of their properties. I will show how\, using these weights\, we can prove
compactness of conformal metrics with critical integrability conditions o
n the scalar curvature. This relates to two problems in differential geome
try: Pinching of the curvature and finding geometrical conditions under wh
ich a sequence of conformal metrics admits a convergent subsequence. The r
esults presented here are joint work with Gilles Carron (University of Nan
tes) and Samuel Tapie (University of Nantes).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (UNAM (Mexico))
DTSTART:20200702T190000Z
DTEND:20200702T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/9
DESCRIPTION:Title: Convergence of manifolds under volume convergence an
d a tensor bound\nby Raquel Perales (UNAM (Mexico)) as part of CUNY Ge
ometric Analysis Seminar\n\n\nAbstract\nGiven a Riemannian manifold $M$ an
d a pair of Riemannian tensors $g_0 \\leq g_j$ on $M$ we have $vol_0(M) \
\leq vol_j(M)$ and the volumes are equal if and only if $g_0=g_j$. In th
is talk I will show that if we have a sequence of Riemmanian tensors $g_j$
such that $g_0\\leq g_j$ and $vol_j(M)\\to vol_0(M)$ then $(M\,g_j)$ conv
erge to $(M\,g_0)$ in the volume preserving intrinsic flat sense. I will
present examples demonstrating that under these conditions we do not neces
sarily obtain smooth\, $C^0$ or Gromov-Hausdorff convergence.\nFurthermore
\, this result can be applied to show stability of graphical tori. \n[Bas
ed on join work with Allen-Sormani and Cabrera Pacheco-Ketterer]\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Mondello (Université de Paris Est Créteil (France))
DTSTART:20200709T180000Z
DTEND:20200709T190000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/10
DESCRIPTION:Title: Non-existence of Yamabe metrics in a singular setti
ng\nby Ilaria Mondello (Université de Paris Est Créteil (France)) as
part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nThe existence of Y
amabe metrics\, that is\, metrics which minimize the Einstein-Hilbert func
tional in a conformal class\, has been proven for compact smooth manifolds
thanks to the celebrated work of Yamabe\, Trudinger\, Aubin and Schoen. W
hen considering manifolds with singularities\, the situation is quite diff
erent: while an existence result due to Akutagawa\, Mazzeo and Carron is a
vailable\, Viaclovsky had constructed in 2010 an example of 4-manifold\, w
ith one orbifold isolated singularity\, for which a Yamabe metric does not
exists. After briefly presenting the singularities we deal with\, we will
discuss a new non-existence result for a class of examples with non isola
ted singularities\, not necessarily orbifold. This is based on a joint wor
k with Kazuo Akutagawa.\n\nPlease note the earlier time than usual. Zoom m
eeting details are sent to our mailing list.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Chul Jang (University of Connecticut)
DTSTART:20200716T190000Z
DTEND:20200716T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/11
DESCRIPTION:Title: Mass rigidity of asymptotically hyperbolic manifold
s\nby Hyun Chul Jang (University of Connecticut) as part of CUNY Geome
tric Analysis Seminar\n\n\nAbstract\nIn this talk\, we present the rigidit
y of positive mass theorem for asymptotically hyperbolic (AH) manifolds. T
hat is\, if the total mass of a given AH manifold is zero\, then the manif
old is isometric to hyperbolic space. The proof of the rigidity used a var
iational approach with the scalar curvature constraint. It also involves a
n investigation of a type of Hessian equation\, which leads to recent spli
tting results with G. J. Galloway. We will briefly discuss them as well. T
his talk is based on the joint works with L.-H. Huang and D. Martin\, and
with G. J. Galloway.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Lee (CUNY Queens College and Graduate Center)
DTSTART:20200723T190000Z
DTEND:20200723T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/12
DESCRIPTION:Title: Bartnik minimizing initial data sets\nby Dan Le
e (CUNY Queens College and Graduate Center) as part of CUNY Geometric Anal
ysis Seminar\n\n\nAbstract\nWe will review what is known about Bartnik min
imizing initial data sets in the time-symmetric case\, and then discuss ne
w results on the general case obtained in joint work with Lan-Hsuan Huang
of the University of Connecticut. Bartnik conjectured that these minimizer
s must be vacuum and admit a global Killing vector. We make partial progre
ss toward the conjecture by proving that Bartnik minimizers must arise fro
m so-called “null dust spacetimes” that admit a global Killing vector
field. In high dimensions\, we find examples that contradict Bartnik’s c
onjecture\, as well as the “strict” positive mass theorem\, though the
se examples have "sub-optimal” asymptotic decay rates.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kerin (NUI Galway (Ireland))
DTSTART:20200730T180000Z
DTEND:20200730T190000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/13
DESCRIPTION:Title: A pot-pourri of non-negatively curved 7-manifolds\nby Martin Kerin (NUI Galway (Ireland)) as part of CUNY Geometric Analy
sis Seminar\n\n\nAbstract\nManifolds with non-negative sectional curvature
are rare and difficult to find\, with interesting topological phenomena t
raditionally being restricted by a dearth of methods of construction. In
this talk\, I will describe a large family of seven-dimensional manifolds
with non-negative curvature\, leading to examples of exotic diffeomorphism
types\, non-standard homotopy types\, and fake versions of familiar non-s
imply connected friends. This is based on joint work with Sebastian Goette
and Krishnan Shankar.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubham Dwivedi (University of Waterloo (Canada))
DTSTART:20200806T190000Z
DTEND:20200806T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/14
DESCRIPTION:Title: Deformation theory of nearly $G_2$ manifolds\nb
y Shubham Dwivedi (University of Waterloo (Canada)) as part of CUNY Geomet
ric Analysis Seminar\n\n\nAbstract\nWe will discuss the deformation theory
of nearly $G_2$ manifolds. After defining nearly $G_2$ manifolds\, we wil
l describe some identities for 2 and 3-forms on such manifolds. We will in
troduce a Dirac type operator which will be used to completely describe th
e cohomology of nearly $G_2$ manifolds. Along the way\, we will give a dif
ferent proof of a result of Alexandrov—Semmelman on the space of infinit
esimal deformation of nearly $G_2$ structures. Finally\, we will prove tha
t the infinitesimal deformations of the homogeneous nearly $G_2$ structure
on the Aloff--Wallach space are obstructed to second order. The talk is b
ased on a joint work with Ragini Singhal (University of Waterloo).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Lange (Universitaet zu Koeln)
DTSTART:20200903T180000Z
DTEND:20200903T190000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/15
DESCRIPTION:Title: Zoll flows on surfaces\nby Christian Lange (Uni
versitaet zu Koeln) as part of CUNY Geometric Analysis Seminar\n\n\nAbstra
ct\nA Riemannian metric is called Zoll if all its geodesics are closed wit
h the same period.\nWe discuss rigidity and flexibility phenomena of such
Riemannian and more general Zoll systems. In particular\, we show that if
a magnetic flow on a torus is Zoll at arbitrarily high energies\, then the
torus is flat. The latter is joint work with Luca Asselle.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariana Smit Vega Garcia (Western Washington University)
DTSTART:20200917T200000Z
DTEND:20200917T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/16
DESCRIPTION:Title: Almost minimizers for obstacle problems\nby Mar
iana Smit Vega Garcia (Western Washington University) as part of CUNY Geom
etric Analysis Seminar\n\n\nAbstract\nIn the applied sciences one is often
confronted with free boundaries\, which arise when the solution to a prob
lem consists of a pair: a function u (often satisfying a partial different
ial equation)\, and a set where this function has a specific behavior. Two
central issues in the study of free boundary problems and related problem
s in the calculus of variations and geometric measure theory are:\n\n(1) W
hat is the optimal regularity of the solution u?\n\n(2) How smooth is the
free boundary (or how smooth is a certain set related to u)?\n\nThe study
of the classical obstacle problem\, one of the most renowned free boundary
problems\, began in the ’60s with the pioneering works of G. Stampacchi
a\, H. Lewy\, and J. L. Lions. During the past five decades\, it has led t
o beautiful and deep developments in the calculus of variations and geomet
ric partial differential equations\, and its study still presents very int
eresting and challenging questions.\nIn contrast to the classical obstacle
problem\, which arises from a minimization problem\, minimizing problems
with noise lead to the notion of almost minimizes. Though deeply connected
to "standard" free boundary problems\, almost minimizers do not satisfy a
PDE as minimizers do\, requiring additional tools from geometric measure
theory to address (1) and (2). \nIn this talk\, I will overview recent dev
elopments on obstacle type problems and almost minimizers for the thin obs
tacle problem\, illustrating techniques that can be used to tackle questio
ns (1) and (2) in various settings.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Adelstein (Yale University)
DTSTART:20200924T200000Z
DTEND:20200924T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/17
DESCRIPTION:Title: The length of the shortest closed geodesic on posit
ively curved 2-spheres\nby Ian Adelstein (Yale University) as part of
CUNY Geometric Analysis Seminar\n\n\nAbstract\nWe start with an intuitive
introduction to the isosystolic inequalities. We then show that the shorte
st closed geodesic on a 2-sphere with non-negative curvature has length bo
unded above by three times the diameter. We prove a new isoperimetric ineq
uality for 2-spheres with pinched curvature\; this allows us to improve ou
r bound on the length of the shortest closed geodesic in the pinched curva
ture setting. This is joint work with Franco Vargas Pallete.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yueh-Ju Lin (Wichita State University)
DTSTART:20201015T200000Z
DTEND:20201015T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/18
DESCRIPTION:Title: Volume comparison of Q-curvature\nby Yueh-Ju Li
n (Wichita State University) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nClassical volume comparison for Ricci curvature is a fundamen
tal result in Riemannian geometry. In general\, scalar curvature as the tr
ace of Ricci curvature\, is too weak to control the volume. However\, with
the additional stability assumption on the closed Einstein manifold\, one
can obtain a volume comparison for scalar curvature. In this talk\, we in
vestigate a similar phenomenon for $Q$-curvature\, a fourth-order analogue
of scalar curvature. In particular\, we prove a volume comparison result
of $Q$-curvature for metrics near stable Einstein metrics by variational t
echniques and a Morse lemma for infinite dimensional manifolds. This is a
joint work with Wei Yuan.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curtis Pro (California State University (Stanislaus))
DTSTART:20201022T200000Z
DTEND:20201022T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/19
DESCRIPTION:Title: Extending a diffeomorphism finiteness theorem to di
mension 4.\nby Curtis Pro (California State University (Stanislaus)) a
s part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nCheeger's Finiten
ess Theorem says: Given numbers $k<$ $K$ in $\\mathbb{R}$ and $v\, D>0$\,
there are at most finitely many differentiable structures on the class of
$n$-manifolds $M$ that support metrics with $k\\leq\\sec M\\leq K\, \\math
rm{vol}\\\,M\\geq v\,$ and $\\mathrm{diam}\\\,M\\leq D.$ In the early 90s
\, Grove\, Petersen\, Wu\, and (independently) Perelman showed in all dime
nsions\, except possibly $n=4$\, this conclusion still holds for the large
r class that has no upper bound on sectional curvature. In this talk\, I'l
l present recent work with Fred Wilhelm that shows this conclusion is also
true in dimension 4.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Zhu (Princeton University)
DTSTART:20201112T210000Z
DTEND:20201112T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/20
DESCRIPTION:Title: Explicit Łojasiewicz inequalities for mean curvatu
re flow shrinkers\nby Jonathan Zhu (Princeton University) as part of C
UNY Geometric Analysis Seminar\n\n\nAbstract\nŁojasiewicz inequalities ar
e a popular tool for studying the stability of geometric structures. For m
ean curvature flow\, Schulze used Simon’s reduction to the classical Ło
jasiewicz inequality to study compact tangent flows. Colding and Minicozzi
instead used a direct method to prove Łojasiewicz inequalities for round
cylinders. We’ll discuss similarly explicit Łojasiewicz inequalities a
nd applications for other shrinking cylinders and Clifford shrinkers.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonçalo Oliveira (Universidade Federal Fluminense (Brazil))
DTSTART:20201001T200000Z
DTEND:20201001T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/21
DESCRIPTION:Title: $G_2$-monopoles (a summary)\nby Gonçalo Olivei
ra (Universidade Federal Fluminense (Brazil)) as part of CUNY Geometric An
alysis Seminar\n\n\nAbstract\nThis talk is aimed at reviewing what is know
n about $G_2$-monopoles and motivate their study. After this\, I will ment
ion some recent results obtained in collaboration with Ákos Nagy and Dani
el Fadel which investigate the asymptotic behaviour of $G_2$-monopoles. Ti
me permitting\, I will mention a few possible future directions regarding
the use of monopoles in $G_2$-geometry.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lin (Dartmouth College)
DTSTART:20201008T200000Z
DTEND:20201008T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/22
DESCRIPTION:Title: Three-dimensional Geometric Structures and the Lapl
ace Spectrum\nby Samuel Lin (Dartmouth College) as part of CUNY Geomet
ric Analysis Seminar\n\n\nAbstract\nThe earliest examples of non-isometric
Laplace-isospectral manifolds have the same local geometries. In fact\, t
he first example of 16-tori given by Milnor and other isospectral pairs ar
ising from the classical group theoretic method of Sunada have the same lo
cal geometries. However\, examples from Gordon\, Schueth\, Sutton\, and An
-Yu-Yu demonstrate that in dimension four and higher\, the local geometry
is not a spectral invariant\, even among locally homogeneous spaces. Thus\
, it is natural to ask whether the local geometry is a spectral invariant
in dimension two and three.\n \nI will present our result in this directio
n\, which provides strong evidence that the local geometry of a three-dime
nsional locally homogeneous space is a spectral invariant. Motivated by th
is problem in spectral geometry\, I will also present a metric classificat
ion of all locally homogeneous three-manifolds covered by topological sphe
res. This talk is based on a joint work with Ben Schmidt and Craig Sutton.
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernani Ribeiro Jr. (Universidade Federal do Ceara (Brazil))
DTSTART:20201029T200000Z
DTEND:20201029T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/23
DESCRIPTION:Title: Four-dimensional gradient shrinking Ricci solitons<
/a>\nby Ernani Ribeiro Jr. (Universidade Federal do Ceara (Brazil)) as par
t of CUNY Geometric Analysis Seminar\n\n\nAbstract\nIn this talk\, we will
discuss 4-dimensional complete (not necessarily compact) gradient shrinki
ng Ricci solitons. We will show that a 4-dimensional complete gradient sh
rinking Ricci soliton satisfying a pointwise condition involving either th
e self-dual or anti-self-dual part of the Weyl tensor is either Einstein\,
or a finite quotient of either the Gaussian shrinking soliton $\\Bbb{R}^4
\,$ or $\\Bbb{S}^{3}\\times\\Bbb{R}$\, or $\\Bbb{S}^{2}\\times\\Bbb{R}^{2}
.$ In addition\, we will present some curvature estimates for 4-dimensiona
l complete gradient Ricci solitons. Some open problems will be also discus
sed. This is a joint work with Huai-Dong Cao and Detang Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Ledwidge (University of Muenster)
DTSTART:20201105T210000Z
DTEND:20201105T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/24
DESCRIPTION:Title: The sharp Li-Yau equality on shrinking Ricci solito
ns\nby Jason Ledwidge (University of Muenster) as part of CUNY Geometr
ic Analysis Seminar\n\n\nAbstract\nIn this talk we will prove a sharp Li-Y
au equality on shrinking Ricci solitons and use this equality to prove the
existence of a minimiser for Perelman's W functional on shrinking Ricci s
olitons. By a result of Haslhofer-Mueller\, the uniqueness of the minimisi
er of the W functional leads to the classification of Type I singularity m
odels to the Ricci flow in four dimensions. If time permits\, we will also
show how the Li-Yau equality leads to a global Isoperimetric inequality o
n shrinkig Ricci solitons. We will be more interested in the importance of
the conjugate heat semigroup and its estimates on shrinking Ricci soliton
s and hence our aim is for the talk not to be too technical.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Neumayer (Northwestern University)
DTSTART:20201119T210000Z
DTEND:20201119T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/25
DESCRIPTION:Title: $d_p$ Convergence and $\\epsilon$-regularity theore
ms for entropy and scalar curvature lower bounds\nby Robin Neumayer (N
orthwestern University) as part of CUNY Geometric Analysis Seminar\n\n\nAb
stract\nIn this talk\, we consider Riemannian manifolds with almost non-ne
gative scalar curvature and Perelman entropy. We establish an $\\epsilon$-
regularity theorem showing that such a space must be close to Euclidean sp
ace in a suitable sense. Interestingly\, such a result is false with respe
ct to the Gromov-Hausdorff and Intrinsic Flat distances\, and more general
ly the metric space structure is not controlled under entropy and scalar l
ower bounds. Instead\, we introduce the notion of the $d_p$ distance betwe
en (in particular) Riemannian manifolds\, which measures the distance betw
een $W^{1\,p}$ Sobolev spaces\, and it is with respect to this distance th
at the $\\epsilon$ regularity theorem holds. We will discuss various appli
cations to manifolds with scalar curvature and entropy lower bounds\, incl
uding a compactness and limit structure theorem for sequences\, a uniform
$L^\\infty$ Sobolev embedding\, and a priori $L^p$ scalar curvature bounds
for $p<1$ This is joint work with Man-Chun Lee and Aaron Naber.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lashi Bandara (Universitaet Potsdam)
DTSTART:20201204T150000Z
DTEND:20201204T160000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/26
DESCRIPTION:Title: The world of rough metrics\nby Lashi Bandara (U
niversitaet Potsdam) as part of CUNY Geometric Analysis Seminar\n\n\nAbstr
act\nRough metrics are measurable coefficient Riemannian structures.\nThey
capture a very large class of natural geometries\, with the quintessentia
l example being Lipschitz pullbacks of smooth metrics.\nAlthough they hav
e implicitly appeared for a very long time\, particularly in the context o
f bounded-measurable coefficient divergence form equations\, they have onl
y been studied explicitly recently.\nThe aim of this talk would be to intr
oduce these metrics\, motivated by an important example - their connection
to the geometric Kato square root problem.\nTheir salient features would
be described\, along with recent results\, such as the existence of heat k
ernels and Weyl asymptotics for associated Laplacians in compact settings.
