BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Anusha Krishnan (Syracuse University)
DTSTART;VALUE=DATE-TIME:20200430T190000Z
DTEND;VALUE=DATE-TIME:20200430T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/1
DESCRIPTION:Title: Diagonalizing the Ricci tensor\nby Anusha Krishnan (Syr
acuse University) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract
\nWe will discuss some recent work on diagonalizing the Ricci tensor of in
variant metrics on compact Lie groups\, homogeneous spaces and cohomogenei
ty one manifolds\, and connections to the Ricci flow.\n\nZoom Meeting ID:
961-8801-7284. The password to join will be sent to the seminar's mailing
list\; if you are not on the mailing list\, please email NKatz(NoSpamPleas
e)citytech.cuny.edu or R.Bettiol(NoSpamPlease)lehman.cuny.edu to receive t
he password directly.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Buttsworth (Cornell University)
DTSTART;VALUE=DATE-TIME:20200507T200000Z
DTEND;VALUE=DATE-TIME:20200507T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/2
DESCRIPTION:Title: The prescribed Ricci curvature problem on manifolds with la
rge symmetry groups\nby Timothy Buttsworth (Cornell University) as par
t of CUNY Geometric Analysis Seminar\n\n\nAbstract\nThe prescribed Ricci c
urvature problem continues to be of fundamental interest in Riemannian geo
metry. In this talk\, I will describe some classical results on this topic
\, as well as some more recent results that have been achieved with homoge
neous and cohomogeneity-one assumptions.\n\nZoom Meeting ID: TBA (will be
posted here and in the seminar's website). The password to join will be se
nt to the seminar's mailing list\; if you are not on the mailing list\, pl
ease email NKatz(NoSpamPlease)citytech.cuny.edu or R.Bettiol(NoSpamPlease)
lehman.cuny.edu to receive the password directly.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ronan Conlon (Florida International University)
DTSTART;VALUE=DATE-TIME:20200514T200000Z
DTEND;VALUE=DATE-TIME:20200514T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/3
DESCRIPTION:Title: Classification results for expanding and shrinking gradient
Kahler-Ricci solitons\nby Ronan Conlon (Florida International Univers
ity) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nA complete
Kahler metric g on a Kahler manifold $M$ is a "gradient Kahler-Ricci solit
on" if there exists a smooth real-valued function $f\\colon M\\to R$ with
$\\nabla f$ holomorphic such that $Ric(g)-Hess(f)+\\lambda g=0$ for $\\la
mbda$ a real number. I will present some classification results for such m
anifolds. This is joint work with Alix Deruelle (Université Paris-Sud) an
d Song Sun (UC Berkeley).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Longa (University of Sao Paulo (Brazil))
DTSTART;VALUE=DATE-TIME:20200528T190000Z
DTEND;VALUE=DATE-TIME:20200528T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/4
DESCRIPTION:Title: Sharp systolic inequalities for 3-manifolds with boundary\nby Eduardo Longa (University of Sao Paulo (Brazil)) as part of CUNY Ge
ometric Analysis Seminar\n\n\nAbstract\nSystolic Geometry dates back to th
e late 1940s\, with the work of Loewner and his doctoral student Pu. This
branch of differential geometry received more attention after the seminal
work of Gromov\, where he proved his famous systolic inequality and introd
uced many important concepts. In this talk I will recall the notion of sys
tole and present some sharp systolic inequalities for free boundary surfac
es in 3-manifolds.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Kröncke (Universität Hamburg)
DTSTART;VALUE=DATE-TIME:20200604T180000Z
DTEND;VALUE=DATE-TIME:20200604T190000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/5
DESCRIPTION:Title: L^p-stability and positive scalar curvature rigidity of Ric
ci-flat ALE manifolds\nby Klaus Kröncke (Universität Hamburg) as par
t of CUNY Geometric Analysis Seminar\n\n\nAbstract\nWe will establish long
-time and derivative estimates for the heat semigroup of various natural S
chrödinger operators on asymptotically locally Euclidean (ALE) manifolds.
These include the Lichnerowicz Laplacian of a Ricci-flat ALE manifold\, p
rovided that it is spin and admits a parallel spinor. The estimates will b
e used to prove its L^p-stability under the Ricci flow for pThe isometry group of spherical quotients\nby Ricardo A
. E. Mendes (University of Oklahoma) as part of CUNY Geometric Analysis Se
minar\n\n\nAbstract\nA special class of Alexandrov metric spaces are the q
uotients $X=S^n/G$ of the round spheres by isometric actions of compact su
bgroups $G$ of $O(n+1)$. We will consider the question of how to compute t
he isometry group of such $X$\, the main result being that every element i
n the identity component of $Isom(X)$ lifts to a $G$-equivariant isometry
of the sphere. The proof relies on a pair of important results about the "
smooth structure" of $X$.\n\nPlease contact organizers for Zoom meeting de
tails.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shih-Kai Chiu (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20200618T190000Z
DTEND;VALUE=DATE-TIME:20200618T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/7
DESCRIPTION:Title: A Liouville type theorem for harmonic 1-forms\nby Shih-
Kai Chiu (University of Notre Dame) as part of CUNY Geometric Analysis Sem
inar\n\n\nAbstract\nThe famous Cheng-Yau gradient estimate implies that on
a\ncomplete Riemannian manifold with nonnegative Ricci curvature\, any\nh
armonic function that grows sublinearly must be a constant. This is\nthe s
ame as saying the function is closed as a 0-form. We prove an\nanalogous r
esult for harmonic 1-forms. Namely\, on a complete\nRicci-flat manifold wi
th Euclidean volume growth\, any harmonic 1-form\nwith polynomial sublinea
r growth must be the differential of a\nharmonic function. We prove this b
y proving an $L^2$ version of the\n"gradient estimate" for harmonic 1-form
s. As a corollary\, we show that\nwhen the manifold is Ricci-flat Kähler
with Euclidean volume growth\,\nthen any subquadratic harmonic function mu
st be pluriharmonic. This\ngeneralizes the result of Conlon-Hein.\n\nConta
ct organizers for Zoom meeting details.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Aldana (Universidad del Norte (Colombia))
DTSTART;VALUE=DATE-TIME:20200625T190000Z
DTEND;VALUE=DATE-TIME:20200625T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/8
DESCRIPTION:Title: Strong $A_\\infty$ weights and compactness of conformal met
rics\nby Clara Aldana (Universidad del Norte (Colombia)) as part of CU
NY Geometric Analysis Seminar\n\n\nAbstract\nIn the talk I will introduce
$A_\\infty$-weights and strong $A_\\infty$-weights and present some of the
ir properties. I will show how\, using these weights\, we can prove compac
tness of conformal metrics with critical integrability conditions on the s
calar curvature. This relates to two problems in differential geometry: Pi
nching of the curvature and finding geometrical conditions under which a s
equence of conformal metrics admits a convergent subsequence. The results
presented here are joint work with Gilles Carron (University of Nantes) an
d Samuel Tapie (University of Nantes).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (UNAM (Mexico))
DTSTART;VALUE=DATE-TIME:20200702T190000Z
DTEND;VALUE=DATE-TIME:20200702T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/9
DESCRIPTION:Title: Convergence of manifolds under volume convergence and a ten
sor bound\nby Raquel Perales (UNAM (Mexico)) as part of CUNY Geometric
Analysis Seminar\n\n\nAbstract\nGiven a Riemannian manifold $M$ and a pai
r of Riemannian tensors $g_0 \\leq g_j$ on $M$ we have $vol_0(M) \\leq v
ol_j(M)$ and the volumes are equal if and only if $g_0=g_j$. In this talk
I will show that if we have a sequence of Riemmanian tensors $g_j$ such t
hat $g_0\\leq g_j$ and $vol_j(M)\\to vol_0(M)$ then $(M\,g_j)$ converge to
$(M\,g_0)$ in the volume preserving intrinsic flat sense. I will present
examples demonstrating that under these conditions we do not necessarily
obtain smooth\, $C^0$ or Gromov-Hausdorff convergence.\nFurthermore\, this
result can be applied to show stability of graphical tori. \n[Based on j
oin work with Allen-Sormani and Cabrera Pacheco-Ketterer]\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilaria Mondello (Université de Paris Est Créteil (France))
DTSTART;VALUE=DATE-TIME:20200709T180000Z
DTEND;VALUE=DATE-TIME:20200709T190000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/10
DESCRIPTION:Title: Non-existence of Yamabe metrics in a singular setting\
nby Ilaria Mondello (Université de Paris Est Créteil (France)) as part o
f CUNY Geometric Analysis Seminar\n\n\nAbstract\nThe existence of Yamabe m
etrics\, that is\, metrics which minimize the Einstein-Hilbert functional
in a conformal class\, has been proven for compact smooth manifolds thanks
to the celebrated work of Yamabe\, Trudinger\, Aubin and Schoen. When con
sidering manifolds with singularities\, the situation is quite different:
while an existence result due to Akutagawa\, Mazzeo and Carron is availabl
e\, Viaclovsky had constructed in 2010 an example of 4-manifold\, with one
orbifold isolated singularity\, for which a Yamabe metric does not exists
. After briefly presenting the singularities we deal with\, we will discus
s a new non-existence result for a class of examples with non isolated sin
gularities\, not necessarily orbifold. This is based on a joint work with
Kazuo Akutagawa.\n\nPlease note the earlier time than usual. Zoom meeting
details are sent to our mailing list.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Chul Jang (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20200716T190000Z
DTEND;VALUE=DATE-TIME:20200716T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/11
DESCRIPTION:Title: Mass rigidity of asymptotically hyperbolic manifolds\n
by Hyun Chul Jang (University of Connecticut) as part of CUNY Geometric An
alysis Seminar\n\n\nAbstract\nIn this talk\, we present the rigidity of po
sitive mass theorem for asymptotically hyperbolic (AH) manifolds. That is\
, if the total mass of a given AH manifold is zero\, then the manifold is
isometric to hyperbolic space. The proof of the rigidity used a variationa
l approach with the scalar curvature constraint. It also involves an inves
tigation of a type of Hessian equation\, which leads to recent splitting r
esults with G. J. Galloway. We will briefly discuss them as well. This tal
k is based on the joint works with L.-H. Huang and D. Martin\, and with G.
J. Galloway.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Lee (CUNY Queens College and Graduate Center)
DTSTART;VALUE=DATE-TIME:20200723T190000Z
DTEND;VALUE=DATE-TIME:20200723T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/12
DESCRIPTION:Title: Bartnik minimizing initial data sets\nby Dan Lee (CUNY
Queens College and Graduate Center) as part of CUNY Geometric Analysis Se
minar\n\n\nAbstract\nWe will review what is known about Bartnik minimizing
initial data sets in the time-symmetric case\, and then discuss new resul
ts on the general case obtained in joint work with Lan-Hsuan Huang of the
University of Connecticut. Bartnik conjectured that these minimizers must
be vacuum and admit a global Killing vector. We make partial progress towa
rd the conjecture by proving that Bartnik minimizers must arise from so-ca
lled “null dust spacetimes” that admit a global Killing vector field.
In high dimensions\, we find examples that contradict Bartnik’s conjectu
re\, as well as the “strict” positive mass theorem\, though these exam
ples have "sub-optimal” asymptotic decay rates.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kerin (NUI Galway (Ireland))
DTSTART;VALUE=DATE-TIME:20200730T180000Z
DTEND;VALUE=DATE-TIME:20200730T190000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
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 Analysis Sem
inar\n\n\nAbstract\nManifolds with non-negative sectional curvature are ra
re and difficult to find\, with interesting topological phenomena traditio
nally being restricted by a dearth of methods of construction. In this ta
lk\, I will describe a large family of seven-dimensional manifolds with no
n-negative curvature\, leading to examples of exotic diffeomorphism types\
, non-standard homotopy types\, and fake versions of familiar non-simply c
onnected friends. This is based on joint work with Sebastian Goette and Kr
ishnan Shankar.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubham Dwivedi (University of Waterloo (Canada))
DTSTART;VALUE=DATE-TIME:20200806T190000Z
DTEND;VALUE=DATE-TIME:20200806T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/14
DESCRIPTION:Title: Deformation theory of nearly $G_2$ manifolds\nby Shubh
am Dwivedi (University of Waterloo (Canada)) as part of CUNY Geometric Ana
lysis Seminar\n\n\nAbstract\nWe will discuss the deformation theory of nea
rly $G_2$ manifolds. After defining nearly $G_2$ manifolds\, we will descr
ibe some identities for 2 and 3-forms on such manifolds. We will introduce
a Dirac type operator which will be used to completely describe the cohom
ology of nearly $G_2$ manifolds. Along the way\, we will give a different
proof of a result of Alexandrov—Semmelman on the space of infinitesimal
deformation of nearly $G_2$ structures. Finally\, we will prove that the i
nfinitesimal deformations of the homogeneous nearly $G_2$ structure on the
Aloff--Wallach space are obstructed to second order. The talk is based on
a joint work with Ragini Singhal (University of Waterloo).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christian Lange (Universitaet zu Koeln)
DTSTART;VALUE=DATE-TIME:20200903T180000Z
DTEND;VALUE=DATE-TIME:20200903T190000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/15
DESCRIPTION:Title: Zoll flows on surfaces\nby Christian Lange (Universita
et zu Koeln) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nA R
iemannian metric is called Zoll if all its geodesics are closed with the s
ame period.\nWe discuss rigidity and flexibility phenomena of such Riemann
ian and more general Zoll systems. In particular\, we show that if a magne
tic 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://researchseminars.org/talk/CUNY_GeometricAnalysis/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariana Smit Vega Garcia (Western Washington University)
DTSTART;VALUE=DATE-TIME:20200917T200000Z
DTEND;VALUE=DATE-TIME:20200917T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/16
DESCRIPTION:Title: Almost minimizers for obstacle problems\nby Mariana Sm
it Vega Garcia (Western Washington University) as part of CUNY Geometric A
nalysis Seminar\n\n\nAbstract\nIn the applied sciences one is often confro
nted with free boundaries\, which arise when the solution to a problem con
sists of a pair: a function u (often satisfying a partial differential equ
ation)\, and a set where this function has a specific behavior. Two centra
l issues in the study of free boundary problems and related problems in th
e calculus of variations and geometric measure theory are:\n\n(1) What is
the optimal regularity of the solution u?\n\n(2) How smooth is the free bo
undary (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 proble
ms\, began in the ’60s with the pioneering works of G. Stampacchia\, H.
Lewy\, and J. L. Lions. During the past five decades\, it has led to beaut
iful and deep developments in the calculus of variations and geometric par
tial differential equations\, and its study still presents very interestin
g and challenging questions.\nIn contrast to the classical obstacle proble
m\, which arises from a minimization problem\, minimizing problems with no
ise lead to the notion of almost minimizes. Though deeply connected to "st
andard" 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 developmen
ts on obstacle type problems and almost minimizers for the thin obstacle p
roblem\, illustrating techniques that can be used to tackle questions (1)
and (2) in various settings.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ian Adelstein (Yale University)
DTSTART;VALUE=DATE-TIME:20200924T200000Z
DTEND;VALUE=DATE-TIME:20200924T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/17
DESCRIPTION:Title: The length of the shortest closed geodesic on positively c
urved 2-spheres\nby Ian Adelstein (Yale University) as part of CUNY Ge
ometric Analysis Seminar\n\n\nAbstract\nWe start with an intuitive introdu
ction to the isosystolic inequalities. We then show that the shortest clos
ed geodesic on a 2-sphere with non-negative curvature has length bounded a
bove by three times the diameter. We prove a new isoperimetric inequality
for 2-spheres with pinched curvature\; this allows us to improve our bound
on the length of the shortest closed geodesic in the pinched curvature se
tting. This is joint work with Franco Vargas Pallete.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yueh-Ju Lin (Wichita State University)
DTSTART;VALUE=DATE-TIME:20201015T200000Z
DTEND;VALUE=DATE-TIME:20201015T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/18
DESCRIPTION:Title: Volume comparison of Q-curvature\nby Yueh-Ju Lin (Wich
ita State University) as part of CUNY Geometric Analysis Seminar\n\n\nAbst
ract\nClassical volume comparison for Ricci curvature is a fundamental res
ult in Riemannian geometry. In general\, scalar curvature as the trace of
Ricci curvature\, is too weak to control the volume. However\, with the ad
ditional stability assumption on the closed Einstein manifold\, one can ob
tain a volume comparison for scalar curvature. In this talk\, we investiga
te a similar phenomenon for $Q$-curvature\, a fourth-order analogue of sca
lar curvature. In particular\, we prove a volume comparison result of $Q$-
curvature for metrics near stable Einstein metrics by variational techniqu
es and a Morse lemma for infinite dimensional manifolds. This is a joint w
ork with Wei Yuan.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curtis Pro (California State University (Stanislaus))
DTSTART;VALUE=DATE-TIME:20201022T200000Z
DTEND;VALUE=DATE-TIME:20201022T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/19
DESCRIPTION:Title: Extending a diffeomorphism finiteness theorem to dimension
4.\nby Curtis Pro (California State University (Stanislaus)) as part
of CUNY Geometric Analysis Seminar\n\n\nAbstract\nCheeger's Finiteness The
orem says: Given numbers $k<$ $K$ in $\\mathbb{R}$ and $v\, D>0$\, there a
re at most finitely many differentiable structures on the class of $n$-man
ifolds $M$ that support metrics with $k\\leq\\sec M\\leq K\, \\mathrm{vol}
\\\,M\\geq v\,$ and $\\mathrm{diam}\\\,M\\leq D.$ In the early 90s\, Grov
e\, Petersen\, Wu\, and (independently) Perelman showed in all dimensions\
, except possibly $n=4$\, this conclusion still holds for the larger class
that has no upper bound on sectional curvature. In this talk\, I'll prese
nt recent work with Fred Wilhelm that shows this conclusion is also true i
n dimension 4.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Zhu (Princeton University)
DTSTART;VALUE=DATE-TIME:20201112T210000Z
DTEND;VALUE=DATE-TIME:20201112T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/20
DESCRIPTION:Title: Explicit Łojasiewicz inequalities for mean curvature flow
shrinkers\nby Jonathan Zhu (Princeton University) as part of CUNY Geo
metric Analysis Seminar\n\n\nAbstract\nŁojasiewicz inequalities are a pop
ular tool for studying the stability of geometric structures. For mean cur
vature flow\, Schulze used Simon’s reduction to the classical Łojasiewi
cz inequality to study compact tangent flows. Colding and Minicozzi instea
d used a direct method to prove Łojasiewicz inequalities for round cylind
ers. We’ll discuss similarly explicit Łojasiewicz inequalities and appl
ications for other shrinking cylinders and Clifford shrinkers.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonçalo Oliveira (Universidade Federal Fluminense (Brazil))
DTSTART;VALUE=DATE-TIME:20201001T200000Z
DTEND;VALUE=DATE-TIME:20201001T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/21
DESCRIPTION:Title: $G_2$-monopoles (a summary)\nby Gonçalo Oliveira (Uni
versidade Federal Fluminense (Brazil)) as part of CUNY Geometric Analysis
Seminar\n\n\nAbstract\nThis talk is aimed at reviewing what is known about
$G_2$-monopoles and motivate their study. After this\, I will mention som
e recent results obtained in collaboration with Ákos Nagy and Daniel Fade