\n\n(Please note the different time for this talk.)\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annachiara Piubello (University of Miami)
DTSTART:20210204T210000Z
DTEND:20210204T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/27
DESCRIPTION:Title: Mass and Riemannian Polyhedra\nby Annachiara Pi
ubello (University of Miami) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nWe show a new formula for the ADM mass as the limit of the to
tal mean curvature plus the total defect of dihedral angle of the boundary
of large polyhedra. In the special case of coordinate cubes\, we will sho
w an integral formula relating the n-dimensional mass with a geometrical q
uantity that determines the (n-1)-dimensional mass. This is joint work wit
h Pengzi Miao.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Lowe (Princeton University)
DTSTART:20210211T210000Z
DTEND:20210211T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/28
DESCRIPTION:Title: Minimal Surfaces in Negatively Curved 3-manifolds\nby Ben Lowe (Princeton University) as part of CUNY Geometric Analysis
Seminar\n\n\nAbstract\nCalegari-Marques-Neves recently initiated the study
of stable properly immersed minimal surfaces in a negatively curved 3-man
ifold from a dynamical perspective. I will survey their work and talk abo
ut some results that I've obtained in this direction.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART:20210218T210000Z
DTEND:20210218T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/29
DESCRIPTION:Title: Manifold submetries\, with applications to Invarian
t Theory\nby Marco Radeschi (University of Notre Dame) as part of CUNY
Geometric Analysis Seminar\n\n\nAbstract\nGiven an orthogonal representat
ion of a Lie group G on a Euclidean vector space V\, Invariant Theory stud
ies the algebra of G-invariant polynomials on V. This setting can be gener
alized by replacing the orbits of the representation with a foliation by t
he fibers of a manifold submetry from the unit sphere S(V)\, and consider
the algebra of polynomials that are constant along these fibers (effective
ly producing an Invariant Theory\, but without groups).\nIn this talk we w
ill exhibit a surprisingly strong relation between the geometric informati
on coming from the submetry and the algebraic information coming from the
corresponding algebra\, with several applications to classical Invariant T
heory.\nThis talk is based on a joint work with Ricardo Mendes.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/2
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weimin Sheng (Zhejiang University)
DTSTART:20210226T000000Z
DTEND:20210226T010000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/30
DESCRIPTION:Title: Removable singularity of positive mass theorem with
continuous metrics\nby Weimin Sheng (Zhejiang University) as part of
CUNY Geometric Analysis Seminar\n\n\nAbstract\nIn this talk\, I consider a
symptotically flat Riemannnian manifolds $(M^n\, g)$ with $C^0$ metric $g$
and $g$ is smooth away from a closed bounded subset $\\Sigma$ and the sca
lar curvature $R_g\\ge 0$ on $M\\setminus \\Sigma$. For given $n\\le p\\l
e \\infty$\, if $g\\in C^0\\cap W^{1\,p}$ and the Hausdorff measure $\\m
athcal{H}^{n-\\frac{p}{p-1}}(\\Sigma)<\\infty$ when $n\\le p<\\infty$ or $
\\mathcal{H}^{n-1}(\\Sigma)=0$ when $p=\\infty$\, then I will show that th
e ADM mass of each end is nonnegative. Furthermore\, if the ADM mass of so
me end is zero\, then I'll show that $(M^n\, g)$ is isometric to the Eucli
dean space by showing the manifold has nonnegative Ricci curvature in RCD
sense. This result extends the result of Dan Lee and P. Lefloch (2015 CMP)
from spin to non-spin\, also improves the result of Shi-Tam [JDG 2002] an
d Lee [PAMS 2013]. Moreover\, for $p=\\infty$\, this confirms a conjecture
of Lee [pAMS 2013].\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitali Kapovitch (University of Toronto)
DTSTART:20210304T210000Z
DTEND:20210304T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/31
DESCRIPTION:Title: Mixed curvature almost flat manifolds\nby Vital
i Kapovitch (University of Toronto) as part of CUNY Geometric Analysis Sem
inar\n\n\nAbstract\nA celebrated theorem of Gromov says that given $n>1$ t
here is an $\\epsilon(n)>0$ such that if a closed Riemannian manifold $M^n
$ satisfies $-\\epsilon<\\sec_M<\\epsilon\, diam(M)< 1$ then $M$ is diffeo
morphic to an infranilmanifold.\nI will show that the lower sectional curv
ature bound in Gromov’s theorem can be weakened to the lower Bakry-Emery
Ricci curvature bound. I will also discuss the relation of this result to
the study of manifolds with Ricci curvature bounded below.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feng Wang (Zhejiang University)
DTSTART:20210311T140000Z
DTEND:20210311T150000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/32
DESCRIPTION:Title: On the singular Yau-Tian-Donaldson conjecture\n
by Feng Wang (Zhejiang University) as part of CUNY Geometric Analysis Semi
nar\n\n\nAbstract\nThe famous Yau-Tian-Donaldson conjecture asserts the eq
uivalence between the stability and existence of canonical metrics. On Fan
o manifolds\, the canonical metric is Kahler-Einstein metric. This case is
solved by Tian and Chen-Donaldson-Sun. In this talk\, we will talk about
the existence of Kahler-Einstein metrics on a class of singular Fano vari
eties. This is a joint work with Chi Li and Professor Gang Tian.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Chul Jang (University of Miami)
DTSTART:20210311T210000Z
DTEND:20210311T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/33
DESCRIPTION:Title: Hyperbolic mass via horospheres\nby Hyun Chul J
ang (University of Miami) as part of CUNY Geometric Analysis Seminar\n\n\n
Abstract\nThe mass of asymptotically hyperbolic manifolds is a geometric i
nvariant that measures its deviation from hyperbolic space. In this talk\,
we present a new mass formula using large coordinate horospheres. The for
mula is stated as a limit of the weighted total difference of mean curvatu
res on large coordinate horospheres. We will remark a few geometric implic
ations of the formula including scalar curvature rigidity of asymptoticall
y hyperbolic manifolds. This talk is based on joint work with Pengzi Miao.
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Li (Rutgers University)
DTSTART:20210408T200000Z
DTEND:20210408T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/34
DESCRIPTION:Title: Recent progresses on the Yau-Tian-Donaldson conject
ure for constant scalar curvature Kahler metrics\nby Chi Li (Rutgers U
niversity) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nFor a
ny polarized projective manifold $(X\, L)$\, the Yau-Tian-Donaldson conjec
ture predicts that the existence of constant scalar curvature Kahler metri
cs in the first Chern class of $L$ is equivalent to an algebraic K-stabili
ty property of $(X\, L)$. We will survey some recent progresses towards th
is conjecture and how it leads to an interesting open question in algebrai
c geometry.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Princeton University)
DTSTART:20210318T200000Z
DTEND:20210318T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/35
DESCRIPTION:Title: Scalar curvature and dihedral rigidity of Riemannia
n polyhedra\nby Chao Li (Princeton University) as part of CUNY Geometr
ic Analysis Seminar\n\n\nAbstract\nIn 2013\, Gromov proposed a geometric c
omparison theorem for metrics with nonnegative scalar curvature\, formulat
ed in terms of the dihedral rigidity phenomenon for Riemannian polyhedrons
: if a Riemannian polyhedron has nonnegative scalar curvature in the inter
ior\, and weakly mean convex faces\, then the dihedral angle between adjac
ent faces cannot be everywhere less than the corresponding Euclidean model
. In this talk\, I will prove this conjecture for a large collection of po
lytopes\, and extend it to metrics with negative scalar curvature lower bo
unds. The strategy is to relate this question with a geometric variational
problem of capillary type\, and apply the Schoen-Yau minimal slicing tech
nique for manifolds with boundary.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davi Maximo (University of Pennsylvania)
DTSTART:20210325T200000Z
DTEND:20210325T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/36
DESCRIPTION:Title: The Waist Inequality and Positive Scalar Curvature<
/a>\nby Davi Maximo (University of Pennsylvania) as part of CUNY Geometric
Analysis Seminar\n\n\nAbstract\nThe topology of three-manifolds with posi
tive scalar curvature has been (mostly) known since the solution of the Po
incare conjecture by Perelman. Indeed\, they consist of connected sums of
spherical space forms and $S^2 \\times S^1$'s. In spite of this\, their "s
hape" remains unknown and mysterious. Since a lower bound of scalar curvat
ure can be preserved by a codimension two surgery\, one may wonder about a
description of the shape of such manifolds based on a codimension two dat
a (in this case\, 1-dimensional manifolds).\n \nIn this talk\, I will show
results from a recent collaboration with Y. Liokumovich elucidating this
question for closed three-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aghil Alaee (Clark University & CMSA Harvard)
DTSTART:20210415T200000Z
DTEND:20210415T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/37
DESCRIPTION:Title: Rich extra dimensions are hidden inside black holes
\nby Aghil Alaee (Clark University & CMSA Harvard) as part of CUNY Geo
metric Analysis Seminar\n\n\nAbstract\nIn 1972\, Kip Thorne conjectured a
formation of a black hole due to an inequality between the mass of a bound
ed region and its size. In this talk\, I review some recent results regard
ing this conjecture and its application to the size of the geometry of ext
ra dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Hallgren (Cornell University)
DTSTART:20210513T200000Z
DTEND:20210513T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/38
DESCRIPTION:Title: Ricci Flow with a Lower Bound on Ricci Curvature an
d Volume\nby Max Hallgren (Cornell University) as part of CUNY Geometr
ic Analysis Seminar\n\n\nAbstract\nIn this talk\, we will investigate the
possible singularity behavior of closed solutions of Ricci flow whose Ricc
i curvature is uniformly bounded below\, and whose volume does not go to z
ero. In four dimensions\, we will see that only orbifold singularities can
arise\, and prove integral curvature estimates on time slices. We will al
so see a rough picture of singularity formation in higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tam Nguyen-Phan (Karlsruhe Institute of Technology)
DTSTART:20210506T190000Z
DTEND:20210506T200000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/39
DESCRIPTION:Title: Flat cycles in the homology of congruence covers of
SL(n\,Z)\\SL(n\,R)/SO(n)\nby Tam Nguyen-Phan (Karlsruhe Institute of
Technology) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nThe
locally symmetric space SL(n\,Z)\\SL(n\,R)/SO(n)\, or the space of flat n-
tori of unit volume\, has immersed\, totally geodesic\, flat tori of dimen
sion (n-1). These tori are natural candidates for nontrivial homology cycl
es of manifold covers of SL(n\,Z)\\SL(n\,R)/SO(n). In joint work with Grig
ori Avramidi\, we show that some of these tori give nontrivial rational ho
mology cycles in congruence covers of SL(n\,Z) \\SL(n\,R)/SO(n). We also s
how that the dimension of the subspace of the (n-1)-homology group spanned
by flat (n-1)-tori grows as one goes up in congruence covers. The prerequ
isite for this talk is very basic linear algebra.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/3
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun (The University of Chicago)
DTSTART:20210909T200000Z
DTEND:20210909T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/40
DESCRIPTION:Title: Initial perturbation of mean curvature flow\nby
Ao Sun (The University of Chicago) as part of CUNY Geometric Analysis Sem
inar\n\n\nAbstract\nWe show that after a perturbation on the initial data
of mean curvature flow\, the perturbed flow can avoid certain non-generic
singularities. This contributes to the program of dynamical approach to me
an curvature flow initiated by Colding and Minicozzi. The key is to prove
that a positive perturbation on initial data would drift to the first eige
nfunction direction after a long time. This result can be viewed as a glob
al unstable manifold theorem in the most unstable direction for a nonlinea
r heat equation. This is joint work with Jinxin Xue (Tsinghua University).
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhou Zhang (The University of Sydney)
DTSTART:20210923T200000Z
DTEND:20210923T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/41
DESCRIPTION:Title: The Modified Kahler-Ricci Flow and Degenerate Calab
i-Yau Equation\nby Zhou Zhang (The University of Sydney) as part of CU
NY Geometric Analysis Seminar\n\n\nAbstract\nThe Kahler-Ricci flow is the
Ricci flow with the initial metric being Kahler. Since H-D Cao’s first p
aper on it\, the featured reduction to a scalar evolution has provided not
iceable flexibility to study variations\, flows of Kahler-Ricci type. More
than a decade ago\, I introduced a modified Kahler-Ricci flow and laid th
e foundation for applications in the study of Calabi-Yau equation with deg
enerate cohomology. Since then\, there have been many developments in the
study of the classic Kahler-Ricci flow and the study of the degenerate Cal
abi-Yau equation using the elliptic continuity method. \n\nMotivated by th
ese\, we further study the modified Kahler-Ricci flow to understand the co
nvergence and eventually singularities of the degenerate Calabi-Yau metric
. This is joint work with Haotian Wu (USyd).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Ville (Université Paris-Est - Créteil Val-de-Marne)
DTSTART:20211118T210000Z
DTEND:20211118T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/42
DESCRIPTION:Title: Minimal surfaces in $\\mathbb R^4$\nby Marina V
ille (Université Paris-Est - Créteil Val-de-Marne) as part of CUNY Geome
tric Analysis Seminar\n\n\nAbstract\nComplete minimal surfaces in $\\mathb
b{R}^4$ are much less well understood than their counterparts in $\\mathbb
{R}^3$. Some basic questions are still quite open\, for example\, what are
the minimal non-holomorphic embeddings of $\\mathbb{R}^2$ in $\\mathbb{R}
^4$?\n\nI will discuss these problems\, define the link/knot /braid at inf
inity of minimal surfaces of finite curvature in $\\mathbb{R}^4$ and expla
in how this object helps us classify these surfaces. I will focus on surfa
ces of small total curvature and show a couple of examples where we deform
/desingularize a classical minimal surface in $\\mathbb{R}^3$ by families
of minimal surfaces in $\\mathbb{R}^4$. Joint work with Marc Soret.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Albin (UIUC)
DTSTART:20210930T200000Z
DTEND:20210930T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/43
DESCRIPTION:Title: The sub-Riemannian limit of a contact manifold\
nby Pierre Albin (UIUC) as part of CUNY Geometric Analysis Seminar\n\n\nAb
stract\nContact manifolds\, which arise naturally in mechanics\, dynamics\
, and geometry\, carry natural Riemannian and sub-Riemannian structures an
d it was shown by Gromov that the latter can be obtained as a limit of the
former. Subsequently\, Rumin found a complex of differential forms reflec
ting the contact structure that computes the singular cohomology of the ma
nifold. He used this complex to describe the behavior of the spectra of th
e Riemannian Hodge Lapacians in the sub-Riemannian limit. As many of the e
igenvalues diverge\, a refined analysis is necessary to determine the beha
vior of global spectral invariants. I will report on joint work with Hadri
an Quan in which we determine the global behavior of the spectrum by expla
ining the structure of the heat kernel along this limit in a uniform way.\
n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangyang Li (Princeton University)
DTSTART:20211028T200000Z
DTEND:20211028T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/44
DESCRIPTION:Title: Minimal hypersurfaces in a generic 8-dimensional cl
osed manifold\nby Yangyang Li (Princeton University) as part of CUNY G
eometric Analysis Seminar\n\n\nAbstract\nIn the recent decade\, the Almgre
n-Pitts min-max theory has advanced the existence theory of minimal surfac
es in a closed Riemannian manifold $(M^{n+1}\, g)$. When $2 \\leq n+1 \\le
q 7$\, many properties of these minimal hypersurfaces (geodesics)\, such a
s areas\, Morse indices\, multiplicities\, and spatial distributions\, hav
e been well studied. However\, in higher dimensions\, singularities may oc
cur in the constructed minimal hypersurfaces. This phenomenon invalidates
many techniques helpful in the low dimensions to investigate these geometr
ic objects. In this talk\, I will discuss how to overcome the difficulty i
n a generic 8-dimensional closed manifold\, utilizing various deformation
arguments. En route to obtaining generic results\, we prove the generic re
gularity of minimal hypersurfaces in dimension 8. This talk is partially b
ased on joint works with Zhihan Wang.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Virginia Agostiniani (University of Trento)
DTSTART:20211202T200000Z
DTEND:20211202T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/45
DESCRIPTION:Title: A Green's function proof of the positive mass theo
rem\nby Virginia Agostiniani (University of Trento) as part of CUNY Ge
ometric Analysis Seminar\n\n\nAbstract\nIn this talk we describe a new mon
otonicity formula holding along the level sets of the Green's function of
an asymptotically flat 3-manifold with nonnegative scalar curvature. Using
such a formula\, we obtain a simple proof of the celebrated positive mass
theorem. In the same context\, and for $1 < p < 3$ a Geroch-type calculat
ion is performed along the level sets of p-harmonic functions\, leading to
a new proof of the Riemannian Penrose Inequality in some case studies. Th
ese results are obtained in collaboration with L. Mazzieri and F. Oronzio.