l which investigate the asymptotic behaviour of $G_2$-monopoles. Time perm
itting\, I will mention a few possible future directions regarding the use
of monopoles in $G_2$-geometry.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lin (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20201008T200000Z
DTEND;VALUE=DATE-TIME:20201008T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/22
DESCRIPTION:Title: Three-dimensional Geometric Structures and the Laplace Spe
ctrum\nby Samuel Lin (Dartmouth College) as part of CUNY Geometric Ana
lysis Seminar\n\n\nAbstract\nThe earliest examples of non-isometric Laplac
e-isospectral manifolds have the same local geometries. In fact\, the firs
t example of 16-tori given by Milnor and other isospectral pairs arising f
rom the classical group theoretic method of Sunada have the same local geo
metries. 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 dime
nsion two and three.\n \nI will present our result in this direction\, whi
ch provides strong evidence that the local geometry of a three-dimensional
locally homogeneous space is a spectral invariant. Motivated by this prob
lem in spectral geometry\, I will also present a metric classification of
all locally homogeneous three-manifolds covered by topological spheres. Th
is talk is based on a joint work with Ben Schmidt and Craig Sutton.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernani Ribeiro Jr. (Universidade Federal do Ceara (Brazil))
DTSTART;VALUE=DATE-TIME:20201029T200000Z
DTEND;VALUE=DATE-TIME:20201029T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/23
DESCRIPTION:Title: Four-dimensional gradient shrinking Ricci solitons\nby
Ernani Ribeiro Jr. (Universidade Federal do Ceara (Brazil)) as part of CU
NY Geometric Analysis Seminar\n\n\nAbstract\nIn this talk\, we will discus
s 4-dimensional complete (not necessarily compact) gradient shrinking Ricc
i solitons. We will show that a 4-dimensional complete gradient shrinking
Ricci soliton satisfying a pointwise condition involving either the self-
dual or anti-self-dual part of the Weyl tensor is either Einstein\, or a f
inite 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 a
ddition\, we will present some curvature estimates for 4-dimensional compl
ete gradient Ricci solitons. Some open problems will be also discussed. Th
is is a joint work with Huai-Dong Cao and Detang Zhou.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Ledwidge (University of Muenster)
DTSTART;VALUE=DATE-TIME:20201105T210000Z
DTEND;VALUE=DATE-TIME:20201105T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/24
DESCRIPTION:Title: The sharp Li-Yau equality on shrinking Ricci solitons\
nby Jason Ledwidge (University of Muenster) as part of CUNY Geometric Anal
ysis Seminar\n\n\nAbstract\nIn this talk we will prove a sharp Li-Yau equa
lity on shrinking Ricci solitons and use this equality to prove the existe
nce of a minimiser for Perelman's W functional on shrinking Ricci solitons
. By a result of Haslhofer-Mueller\, the uniqueness of the minimisier of t
he W functional leads to the classification of Type I singularity models t
o the Ricci flow in four dimensions. If time permits\, we will also show h
ow the Li-Yau equality leads to a global Isoperimetric inequality on shrin
kig Ricci solitons. We will be more interested in the importance of the co
njugate heat semigroup and its estimates on shrinking Ricci solitons and h
ence our aim is for the talk not to be too technical.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robin Neumayer (Northwestern University)
DTSTART;VALUE=DATE-TIME:20201119T210000Z
DTEND;VALUE=DATE-TIME:20201119T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/25
DESCRIPTION:Title: $d_p$ Convergence and $\\epsilon$-regularity theorems for
entropy and scalar curvature lower bounds\nby Robin Neumayer (Northwes
tern University) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\
nIn this talk\, we consider Riemannian manifolds with almost non-negative
scalar curvature and Perelman entropy. We establish an $\\epsilon$-regular
ity theorem showing that such a space must be close to Euclidean space in
a suitable sense. Interestingly\, such a result is false with respect to t
he Gromov-Hausdorff and Intrinsic Flat distances\, and more generally the
metric space structure is not controlled under entropy and scalar lower bo
unds. Instead\, we introduce the notion of the $d_p$ distance between (in
particular) Riemannian manifolds\, which measures the distance between $W^
{1\,p}$ Sobolev spaces\, and it is with respect to this distance that the
$\\epsilon$ regularity theorem holds. We will discuss various applications
to manifolds with scalar curvature and entropy lower bounds\, including a
compactness and limit structure theorem for sequences\, a uniform $L^\\in
fty$ 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://researchseminars.org/talk/CUNY_GeometricAnalysis/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lashi Bandara (Universitaet Potsdam)
DTSTART;VALUE=DATE-TIME:20201204T150000Z
DTEND;VALUE=DATE-TIME:20201204T160000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/26
DESCRIPTION:Title: The world of rough metrics\nby Lashi Bandara (Universi
taet Potsdam) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nRo
ugh metrics are measurable coefficient Riemannian structures.\nThey captur
e a very large class of natural geometries\, with the quintessential examp
le being Lipschitz pullbacks of smooth metrics.\nAlthough they have impli
citly appeared for a very long time\, particularly in the context of bound
ed-measurable coefficient divergence form equations\, they have only been
studied explicitly recently.\nThe aim of this talk would be to introduce t
hese metrics\, motivated by an important example - their connection to the
geometric Kato square root problem.\nTheir salient features would be desc
ribed\, along with recent results\, such as the existence of heat kernels
and Weyl asymptotics for associated Laplacians in compact settings.\n\n(Pl
ease note the different time for this talk.)\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annachiara Piubello (University of Miami)
DTSTART;VALUE=DATE-TIME:20210204T210000Z
DTEND;VALUE=DATE-TIME:20210204T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/27
DESCRIPTION:Title: Mass and Riemannian Polyhedra\nby Annachiara Piubello
(University of Miami) as part of CUNY Geometric Analysis Seminar\n\n\nAbst
ract\nWe show a new formula for the ADM mass as the limit of the total mea
n curvature plus the total defect of dihedral angle of the boundary of lar
ge polyhedra. In the special case of coordinate cubes\, we will show an in
tegral formula relating the n-dimensional mass with a geometrical quantity
that determines the (n-1)-dimensional mass. This is joint work with Pengz
i Miao.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Lowe (Princeton University)
DTSTART;VALUE=DATE-TIME:20210211T210000Z
DTEND;VALUE=DATE-TIME:20210211T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
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 sta
ble properly immersed minimal surfaces in a negatively curved 3-manifold f
rom a dynamical perspective. I will survey their work and talk about some
results that I've obtained in this direction.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20210218T210000Z
DTEND;VALUE=DATE-TIME:20210218T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/29
DESCRIPTION:Title: Manifold submetries\, with applications to Invariant Theor
y\nby Marco Radeschi (University of Notre Dame) as part of CUNY Geomet
ric Analysis Seminar\n\n\nAbstract\nGiven an orthogonal representation of
a Lie group G on a Euclidean vector space V\, Invariant Theory studies the
algebra of G-invariant polynomials on V. This setting can be generalized
by replacing the orbits of the representation with a foliation by the fibe
rs of a manifold submetry from the unit sphere S(V)\, and consider the alg
ebra of polynomials that are constant along these fibers (effectively prod
ucing an Invariant Theory\, but without groups).\nIn this talk we will exh
ibit a surprisingly strong relation between the geometric information comi
ng from the submetry and the algebraic information coming from the corresp
onding algebra\, with several applications to classical Invariant Theory.\
nThis talk is based on a joint work with Ricardo Mendes.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weimin Sheng (Zhejiang University)
DTSTART;VALUE=DATE-TIME:20210226T000000Z
DTEND;VALUE=DATE-TIME:20210226T010000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/30
DESCRIPTION:Title: Removable singularity of positive mass theorem with contin
uous metrics\nby Weimin Sheng (Zhejiang University) as part of CUNY Ge
ometric Analysis Seminar\n\n\nAbstract\nIn this talk\, I consider asymptot
ically flat Riemannnian manifolds $(M^n\, g)$ with $C^0$ metric $g$ and $g
$ is smooth away from a closed bounded subset $\\Sigma$ and the scalar cur
vature $R_g\\ge 0$ on $M\\setminus \\Sigma$. For given $n\\le p\\le \\inf
ty$\, if $g\\in C^0\\cap W^{1\,p}$ and the Hausdorff measure $\\mathcal{
H}^{n-\\frac{p}{p-1}}(\\Sigma)<\\infty$ when $n\\le p<\\infty$ or $\\mathc
al{H}^{n-1}(\\Sigma)=0$ when $p=\\infty$\, then I will show that the ADM m
ass of each end is nonnegative. Furthermore\, if the ADM mass of some end
is zero\, then I'll show that $(M^n\, g)$ is isometric to the Euclidean sp
ace 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 s
pin to non-spin\, also improves the result of Shi-Tam [JDG 2002] and Lee [
PAMS 2013]. Moreover\, for $p=\\infty$\, this confirms a conjecture of Lee
[pAMS 2013].\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vitali Kapovitch (University of Toronto)
DTSTART;VALUE=DATE-TIME:20210304T210000Z
DTEND;VALUE=DATE-TIME:20210304T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/31
DESCRIPTION:Title: Mixed curvature almost flat manifolds\nby Vitali Kapov
itch (University of Toronto) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nA celebrated theorem of Gromov says that given $n>1$ there is
an $\\epsilon(n)>0$ such that if a closed Riemannian manifold $M^n$ satis
fies $-\\epsilon<\\sec_M<\\epsilon\, diam(M)< 1$ then $M$ is diffeomorphic
to an infranilmanifold.\nI will show that the lower sectional curvature b
ound 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 st
udy of manifolds with Ricci curvature bounded below.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Feng Wang (Zhejiang University)
DTSTART;VALUE=DATE-TIME:20210311T140000Z
DTEND;VALUE=DATE-TIME:20210311T150000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/32
DESCRIPTION:Title: On the singular Yau-Tian-Donaldson conjecture\nby Feng
Wang (Zhejiang University) as part of CUNY Geometric Analysis Seminar\n\n
\nAbstract\nThe famous Yau-Tian-Donaldson conjecture asserts the equivalen
ce between the stability and existence of canonical metrics. On Fano manif
olds\, 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 exi
stence of Kahler-Einstein metrics on a class of singular Fano varieties.
This is a joint work with Chi Li and Professor Gang Tian.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyun Chul Jang (University of Miami)
DTSTART;VALUE=DATE-TIME:20210311T210000Z
DTEND;VALUE=DATE-TIME:20210311T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/33
DESCRIPTION:Title: Hyperbolic mass via horospheres\nby Hyun Chul Jang (Un
iversity of Miami) as part of CUNY Geometric Analysis Seminar\n\n\nAbstrac
t\nThe mass of asymptotically hyperbolic manifolds is a geometric invarian
t that measures its deviation from hyperbolic space. In this talk\, we pre
sent a new mass formula using large coordinate horospheres. The formula is
stated as a limit of the weighted total difference of mean curvatures on
large coordinate horospheres. We will remark a few geometric implications
of the formula including scalar curvature rigidity of asymptotically hyper
bolic manifolds. This talk is based on joint work with Pengzi Miao.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chi Li (Rutgers University)
DTSTART;VALUE=DATE-TIME:20210408T200000Z
DTEND;VALUE=DATE-TIME:20210408T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/34
DESCRIPTION:Title: Recent progresses on the Yau-Tian-Donaldson conjecture for
constant scalar curvature Kahler metrics\nby Chi Li (Rutgers Universi
ty) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nFor any pola
rized projective manifold $(X\, L)$\, the Yau-Tian-Donaldson conjecture pr
edicts that the existence of constant scalar curvature Kahler metrics in t
he first Chern class of $L$ is equivalent to an algebraic K-stability prop
erty of $(X\, L)$. We will survey some recent progresses towards this conj
ecture and how it leads to an interesting open question in algebraic geome
try.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chao Li (Princeton University)
DTSTART;VALUE=DATE-TIME:20210318T200000Z
DTEND;VALUE=DATE-TIME:20210318T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/35
DESCRIPTION:Title: Scalar curvature and dihedral rigidity of Riemannian polyh
edra\nby Chao Li (Princeton University) as part of CUNY Geometric Anal
ysis Seminar\n\n\nAbstract\nIn 2013\, Gromov proposed a geometric comparis
on theorem for metrics with nonnegative scalar curvature\, formulated in t
erms of the dihedral rigidity phenomenon for Riemannian polyhedrons: if a
Riemannian polyhedron has nonnegative scalar curvature in the interior\, a
nd weakly mean convex faces\, then the dihedral angle between adjacent fac
es cannot be everywhere less than the corresponding Euclidean model. In th
is talk\, I will prove this conjecture for a large collection of polytopes
\, and extend it to metrics with negative scalar curvature lower bounds. T
he strategy is to relate this question with a geometric variational proble
m of capillary type\, and apply the Schoen-Yau minimal slicing technique f
or manifolds with boundary.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davi Maximo (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20210325T200000Z
DTEND;VALUE=DATE-TIME:20210325T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/36
DESCRIPTION:Title: The Waist Inequality and Positive Scalar Curvature\nby
Davi Maximo (University of Pennsylvania) as part of CUNY Geometric Analys
is Seminar\n\n\nAbstract\nThe topology of three-manifolds with positive sc
alar curvature has been (mostly) known since the solution of the Poincare
conjecture by Perelman. Indeed\, they consist of connected sums of spheric
al space forms and $S^2 \\times S^1$'s. In spite of this\, their "shape" r
emains unknown and mysterious. Since a lower bound of scalar curvature can
be preserved by a codimension two surgery\, one may wonder about a descri
ption of the shape of such manifolds based on a codimension two data (in t
his case\, 1-dimensional manifolds).\n \nIn this talk\, I will show result
s from a recent collaboration with Y. Liokumovich elucidating this questio
n for closed three-manifolds.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aghil Alaee (Clark University & CMSA Harvard)
DTSTART;VALUE=DATE-TIME:20210415T200000Z
DTEND;VALUE=DATE-TIME:20210415T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/37
DESCRIPTION:Title: Rich extra dimensions are hidden inside black holes\nb
y Aghil Alaee (Clark University & CMSA Harvard) as part of CUNY Geometric
Analysis Seminar\n\n\nAbstract\nIn 1972\, Kip Thorne conjectured a formati
on of a black hole due to an inequality between the mass of a bounded regi
on and its size. In this talk\, I review some recent results regarding thi
s conjecture and its application to the size of the geometry of extra dime
nsions.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Max Hallgren (Cornell University)
DTSTART;VALUE=DATE-TIME:20210513T200000Z
DTEND;VALUE=DATE-TIME:20210513T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/38
DESCRIPTION:Title: Ricci Flow with a Lower Bound on Ricci Curvature and Volum
e\nby Max Hallgren (Cornell University) as part of CUNY Geometric Anal
ysis Seminar\n\n\nAbstract\nIn this talk\, we will investigate the possibl
e singularity behavior of closed solutions of Ricci flow whose Ricci curva
ture is uniformly bounded below\, and whose volume does not go to zero. In
four dimensions\, we will see that only orbifold singularities can arise\
, and prove integral curvature estimates on time slices. We will also see
a rough picture of singularity formation in higher dimensions.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tam Nguyen-Phan (Karlsruhe Institute of Technology)
DTSTART;VALUE=DATE-TIME:20210506T190000Z
DTEND;VALUE=DATE-TIME:20210506T200000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
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 Technol
ogy) 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 dimension (n
-1). These tori are natural candidates for nontrivial homology cycles of m
anifold covers of SL(n\,Z)\\SL(n\,R)/SO(n). In joint work with Grigori Avr
amidi\, we show that some of these tori give nontrivial rational homology
cycles in congruence covers of SL(n\,Z) \\SL(n\,R)/SO(n). We also show tha
t the dimension of the subspace of the (n-1)-homology group spanned by fla
t (n-1)-tori grows as one goes up in congruence covers. The prerequisite f
or this talk is very basic linear algebra.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun (The University of Chicago)
DTSTART;VALUE=DATE-TIME:20210909T200000Z
DTEND;VALUE=DATE-TIME:20210909T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
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 Seminar\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 singula
rities. This contributes to the program of dynamical approach to mean curv
ature flow initiated by Colding and Minicozzi. The key is to prove that a
positive perturbation on initial data would drift to the first eigenfuncti
on direction after a long time. This result can be viewed as a global unst
able manifold theorem in the most unstable direction for a nonlinear heat
equation. This is joint work with Jinxin Xue (Tsinghua University).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhou Zhang (The University of Sydney)
DTSTART;VALUE=DATE-TIME:20210923T200000Z
DTEND;VALUE=DATE-TIME:20210923T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/41
DESCRIPTION:Title: The Modified Kahler-Ricci Flow and Degenerate Calabi-Yau E
quation\nby Zhou Zhang (The University of Sydney) as part of CUNY Geom
etric Analysis Seminar\n\n\nAbstract\nThe Kahler-Ricci flow is the Ricci f
low with the initial metric being Kahler. Since H-D Cao’s first paper on
it\, the featured reduction to a scalar evolution has provided noticeable
flexibility to study variations\, flows of Kahler-Ricci type. More than a
decade ago\, I introduced a modified Kahler-Ricci flow and laid the found
ation for applications in the study of Calabi-Yau equation with degenerate
cohomology. Since then\, there have been many developments in the study o
f the classic Kahler-Ricci flow and the study of the degenerate Calabi-Yau
equation using the elliptic continuity method. \n\nMotivated by these\, w
e further study the modified Kahler-Ricci flow to understand the convergen
ce and eventually singularities of the degenerate Calabi-Yau metric. This
is joint work with Haotian Wu (USyd).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Ville (Université Paris-Est - Créteil Val-de-Marne)
DTSTART;VALUE=DATE-TIME:20211118T210000Z
DTEND;VALUE=DATE-TIME:20211118T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/42
DESCRIPTION:Title: Minimal surfaces in $\\mathbb R^4$\nby Marina Ville (U
niversité Paris-Est - Créteil Val-de-Marne) as part of CUNY Geometric An
alysis Seminar\n\n\nAbstract\nComplete minimal surfaces in $\\mathbb{R}^4$
are much less well understood than their counterparts in $\\mathbb{R}^3$.