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengwen Wang (University of Warwick)
DTSTART:20210916T200000Z
DTEND:20210916T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/46
DESCRIPTION:Title: A Brakke type regularity for the parabolic Allen-Ca
hn equation\nby Shengwen Wang (University of Warwick) as part of CUNY
Geometric Analysis Seminar\n\n\nAbstract\nWe will talk about an analogue o
f the Brakke's local regularity theorem for the $\\epsilon$ parabolic Alle
n-Cahn equation. In particular\, we show uniform $C_{2\,\\alpha}$ regulari
ty for the transition layers converging to smooth mean curvature flows as
$\\epsilon$ tend to 0 under the almost unit-density assumption. This can b
e viewed as a diffused version of the Brakke regularity for the limit mean
curvature flow. This is joint work with Huy Nguyen.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaochun Rong (Rutgers University)
DTSTART:20211209T210000Z
DTEND:20211209T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/48
DESCRIPTION:Title: Open Alexandrov spaces of non-negative curvature\nby Xiaochun Rong (Rutgers University) as part of CUNY Geometric Analysi
s Seminar\n\n\nAbstract\nWe will discuss some recent work on geometric and
topological structures of an open (complete and non-compact) Alexandrov s
pace of non-negative curvature\, which can be viewed as counterparts of re
sults on open Riemannian manifolds of non-negative sectional curvature. Th
is is a joint work with Xueping Li of Jiangsu Normal University\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruojing Jiang (University of Chicago)
DTSTART:20211104T200000Z
DTEND:20211104T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/49
DESCRIPTION:Title: Minimal Surface Entropy in Negatively Curved N-mani
folds and Rigidity\nby Ruojing Jiang (University of Chicago) as part o
f CUNY Geometric Analysis Seminar\n\n\nAbstract\nWe focus on an odd-dimens
ional closed manifold M that admits a hyperbolic metric. For any metric on
M with sectional curvature less than or equal to -1\, we introduce the mi
nimal surface entropy to count the number of surface subgroups. It attains
the minimum if and only if the metric is hyperbolic. This is an extension
of the work on 3-manifolds by Calegari-Marques-Neves. I'm going to introd
uce their ideas for dimension 3\, and talk about the problems and solution
s for higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/4
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nan Li (NYCCT CUNY)
DTSTART:20211021T200000Z
DTEND:20211021T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/50
DESCRIPTION:Title: Curvature measure on singular spaces with lower cur
vature bounds\nby Nan Li (NYCCT CUNY) as part of CUNY Geometric Analys
is Seminar\n\n\nAbstract\nWe will discuss some recent progress on the foll
owing problems.\n\n1. Is there an upper bound of curvature integrals\, pro
vided that certain curvature is bounded from below?\n
\n2. As a measure in the Gromov-Hausdorff limit of manifold
s\, what is the behavior of the limit of the curvature integral? The curva
ture should concentrate at singular points.\n
\n3. What is the notion of curvature measure in singular spaces wit
h curvature bounded from below?\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Vargas Pallete (Yale University)
DTSTART:20211014T200000Z
DTEND:20211014T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/51
DESCRIPTION:Title: Mean curvature flow and foliations in Hyperbolic 3-
manifolds\nby Franco Vargas Pallete (Yale University) as part of CUNY
Geometric Analysis Seminar\n\n\nAbstract\nIn this talk we explore some pro
perties of the mean curvature flow with surgery and the level-set flow in
negative curvature. We combine those with min-max theory to conclude that
any quasi-Fuchsian and any hyperbolic 3-manifolds fibered over $S^1$ admit
s a foliation where every leaf is minimal or has non-vanishing mean curvat
ure. We will also discuss outermost minimal surfaces in this setup. This i
s joint work with Marco Guaraco (Imperial College) and Vanderson Lima (Uni
versidade Federal do Rio Grande do Sul).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Zamora (Penn State)
DTSTART:20211007T200000Z
DTEND:20211007T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/52
DESCRIPTION:Title: Structure of collapse and fundamental groups\nb
y Sergio Zamora (Penn State) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nGromov's compactness criterion implies that the family $M_{se
c}(d\,D\,c)$ (resp. $M_{Ric}(d\,D\,c)$) of closed Riemannian manifolds wit
h dimension $\\leq d$\, diameter $\\leq D$\, and sectional curvature $\\ge
q c$ (resp. Ricci curvature $\\geq c$)\, is pre-compact with respect to th
e Hausdorff topology in the space of compact metric spaces.\nThe general b
ehavior of a sequence $X_i$ in one of those families is very different dep
ending on whether vol$(X_i) \\to 0$\, or vol$(X_i)\\geq \\delta >0$. In t
his talk I will present some topological obstructions\, involving the fund
amental groups of the spaces $X_i$\, for the second situation to occur.\nT
he main tools used in this kind of results are systolic inequalities\, and
the Yamaguchi--Burago--Gromov--Perelman fibration theorem in the case of
lower sectional curvature bounds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhui Wu (Tsinghua Univ.)
DTSTART:20220211T000000Z
DTEND:20220211T010000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/53
DESCRIPTION:Title: Recent progress on first eigenvalues of hyperbolic
surfaces for large genus\nby Yunhui Wu (Tsinghua Univ.) as part of CUN
Y Geometric Analysis Seminar\n\n\nAbstract\nIn this talk we will discuss s
everal recent results on first eigenvalues of closed hyperbolic surfaces f
or large genus. For example\, we show that a random hyperbolic surface of
large genus has first eigenvalue greater than $\\frac{3}{16}-\\epsilon$\,
extending Mirzakhani's lower bound $0.0024$. This talk is based on several
joint works with Yuhao Xue.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ravi Shankar (NSF and University of Oklahoma)
DTSTART:20220428T201500Z
DTEND:20220428T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/54
DESCRIPTION:Title: Growth Competitions in Non-positive Curvature\n
by Ravi Shankar (NSF and University of Oklahoma) as part of CUNY Geometric
Analysis Seminar\n\nLecture held in CUNY Graduate Center (Room 6495).\n\n
Abstract\n[ATTENTION: THIS TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 649
5\, AND SIMULTANEOUSLY TRANSMITTED VIA ZOOM]\n\nThe notion of a growth com
petition between two deterministically growing clusters in a complete\, no
n-compact metric space (or graph) was first proposed by I. Benjamini and r
ecently explored in the case of 2-dimensional Euclidean and hyperbolic spa
ces by his student\, R. Assouline. A growth competition in a non-compact\
, complete Riemannian manifold\, $X$\, (or more generally a complete\, non
-compact geodesic metric space) is the existence of two sets\, $A_t$ (fast
) and $B_t$ (slow)\, $t \\geq 0$\, that grow from singletons according to
the following simple rules:\n\n(i) $A_0 = \\{q\\}\, B_0 = \\{p \\}$ and $p
\\neq q$.\n\n(ii) $\\{A_t\\}_{t\\geq 0}$ is a parametrized family of subse
ts defined as\, $A_t := \\cup_{\\alpha} \\alpha([0\,t])$\, where $\\alpha(
s)$ is a $\\lambda$-Lipschitz curve in $X$\, with $\\lambda > 1$ such that
$\\alpha(s) \\not\\in B_s$ for all $s \\in [0\,t]$. The collection of se
ts $A_t$ are the fast sets.\n\n(iii) $\\{B_t\\}_{t\\geq 0}$ is a parametri
zed family of subsets defined as\, $B_t := \\cup_{\\beta} \\beta([0\,t))$\
, where $\\beta(s)$ is a 1-Lipschitz curve in $X$ and $\\beta(s) \\not\\in
A_s$ for all $s \\in [0\,t]$. The collection of sets $B_t$ are the slow
sets.\n\n(iv) The limiting sets are denoted as $A_\\infty = \\cup_{t \\geq
0} A_t$ and $B_\\infty = \\cup_{t \\geq 0} B_t$.\n\nA key result shown by
Assouline is that given any two distinct points $p\,q$ in a path connecte
d\, complete\, geodesic metric space $X$ and a real number $\\lambda >1$\,
there exists a unique growth competition satisfying the above conditions.
A basic geometric question one may ask in this setting is: Under what ci
rcumstances is the slow set\, $B_\\infty$\, totally bounded (surrounded) b
y the fast set\, $A_\\infty$\, versus when are they both unbounded (co-exi
stence)? The applications of this geometric exploration are evident in a
variety of settings (including disease/vaccine vectors\, flow of misinform
ation or the control of forest fires).\n\nIn recent work with Benjamin Sch
midt and Ralf Spatzier we have been exploring the above question in the se
tting of non-positive curvature. In this talk we introduce growth competit
ions and give a preview of some results and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhichao Wang (University of British Columbia)
DTSTART:20220217T210000Z
DTEND:20220217T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/55
DESCRIPTION:Title: Min-max minimal hypersurfaces with higher multiplic
ity\nby Zhichao Wang (University of British Columbia) as part of CUNY
Geometric Analysis Seminar\n\n\nAbstract\nRecently\, X. Zhou proved that t
he Almgren-Pitts min-max solution has multiplicity one for bumpy metrics (
Multiplicity One Theorem). In this talk\, we exhibit the first set of exam
ples of non-bumpy metrics on the $(n+1)$-sphere ($2\\leq n\\leq 6$) in whi
ch the varifold associated with the two-parameter min-max construction mus
t be a multiplicity-two minimal $n$-sphere. This is proved by a new area-a
nd-separation estimate for certain minimal hypersurfaces with Morse index
two inspired by an early work of Colding-Minicozzi. This is a joint work w
ith X. Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otis Chodosh (Stanford University)
DTSTART:20220317T200000Z
DTEND:20220317T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/56
DESCRIPTION:Title: Stability of minimal hypersurfaces in 4-manifolds\nby Otis Chodosh (Stanford University) as part of CUNY Geometric Analys
is Seminar\n\n\nAbstract\nI will discuss recent joint work with Chao Li an
d Doug Stryker concerning stability of (non-compact) minimal hypersurfaces
in 4-manifolds. I will discuss ambient curvature conditions that do and d
o not admit complete such hypersurfaces\, as well as indicating some appli
cations to comparison geometry.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erin Griffin (Seattle Pacific University)
DTSTART:20220414T200000Z
DTEND:20220414T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/57
DESCRIPTION:Title: The Case for a General $q$-flow: An Investigation o
f Ambient Obstruction Solitons\nby Erin Griffin (Seattle Pacific Unive
rsity) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nWe will d
iscuss a new program of studying ambient obstruction solitons and homogene
ous gradient Bach solitons using a geometric flow for a general tensor $q$
. We begin by establishing a number of results for solitons to the geometr
ic flow for a general tensor\, $q$. Moving on\, we will apply these result
s to the ambient obstruction flow to see that any homogeneous ambient obst
ruction soliton is ambient obstruction flat. Then\, focusing on dimension
$n=4$\, we show that any homogeneous gradient Bach soliton that is steady
must be Bach flat\; that the only homogeneous\, non-Bach-flat\, shrinking
gradient solitons are product metrics on $\\mathbb R^2 \\times \\mathbb S^
2$ and $\\mathbb R^2 \\times\\mathbb H^2$\; and there is a homogeneous\,
non-Bach-flat\, expanding gradient Bach soliton.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Ambrozio (IMPA)
DTSTART:20220310T210000Z
DTEND:20220310T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/58
DESCRIPTION:Title: Analogues of Zoll metrics in minimal submanifolds t
heory\nby Lucas Ambrozio (IMPA) as part of CUNY Geometric Analysis Sem
inar\n\n\nAbstract\nA Riemannian metric on a closed manifold is called Zol
l when all of its geodesics are closed and have the same period. Zoll metr
ics on the two-sphere were constructed by Zoll in the beginning of the 190
0's\, but many questions about them are still open. It seems that higher-d
imensional analogues of Zoll metrics\, where closed geodesics are replaced
by closed embedded minimal hypersurfaces\, could be very interesting obje
cts to be investigated in relation to isodiastolic inequalities and other
geometric problems\, but also on their own account. In this talk\, I will
discuss some recent results about the construction and geometric understan
ding of these new Zoll-like geometries. This is a joint project with F. Ma
rques (Princeton) and A. Neves (UChicago).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiayin Pan (Fields Institute and UC Santa Cruz)
DTSTART:20220224T210000Z
DTEND:20220224T220000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/59
DESCRIPTION:Title: Nonnegative Ricci curvature\, metric cones\, and vi
rtual abelianness\nby Jiayin Pan (Fields Institute and UC Santa Cruz)
as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nLet M be an open
$n$-manifold with nonnegative Ricci curvature. We prove that if its escap
e rate is not $1/2$ and its Riemannian universal cover is conic at infinit
y\, that is\, every asymptotic cone $(Y\,y)$ of the universal cover is a m
etric cone with vertex $y$\, then $\\pi_1(M)$ contains an abelian subgroup
of finite index. If in addition the universal cover has Euclidean volume
growth of constant at least $L$\, we can further bound the index by a cons
tant $C(n\,L)$.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/5
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Song Sun (UC Berkeley)
DTSTART:20220505T200000Z
DTEND:20220505T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/60
DESCRIPTION:Title: Collapsing geometry of hyperkahler 4 manifolds\
nby Song Sun (UC Berkeley) as part of CUNY Geometric Analysis Seminar\n\n\
nAbstract\nA Riemannian 4-manifold is hyperkahler if its holonomy group is
contained in SU(2). This is the simplest nontrivial model of Ricci-flat m
anifolds. To understand the geometry of these metrics\, one is lead to und
erstand the interesting phenomenon of ''collapsing'' to lower dimensions.
In this talk I will discuss the analysis of collapsing geometry of these
metrics and some applications. This talk is based on joint work with Ruob
ing Zhang (Princeton).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Wylie (Syracuse University)
DTSTART:20220407T201500Z
DTEND:20220407T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/61
DESCRIPTION:Title: Weighted Sectional Curvature\nby William Wylie
(Syracuse University) as part of CUNY Geometric Analysis Seminar\n\nLectur
e held in CUNY Graduate Center (Room 6495).\n\nAbstract\n[ATTENTION: THIS
TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 6495\, AND SIMULTANEOUSLY TRAN
SMITTED VIA ZOOM]\n\nRicci curvature for manifolds with density has been e
xtensively studied recently and has many applications. A corresponding the
ory of sectional curvature has not been as well developed. Perhaps one rea
son for this is technical issues in making a suitable definition. In this
talk I'll discuss one attempt to make such a definition and survey some re
sults as well as open questions. This is based on joint work with Kennard
and Kennard-Yeroshkin.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Fernandez (UNAM)
DTSTART:20220324T200000Z
DTEND:20220324T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/62
DESCRIPTION:Title: Yamabe type problems in the presence of singular Ri
emannian foliations\nby Juan Carlos Fernandez (UNAM) as part of CUNY G
eometric Analysis Seminar\n\n\nAbstract\nIn this talk we will study how th
e generalized symmetries given by singular Riemannian foliations give rise
to sign-changing solutions to some semilinear elliptic equations with pow
er nonlinearity\, which are constant on the leaves of the foliation. In pa
rticular\, we give new solutions to the Yamabe problem on the sphere\, con
stant on the leaves of RFKM-foliations.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paula Burkhardt-Guim (NYU)
DTSTART:20220331T201500Z
DTEND:20220331T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/63
DESCRIPTION:Title: Lower scalar curvature bounds for $C^0$ metrics: a
Ricci flow approach\nby Paula Burkhardt-Guim (NYU) as part of CUNY Geo
metric Analysis Seminar\n\nLecture held in CUNY Graduate Center (Room 6495
).\n\nAbstract\n[ATTENTION: THIS TALK WILL BE HELD IN PERSON AT CUNY GC RO
OM 6495\, AND SIMULTANEOUSLY TRANSMITTED VIA ZOOM]\n\nWe describe some rec
ent work that has been done to generalize the notion of lower scalar curva
ture bounds to $C^0$ metrics\, including a localized Ricci flow approach.
In particular\, we show the following: that there is a Ricci flow definiti
on which is stable under greater-than-second-order perturbation of the met
ric\, that there exists a reasonable notion of a Ricci flow starting from
$C^0$ initial data which is smooth for positive times\, and that the weak
lower scalar curvature bounds are preserved under evolution by the Ricci f
low from $C^0$ initial data.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Schwahn (Universitaet Stuttgart)
DTSTART:20220512T201500Z
DTEND:20220512T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/64
DESCRIPTION:Title: Stability and rigidity of normal homogeneous Einste
in manifolds\nby Paul Schwahn (Universitaet Stuttgart) as part of CUNY
Geometric Analysis Seminar\n\n\nAbstract\n[ATTENTION: THIS TALK WILL BE H
ELD IN PERSON AT CUNY GC ROOM 6495\, AND SIMULTANEOUSLY TRANSMITTED VIA ZO
OM]\n\nThe stability of an Einstein metric is decided by the (non-)existen
ce of small eigenvalues of the Lichnerowicz Laplacian on tt-tensors. In th
e homogeneous setting\, harmonic analysis allows us to approach the comput
ation of these eigenvalues. This easy on symmetric spaces\, but considerab
ly more difficult in the non-symmetric case. I review the case of irreduci
ble symmetric spaces of compact type\, prove the existence of a non-symmet
ric stable Einstein metric of positive scalar curvature\, and give an outl
ook on how to investigate the normal homogeneous case. Furthermore\, I exp
lore the rigidity and infinitesimal deformability of homogeneous Einstein
metrics.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20220908T200000Z
DTEND:20220908T210000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/65
DESCRIPTION:by TBA as part of CUNY Geometric Analysis Seminar\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhihan Wang (Princeton University)
DTSTART:20221006T201500Z
DTEND:20221006T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/66
DESCRIPTION:Title: Translating mean curvature flow with simple ends\nby Zhihan Wang (Princeton University) as part of CUNY Geometric Analysi
s Seminar\n\n\nAbstract\nTranslators are known as candidates of Type II bl
ow-up model for mean curvature flows. Various examples of mean curvature
flow translators have been constructed in the convex case and semi-graphic
al cases\, most of which have either infinite entropy or higher multiplici
ty asymptotics near infinity. In this talk\, we shall present the constru
ction of a new family of translators with prescribed end. This is joint wo
rk with Ao Sun.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernani Ribeiro Jr (Universidade Federal do Ceara (Brazil))
DTSTART:20221020T201500Z
DTEND:20221020T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/67
DESCRIPTION:Title: On the Hitchin-Thorpe inequality for four-dimension
al compact Ricci solitons\nby Ernani Ribeiro Jr (Universidade Federal
do Ceara (Brazil)) as part of CUNY Geometric Analysis Seminar\n\nLecture h
eld in GC 6496.\n\nAbstract\nIn this talk\, we will discuss the geometry o
f 4-dimensional compact gradient Ricci solitons. We will show that\, under
an upper bound condition on the range of the potential function\, a 4-dim
ensional compact gradient Ricci soliton must satisfy the classical Hitchin
-Thorpe inequality. In addition\, some volume estimates will be presented.
This is joint work with Xu Cheng and Detang Zhou.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Allen (CUNY Lehman College)
DTSTART:20220915T201500Z
DTEND:20220915T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/68
DESCRIPTION:Title: Stability of the Positive Mass Theorem under Integr
al Ricci Bounds\nby Brian Allen (CUNY Lehman College) as part of CUNY
Geometric Analysis Seminar\n\nLecture held in 6496.\n\nAbstract\n[ATTENTIO
N: THIS TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 6496\, AND SIMULTANEOU
SLY TRANSMITTED VIA ZOOM. THIS IS THE FIRST OF TWO TALKS ON THIS DAY.]\n\n
Recently\, Bray\, Kazaras\, Khuri\, and Stern have provided a formula rela
ting the mass of an asymptotically flat manifold to asymptotically linear
harmonic functions. This formula has already been used to show Gromov-Haus
dorff stability of the positive mass theorem under lower bounds on the Ric
ci curvature by Kazaras\, Khuri\, and Lee. We will discuss new results wit
h Bryden and Kazaras where we use the mass formula to show quantitative $C
^{\\alpha}$ stability of the positive mass theorem. We will see that three
distinct harmonic functions\, which a priori do not provide a global coor
dinate system\, under integral Ricci curvature\, Neumann isoperimetric bou
nds\, and small mass do provide a global coordinate system. We then use th
is coordinate system to control the metric by the mass in the $C^{\\alpha}
$ norm.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José M Espinar (Universidad de Cadiz)
DTSTART:20221013T201500Z
DTEND:20221013T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/69
DESCRIPTION:Title: On Fraser-Li conjecture with anti-prismatic symmetr
y and one boundary component\nby José M Espinar (Universidad de Cadiz
) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n
\nAbstract\nLet $\\sigma_1$ be the first Steklov eigenvalue on an embedded
free boundary minimal surface in $B^3$. We show that an embedded free bou
ndary minimal surface $\\Sigma_{\\bf g}$ of genus $1 \\leq {\\bf g} \\in \
\mathbb{N}$\, one boundary component and anti-prismatic symmetry satisfy $
\\sigma_1 (\\Sigma _{\\bf g}) =1$. In particular\, the family constructed
by Kapouleas--Wiygul satisfies a such condition.\n\nThis talk will be held
in person at CUNY GC and simultaneously transmitted via Zoom.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/6
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Petrúcio Cavalcante (Princeton University and Universidade
Federal de Alagoas)
DTSTART:20221117T211500Z
DTEND:20221117T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/70
DESCRIPTION:Title: Index bounds for CMC surfaces\nby Marcos Petrú
cio Cavalcante (Princeton University and Universidade Federal de Alagoas)
as part of CUNY Geometric Analysis Seminar\n\nLecture held in 6496.\n\nAbs
tract\nConstant mean curvature surfaces are critical points for the area f
unctional under volume preserving variations. From this variational point
of view\, it is natural to study the index and its relations to the geomet
ry and topology of these surfaces. In this talk\, I will describe some cla
ssical and new results in this theme\, as well as some open problems.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prosenjit Roy (Indian Institute of Technology Kanpur)
DTSTART:20220915T211500Z
DTEND:20220915T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/71
DESCRIPTION:Title: Asymptotic Analysis of Eigenvalue Problems on cylin
drical domains whose length tends to infinity\nby Prosenjit Roy (India
n Institute of Technology Kanpur) as part of CUNY Geometric Analysis Semin
ar\n\n\nAbstract\n[ATTENTION: THIS TALK WILL BE HELD IN PERSON AT CUNY GC
ROOM 6496\, AND SIMULTANEOUSLY TRANSMITTED VIA ZOOM. THIS IS THE SECOND OF
TWO TALKS ON THIS DAY.]\n\nThe primary aim of this talk is to study the a
symptotic behaviour of eigenvalue problem\, with Neumann boundary conditio
ns on the sides and Dirichlet boundary conditions on the lateral part of t
he cylindrical domain\, as the length of the cylinder goes to infinity. Be
fore discussing this problem\, I will present the analysis of analogous pr
oblems for full Dirichlet boundary conditions and some other literature fo
r such problems.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bernstein (IAS and Johns Hopkins University)
DTSTART:20221208T211500Z
DTEND:20221208T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/72
DESCRIPTION:Title: Colding-Minicozzi Entropies in Cartan-Hadamard Mani
folds\nby Jacob Bernstein (IAS and Johns Hopkins University) as part o
f CUNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\
nWe discuss a new family of functionals on submanifolds of Cartan-Hadamard
manifolds that generalize the Colding-Minicozzi entropy of submanifolds o
f Euclidean space. These quantities are monotone under mean curvature flo
w under natural conditions. As a consequence\, we obtain sharp lower bound
s on them for certain closed hypersurfaces and observe a novel rigidity ph
enomenon. This is joint work with A. Bhattacharya.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demetre Kazaras (Duke University)
DTSTART:20221027T201500Z
DTEND:20221027T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/73
DESCRIPTION:Title: The positive mass theorem\, comparison geometry\, a
nd spacetime harmonic functions\nby Demetre Kazaras (Duke University)
as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nComparison theor
ems are the basis for our geometric understanding of Riemannian manifolds
satisfying a given curvature condition. A remarkable example is the Gromov
-Lawson toric band inequality\, which bounds the distance between the two
sides of a Riemannian torus-cross-interval with positive scalar curvature
in terms of the scalar curvature's minimum. We will give a new qualitative
version of this and similar "band-width" type inequalities using the noti
on of spacetime harmonic functions\, which recently played the lead role i
n a proof of the positive mass theorem. Other applications include new ver
sions of the Bonnet-Meyer diameter estimate for positive Ricci curvature a
nd Llarull's theorem which do not require a completeness assumption. Conne
ctions will be made with minimal surface and spinorial methods. I will als
o discuss the question "How flat is an isolated gravitational system with
little total mass?" and present work which partially addresses questions o
f Sormani and Gromov.\n\nThis will be an online talk.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Song (Rutgers University)
DTSTART:20221103T201500Z
DTEND:20221103T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/74
DESCRIPTION:Title: Diameter estimates in Kähler geometry\nby Jian
Song (Rutgers University) as part of CUNY Geometric Analysis Seminar\n\nL
ecture held in GC 6496.\n\nAbstract\nWe establish diameter estimates for K
ähler metrics\, requiring only an entropy bound and no lower bound on the
Ricci curvature. As a consequence\, diameter bounds are obtained for long
-time solutions of the Kähler-Ricci flow and finite-time solutions when t
he limiting class is big\, as well as for special fibrations of Calabi-Yau
manifolds.\n\nJoint session with CUNY Nonlinear Analysis and PDEs Seminar
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Henrique Andrade (University of British Columbia / Universid
ade de São Paulo)
DTSTART:20221201T211500Z
DTEND:20221201T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/75
DESCRIPTION:Title: Multiplicity of solutions to the multiphasic Allen-
-Cahn--Hilliard system with a small volume constraint on closed paralleliz
able manifolds\nby João Henrique Andrade (University of British Colum
bia / Universidade de São Paulo) as part of CUNY Geometric Analysis Semin
ar\n\n\nAbstract\nWe prove the existence of multiple solutions to the Alle
n--Cahn--Hilliard (ACH) vectorial equation (with two equations) involving
a triple-well (triphasic) potential with a small volume constraint on a cl
osed parallelizable Riemannian manifold.\nMore precisely\, we find a lower
bound for the number of solutions depending on some topological invariant
s of the underlying manifold. The phase transition potential is considered
to have a finite set of global minima\, where it also vanishes\, and a su
bcritical growth at infinity. Our strategy is to employ the Lusternik--Sch
nirelmann and infinite-dimensional Morse theories for the vectorial energy
functional. To this end\, we exploit that the associated ACH energy $\\Ga
mma$-converges to the weighted multi-perimeter for clusters\, which combin
ed with some deep theorems from isoperimetric theory yields the suitable s
etup to apply the photography method. Along the way\, the lack of a closed
analytic expression for the multi-isoperimetric function for clusters imp
oses a delicate issue. Furthermore\, using a transversality theorem\, we a
lso show the genericity of the set of metrics for which solutions to the A
CH system are nondegenerate.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Nardulli (Universidad Federal do ABC)
DTSTART:20221110T211500Z
DTEND:20221110T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/76
DESCRIPTION:Title: Lusternik-Schnirelman and Morse Theory for the Van
der Waals-Cahn-Hilliard equation with volume constraint\nby Stefano Na
rdulli (Universidad Federal do ABC) as part of CUNY Geometric Analysis Sem
inar\n\n\nAbstract\nWe give a multiplicity result for solutions of the Van
der Waals-Cahn-Hilliard two phase transition equation with volume constra
ints on a closed Riemannian manifold. Our proof employs some results from
the classical Lusternik–Schnirelman and Morse theory\, together with a t
echnique\, the so-called photography method\, which allows us to obtain lo
wer bounds on the number of solutions in terms of topological invariants o
f the underlying manifold. The setup for the photography method employs re
cent results from Riemannian isoperimetry for small volumes. This is joint
work with Vieri Benci\, Luis Eduardo Osorio Acevedo\, Paolo Piccione.\n\n
Joint session with CUNY Nonlinear Analysis and PDEs Seminar.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conghan Dong (Stony Brook)
DTSTART:20230209T211500Z
DTEND:20230209T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/77
DESCRIPTION:Title: Stability of the Euclidean 3-space for the positive
mass theorem\nby Conghan Dong (Stony Brook) as part of CUNY Geometric
Analysis Seminar\n\n\nAbstract\nThe Positive Mass Theorem of R. Schoen an
d S.-T. Yau in dimension 3 states that if $(M^3\, g)$ is asymptotically fl
at and has nonnegative scalar curvature\, then its ADM mass $m(g)$ satisfi
es $m(g) \\geq 0$\, and equality holds only when $(M\, g)$ is the flat Euc
lidean 3-space $\\mathbb{R}^3$. We show that $\\mathbb{R}^3$ is stable in
the following sense. Let $(M^3_i\, g_i)$ be a sequence of asymptotically f
lat 3-manifolds with nonnegative scalar curvature and suppose that $m(g_i)
$ converges to 0. Then for all i\, there is a subset $Z_i$ in $M_i$ such t
hat the area of the boundary $\\partial Z_i$ converges to zero and the seq
uence $(M_i \\setminus Z_i \, \\hat{d}_{g_i} \, p_i )$\, with induced leng
th metric $\\hat{d}_{g_i}$ and any base point $p_i \\in M_i \\setminus Z_i
$\, converges to $\\mathbb{R}^3$ in the pointed measured Gromov-Hausdorff
topology. This confirms a conjecture of G. Huisken and T. Ilmanen. We also
find an almost optimal bound for the area of $\\partial Z_i$ in terms of
$m(g_i)$. This is a joint work with Antoine Song.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiewon Park (Yale University)
DTSTART:20230323T201500Z
DTEND:20230323T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/78
DESCRIPTION:Title: A Compactness Theorem for Rotationally Symmetric Ri
emannian Manifolds with Positive Scalar Curvature\nby Jiewon Park (Yal
e University) as part of CUNY Geometric Analysis Seminar\n\nLecture held i
n GC 6496.\n\nAbstract\nIt is a conjecture of Gromov and Sormani that sequ
ences of compact Riemannian manifolds with nonnegative scalar curvature an
d area of minimal surfaces bounded below should have subsequences which co
nverge in the intrinsic flat sense to limit spaces which have nonnegative
generalized scalar curvature and Euclidean tangent cones almost everywhere
. In this talk I will present a joint work with Wenchuan Tian and Changlia
ng Wang\, where we proved this conjecture for rotationally symmetric manif
olds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Mendes (University of Oklahoma)
DTSTART:20230316T201500Z
DTEND:20230316T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/79
DESCRIPTION:Title: A Weyl Law for singular Riemannian foliations\n
by Ricardo Mendes (University of Oklahoma) as part of CUNY Geometric Analy
sis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nA classic version of
the Weyl Law describes the asymptotic behavior of the eigenvalues of the L
aplace operator on a closed Riemannian manifold $M$ in terms of its dimens
ion and volume. In the 1970's\, Donnelly and Bruenning--Heintze establishe
d a version when a compact group $G$ acts on $M$ by isometries: the rate o
f growth of eigenvalues associated to $G$-invariant eigenfunctions is cont
rolled by the dimension and volume of the orbit space $M/G$. I will descri
be a generalization where the decomposition of $M$ into $G$-orbits is repl
aced with a singular Riemannian foliation. This is based on joint work-in-
progress with Marco Radeschi and Samuel Lin.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/7
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Mouillé
DTSTART:20230223T211500Z
DTEND:20230223T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/80
DESCRIPTION:Title: Positive intermediate Ricci curvature with maximal
symmetry rank\nby Lawrence Mouillé as part of CUNY Geometric Analysis
Seminar\n\nLecture held in GC 6496.\n\nAbstract\nPositive $k$th-intermedi
ate Ricci curvature is a condition on an $n$-manifold that interpolates be
tween positive sectional curvature ($k = 1$) and positive Ricci curvature
($k = n - 1$). In a foundational result for the study of closed manifolds
with positive sectional curvature and large isometry group\, Grove and Sea
rle classified those with maximal symmetry rank (i.e. rank of the isometry
group = rank of $O(n+1)$). In this talk\, I will present a generalization
of this rigidity result to manifolds with positive 2nd-intermediate Ricci
curvature. The exceptional cases are dimension 4\, in which we rule out s
everal candidates using a Frankel-type argument\, and dimension 6\, in whi
ch it is known that a product of 3-spheres admits a metric with positive 2
nd-intermediate Ricci curvature and maximal symmetry rank. This talk is ba
sed on joint work with Lee Kennard.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART:20230420T201500Z
DTEND:20230420T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/81
DESCRIPTION:Title: Minimal Surfaces in Hyperbolic 3-manifolds\nby
Baris Coskunuzer (UT Dallas) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nIn this talk\, we will show the existence of smoothly embedde
d closed minimal surfaces in infinite volume hyperbolic 3-manifolds. The t
alk will be non-technical\, and accessible to graduate students.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Johne (Columbia University)
DTSTART:20230216T211500Z
DTEND:20230216T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/82
DESCRIPTION:Title: A generalization of Geroch's conjecture\nby Flo
rian Johne (Columbia University) as part of CUNY Geometric Analysis Semina
r\n\nLecture held in 6496.\n\nAbstract\nClosed manifolds with topology $N
= M \\times S^1$ do not admit metrics of positive Ricci curvature by the t
heorem of Bonnet-Myers\, while the the resolution of the Geroch conjecture
implies that the torus $T^n$ does not admit a metric of positive scalar c
urvature. In this talk we explain a non-existence result for metrics of p
ositive m-intermediate curvature (a notion of curvature reducing to Ricci
curvature for $m = 1$\, and scalar curvature for $m = n-1$) on closed mani
folds with topology $N^n = M^{n-m} \\times T^m$ for $n \\leq 7$. Our proof
uses minimization of weighted areas\, the associated stability inequalit
y\, and delicate estimates on the second fundamental form. This is joint w
ork with Simon Brendle and Sven Hirsch\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Stufflebeam (University of Pennsylvania)
DTSTART:20230309T211500Z
DTEND:20230309T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/83
DESCRIPTION:Title: Stability of Convex Disks\nby Hunter Stufflebea
m (University of Pennsylvania) as part of CUNY Geometric Analysis Seminar\
n\nLecture held in GC 6496.\n\nAbstract\nWe prove that topological disks w
ith positive curvature and strictly convex boundary of large length are cl
ose to round spherical caps of constant boundary curvature in the Gromov-H
ausdorff and Sormani-Wenger Intrinsic Flat senses. This proves stability f
or a theorem of F. Hang and X. Wang.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eris Runa (Gran Sasso Science Institute\, L’Aquila)