Some basic questions are still quite open\, for example\, what are the mi
nimal non-holomorphic embeddings of $\\mathbb{R}^2$ in $\\mathbb{R}^4$?\n\
nI will discuss these problems\, define the link/knot /braid at infinity o
f minimal surfaces of finite curvature in $\\mathbb{R}^4$ and explain how
this object helps us classify these surfaces. I will focus on surfaces of
small total curvature and show a couple of examples where we deform/desing
ularize a classical minimal surface in $\\mathbb{R}^3$ by families of min
imal surfaces in $\\mathbb{R}^4$. Joint work with Marc Soret.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Albin (UIUC)
DTSTART;VALUE=DATE-TIME:20210930T200000Z
DTEND;VALUE=DATE-TIME:20210930T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/43
DESCRIPTION:Title: The sub-Riemannian limit of a contact manifold\nby Pie
rre Albin (UIUC) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\
nContact manifolds\, which arise naturally in mechanics\, dynamics\, and g
eometry\, carry natural Riemannian and sub-Riemannian structures and it wa
s shown by Gromov that the latter can be obtained as a limit of the former
. Subsequently\, Rumin found a complex of differential forms reflecting th
e contact structure that computes the singular cohomology of the manifold.
He used this complex to describe the behavior of the spectra of the Riema
nnian Hodge Lapacians in the sub-Riemannian limit. As many of the eigenval
ues diverge\, a refined analysis is necessary to determine the behavior of
global spectral invariants. I will report on joint work with Hadrian Quan
in which we determine the global behavior of the spectrum by explaining t
he structure of the heat kernel along this limit in a uniform way.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangyang Li (Princeton University)
DTSTART;VALUE=DATE-TIME:20211028T200000Z
DTEND;VALUE=DATE-TIME:20211028T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/44
DESCRIPTION:Title: Minimal hypersurfaces in a generic 8-dimensional closed ma
nifold\nby Yangyang Li (Princeton University) as part of CUNY Geometri
c Analysis Seminar\n\n\nAbstract\nIn the recent decade\, the Almgren-Pitts
min-max theory has advanced the existence theory of minimal surfaces in a
closed Riemannian manifold $(M^{n+1}\, g)$. When $2 \\leq n+1 \\leq 7$\,
many properties of these minimal hypersurfaces (geodesics)\, such as areas
\, Morse indices\, multiplicities\, and spatial distributions\, have been
well studied. However\, in higher dimensions\, singularities may occur in
the constructed minimal hypersurfaces. This phenomenon invalidates many te
chniques helpful in the low dimensions to investigate these geometric obje
cts. In this talk\, I will discuss how to overcome the difficulty in a gen
eric 8-dimensional closed manifold\, utilizing various deformation argumen
ts. En route to obtaining generic results\, we prove the generic regularit
y of minimal hypersurfaces in dimension 8. This talk is partially based on
joint works with Zhihan Wang.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Virginia Agostiniani (University of Trento)
DTSTART;VALUE=DATE-TIME:20211202T200000Z
DTEND;VALUE=DATE-TIME:20211202T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/45
DESCRIPTION:Title: A Green's function proof of the positive mass theorem
\nby Virginia Agostiniani (University of Trento) as part of CUNY Geometric
Analysis Seminar\n\n\nAbstract\nIn this talk we describe a new monotonici
ty formula holding along the level sets of the Green's function of an asym
ptotically flat 3-manifold with nonnegative scalar curvature. Using such a
formula\, we obtain a simple proof of the celebrated positive mass theore
m. In the same context\, and for $1 < p < 3$ a Geroch-type calculation is
performed along the level sets of p-harmonic functions\, leading to a new
proof of the Riemannian Penrose Inequality in some case studies. These res
ults are obtained in collaboration with L. Mazzieri and F. Oronzio.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shengwen Wang (University of Warwick)
DTSTART;VALUE=DATE-TIME:20210916T200000Z
DTEND;VALUE=DATE-TIME:20210916T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/46
DESCRIPTION:Title: A Brakke type regularity for the parabolic Allen-Cahn equa
tion\nby Shengwen Wang (University of Warwick) as part of CUNY Geometr
ic Analysis Seminar\n\n\nAbstract\nWe will talk about an analogue of the B
rakke's local regularity theorem for the $\\epsilon$ parabolic Allen-Cahn
equation. In particular\, we show uniform $C_{2\,\\alpha}$ regularity for
the transition layers converging to smooth mean curvature flows as $\\epsi
lon$ tend to 0 under the almost unit-density assumption. This can be viewe
d as a diffused version of the Brakke regularity for the limit mean curvat
ure flow. This is joint work with Huy Nguyen.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaochun Rong (Rutgers University)
DTSTART;VALUE=DATE-TIME:20211209T210000Z
DTEND;VALUE=DATE-TIME:20211209T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/48
DESCRIPTION:Title: Open Alexandrov spaces of non-negative curvature\nby X
iaochun Rong (Rutgers University) as part of CUNY Geometric Analysis Semin
ar\n\n\nAbstract\nWe will discuss some recent work on geometric and topolo
gical structures of an open (complete and non-compact) Alexandrov space of
non-negative curvature\, which can be viewed as counterparts of results o
n open Riemannian manifolds of non-negative sectional curvature. This is a
joint work with Xueping Li of Jiangsu Normal University\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruojing Jiang (University of Chicago)
DTSTART;VALUE=DATE-TIME:20211104T200000Z
DTEND;VALUE=DATE-TIME:20211104T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/49
DESCRIPTION:Title: Minimal Surface Entropy in Negatively Curved N-manifolds a
nd Rigidity\nby Ruojing Jiang (University of Chicago) as part of CUNY
Geometric Analysis Seminar\n\n\nAbstract\nWe focus on an odd-dimensional c
losed manifold M that admits a hyperbolic metric. For any metric on M with
sectional curvature less than or equal to -1\, we introduce the minimal s
urface entropy to count the number of surface subgroups. It attains the mi
nimum 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 introduce the
ir ideas for dimension 3\, and talk about the problems and solutions for h
igher dimensions.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nan Li (NYCCT CUNY)
DTSTART;VALUE=DATE-TIME:20211021T200000Z
DTEND;VALUE=DATE-TIME:20211021T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/50
DESCRIPTION:Title: Curvature measure on singular spaces with lower curvature
bounds\nby Nan Li (NYCCT CUNY) as part of CUNY Geometric Analysis Semi
nar\n\n\nAbstract\nWe will discuss some recent progress on the following p
roblems.\n\n1. Is there an upper bound of curvature integrals\, provided t
hat certain curvature is bounded from below?\n
\n2. As a measure in the Gromov-Hausdorff limit of manifolds\, wha
t is the behavior of the limit of the curvature integral? The curvature sh
ould concentrate at singular points.\n
\n3. What is the notion of curvature measure in singular spaces with curva
ture bounded from below?\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Franco Vargas Pallete (Yale University)
DTSTART;VALUE=DATE-TIME:20211014T200000Z
DTEND;VALUE=DATE-TIME:20211014T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/51
DESCRIPTION:Title: Mean curvature flow and foliations in Hyperbolic 3-manifol
ds\nby Franco Vargas Pallete (Yale University) as part of CUNY Geometr
ic Analysis Seminar\n\n\nAbstract\nIn this talk we explore some properties
of the mean curvature flow with surgery and the level-set flow in negativ
e curvature. We combine those with min-max theory to conclude that any qua
si-Fuchsian and any hyperbolic 3-manifolds fibered over $S^1$ admits a fol
iation where every leaf is minimal or has non-vanishing mean curvature. We
will also discuss outermost minimal surfaces in this setup. This is joint
work with Marco Guaraco (Imperial College) and Vanderson Lima (Universida
de Federal do Rio Grande do Sul).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Zamora (Penn State)
DTSTART;VALUE=DATE-TIME:20211007T200000Z
DTEND;VALUE=DATE-TIME:20211007T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/52
DESCRIPTION:Title: Structure of collapse and fundamental groups\nby Sergi
o Zamora (Penn State) as part of CUNY Geometric Analysis Seminar\n\n\nAbst
ract\nGromov's compactness criterion implies that the family $M_{sec}(d\,D
\,c)$ (resp. $M_{Ric}(d\,D\,c)$) of closed Riemannian manifolds with dimen
sion $\\leq d$\, diameter $\\leq D$\, and sectional curvature $\\geq c$ (r
esp. Ricci curvature $\\geq c$)\, is pre-compact with respect to the Hausd
orff topology in the space of compact metric spaces.\nThe general behavior
of a sequence $X_i$ in one of those families is very different depending
on whether vol$(X_i) \\to 0$\, or vol$(X_i)\\geq \\delta >0$. In this tal
k I will present some topological obstructions\, involving the fundamental
groups of the spaces $X_i$\, for the second situation to occur.\nThe main
tools used in this kind of results are systolic inequalities\, and the Ya
maguchi--Burago--Gromov--Perelman fibration theorem in the case of lower s
ectional curvature bounds.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhui Wu (Tsinghua Univ.)