DTSTART:20230216T223000Z
DTEND:20230216T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/85
DESCRIPTION:Title: Energy driven pattern formation for local/non-local
systems\nby Eris Runa (Gran Sasso Science Institute\, L’Aquila) as
part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nIn this talk we wil
l consider a class of local/nonlocal interaction functionals motivated by
the physics literature. The functionals contain a local term which penaliz
es interfaces\, and a non-local term which favors oscillations. The equili
brium between these two terms is expected to result in\nthe emergence of p
attern formation. We will show that minimizers are periodic stripes and in
particular that the functional exhibits the phenomenon of symmetry breaki
ng.\n\nThis talk is presented jointly with the Nonlinear Analysis and PDEs
Seminar.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jackson Goodman (UC Berkeley)
DTSTART:20230330T201500Z
DTEND:20230330T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/86
DESCRIPTION:Title: Curvature operators and rational cobordism\nby
Jackson Goodman (UC Berkeley) as part of CUNY Geometric Analysis Seminar\n
\n\nAbstract\nWe give new conditions on positivity of certain linear combi
nations of eigenvalues of the curvature operator of a Riemannian manifold
which imply the vanishing of the indices of Dirac operators twisted with b
undles of tensors. The vanishing indices in turn have topological implicat
ions in terms of the Pontryagin classes\, rational cobordism type\, and Wi
tten genus of the manifolds. To prove our results we generalize new method
s developed by Petersen and Wink to apply the Bochner technique to Laplaci
ans on bundles of tensors. This is joint work with Renato Bettiol.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Lejmi (Bronx Community College)
DTSTART:20230309T223000Z
DTEND:20230309T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/87
DESCRIPTION:Title: Special metrics in almost-Hermitian geometry\nb
y Mehdi Lejmi (Bronx Community College) as part of CUNY Geometric Analysis
Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn this talk\, we discus
s the existence of some canonical metrics on compact almost-Hermitian mani
folds. For example\, we study an analogue of the Yamabe problem in Hermiti
an geometry. We also discuss Einstein-like metrics in Hermitian geometry.\
n\nThis talk is presented jointly with the Nonlinear Analysis and PDEs Sem
inar.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Sweeney (Stony Brook)
DTSTART:20230511T201500Z
DTEND:20230511T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/88
DESCRIPTION:Title: Examples for Scalar Sphere Stability\nby Paul S
weeney (Stony Brook) as part of CUNY Geometric Analysis Seminar\n\n\nAbstr
act\nTwo different ways scalar curvature can characterize the sphere are d
escribed by the rigidity theorems of Llarull and of Marques-Neves. Associa
ted with these rigidity theorems are two stability conjectures. In this ta
lk\, we will produce examples related to these stability conjectures. The
first set of examples demonstrates the necessity of including a condition
on the minimum area of all minimal surfaces to prevent bubbling along the
sequence. The second set of examples are sequences that do not converge in
the Gromov-Hausdorff sense but do converge in the volume-preserving intri
nsic flat sense. In order to construct such sequences\, we improve the Gro
mov-Lawson tunnel construction so that one can attach wells and tunnels to
a manifold with scalar curvature bounded below and only decrease the scal
ar curvature by an arbitrarily small amount. This allows a generalization
of other examples that use tunnels such as the sewing construction of Basi
lio\, Dodziuk\, and Sormani\, and the construction due to Basilio\, Kazara
s\, and Sormani of an intrinsic flat limit with no geodesics.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Mira (Universidad Politecnica de Cartagena)
DTSTART:20230420T213000Z
DTEND:20230420T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/89
DESCRIPTION:Title: Minimal annuli with free boundary in the unit ball<
/a>\nby Pablo Mira (Universidad Politecnica de Cartagena) as part of CUNY
Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn thi
s talk we will construct a family of free boundary minimal annuli immersed
in the unit ball of Euclidean 3-space\, the first such examples other tha
n the critical catenoid. Their existence answers in the negative a problem
of the theory that dates back to Nitsche in 1985\, who claimed that such
annuli could not exist. We will explain the geometry of these examples and
discuss several open problems. We will also show how our method produces
embedded capillary minimal annuli in the unit ball that are not rotational
\, thus solving a problem by Wente (1995). Joint work with Isabel Fernande
z and Laurent Hauswirth.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/8
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Wang (Stony Brook)
DTSTART:20230427T201500Z
DTEND:20230427T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/90
DESCRIPTION:Title: Topology of complete $3$-manifolds with uniformly p
ositive scalar curvature\nby Jian Wang (Stony Brook) as part of CUNY G
eometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nA well-
known question posed by S.T. Yau is how to classify 3-manifolds admitting
a complete metric with (uniformly) positive scalar curvature up to diffeo
morphism. It was resolved by G.Perelman for closed $3$-manifolds. However\
, the non-compact case is complicated. In this talk\, I will give a comple
te topological characterization for complete open $3$-manifolds with unifo
rmly positive scalar curvature. Furthermore\, we will talk about its gener
alization for $3$-manifolds with boundaries.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niels Moller (University of Copenhagen)
DTSTART:20230921T201500Z
DTEND:20230921T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/91
DESCRIPTION:Title: Rigidity of the grim reaper cylinder as a collapsed
self-translating soliton\nby Niels Moller (University of Copenhagen)
as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\n
Abstract\nMean curvature flow self-translating solitons are minimal hypers
urfaces for a certain incomplete conformal background metric\, and are amo
ng the possible singularity models for the flow. In the collapsed case\, t
hey are confined to slabs in space. The simplest non-trivial such example\
, the grim reaper curve $\\Gamma$ in $\\mathbb{R}^2$\, has been known sinc
e 1956\, as an explicit ODE-solution\, which also easily gave its uniquene
ss.\n\nWe consider here the case of surfaces\, where the rigidity result f
or $\\Gamma\\times\\mathbb{R}$ that we'll show is:\nThe grim reaper cylind
er is the unique (up to rigid motions) finite entropy unit speed self-tran
slating surface which has width equal to $\\pi$ and is bounded from below.
(Joint w/ Impera & Rimoldi.)\n\nTime permitting\, we'll also discuss rece
nt uniqueness results in the collapsed simply-connected low entropy case (
joint w/ Gama & Martín)\, using Morse theory and nodal set techniques\, w
hich extend Chini's classification.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Hirsch (IAS)
DTSTART:20230914T201500Z
DTEND:20230914T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/93
DESCRIPTION:Title: Hawking mass monotonicity for initial data sets
\nby Sven Hirsch (IAS) as part of CUNY Geometric Analysis Seminar\n\nLectu
re held in GC 6496.\n\nAbstract\nAn interesting feature of General Relativ
ity is the presence of singularities which can occur in even the simplest
examples such as the Schwarzschild spacetime. However\, in this case the s
ingularity is cloaked behind the event horizon of the black hole which has
been conjectured to be generically the case. To analyze this so-called Co
smic Censorship Conjecture\, Roger Penrose proposed in 1973 a test which i
nvolves Hawking's area theorem\, the final state conjecture and a geometri
c inequality on initial data sets $(M\,g\,k)$. For $k=0$ this so-called Pe
nrose inequality has been proven by Gerhard Huisken and Tom Ilmanen via in
verse mean curvature flow and by Hubert Bray using the conformal flow\, bu
t in general the question is wide open. We will present several approaches
to generalize the Hawking mass monotonicity formula to arbitrary initial
data sets including a new one based on double null foliations. For this pu
rpose\, we start with recalling spacetime harmonic functions and their app
lications which have been introduced together with Demetre Kazaras and Mar
cus Khuri in the context of the spacetime positive mass theorem.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Nikolayevsky (La Trobe University)
DTSTART:20230907T201500Z
DTEND:20230907T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/94
DESCRIPTION:Title: Einstein hypersurfaces in irreducible symmetric spa
ces\nby Yuri Nikolayevsky (La Trobe University) as part of CUNY Geomet
ric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn this talk
\, I will present the results of a joint paper of Jeong Hyeong Park and my
self in which we give a classification of Einstein hypersurfaces in irredu
cible symmetric spaces. The main theorem states that there are three class
es of such hypersurfaces\, belonging to three different geometries: homoge
neous geometry (for Einstein hypersurfaces in noncompact symmetric spaces)
\, Legendrian geometry (Einstein hypersurfaces in SU(3)/SO(3) and affine g
eometry (Einstein hypersurfaces in SL(3)/SO(3)).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Tony (WWU Muenster)
DTSTART:20231130T211500Z
DTEND:20231130T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/95
DESCRIPTION:Title: Scalar curvature comparison geometry and the higher
mapping degree\nby Thomas Tony (WWU Muenster) as part of CUNY Geometr
ic Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nLlarull prove
d in the late '90s that the round $n$-sphere is area-extremal in the sense
that one cannot increase the scalar curvature and the metric simultaneous
ly. Goette and Semmelmann generalized Llarull's work and proved an extrema
lity and rigidity statement for area-non-increasing spin maps $f\\colon M\
\to N$ of non-zero $\\hat{A}$-degree between two closed connected oriented
Riemannian manifolds.\n\nIn this talk\, I will extend this classical resu
lt to maps between not necessarily orientable manifolds and replace the to
pological condition on the $\\hat{A}$-degree with a less restrictive condi
tion involving the so-called higher mapping degree. For that purpose\, I w
ill first present an index formula connecting the higher mapping degree an
d the Euler characteristic of $N$ with the index of a certain Dirac operat
or linear over a $\\mathrm{C}^\\ast$-algebra. Second\, I will use this ind
ex formula to show that the topological assumptions\, together with our ex
tremal geometric situation\, give rise to a family of almost constant sect
ions that can be used to deduce the extremality and rigidity statements.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Harvie (National Taiwan University)
DTSTART:20231116T211500Z
DTEND:20231116T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/96
DESCRIPTION:Title: The equality case of the static Minkowski inequalit
y and applications\nby Brian Harvie (National Taiwan University) as pa
rt of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstr
act\nAsymptotically flat static spaces are Riemannian manifolds that corre
spond to static vacuum spacetimes in general relativity. The most importan
t example is the Schwarzschild space\, a rotationally symmetric Riemannian
manifold corresponding to the Schwarzschild spacetime. A number of import
ant questions about the uniqueness of the Schwarzschild spacetime may be p
osed as rigidity questions for AF static spaces. These include the famous
static black hole uniqueness theorems of Israel and Bunting/Masood-ul-Alam
as well as the more recent uniqueness theorems for static spacetimes cont
aining photon surfaces.\n\nIn this talk\, I will present a new approach to
these questions that is based on a Minkowski-type inequality for AF stati
c spaces. Like the Minkowski inequality for convex hypersurfaces in Euclid
ean space\, this inequality gives a bound from below on the total mean cur
vature of the boundary of the manifold. First\, I will characterize rigidi
ty within this inequality\, showing under suitable boundary assumptions th
at the equality is achieved only by rotationally symmetric regions of Schw
arzschild space. As an application\, I will show uniqueness of suitably-de
fined static metric extensions for the Bartnik data of Schwarzschild coord
inate spheres. This talk is based on joint work with Ye-Kai Wang of NYCU.\
n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfgang Ziller (University of Pennsylvania)
DTSTART:20231026T201500Z
DTEND:20231026T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/97
DESCRIPTION:Title: Hypersurfaces with constant Ricci curvature\nby
Wolfgang Ziller (University of Pennsylvania) as part of CUNY Geometric An
alysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nWe will talk about
a classification of hypersurfaces in $S^4(1)$ and $H^4$ with the property
that the eigenvalues of the Ricci curvature are constant (and hence the c
urvature tensor is “constant"). They can be described as the embedding o
f a surface\, which is algebraic (with singularities).\n \nThis is joint w
ork with Robert Bryant and Luis Florit.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Skorobogatova (Princeton University)
DTSTART:20231109T211500Z
DTEND:20231109T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/98
DESCRIPTION:Title: Higher codimension area-minimizers: structure of si
ngularities and uniqueness of tangent cones\nby Anna Skorobogatova (Pr
inceton University) as part of CUNY Geometric Analysis Seminar\n\nLecture
held in GC 6496.\n\nAbstract\nThe problem of determining the size and stru
cture of the interior singular set of area-minimizing surfaces has been st
udied thoroughly in a number of different frameworks\, with many ground-br
eaking contributions. In the framework of integral currents\, when the cod
imension of the surface is higher than 1\, the presence of singular points
with flat tangent cones creates an obstruction to easily understanding th
e interior singularities. Little progress has been made in full generality
since Almgren’s celebrated $(m-2)$-Hausdorff dimension bound on the sin
gular set for an $m$-dimensional area-minimizing integral current\, which
was since revisited and simplified by De Lellis and Spadaro.\n\nIn this ta
lk I will discuss recent joint works with Camillo De Lellis and Paul Minte
r\, where we establish $(m-2)$-rectifiability of the interior singular set
of an $m$-dimensional area-minimizing integral current and show that the
tangent cone is unique at $\\mathcal{H}^{m-2}$-a.e. interior point.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingbo Wan (Columbia University)
DTSTART:20230928T201500Z
DTEND:20230928T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/99
DESCRIPTION:Title: Rigidity of contracting maps using harmonic map hea
t flow\nby Jingbo Wan (Columbia University) as part of CUNY Geometric
Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn this talk\, w
e are going to consider the rigidity of map between positively curved clos
ed manifolds\, which is motivated by the recent work of Tsai-Tsui-Wang. We
show that distance non-increasing map between complex projective spaces i
s either an isometry or homotopically trivial. The rigidity result also ho
lds on a wider class of manifolds with positive curvature and weaker contr
acting property on the map in between distance non-increasing and area non
-increasing. This is based on the harmonic map heat flow and it partially
answer a question raised by Tsai-Tsui-Wang. This is a joint work with Prof
. Man-Chun Lee in CUHK.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/9
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Santiago Cordero Misteli (Stony Brook University)
DTSTART:20231019T201500Z
DTEND:20231019T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/100
DESCRIPTION:Title: Morse index bounds for free boundary minimal hyper
surfaces through covering arguments\nby Santiago Cordero Misteli (Ston
y Brook University) as part of CUNY Geometric Analysis Seminar\n\nLecture
held in GC 6496.\n\nAbstract\nHow complicated can a minimal surface be? Th
is question has led to interesting discoveries about the relationships bet
ween various notions of complexity. In this context\, an important open qu
estion is the Schoen conjecture\, which roughly says that the Morse index
dominates the topology. This conjecture has been established in certain ca
ses under some assumptions on the ambient curvature. In 2019\, Antoine Son
g introduced a novel approach to prove a similar bound on the Betti number
s in terms of the Morse index. This new proof doesn't impose any ambient c
urvature assumptions but requires a control on the area. In this talk I wi
ll explain joint work with Giada Franz\, where we generalize Song's approa
ch to prove a similar statement for free boundary minimal hypersurfaces.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
00/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongyeong Ko (Rutgers University)
DTSTART:20231012T201500Z
DTEND:20231012T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/102
DESCRIPTION:Title: Capillary and Free boundary embedded geodesics on
Riemannian 2-disks with a strictly convex boundary\nby Dongyeong Ko (R
utgers University) as part of CUNY Geometric Analysis Seminar\n\nLecture h
eld in GC 6496.\n\nAbstract\nThe existence of embedded geodesics on surfac
es is a foundational problem. I will explain the existence of two capillar
y embedded geodesics on Riemannian 2-disks with a strictly convex boundary
with a certain condition via a multi-parameter min-max construction. I wi
ll then explain the existence of two free boundary embedded geodesics on R
iemannian 2-disks with a strictly convex boundary by free boundary curve s
hortening flow on surfaces\, which is a free boundary analog of Grayson’
s theorem of 1989. Finally\, I will explain the Morse Index bound of such
geodesics.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
02/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Hanke (Universitaet Augsburg)
DTSTART:20231207T223000Z
DTEND:20231207T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/103
DESCRIPTION:Title: New developments in the scalar curvature rigidity
of spheres\nby Bernhard Hanke (Universitaet Augsburg) as part of CUNY
Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nLower
scalar curvature bounds on spin Riemannian manifolds exhibit remarkable ex
tremality and rigidity phenomena determined by spectral properties of Dira
c operators. For example\, a fundamental result of Llarull states that the
re is no smooth Riemannian metric on the n-sphere which dominates the roun
d metric and whose scalar curvature is greater than or equal to the scalar
curvature of the round metric\, except for the round metric itself. A sim
ilar result holds for smooth comparison maps from spin Riemannian manifold
s to round spheres. \n\nAnswering questions posed by Gromov in his "Four
Lectures"\, we generalize these results in two directions: First\, to Riem
annian metrics with regularity less than $C^1$ and Lipschitz comparison ma
ps\, and second\, to spheres with two antipodal points removed. This is jo
int work with Cecchini-Schick and with Bär-Brendle-Wang\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
03/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun (Lehigh University)
DTSTART:20240307T211500Z
DTEND:20240307T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/104
DESCRIPTION:Title: Interpolation method in mean curvature flow\nb
y Ao Sun (Lehigh University) as part of CUNY Geometric Analysis Seminar\n\
nLecture held in GC 6417.\n\nAbstract\nThe interpolation method is a very
powerful tool to construct special solutions in geometric analysis. I will
present two applications in mean curvature flow: one is constructing a ne
w genus one self-shrinking mean curvature flow\, and another one is constr
ucting immortal mean curvature flow with higher multiplicity convergence.
The talk is based on joint work with Adrian Chu (UChicago) and joint work
with Jingwen Chen (UPenn).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
04/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doug Stryker (Princeton University)
DTSTART:20240314T201500Z
DTEND:20240314T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/105
DESCRIPTION:Title: Stable minimal hypersurfaces in $\\mathbb R^5$
\nby Doug Stryker (Princeton University) as part of CUNY Geometric Analysi
s Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI will discuss why ever
y complete two-sided stable minimal hypersurface in $\\mathbb R^5$ is flat
\, based on joint work with Otis Chodosh\, Chao Li\, and Paul Minter.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
05/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Sarnataro (Princeton University)
DTSTART:20240314T213000Z
DTEND:20240314T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/106
DESCRIPTION:Title: The Allen—Cahn equation and free boundary minima
l surfaces\nby Lorenzo Sarnataro (Princeton University) as part of CUN
Y Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nIn r
ecent years\, the combined work of Guaraco\, Hutchinson\, Tonegawa\, and W
ickramasekera have established a min-max construction of minimal hypersurf
aces in closed Riemannian manifolds\, based on the analysis of singular li
mits of sequences of solutions of the Allen—Cahn equation\, a semi-linea
r elliptic equation arising in the theory of phase transitions. In this ta
lk\, I will describe some recent boundary regularity results for such limi
t-interfaces\, which provide the first step towards an Allen—Cahn min-ma
x construction of free boundary minimal hypersurfaces in Riemannian manifo
lds with boundary. \nThis is based on joint work with Martin Li (CUHK) and
Davide Parise (UCSD).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
06/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Martin (Universidad de Granada)
DTSTART:20240418T201500Z
DTEND:20240418T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/107
DESCRIPTION:Title: Some new examples of translating solitons for the
mean curvature flow: Annuloids and Delta-wings\nby Francisco Martin (U
niversidad de Granada) as part of CUNY Geometric Analysis Seminar\n\nLectu
re held in GC 6417.\n\nAbstract\nIn this presentation\, we shall describe
new annular examples of complete translating solitons for the mean curvatu
re flow and how they are related to a family of translating graphs\, the D
elta-wings. In addition\, we will prove some related results that answer q
uestions that arise naturally in this investigation. These results apply t
o translators in general\, not just to graphs or annuli. This is a joint w
ork with David Hoffman and Brian White.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
07/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lu Wang (Yale University)
DTSTART:20240321T201500Z
DTEND:20240321T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/108
DESCRIPTION:Title: A mean curvature flow approach to density of minim
al cones\nby Lu Wang (Yale University) as part of CUNY Geometric Analy
sis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nMinimal cones are mod
els for singularities in minimal submanifolds\, as well as stationary solu
tions to the mean curvature flow. In this talk\, I will explain how to uti
lize mean curvature flow to yield near optimal estimates on density of top
ologically nontrivial minimal cones. This is joint with Jacob Bernstein.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
08/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tin Yau Tsang (NYU)
DTSTART:20240229T211500Z
DTEND:20240229T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/109
DESCRIPTION:Title: Another aspect of Gromov's conjectures\nby Tin
Yau Tsang (NYU) as part of CUNY Geometric Analysis Seminar\n\nLecture hel
d in GC 6417.\n\nAbstract\nIn this talk\, we will discuss some of Gromov's
conjectures on scalar curvature from the perspective of general relativit
y\, in particular their partial solutions by the positive mass theorem.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
09/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Giorgi (Columbia University)
DTSTART:20240215T211500Z
DTEND:20240215T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/110
DESCRIPTION:Title: The nonlinear stability of black holes: an overvie
w\nby Elena Giorgi (Columbia University) as part of CUNY Geometric Ana
lysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nBlack holes are the
most striking predictions of General Relativity and are by now understood
to be fundamental objects in our universe. In this colloquium talk\, I wi
ll provide an overview of their mathematical properties\, in particular co
ncerning their stability as solutions to the Einstein equation\, and give
a bird’s-eye view of the recent proof of the nonlinear stability of the
slowly rotating Kerr black holes (joint with Klainerman-Szeftel).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Piccione (Universidade de Sao Paulo)
DTSTART:20240328T201500Z
DTEND:20240328T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/111
DESCRIPTION:Title: A multiplicity result for solutions of Yamabe-type
problems\nby Paolo Piccione (Universidade de Sao Paulo) as part of CU
NY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI w
ill discuss a general nonuniqueness result for conformally variational inv
ariants on the universal cover of closed Riemannian manifolds whose fundam
ental group has infinite profinite completion. This is based on works in c
ollaboration with R. Bettiol\, J. H. Andrade\, J. Case and J. Wei.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Ratzkin (Universität Würzburg)
DTSTART:20240328T213000Z
DTEND:20240328T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/113
DESCRIPTION:Title: Stability estimates for the total Q-curvature func
tional\nby Jesse Ratzkin (Universität Würzburg) as part of CUNY Geom
etric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI will dis
cuss stability estimates for metrics close to those minimizing the total Q
-curvature functional on compact manifolds\, generalizing previous stabili
ty estimates for the classical Sobolev inequality due to Bianchi and Egnel
l and stability of minimizing Yamabe metrics\, due to Engelstein\, Neumeye
r and Spolaor. Generically\, the distance to the set of minimizing metrics
is controlled by the square of the Q-curvature deficit. We are also able
to characterize some examples where this distance is controlled by a highe
r power of the Q-curvature deficit\, and I will discuss these examples in
some detail. This is joint work with Joāo Henrique Andrade\, Tobias Köni
g and Juncheng Wei.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Pérez-Ayala (Princeton University)
DTSTART:20240208T211500Z
DTEND:20240208T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/114
DESCRIPTION:Title: Extremal Eigenvalues for the Paneitz Operator in 4
-Dimensional Manifolds\nby Samuel Pérez-Ayala (Princeton University)
as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\n
Abstract\nOn any closed Riemannian manifold\, we can consider the Laplace-
Beltrami operator together with its sequence of eigenvalues. As the metric
is varied conformally\, the eigenvalues change\, leading to a natural var
iational problem of finding conformal metrics that extremize a specific ei
genvalue under a volume constraint. A beautiful observation by Nadirashvil
i says that these special extremal metrics are in correspondence
with the existence of harmonic maps into higher dimensional spheres. In th
is talk\, I will explain a similar connection for the Paneitz operator in
four manifolds and conformal-harmonic maps. Additionally\, I will report i
n some recent work with A.Chang and M.Gursky\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianxiong Wang (University of Connecticut)
DTSTART:20240418T213000Z
DTEND:20240418T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/115
DESCRIPTION:Title: Higher order conformal equations on hyperbolic spa
ces and the symmetry of solutions\nby Jianxiong Wang (University of Co
nnecticut) as part of CUNY Geometric Analysis Seminar\n\nLecture held in G
C 6417.\n\nAbstract\nThe classification of solutions for semilinear PDEs\,
as well as the classification of critical points of the corresponding fun
ctionals\, have wide applications in the study of partial differential equ
ations and differential geometry. The classical moving plane method and th
e moving sphere method in Euclidean space provide an effective approach to
capturing the symmetry of solutions. In this talk\, we develop a moving s
phere approach for integral equations in the hyperbolic space\, to obtain
the symmetry property as well as a characterization result towards positiv
e solutions for nonlinear problems involving the GJMS operators (a general
ization of the Paneitz operator). Our methods also rely on Helgason-Fourie
r analysis and Hardy-Littlewood-Sobolev inequalities on hyperbolic spaces
together with a Kelvin transform.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Ville (CNRS\, Université Paris-Est Créteil)
DTSTART:20240411T201500Z
DTEND:20240411T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/116
DESCRIPTION:Title: Branched surfaces in 4-manifolds\nby Marina Vi
lle (CNRS\, Université Paris-Est Créteil) as part of CUNY Geometric Anal
ysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nIn the 1980s\, geome
ters studied the twistor degree of a surface $S$ in a 4-manifold $M$\, giv
en by the sum of its tangent and normal bundles\, $TS$ and $NS$. A questio
n arose: if a sequence $(S_n)$ of immersed surfaces in $M$ degenerates int
o a branched surface $S_0$\, how do the twistors degree of $S_0$ compare w
ith those of the $S_n$'s? I go back to this problem and treat it locally a
round a branch point $p$ of $S_0$. It means comparing the amount of curvat
ures of $TS_n$ and $NS_n$ which concentrate close to $p$ when $n$ tends to
infinity. I approach this question with topological tools (braids) rather
than analytic ones and I give a few cases where an extra assumption\, eit
her geometrical or topological\, allows to get some answers.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liam Mazurowski (Cornell University)
DTSTART:20240509T201500Z
DTEND:20240509T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/117
DESCRIPTION:Title: Stability for the Yamabe Invariant of S^3\nby
Liam Mazurowski (Cornell University) as part of CUNY Geometric Analysis Se
minar\n\nLecture held in GC 6417.\n\nAbstract\nThe Yamabe problem asks whe
ther every closed Riemannian manifold admits a conformal metric with const
ant scalar curvature. The Yamabe problem has been fully resolved in the af
firmative by the work of Yamabe\, Trudinger\, Aubin\, and Schoen. The reso
lution of the Yamabe problem is closely connected to an inequality for the
total scalar curvature: the total scalar curvature of (M^n\,g) is at mos
t that of the round sphere with the same volume. Moreover\, if equality ho
lds then (M^n\,g) is conformal to a round sphere. It is natural to invest
igate the stability of this inequality. In this talk\, we will show that i
f the total scalar curvature of (S^3\,g) is close to that of the round 3-s
phere with the same volume\, then some metric in the conformal class of g
is close to round in a certain sense. This is joint work with Xuan Yao.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junming Xie (Rutgers University)
DTSTART:20240912T201500Z
DTEND:20240912T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/118
DESCRIPTION:Title: Four-dimensional gradient Ricci solitons with nonn
egative (or half nonnegative) isotropic curvature.\nby Junming Xie (Ru
tgers University) as part of CUNY Geometric Analysis Seminar\n\nLecture he
ld in GC 6417.\n\nAbstract\nRicci solitons\, introduced by R. Hamilton in
the mid-80s\, are self-similar solutions to the Ricci flow and natural ext
ensions of Einstein manifolds. They often arise as singularity models and
hence play a significant role in the study of Ricci flow. In this talk\, w
e will present some recent progress on the geometry and classifications of
4-dimensional gradient Ricci solitons with nonnegative\, or half nonnegat
ive\, isotropic curvature. This talk is based on a joint work with Huai-Do
ng Cao.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Friedemann Schuricht (Technische Universität Dresden\, Germany)
DTSTART:20240912T213000Z
DTEND:20240912T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/119
DESCRIPTION:Title: Theory of Traces and the Divergence Theorem\nb
y Friedemann Schuricht (Technische Universität Dresden\, Germany) as part
of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstrac
t\nWe introduce a general approach to traces that we consider\nas linear c
ontinuous functionals on some function space.\nHere we focus on special ch
oices and obtain an integral\ncalculus for traces based on finitely additi
ve measures.\nThis allows the computation of the precise representative of
an integrable\nfunction and of the trace of a Sobolev or BV function by i
ntegrals instead of\nthe usual limit of averages. For integrable vector\nf
ields where the distributional divergence is a measure\, we also derive\nG
auss-Green formulas on arbitrary Borel sets. It turns out that a second\nb
oundary integral is needed to treat singularities that had not been\nacces
sible before. The advantage of the integral calculus\nis that neither a no
rmal field nor a trace function on the boundary is needed.\nAlso inner bou
ndaries and concentrations on the boundary can be treated this\nway. The G
auss-Green formulas are also available for Sobolev and BV functions.\nAs a
pplication the existence of a weak solution of a boundary value problem\nc
ontaining the p-Laplace operator can be shown.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paula Burkhardt-Guim (Stony Brook University)
DTSTART:20241017T201500Z
DTEND:20241017T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/120
DESCRIPTION:Title: Smoothing $L^\\infty$ Riemannian metrics with nonn
egative scalar curvature outside of a singular set\nby Paula Burkhardt
-Guim (Stony Brook University) as part of CUNY Geometric Analysis Seminar\
n\nLecture held in GC 6417.\n\nAbstract\nWe show that any $L^\\infty$ Riem
annian metric $g$ on $\\R^n$ that is smooth with nonnegative scalar curvat
ure away from a singular set of finite $(n-\\alpha)$-dimensional Minkowski
content\, for some $\\alpha>2$\, admits an approximation by smooth Rieman
nian metrics with nonnegative scalar curvature\, provided that $g$ is suff
iciently close in $L^\\infty$ to the Euclidean metric. The approximation i
s given by time slices of the Ricci-DeTurck flow\, which converge locally
in $C^\\infty$ to $g$ away from the singular set. We also identify conditi
ons under which a smooth Ricci-DeTurck flow starting from a $L^\\infty$ me
tric that is uniformly bilipschitz to Euclidean space and smooth with nonn
egative scalar curvature away from a finite set of points must have nonneg
ative scalar curvature for positive times.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Li (John Jay College of Criminal Justice and CUNY Grad Center)
DTSTART:20241017T213000Z
DTEND:20241017T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/121
DESCRIPTION:Title: Monotone properties of the eigenfunctions of Neuma
nn problems\nby Yi Li (John Jay College of Criminal Justice and CUNY G
rad Center) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6417.\n\nAbstract\nIn this talk we prove the hot spots conjecture for l
ong rotationally symmetric domains of Euclidean space by the continuity me
thod. More precisely\, we show that the odd Neumann eigenfunction in $x_n$
associated with lowest nonzero eigenvalue is a Morse function on the boun
dary\, which has exactly two critical points and is monotone in the direct
ion from its minimum point to its maximum point. As a consequence\, we pro
ve that the Jerison and Nadirashvili’s conjecture 8.3 holds true for rot
ationally symmetric domains and are also able to obtain a sharp lower boun
d for the Neumann eigenvalue.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (New York University)
DTSTART:20241114T211500Z
DTEND:20241114T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/122
DESCRIPTION:Title: Boundary regularity of capillary minimizing hypers
urfaces\nby Chao Li (New York University) as part of CUNY Geometric An
alysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nCapillary minimizi
ng hypersurfaces are the mathematical model for interfaces between incompr
essible fluids. I will describe some progress in understanding the boundar
y regularity of such surfaces. In particular\, some of our analysis is bas
ed on a connection between the capillary problem and the one-phase Bernoul
li problem\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcello Lucia (College of Staten Island and CUNY Grad Center)
DTSTART:20241114T223000Z
DTEND:20241114T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/123
DESCRIPTION:Title: A Mountain pass Theorem and moduli spaces of minim
al immersions in hyperbolic 3-manifolds\nby Marcello Lucia (College of
Staten Island and CUNY Grad Center) as part of CUNY Geometric Analysis Se
minar\n\nLecture held in GC 6417.\n\nAbstract\nA minimal immersion of an o
riented closed surface in a hyperbolic 3-manifold gives rise to a complex
structure and a holomorphic quadratic differential that describes the sec
ond fundamental form. Another set of data is provided by a dual formulati
on proposed by Gonçalves-Uhlenbeck\, and in fact from such given ``dual d
ata" it is always possible to reconstruct a minimal immersion. This can be
proved in a variational framework and leads to a general Mountain Pass Th
eorem for a class of systems that will be presented in this talk.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Rodriguez Vazquez (Université Libre de Bruxelles)
DTSTART:20241107T211500Z
DTEND:20241107T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/124
DESCRIPTION:Title: Positive Ric2 curvature on products of spheres and
their quotients via intermediate fatness\nby Alberto Rodriguez Vazque
z (Université Libre de Bruxelles) as part of CUNY Geometric Analysis Semi
nar\n\nLecture held in GC 6417.\n\nAbstract\nI will present joint work wit
h Miguel Domínguez Vázquez\, David González-Álvaro\, and Jason DeVito\
, focused on constructing the first examples of compact Riemannian manifol
ds with Ric2>0 curvature in dimensions 10\, 11\, 12\, 13\, and 14. The con
dition Ric2 > 0 is an intermediate curvature condition that interpolates b
etween positive sectional curvature (sec> 0) and positive Ricci curvature
(Ric> 0). We achieve this using a generalization of the fat bundle notion.