DTSTART;VALUE=DATE-TIME:20220211T000000Z
DTEND;VALUE=DATE-TIME:20220211T010000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/53
DESCRIPTION:Title: Recent progress on first eigenvalues of hyperbolic surface
s for large genus\nby Yunhui Wu (Tsinghua Univ.) as part of CUNY Geome
tric Analysis Seminar\n\n\nAbstract\nIn this talk we will discuss several
recent results on first eigenvalues of closed hyperbolic surfaces for larg
e genus. For example\, we show that a random hyperbolic surface of large g
enus has first eigenvalue greater than $\\frac{3}{16}-\\epsilon$\, extendi
ng Mirzakhani's lower bound $0.0024$. This talk is based on several joint
works with Yuhao Xue.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ravi Shankar (NSF and University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20220428T201500Z
DTEND;VALUE=DATE-TIME:20220428T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/54
DESCRIPTION:Title: Growth Competitions in Non-positive Curvature\nby Ravi
Shankar (NSF and University of Oklahoma) as part of CUNY Geometric Analys
is Seminar\n\nLecture held in CUNY Graduate Center (Room 6495).\n\nAbstrac
t\n[ATTENTION: THIS TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 6495\, AND
SIMULTANEOUSLY TRANSMITTED VIA ZOOM]\n\nThe notion of a growth competitio
n between two deterministically growing clusters in a complete\, non-compa
ct metric space (or graph) was first proposed by I. Benjamini and recently
explored in the case of 2-dimensional Euclidean and hyperbolic spaces by
his student\, R. Assouline. A growth competition in a non-compact\, compl
ete Riemannian manifold\, $X$\, (or more generally a complete\, non-compac
t 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 fol
lowing 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 subsets defi
ned as\, $A_t := \\cup_{\\alpha} \\alpha([0\,t])$\, where $\\alpha(s)$ is
a $\\lambda$-Lipschitz curve in $X$\, with $\\lambda > 1$ such that $\\alp
ha(s) \\not\\in B_s$ for all $s \\in [0\,t]$. The collection of sets $A_t
$ are the fast sets.\n\n(iii) $\\{B_t\\}_{t\\geq 0}$ is a parametrized fam
ily of subsets defined as\, $B_t := \\cup_{\\beta} \\beta([0\,t))$\, where
$\\beta(s)$ is a 1-Lipschitz curve in $X$ and $\\beta(s) \\not\\in A_s$ f
or 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 Assoul
ine is that given any two distinct points $p\,q$ in a path connected\, com
plete\, geodesic metric space $X$ and a real number $\\lambda >1$\, there
exists a unique growth competition satisfying the above conditions. A bas
ic geometric question one may ask in this setting is: Under what circumsta
nces is the slow set\, $B_\\infty$\, totally bounded (surrounded) by the f
ast set\, $A_\\infty$\, versus when are they both unbounded (co-existence)
? The applications of this geometric exploration are evident in a variety
of settings (including disease/vaccine vectors\, flow of misinformation o
r the control of forest fires).\n\nIn recent work with Benjamin Schmidt an
d Ralf Spatzier we have been exploring the above question in the setting o
f non-positive curvature. In this talk we introduce growth competitions an
d give a preview of some results and open problems.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhichao Wang (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20220217T210000Z
DTEND;VALUE=DATE-TIME:20220217T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/55
DESCRIPTION:Title: Min-max minimal hypersurfaces with higher multiplicity
\nby Zhichao Wang (University of British Columbia) as part of CUNY Geometr
ic Analysis Seminar\n\n\nAbstract\nRecently\, X. Zhou proved that the Almg
ren-Pitts min-max solution has multiplicity one for bumpy metrics (Multipl
icity One Theorem). In this talk\, we exhibit the first set of examples of
non-bumpy metrics on the $(n+1)$-sphere ($2\\leq n\\leq 6$) in which the
varifold associated with the two-parameter min-max construction must be a
multiplicity-two minimal $n$-sphere. This is proved by a new area-and-sepa
ration estimate for certain minimal hypersurfaces with Morse index two ins
pired by an early work of Colding-Minicozzi. This is a joint work with X.
Zhou.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Otis Chodosh (Stanford University)
DTSTART;VALUE=DATE-TIME:20220317T200000Z
DTEND;VALUE=DATE-TIME:20220317T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/56
DESCRIPTION:Title: Stability of minimal hypersurfaces in 4-manifolds\nby
Otis Chodosh (Stanford University) as part of CUNY Geometric Analysis Semi
nar\n\n\nAbstract\nI will discuss recent joint work with Chao Li and Doug
Stryker concerning stability of (non-compact) minimal hypersurfaces in 4-m
anifolds. I will discuss ambient curvature conditions that do and do not a
dmit complete such hypersurfaces\, as well as indicating some applications
to comparison geometry.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erin Griffin (Seattle Pacific University)
DTSTART;VALUE=DATE-TIME:20220414T200000Z
DTEND;VALUE=DATE-TIME:20220414T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/57
DESCRIPTION:Title: The Case for a General $q$-flow: An Investigation of Ambie
nt Obstruction Solitons\nby Erin Griffin (Seattle Pacific University)
as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nWe will discuss
a new program of studying ambient obstruction solitons and homogeneous gra
dient Bach solitons using a geometric flow for a general tensor $q$. We be
gin by establishing a number of results for solitons to the geometric flow
for a general tensor\, $q$. Moving on\, we will apply these results to th
e ambient obstruction flow to see that any homogeneous ambient obstruction
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 gradien
t 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-Bac
h-flat\, expanding gradient Bach soliton.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Ambrozio (IMPA)
DTSTART;VALUE=DATE-TIME:20220310T210000Z
DTEND;VALUE=DATE-TIME:20220310T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/58
DESCRIPTION:Title: Analogues of Zoll metrics in minimal submanifolds theory\nby Lucas Ambrozio (IMPA) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nA Riemannian metric on a closed manifold is called Zoll when
all of its geodesics are closed and have the same period. Zoll metrics on
the two-sphere were constructed by Zoll in the beginning of the 1900's\, b
ut many questions about them are still open. It seems that higher-dimensio
nal analogues of Zoll metrics\, where closed geodesics are replaced by clo
sed embedded minimal hypersurfaces\, could be very interesting objects to
be investigated in relation to isodiastolic inequalities and other geometr
ic problems\, but also on their own account. In this talk\, I will discuss
some recent results about the construction and geometric understanding of
these new Zoll-like geometries. This is a joint project with F. Marques (
Princeton) and A. Neves (UChicago).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiayin Pan (Fields Institute and UC Santa Cruz)
DTSTART;VALUE=DATE-TIME:20220224T210000Z
DTEND;VALUE=DATE-TIME:20220224T220000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/59
DESCRIPTION:Title: Nonnegative Ricci curvature\, metric cones\, and virtual a
belianness\nby Jiayin Pan (Fields Institute and UC Santa Cruz) as part
of CUNY Geometric Analysis Seminar\n\n\nAbstract\nLet M be an open $n$-ma
nifold with nonnegative Ricci curvature. We prove that if its escape rate
is not $1/2$ and its Riemannian universal cover is conic at infinity\, tha
t is\, every asymptotic cone $(Y\,y)$ of the universal cover is a metric c
one with vertex $y$\, then $\\pi_1(M)$ contains an abelian subgroup of fin
ite index. If in addition the universal cover has Euclidean volume growth
of constant at least $L$\, we can further bound the index by a constant $C
(n\,L)$.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Song Sun (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20220505T200000Z
DTEND;VALUE=DATE-TIME:20220505T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/60
DESCRIPTION:Title: Collapsing geometry of hyperkahler 4 manifolds\nby Son
g Sun (UC Berkeley) as part of CUNY Geometric Analysis Seminar\n\n\nAbstra
ct\nA Riemannian 4-manifold is hyperkahler if its holonomy group is contai
ned in SU(2). This is the simplest nontrivial model of Ricci-flat manifold
s. To understand the geometry of these metrics\, one is lead to understand
the interesting phenomenon of ''collapsing'' to lower dimensions. In th
is talk I will discuss the analysis of collapsing geometry of these metric
s and some applications. This talk is based on joint work with Ruobing Zha
ng (Princeton).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Wylie (Syracuse University)
DTSTART;VALUE=DATE-TIME:20220407T201500Z
DTEND;VALUE=DATE-TIME:20220407T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/61
DESCRIPTION:Title: Weighted Sectional Curvature\nby William Wylie (Syracu
se University) as part of CUNY Geometric Analysis Seminar\n\nLecture held
in CUNY Graduate Center (Room 6495).\n\nAbstract\n[ATTENTION: THIS TALK WI
LL BE HELD IN PERSON AT CUNY GC ROOM 6495\, AND SIMULTANEOUSLY TRANSMITTED
VIA ZOOM]\n\nRicci curvature for manifolds with density has been extensiv
ely studied recently and has many applications. A corresponding theory of
sectional curvature has not been as well developed. Perhaps one reason 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 results a
s well as open questions. This is based on joint work with Kennard and Ken
nard-Yeroshkin.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Fernandez (UNAM)
DTSTART;VALUE=DATE-TIME:20220324T200000Z
DTEND;VALUE=DATE-TIME:20220324T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/62
DESCRIPTION:Title: Yamabe type problems in the presence of singular Riemannia
n foliations\nby Juan Carlos Fernandez (UNAM) as part of CUNY Geometri
c Analysis Seminar\n\n\nAbstract\nIn this talk we will study how the gener
alized symmetries given by singular Riemannian foliations give rise to sig
n-changing solutions to some semilinear elliptic equations with power nonl
inearity\, which are constant on the leaves of the foliation. In particula
r\, we give new solutions to the Yamabe problem on the sphere\, constant o
n the leaves of RFKM-foliations.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paula Burkhardt-Guim (NYU)
DTSTART;VALUE=DATE-TIME:20220331T201500Z
DTEND;VALUE=DATE-TIME:20220331T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/63
DESCRIPTION:Title: Lower scalar curvature bounds for $C^0$ metrics: a Ricci f
low approach\nby Paula Burkhardt-Guim (NYU) as part of CUNY Geometric
Analysis Seminar\n\nLecture held in CUNY Graduate Center (Room 6495).\n\nA
bstract\n[ATTENTION: THIS TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 6495
\, AND SIMULTANEOUSLY TRANSMITTED VIA ZOOM]\n\nWe describe some recent wor
k that has been done to generalize the notion of lower scalar curvature bo
unds to $C^0$ metrics\, including a localized Ricci flow approach. In part
icular\, we show the following: that there is a Ricci flow definition whic
h is stable under greater-than-second-order perturbation of the metric\, t
hat there exists a reasonable notion of a Ricci flow starting from $C^0$ i
nitial data which is smooth for positive times\, and that the weak lower s
calar curvature bounds are preserved under evolution by the Ricci flow fro
m $C^0$ initial data.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Schwahn (Universitaet Stuttgart)
DTSTART;VALUE=DATE-TIME:20220512T201500Z
DTEND;VALUE=DATE-TIME:20220512T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/64
DESCRIPTION:Title: Stability and rigidity of normal homogeneous Einstein mani
folds\nby Paul Schwahn (Universitaet Stuttgart) as part of CUNY Geomet
ric Analysis Seminar\n\n\nAbstract\n[ATTENTION: THIS TALK WILL BE HELD IN
PERSON AT CUNY GC ROOM 6495\, AND SIMULTANEOUSLY TRANSMITTED VIA ZOOM]\n\n
The stability of an Einstein metric is decided by the (non-)existence of s
mall eigenvalues of the Lichnerowicz Laplacian on tt-tensors. In the homog
eneous setting\, harmonic analysis allows us to approach the computation o
f these eigenvalues. This easy on symmetric spaces\, but considerably more
difficult in the non-symmetric case. I review the case of irreducible sym
metric spaces of compact type\, prove the existence of a non-symmetric sta
ble Einstein metric of positive scalar curvature\, and give an outlook on
how to investigate the normal homogeneous case. Furthermore\, I explore th
e rigidity and infinitesimal deformability of homogeneous Einstein metrics
.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20220908T200000Z
DTEND;VALUE=DATE-TIME:20220908T210000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/65
DESCRIPTION:by TBA as part of CUNY Geometric Analysis Seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhihan Wang (Princeton University)
DTSTART;VALUE=DATE-TIME:20221006T201500Z
DTEND;VALUE=DATE-TIME:20221006T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/66
DESCRIPTION:Title: Translating mean curvature flow with simple ends\nby Z
hihan Wang (Princeton University) as part of CUNY Geometric Analysis Semin
ar\n\n\nAbstract\nTranslators are known as candidates of Type II blow-up m
odel for mean curvature flows. Various examples of mean curvature flow tr
anslators have been constructed in the convex case and semi-graphical case
s\, most of which have either infinite entropy or higher multiplicity asym
ptotics near infinity. In this talk\, we shall present the construction o
f a new family of translators with prescribed end. This is joint work with
Ao Sun.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernani Ribeiro Jr (Universidade Federal do Ceara (Brazil))
DTSTART;VALUE=DATE-TIME:20221020T201500Z
DTEND;VALUE=DATE-TIME:20221020T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/67
DESCRIPTION:Title: On the Hitchin-Thorpe inequality for four-dimensional comp
act Ricci solitons\nby Ernani Ribeiro Jr (Universidade Federal do Cear
a (Brazil)) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6496.\n\nAbstract\nIn this talk\, we will discuss the geometry of 4-dim
ensional compact gradient Ricci solitons. We will show that\, under an upp
er bound condition on the range of the potential function\, a 4-dimensiona
l compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe
inequality. In addition\, some volume estimates will be presented. This i
s joint work with Xu Cheng and Detang Zhou.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Allen (CUNY Lehman College)
DTSTART;VALUE=DATE-TIME:20220915T201500Z
DTEND;VALUE=DATE-TIME:20220915T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/68
DESCRIPTION:Title: Stability of the Positive Mass Theorem under Integral Ricc
i Bounds\nby Brian Allen (CUNY Lehman College) as part of CUNY Geometr
ic Analysis Seminar\n\nLecture held in 6496.\n\nAbstract\n[ATTENTION: THIS
TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 6496\, AND SIMULTANEOUSLY TRA
NSMITTED VIA ZOOM. THIS IS THE FIRST OF TWO TALKS ON THIS DAY.]\n\nRecentl
y\, Bray\, Kazaras\, Khuri\, and Stern have provided a formula relating th
e mass of an asymptotically flat manifold to asymptotically linear harmoni
c functions. This formula has already been used to show Gromov-Hausdorff s
tability of the positive mass theorem under lower bounds on the Ricci curv
ature by Kazaras\, Khuri\, and Lee. We will discuss new results with Bryde
n and Kazaras where we use the mass formula to show quantitative $C^{\\alp
ha}$ stability of the positive mass theorem. We will see that three distin
ct harmonic functions\, which a priori do not provide a global coordinate
system\, under integral Ricci curvature\, Neumann isoperimetric bounds\, a
nd small mass do provide a global coordinate system. We then use this coor
dinate system to control the metric by the mass in the $C^{\\alpha}$ norm.