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangyang Li (University of Chicago)
DTSTART:20241031T201500Z
DTEND:20241031T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/125
DESCRIPTION:Title: Existence and regularity of anisotropic minimal hy
persurfaces\nby Yangyang Li (University of Chicago) as part of CUNY Ge
ometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nAnisotro
pic area\, a generalization of the area functional\, arises naturally in m
odels of crystal surfaces. The regularity theory for its critical points\,
anisotropic minimal (hyper)surfaces\, is significantly more challenging t
han the area functional case\, mainly due to the lack of a monotonicity\nf
ormula. In this talk\, I will discuss how one can overcome this difficulty
and construct a smooth anisotropic minimal surface and optimally regular
minimal hypersurfaces for elliptic integrands in closed Riemannian manifol
ds through min-max theory. This confirms a conjecture by Allard in 1983. T
he talk is based on joint work with Guido De Philippis and Antonio De Rosa
.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernani Ribeiro Jr (Universidade Federal do Ceara (Brazil))
DTSTART:20250320T201500Z
DTEND:20250320T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/126
DESCRIPTION:Title: Rigidity of compact quasi-Einstein manifolds with
boundary\nby Ernani Ribeiro Jr (Universidade Federal do Ceara (Brazil)
) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n
\nAbstract\nIt is known by the classical book "Einstein Manifolds" (Besse\
, 1984) that quasi-Einstein manifolds correspond to a base of a warped pro
duct Einstein metric. Another interesting motivation to investigate quasi-
Einstein manifolds derives from the study of diffusion operators by Bakry
and Emery (1985)\, which is linked to the theories of smooth metric measur
e space\, static spaces and Ricci solitons. In this talk\, we will show th
at a 3-dimensional simply connected compact quasi-Einstein manifold with b
oundary and constant scalar curvature must be isometric to either the stan
dard hemisphere $S^3_{+}$\, or the cylinder $R \\times S^2$ with product m
etric. For dimension n=4\, we will show that a 4-dimensional simply connec
ted compact quasi-Einstein manifold with boundary and constant scalar curv
ature is isometric to either the standard hemisphere $S^4_+$\, or the cyli
nder $I \\times S^3$ with product metric\, or the product space $S^2_+ \\t
imes S^2$ with the product metric. This is a joint work with D. Zhou and J
. Costa.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kazuo Akutagawa (Chuo University)
DTSTART:20250307T164500Z
DTEND:20250307T174500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/127
DESCRIPTION:Title: Harmonic maps from the product of hyperbolic space
s to hyperbolic spaces\nby Kazuo Akutagawa (Chuo University) as part o
f CUNY Geometric Analysis Seminar\n\nLecture held in GC 4419.\n\nAbstract\
nIn this talk\, we will consider the asymptotic Dirichlet problem \nfor ha
rmonic maps from the product $\\mathbb{H}^{m_1} \\times \\mathbb{H}^{m_2}$
of two hyperbolic spaces \nto hyperbolic spaces. \nIt remarks that $\\mat
hbb{H}^{m_1} \\times \\mathbb{H}^{m_2}$ is a higher rank symmetric space o
f noncompact type. \nWe first show uniqueness and non-existence results\,
particularly the existence of such harmonic maps (with some natural condit
ions) \nimplies that it must be $m _1 = m_2 = 2$. \nWe also show an existe
nce result for harmonic maps from $\\mathbb{H}^2 \\times \\mathbb{H}^2$ \n
to hyperbolic spaces. \nThis is a joint work with Yoshihiko Matsumoto.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Lowe (University of Chicago)
DTSTART:20250227T211500Z
DTEND:20250227T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/128
DESCRIPTION:Title: Minimal Surfaces in Negative Curvature\nby Ben
Lowe (University of Chicago) as part of CUNY Geometric Analysis Seminar\n
\nLecture held in GC 6417.\n\nAbstract\nKahn-Markovic showed that every cl
osed negatively curved 3-manifold contains essential minimal surfaces in g
reat abundance. Since then the goal of understanding the geometry of these
minimal surfaces has been a focus of activity\, both in analogy to the ge
odesic flow one dimension lower and the more positive-curvature-centric mi
n-max theory of minimal surfaces. This talk will survey recent development
s in this area\, which brings together techniques from dynamical systems\,
geometric analysis\, and hyperbolic geometry.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiahua Zou (Rutgers University)
DTSTART:20250227T223000Z
DTEND:20250227T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/129
DESCRIPTION:Title: Minimal hypersurfaces in $\\mathbb{S}^{4}(1)$ by d
oubling the equatorial $\\mathbb{S}^{3}$\nby Jiahua Zou (Rutgers Unive
rsity) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 64
17.\n\nAbstract\nFor each large enough $m\\in\\mathbb{N}$ we construct by
PDE gluing\nmethods a closed embedded smooth minimal hypersurface ${\\brev
e{M}_m}$\ndoubling the equatorial three-sphere $\\mathbb{S_\\mathrm{eq}}^3
$ in\n$\\mathbb{S}^4(1)$. This answers a long-standing question of Yau in
the\ncase of $\\mathbb S^4(1)$ and long-standing questions of Hsiang. Simi
larly we\nconstruct a self-shrinker ${\\breve{M}_{\\mathrm{shr}\,m}}$ of t
he Mean\nCurvature Flow in $\\mathbb{R}^4$ doubling the three-dimensional\
nspherical self-shrinker $\\mathbb{S}_{\\mathrm{shr}}^3\\subset\\R^4$. A\n
brief survey on two-dimensional case will also be given. This talk is\nbas
ed on joint work with Kapouleas.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stephen Preston (CUNY)
DTSTART:20250220T211500Z
DTEND:20250220T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/130
DESCRIPTION:Title: Nearly bi-invariant metrics on Lie groups\nby
Stephen Preston (CUNY) as part of CUNY Geometric Analysis Seminar\n\nLectu
re held in GC 6417.\n\nAbstract\nI will present some results on finite-dim
ensional Lie groups with left-invariant Riemannian metrics that are close
to bi-invariant metrics\, in the sense that they are generated from an ine
rtia operator with an underlying bi-invariant form. Examples include SO(n)
with the rigid body metric\, the Zeitlin models on SU(n) for ideal fluid
mechanics on the 2-sphere\, and Berger spheres. I will describe some resul
ts on Ricci curvature\, geodesics\, and conjugate points\, based on a rece
nt preprint with Alice Le Brigant and Leandro Lichtenfelz.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeno Huang (CUNY)
DTSTART:20250328T174500Z
DTEND:20250328T184500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/131
DESCRIPTION:Title: The asymptotic Plateau problem\nby Zeno Huang
(CUNY) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 64
17.\n\nAbstract\nThe asymptotic Plateau problem is a set of problems askin
g the existence and multiplicity for a minimal surface (or disk) in $H^3$
asymptotic to a given Jordan curve on the sphere at infinity. I will descr
ibe the problems and current solutions to some of them as well as some ope
n problems. Much of the talk is based on recent work with Lowe and Seppi.
\n\nThis event is a special meeting held jointly with the Complex Analysis
and Dynamics Seminar https://userhome.brooklyn.cuny.edu/aulicino/seminar/
\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongyi Liu (Princeton University)
DTSTART:20250320T213000Z
DTEND:20250320T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/132
DESCRIPTION:Title: Compactness theorems for Einstein 4-manifolds with
boundary\nby Hongyi Liu (Princeton University) as part of CUNY Geomet
ric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nEinstein 4-m
anifolds have been widely studied in both the compact and complete non-com
pact settings\, particularly when additional geometric structures are pres
ent. However\, the case of Einstein manifolds with boundary remains less e
xplored. In this talk\, I will discuss compactness theorems for Einstein 4
-manifolds with boundary\, considering two distinct frameworks: when the b
oundary is at a finite distance and in the conformally compact setting.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zilu Ma (Rutgers)
DTSTART:20250424T201500Z
DTEND:20250424T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/133
DESCRIPTION:Title: Examples of Bubble-Sheet Singularities in Ricci Fl
ow\nby Zilu Ma (Rutgers) as part of CUNY Geometric Analysis Seminar\n\
nLecture held in GC 6417.\n\nAbstract\nTwo-cylinders or bubble-sheets are
new singularities arising in 4D Ricci flow\, and they are generally hard t
o study compared to three-cylinders. In this talk\, we shall discuss some
recent constructions of compact Ricci flows producing such a singularity m
odel. More precisely\, we show that starting from an open set of initial d
ata with warped product geometries over a surface\, the Ricci flow develop
s a unique bubble-sheet singularity. This is based on the join work with J
. Isenberg\, D. Knopf\, and N. Šešum.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Riccardo Caniato (Caltech)
DTSTART:20250515T201500Z
DTEND:20250515T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/135
DESCRIPTION:Title: Area rigidity for the regular representation of su
rface groups\nby Riccardo Caniato (Caltech) as part of CUNY Geometric
Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nStarting from th
e celebrated results of Eells and Sampson\, a rich and flourishing literat
ure has developed around equivariant harmonic maps from the universal cove
r of Riemann surfaces into nonpositively curved target spaces. In particul
ar\, such maps are known to be rigid\, in the sense that they are unique u
p to natural equivalence. Unfortunately\, this rigidity property fails whe
n the target space has positive curvature\, and comparatively little is kn
own in this framework.\n\nIn this talk\, given a closed Riemann surface wi
th strictly negative Euler characteristic and a unitary representation of
its fundamental group on a separable complex Hilbert space H which is weak
ly equivalent to the regular representation\, we aim to discuss a lower bo
und on the Dirichlet energy of equivariant harmonic maps from the universa
l cover of the surface into the unit sphere S of H\, and to give a complet
e classification of the cases in which the equality is achieved. As a rema
rkable corollary\, we obtain a lower bound on the area of equivariant mini
mal surfaces in S\, and we determine all the representations for which the
re exists an equivariant\, area-minimizing minimal surface in S.\n\nThe su
bject matter of this talk is a joint work with Antoine Song (Caltech) and
Xingzhe Li (Cornell University).\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Harvie (Columbia)
DTSTART:20250501T201500Z
DTEND:20250501T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/137
DESCRIPTION:Title: A uniqueness theorem for the anti-de-Sitter Schwar
zschild metric\nby Brian Harvie (Columbia) as part of CUNY Geometric A
nalysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nIn 1967\, W. Isra
el proved that the Schwarzschild spacetime is the only isolated static vac
uum black hole with zero cosmological constant in general relativity. Desp
ite many generalizations of Israel's theorem in subsequent years\, static
black hole uniqueness for a negative cosmological constant remains an outs
tanding problem. Here\, one hopes to show that a Lorentzian warped product
metric with constant negative Ricci curvature which contains a Killing ho
rizon and is asymptotic to anti-de-Sitter is isometric to an anti-de-Sitte
r-Schwarzschild spacetime. This is closely related to the Penrose inequali
ty\, and like the Penrose inequality in the asymptotically hyperbolic sett
ing the problem is quite resistant to proof.\n\nIn this talk\, I will pres
ent a partial uniqueness theorem for static vacuum black holes with a nega
tive cosmological constant. Namely\, the ADS-Schwarzschild metric with lea
st surface gravity is unique\, and in general a static black hole with the
same surface gravity and horizon area as an ADS-Schwarzschild solution is
isometric to that solution. This is joint work with Ye-Kai-Wang of NYCU.\
n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessandro Carlotto (University of Trento)
DTSTART:20250508T201500Z
DTEND:20250508T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/138
DESCRIPTION:Title: Non-persistence of strongly isolated singularities
\, and geometric applications\nby Alessandro Carlotto (University of T
rento) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 64
17.\n\nAbstract\nIn this lecture\, based on recent joint work with Yangyan
g Li (University of Chicago) and Zhihan Wang (Cornell University)\, I will
present a generic regularity result for stationary integral $n$-varifolds
with only strongly isolated singularities inside $N$-dimensional Riemanni
an manifolds\, in absence of any restriction on the dimension ($n\\geq 2$)
and codimension. As a special case\, we prove that for any $n\\geq 2$ and
any compact $(n+1)$-dimensional manifold $M$ the following holds: for a g
eneric choice of the background metric $g$ all stationary integral $n$-var
ifolds in $(M\,g)$ will either be entirely smooth or have at least one sin
gular point that is not strongly isolated. In other words\, for a generi
c metric only ``more complicated'' singularities may possibly persist. Thi
s implies\, for instance\, a generic finiteness result for the class of al
l closed minimal hypersurfaces of area at most $4\\pi^2-\\varepsilon$ (for
any $\\varepsilon>0$) in nearly round four-spheres: we can thus give prec
ise answers\, in the negative\, to the well-known questions of persistence
of the Clifford football and of Hsiang's hyperspheres in nearly round met
rics. The aforementioned main regularity result is achieved as a conseq
uence of the fine analysis of the Fredholm index of the Jacobi operator fo
r such varifolds: we prove on the one hand an exact formula relating that
number to the Morse indices of the conical links at the singular points\,
while on the other hand we show that the same number is non-negative for a
ll such varifolds if the ambient metric is generic.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nan Li (CUNY)
DTSTART:20250515T213000Z
DTEND:20250515T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/139
DESCRIPTION:Title: Bounding the curvature integral on manifold with s
ingularities\nby Nan Li (CUNY) as part of CUNY Geometric Analysis Semi
nar\n\nLecture held in GC 6417.\n\nAbstract\nLet $X$ be an $n$-dimensional
Alexandrov space with curvature $\\ge\\kappa$. Let $\\mathcal S(X)$ be th
e set of points in $X$ whose tangent cones are not isometric to $\\dR^n$.
Let $p\\in X$ and assume that $M=B_2(p)\\setminus \\mathcal S(X)$ is a smo
oth manifold\, equipped with the Riemannian metric induced by the metric o
f $X$. We show that the integral of scalar curvature of $M$ over $B_1(p)\\
subseteq X$\, is bounded from above by a constant depending only on $n$ an
d $\\kappa$. As a special case\, this generalizes Petrunin's similar resu
lt on smooth manifolds to the setting of smooth Alexandrov spaces with bou
ndary.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yipeng Wang (Columbia)
DTSTART:20250508T213000Z
DTEND:20250508T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/140
DESCRIPTION:Title: Rigidity Results Involving Stabilized Scalar Curva
ture\nby Yipeng Wang (Columbia) as part of CUNY Geometric Analysis Sem
inar\n\nLecture held in GC 6417.\n\nAbstract\nGromov introduced the notion
of stabilized scalar curvature\, which arises naturally in the context of
warped product extensions. This concept also appears in the study of the
geometry of weighted manifolds and in Perelman's work on the Ricci flow. I
n this talk\, I will explore the relationship between various formulations
of stabilized scalar curvature and explain how several classical scalar c
urvature rigidity results can be extended to this more general setting.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junsheng Zhang (NYU Courant)
DTSTART:20250911T201500Z
DTEND:20250911T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/142
DESCRIPTION:Title: Kähler-Ricci Shrinkers and Polarized Fano Fibrati
ons\nby Junsheng Zhang (NYU Courant) as part of CUNY Geometric Analysi
s Seminar\n\nLecture held in GC 6417.\n\nAbstract\nWe prove that every (no
n-compact) Kähler-Ricci shrinker is naturally a polarized Fano fibration.
The proof relies on Kähler reductions and boundedness result in biration
al geometry. Moreover\, we propose several conjectures for Kähler-Ricci s
hrinkers\, unifying the well-developed theories of Kähler-Einstein metric
s and Calabi-Yau cones. This is joint work with Song Sun.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio de Rosa (Bocconi University (Italy))
DTSTART:20251030T201500Z
DTEND:20251030T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/143
DESCRIPTION:Title: Rigidity of critical points of hydrophobic capilla
ry functionals\nby Antonio de Rosa (Bocconi University (Italy)) as par
t of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstra
ct\nWe prove the rigidity\, among sets of finite perimeter\, of volume-pre
serving critical points of the capillary energy in the half space\, in the
case where the prescribed interior contact angle is between 90$^o$ and 12
0$^o$. No structural or regularity assumption is required on the finite pe
rimeter sets. Assuming that the “tangential” part of the capillary bou
ndary is $H^n$-null\, this rigidity theorem extends to the full hydrophobi
c regime of interior contact angles between 90$^o$ and 180$^o$. Furthermor
e\, we establish the anisotropic counterpart of this theorem under the ass
umption of lower density bounds. This is joint work with R. Neumayer and R
. Resende.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayush Khaitan (Rutgers University)
DTSTART:20251009T201500Z
DTEND:20251009T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/144
DESCRIPTION:Title: On geometric analysis and the permanent problem\nby Ayush Khaitan (Rutgers University) as part of CUNY Geometric Analysi
s Seminar\n\nLecture held in GC 6417.\n\nAbstract\nFinding non-trivial and
sharp lower bounds on the permanent of a matrix is an old\, central probl
em in combinatorics\, statistical mechanics and theoretical computer scien
ce. Calculating the permanent is known to be #P-complete\, and hence findi
ng good lower bounds has attracted sustained attention across multiple are
as. We explore the surprising applicability of geometric analysis in study
ing and partially resolving this problem. This is joint work with Ishan Ma
ta and Bhargav Narayanan.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ali Maaloui (Clark University)
DTSTART:20251120T211500Z
DTEND:20251120T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/145
DESCRIPTION:Title: Conformally Invariant Fractional Dirac Operator: C
onstruction and Associated Sobolev Inequalities\nby Ali Maaloui (Clark
University) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6417.\n\nAbstract\nIn this talk I will discuss the construction of the
fractional Dirac operator via scattering theory. This provides a continuo
us family of pseudo-differential operators acting on spinors similar to th
e case of the fractional conformal Laplacian. Then I will introduce a Caff
arelli-Silvestre type extension allowing an alternative definition of thes
e operators as a Dirichlet-to-Neumann type\noperators and also an associat
ed Sobolev type inequality.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Weinkove (Northwestern University)
DTSTART:20251211T223000Z
DTEND:20251211T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/146
DESCRIPTION:Title: Parabolic equations with no boundary conditions\nby Ben Weinkove (Northwestern University) as part of CUNY Geometric Ana
lysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI will discuss the
existence of smooth solutions of (degenerate) parabolic equations with no
boundary conditions. In the linear setting I will describe a result of K
ohn-Nirenberg type and show how it can be applied to prove smooth short ti
me existence results for nonlinear equations including the porous medium e
quation\, the p-Laplacian evolution equation and the Gauss curvature flow
with a flat side. This is joint work with Albert Chau.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philip Korman (University of Cinncinati)
DTSTART:20251120T223000Z
DTEND:20251120T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/148
DESCRIPTION:Title: Some special super-critical equations\nby Phil
ip Korman (University of Cinncinati) as part of CUNY Geometric Analysis Se
minar\n\nLecture held in GC 6417.\n\nAbstract\nFor special super-critical
equations it is possible to determine exactly all positive solutions on a
ball in $R^n$\, and give precise information on the entire solution curves
. These equations can serve as prototypes for other similar equations. The
special equations include Gelfand's equation\, Lin-Ni equation\, MEMS\, a
nd $\\Delta u+u^{\\frac{n+2}{n-2}}=0$.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Yao (Stony Brook)
DTSTART:20251016T201500Z
DTEND:20251016T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/149
DESCRIPTION:Title: Asymptotics for Homogeneous Complex Monge-Ampere E
quations on ALE Kahler Ends\nby Qi Yao (Stony Brook) as part of CUNY G
eometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI will
present a new analytic framework for the holomorphic-disc approach to Homo
geneous complex Monge–Ampère equations (HCMA) on noncompact Kähler man
ifolds with ALE ends\, product with a disc. I will first set up a Bedford
–Taylor–type pluripotential package adapted to noncompact settings so
that comparison principles and envelope constructions work cleanly on ALE
ends. Initiated by Semmes\, Donaldson\, I construct a tame holomorphic–d
isc foliation near infinity and\, at that very stage\, we observe and addr
ess a small but essential “loss of regularity in a parameter” by a bri
ef BMO/Nash–Moser argument. The foliation allows the construction of a g
lobal $\\Omega$-psh subsolution F that is exact on the end--$F= \\Phi$ out
side a large compact set\, where $\\Phi$ is the solution to the HCMA equat
ion. From this exactness\, one obtains sharp weighted asymptotics for $\\P
hi$. If time permits\, I will discuss some further development. The framew
ork extends with minor changes to other infinite-end geometries and to the
local ball settings. These results also connect directly to questions abo
ut the uniqueness of canonical metrics on open K\\”ahler manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helge Frerichs (University of Augsburg)
DTSTART:20251204T211500Z
DTEND:20251204T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/150
DESCRIPTION:Title: Scalar curvature deformations with non-compact bou
ndaries\nby Helge Frerichs (University of Augsburg) as part of CUNY Ge
ometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nWe devel
op a general deformation principle for families of Riemannian metrics on s
mooth manifolds with possibly non-compact boundary\, preserving lower scal
ar curvature bounds. The principle is used to strengthen boundary conditio
ns from mean convex to totally geodesic or doubling. The deformation princ
iple preserves further geometric properties such as completeness and a giv
en quasi-isometry type.\n\nAs an application\, we prove non-existence resu
lts for Riemannian metrics with uniformly positive scalar curvature and me
an convex boundary\, including some investigation of the Whitehead manifol
d.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyan Li (Rutgers University)
DTSTART:20251113T211500Z
DTEND:20251113T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/151
DESCRIPTION:Title: Symmetry of hypersurfaces and the Hopf Lemma\n
by Yanyan Li (Rutgers University) as part of CUNY Geometric Analysis Semin
ar\n\nLecture held in GC 6417.\n\nAbstract\nIn 1945\, S.S. Chern provided
the following characterization of spheres in three-dimensional Euclidean s
pace: Let $M$ be a closed convex surface satisfying $F (\\kappa_1 \, \\kap
pa_2 ) = 1$\, where $\\kappa_1$ and $\\kappa_2$ denote the principal curva
tures\, and \\(F\\) is elliptic in the sense that\n\\(\\partial\\kappa_i F
> 0\\). Then \\(M\\) must be a sphere.\n\nImportant special cases include
\\(F (\\kappa_1 \, \\kappa_2 ) = \\kappa_1 + \\kappa_2\\) and \\(F (\\kap
pa_1 \, \\kappa_2 ) = \\kappa_1 \\kappa_2\\)\, corresponding to prescribed
mean curvature and prescribed Gaussian curvature\, respectively.\n\nNiren
berg and I explored extensions of this problem and proposed the following
conjecture: Let \\(M\\) be a closed convex surface in three-dimensional Eu
clidean space\, and let \\(F\\) be elliptic. Suppose that for any two poin
ts $(X_1 \, X_2 \, X_3 )$ and $(X_1 \, X_2 \, \\hat X_3 )$ on $M$ with $X_
3 \\geq \\hat X_3$\, the inequality \\(F (\\kappa_1 \, \\kappa_2 )(X_1 \,
X_2 \, X_3 ) \\leq F (\\kappa_1 \, \\kappa_2 )(X_1 \, X_2 \, \\hat X_3 )\\
) holds. Then \\(M\\) must be symmetric about some hyperplane \\(X_3 =\\\,
\\)constant.\n\nIn this talk\, I will survey developments in this area and
present open problems\, both related to resolving this conjecture and to
broader conjectures concerning extensions of the Hopf Lemma.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Hirsch (Columbia University)
DTSTART:20260205T211500Z
DTEND:20260205T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/152
DESCRIPTION:Title: Causal character of imaginary Killing spinors and
spinorial slicings\nby Sven Hirsch (Columbia University) as part of CU
NY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nWe
characterize spin initial data sets that saturate the BPS bound in the asy
mptotically AdS setting. This includes both gravitational waves and rotati
ng black holes in higher dimensions\, and we establish a sharp dimension t
hreshold in each case. A key ingredient in our argument is a theorem provi
ding a general criterion for when an imaginary Killing spinor of mixed cau
sal type can be replaced by one that is strictly timelike or null. Moreove
r\, in analogy with the minimal surface method\, we demonstrate that spino
rs can be used to construct a codimension-2 slicing. This is based upon jo
int work with Yiyue Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Víctor Sanmartín-López (Universidade de Santiago de Compostela)
DTSTART:20260326T201500Z
DTEND:20260326T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/153
DESCRIPTION:Title: Submanifold geometry in symmetric spaces of non-co
mpact type\nby Víctor Sanmartín-López (Universidade de Santiago de
Compostela) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6417.\n\nAbstract\nIn submanifold geometry\, it is natural to begin by
investigating those submanifolds with a high degree of symmetry\, such as
homogeneous hypersurfaces\, or\, equivalently\, those arising as principal
orbits of cohomogeneity one actions. Indeed\, one of the main goals of th
is talk is to present the classification of cohomogeneity one actions on s
ymmetric spaces of non-compact type.\n \nFurthermore\, we will also compar
e the class of homogeneous hypersurfaces with some other important familie
s including\, for instance\, isoparametric hypersurfaces\, hypersurfaces w
ith constant principal curvatures\, or curvature-adapted hypersurfaces. Th
is comparison will naturally bring other classes of submanifolds into the
picture\, such as totally geodesic\, austere\, minimal\, or CPC submanifol
ds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eunice Ng (Stony Brook University)
DTSTART:20260430T201500Z
DTEND:20260430T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/154
DESCRIPTION:by Eunice Ng (Stony Brook University) as part of CUNY Geometri
c Analysis Seminar\n\nLecture held in GC 6417.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Chu (Cornell University)
DTSTART:20260423T201500Z
DTEND:20260423T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/155
DESCRIPTION:by Adrian Chu (Cornell University) as part of CUNY Geometric A
nalysis Seminar\n\nLecture held in GC 6417.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xuan Yao (Princeton University)
DTSTART:20260319T201500Z
DTEND:20260319T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/156
DESCRIPTION:Title: Capillary minimal slicing and scalar curvature rig
idity in dimension 4\nby Xuan Yao (Princeton University) as part of CU
NY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nWe
develop a capillary minimal slicing technique and prove a scalar curvature
comparison-rigidity result in dimension 4. This is a joint work with Dong
yeong Ko.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andras Balogh (College of Staten Island CUNY)
DTSTART:20260326T213000Z
DTEND:20260326T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/157
DESCRIPTION:Title: Global Solutions of the Higgs Boson Equation in de
Sitter Spacetime\nby Andras Balogh (College of Staten Island CUNY) as
part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAb
stract\nIn this work\, we investigate the Higgs Boson Equation in de Sitte
r Spacetime. We prove the existence and uniqueness of global–in–time s
olutions for initial data of arbitrary size with compact support. The proo
f uses Galerkin's method\, based on a priori energy estimates. High–perf
ormance computer simulations are presented to demonstrate the theoretical
results and to provide further conjectures about bubble formation and long
–time behavior.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mohameden Ahmedou (Universitaet Giessen)
DTSTART:20260423T213000Z
DTEND:20260423T223000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/158
DESCRIPTION:by Mohameden Ahmedou (Universitaet Giessen) as part of CUNY Ge
ometric Analysis Seminar\n\nLecture held in GC 6417.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mingyang Li (SCGP/Stony Brook University)
DTSTART:20260226T223000Z
DTEND:20260226T233000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/159
DESCRIPTION:Title: Gravitational instantons and harmonic maps\nby
Mingyang Li (SCGP/Stony Brook University) as part of CUNY Geometric Analy
sis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nIt is known from gene
ral relativity that axisymmetric stationary black holes can be reduced to
axisymmetric harmonic maps into the hyperbolic plane $H^2$\, while in the
Riemannian setting\, 4d Ricci-flat metrics with torus symmetry can also be
locally reduced to such harmonic maps satisfying a tameness condition. We
study such harmonic maps and application includes a construction of infin
itely many new complete\, asymptotically flat\, Ricci-flat 4-manifolds wit
h arbitrarily large second Betti number $b_2$. Joint work with Song Sun.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Angel Javaloyes (Universidad de Murcia)
DTSTART:20260312T213000Z
DTEND:20260312T221000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/160
DESCRIPTION:Title: Cone structure and metrics that depend on time
\nby Miguel Angel Javaloyes (Universidad de Murcia) as part of CUNY Geomet
ric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nHow can a me
tric that depends on time be studied? In General Relativity\, space and ti
me are intertwined in such a way that they cannot be understood separately
\, and moreover\, time is relative\, depending on a choice of reference fr
ame. But our goal in this lecture will be different. We will show that it
makes sense to work with an absolute time and still consider time-dependen
t metrics. The role of length will be played by time\, and the Riemannian
metric will determine the velocity of objects in each direction. Geodesics
will be defined as the fastest trajectories\, which\, by applying the rel
ativistic Fermat principle\, can be calculated as light-like geodesics on
a Finsler spacetime\, most generally\, from a cone structure. Finally\, we
will demonstrate that these structures can be applied to the study of for
est fires and that we can also define a curvature that measures how geodes
ics diverge using the degenerate curvature introduced by Harris in Lorentz
ian manifolds. This curvature helps to identify focal points\, which are c
rucial for firefighters. Moreover\, we will give an interpretation of curv
ature in terms of Jacobi fields and will obtain some applications to compu
te flag curvature in Finsler manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erasmo Caponio (Politecnico di Bari)
DTSTART:20260312T222000Z
DTEND:20260312T230000Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/161
DESCRIPTION:Title: Massive particle surfaces and Jacobi-Randers metri
cs\nby Erasmo Caponio (Politecnico di Bari) as part of CUNY Geometric
Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nThe geometry of
photon surfaces -- timelike hypersurfaces trapping light rays -- is well-c
haracterized in General Relativity by the condition of total umbilicity. H
owever\, realistic astrophysical environments around black holes also invo
lve massive charged particles. Unlike photons\, these particles are gover
ned by the Lorentz force and depend on a fixed charge-to-mass ratio $\\rho
$. Moreover\, if there exists a timelike Killing vector $K$ field and the
electromagnetic field is also $K$-invariant\, they also have a well-define
d specific energy $\\varepsilon$. Recent literature has shown that surfa
ces trapping such particles\, known as massive particle surfaces (MPS) sat
isfy an extrinsic condition of ``partial umbilicity''.\n\nIn this talk\, I
present a characterization of an MPS in a stationary spacetimes using Fin
sler geometry. Working within a standard stationary splitting\, we can ob
tain conditions under which the dynamics of charged massive particles wit
h fixed $(\\rho\,\\varepsilon)$ reduces to the geodesic flow of a Jacobi
-Randers type metric defined on the spatial slice.\nUnder these conditions
\, a Killing-invariant hypersurface $\\mathbb{R} \\times S_0$ is then a
$(\\rho\, \\varepsilon)$-MPS if and only if its spatial section $S_0$ is
totally geodesic with respect to the associated Jacobi-Randers metric. \n
\nWe will also discuss applications of this framework\, including the deri
vation of the ``master equation'' for the kinetic energy along the surface
and existence results for $(\\rho\, \\varepsilon)$-trajectories connecti
ng an event to a flow line of the timelike Killing vector field.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Bryant (Duke University)
DTSTART:20260305T211500Z
DTEND:20260305T221500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/162
DESCRIPTION:Title: Curvature-homogeneous hypersurfaces in space forms
\nby Robert Bryant (Duke University) as part of CUNY Geometric Analysi
s Seminar\n\nLecture held in GC 6417.\n\nAbstract\nIn a recent work with L
. Florit and W. Ziller\, we completed the classification of curvature-homo
geneous hypersurfaces in spaces of constant curvature. It was a surprise t
o find that\, in the previously unsolved cases\, there exists an exotic fa
mily of solutions that are not homogeneous as hypersurfaces\, and it turns
out that a variety of techniques are needed to understand them fully.\n\n
I’ll begin by surveying the history of the problem\, starting with the c
lassic works of É. Cartan and H.-F. Münzer on isoparametric hypersurface
s\, as well as more recent work on the isoparametric case and the more gen
eral curvature-homogeneous problem. Then I’ll explain the ideas and tec
hniques (including using symbolic calculation software and Gröbner bases)
that led to the resolution of the final cases (and why these were needed)
.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiaochu Ma (Texas A&M University)
DTSTART:20260416T201500Z
DTEND:20260416T211500Z
DTSTAMP:20260404T110746Z
UID:CUNY_GeometricAnalysis/163
DESCRIPTION:Title: Small Scale Index Theory\, Scalar Curvature\, and
Gromov’s Simplicial Norm\nby Qiaochu Ma (Texas A&M University) as pa
rt of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstr
act\nScalar curvature encodes the volume information of small geodesic bal
ls within a Riemannian manifold\, making it\, to some extent\, the weakest
curvature invariant. This raises a natural question: what topological con
straints does scalar curvature impose on manifolds? In this talk\, we shal
l show that for a manifold with a scalar curvature lower bound\, the simpl
icial norm of certain characteristic classes can be controlled by its volu
me and the injectivity radius of its universal covering. This is joint wo
rk with Guoliang Yu.\n
LOCATION:https://stable.researchseminars.org/talk/CUNY_GeometricAnalysis/1
63/
END:VEVENT
END:VCALENDAR