\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:José M Espinar (Universidad de Cadiz)
DTSTART;VALUE=DATE-TIME:20221013T201500Z
DTEND;VALUE=DATE-TIME:20221013T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/69
DESCRIPTION:Title: On Fraser-Li conjecture with anti-prismatic symmetry and o
ne boundary component\nby José M Espinar (Universidad de Cadiz) as pa
rt of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstr
act\nLet $\\sigma_1$ be the first Steklov eigenvalue on an embedded free b
oundary minimal surface in $B^3$. We show that an embedded free boundary m
inimal 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 Kapo
uleas--Wiygul satisfies a such condition.\n\nThis talk will be held in per
son at CUNY GC and simultaneously transmitted via Zoom.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Petrúcio Cavalcante (Princeton University and Universidade
Federal de Alagoas)
DTSTART;VALUE=DATE-TIME:20221117T211500Z
DTEND;VALUE=DATE-TIME:20221117T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/70
DESCRIPTION:Title: Index bounds for CMC surfaces\nby Marcos Petrúcio Cav
alcante (Princeton University and Universidade Federal de Alagoas) as part
of CUNY Geometric Analysis Seminar\n\nLecture held in 6496.\n\nAbstract\n
Constant mean curvature surfaces are critical points for the area function
al under volume preserving variations. From this variational point of view
\, it is natural to study the index and its relations to the geometry and
topology of these surfaces. In this talk\, I will describe some classical
and new results in this theme\, as well as some open problems.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prosenjit Roy (Indian Institute of Technology Kanpur)
DTSTART;VALUE=DATE-TIME:20220915T211500Z
DTEND;VALUE=DATE-TIME:20220915T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/71
DESCRIPTION:Title: Asymptotic Analysis of Eigenvalue Problems on cylindrical
domains whose length tends to infinity\nby Prosenjit Roy (Indian Insti
tute of Technology Kanpur) as part of CUNY Geometric Analysis Seminar\n\n\
nAbstract\n[ATTENTION: THIS TALK WILL BE HELD IN PERSON AT CUNY GC ROOM 64
96\, AND SIMULTANEOUSLY TRANSMITTED VIA ZOOM. THIS IS THE SECOND OF TWO TA
LKS ON THIS DAY.]\n\nThe primary aim of this talk is to study the asymptot
ic behaviour of eigenvalue problem\, with Neumann boundary conditions on t
he sides and Dirichlet boundary conditions on the lateral part of the cyli
ndrical domain\, as the length of the cylinder goes to infinity. Before di
scussing this problem\, I will present the analysis of analogous problems
for full Dirichlet boundary conditions and some other literature for such
problems.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Bernstein (IAS and Johns Hopkins University)
DTSTART;VALUE=DATE-TIME:20221208T211500Z
DTEND;VALUE=DATE-TIME:20221208T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/72
DESCRIPTION:Title: Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds\nby Jacob Bernstein (IAS and Johns Hopkins University) as part of CUNY
Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nWe dis
cuss a new family of functionals on submanifolds of Cartan-Hadamard manifo
lds that generalize the Colding-Minicozzi entropy of submanifolds of Eucli
dean space. These quantities are monotone under mean curvature flow under
natural conditions. As a consequence\, we obtain sharp lower bounds on th
em for certain closed hypersurfaces and observe a novel rigidity phenomeno
n. This is joint work with A. Bhattacharya.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Demetre Kazaras (Duke University)
DTSTART;VALUE=DATE-TIME:20221027T201500Z
DTEND;VALUE=DATE-TIME:20221027T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/73
DESCRIPTION:Title: The positive mass theorem\, comparison geometry\, and spac
etime harmonic functions\nby Demetre Kazaras (Duke University) as part
of CUNY Geometric Analysis Seminar\n\n\nAbstract\nComparison theorems are
the basis for our geometric understanding of Riemannian manifolds satisfy
ing a given curvature condition. A remarkable example is the Gromov-Lawson
toric band inequality\, which bounds the distance between the two sides o
f a Riemannian torus-cross-interval with positive scalar curvature in term
s of the scalar curvature's minimum. We will give a new qualitative versio
n of this and similar "band-width" type inequalities using the notion of s
pacetime harmonic functions\, which recently played the lead role in a pro
of of the positive mass theorem. Other applications include new versions o
f the Bonnet-Meyer diameter estimate for positive Ricci curvature and Llar
ull's theorem which do not require a completeness assumption. Connections
will be made with minimal surface and spinorial methods. I will also discu
ss the question "How flat is an isolated gravitational system with little
total mass?" and present work which partially addresses questions of Sorma
ni and Gromov.\n\nThis will be an online talk.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Song (Rutgers University)
DTSTART;VALUE=DATE-TIME:20221103T201500Z
DTEND;VALUE=DATE-TIME:20221103T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/74
DESCRIPTION:Title: Diameter estimates in Kähler geometry\nby Jian Song (
Rutgers University) as part of CUNY Geometric Analysis Seminar\n\nLecture
held in GC 6496.\n\nAbstract\nWe establish diameter estimates for Kähler
metrics\, requiring only an entropy bound and no lower bound on the Ricci
curvature. As a consequence\, diameter bounds are obtained for long-time s
olutions of the Kähler-Ricci flow and finite-time solutions when the limi
ting class is big\, as well as for special fibrations of Calabi-Yau manifo
lds.\n\nJoint session with CUNY Nonlinear Analysis and PDEs Seminar\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Henrique Andrade (University of British Columbia / Universid
ade de São Paulo)
DTSTART;VALUE=DATE-TIME:20221201T211500Z
DTEND;VALUE=DATE-TIME:20221201T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/75
DESCRIPTION:Title: Multiplicity of solutions to the multiphasic Allen--Cahn--
Hilliard system with a small volume constraint on closed parallelizable ma
nifolds\nby João Henrique Andrade (University of British Columbia / U
niversidade de São Paulo) as part of CUNY Geometric Analysis Seminar\n\n\
nAbstract\nWe prove the existence of multiple solutions to the Allen--Cahn
--Hilliard (ACH) vectorial equation (with two equations) involving a tripl
e-well (triphasic) potential with a small volume constraint on a closed pa
rallelizable Riemannian manifold.\nMore precisely\, we find a lower bound
for the number of solutions depending on some topological invariants of th
e underlying manifold. The phase transition potential is considered to hav
e a finite set of global minima\, where it also vanishes\, and a subcritic
al growth at infinity. Our strategy is to employ the Lusternik--Schnirelma
nn and infinite-dimensional Morse theories for the vectorial energy functi
onal. To this end\, we exploit that the associated ACH energy $\\Gamma$-co
nverges to the weighted multi-perimeter for clusters\, which combined with
some deep theorems from isoperimetric theory yields the suitable setup to
apply the photography method. Along the way\, the lack of a closed analyt
ic expression for the multi-isoperimetric function for clusters imposes a
delicate issue. Furthermore\, using a transversality theorem\, we also sho
w the genericity of the set of metrics for which solutions to the ACH syst
em are nondegenerate.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Nardulli (Universidad Federal do ABC)
DTSTART;VALUE=DATE-TIME:20221110T211500Z
DTEND;VALUE=DATE-TIME:20221110T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/76
DESCRIPTION:Title: Lusternik-Schnirelman and Morse Theory for the Van der Waa
ls-Cahn-Hilliard equation with volume constraint\nby Stefano Nardulli
(Universidad Federal do ABC) as part of CUNY Geometric Analysis Seminar\n\
n\nAbstract\nWe give a multiplicity result for solutions of the Van der Wa
als-Cahn-Hilliard two phase transition equation with volume constraints on
a closed Riemannian manifold. Our proof employs some results from the cla
ssical Lusternik–Schnirelman and Morse theory\, together with a techniqu
e\, the so-called photography method\, which allows us to obtain lower bou
nds on the number of solutions in terms of topological invariants of the u
nderlying manifold. The setup for the photography method employs recent re
sults from Riemannian isoperimetry for small volumes. This is joint work w
ith Vieri Benci\, Luis Eduardo Osorio Acevedo\, Paolo Piccione.\n\nJoint s
ession with CUNY Nonlinear Analysis and PDEs Seminar.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conghan Dong (Stony Brook)
DTSTART;VALUE=DATE-TIME:20230209T211500Z
DTEND;VALUE=DATE-TIME:20230209T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/77
DESCRIPTION:Title: Stability of the Euclidean 3-space for the positive mass t
heorem\nby Conghan Dong (Stony Brook) as part of CUNY Geometric Analys
is Seminar\n\n\nAbstract\nThe Positive Mass Theorem of R. Schoen and S.-T.
Yau in dimension 3 states that if $(M^3\, g)$ is asymptotically flat and
has nonnegative scalar curvature\, then its ADM mass $m(g)$ satisfies $m(g
) \\geq 0$\, and equality holds only when $(M\, g)$ is the flat Euclidean
3-space $\\mathbb{R}^3$. We show that $\\mathbb{R}^3$ is stable in the fol
lowing sense. Let $(M^3_i\, g_i)$ be a sequence of asymptotically flat 3-m
anifolds with nonnegative scalar curvature and suppose that $m(g_i)$ conve
rges to 0. Then for all i\, there is a subset $Z_i$ in $M_i$ such that the
area of the boundary $\\partial Z_i$ converges to zero and the sequence $
(M_i \\setminus Z_i \, \\hat{d}_{g_i} \, p_i )$\, with induced length metr
ic $\\hat{d}_{g_i}$ and any base point $p_i \\in M_i \\setminus Z_i$\, con
verges to $\\mathbb{R}^3$ in the pointed measured Gromov-Hausdorff topolog
y. This confirms a conjecture of G. Huisken and T. Ilmanen. We also find a
n 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://researchseminars.org/talk/CUNY_GeometricAnalysis/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiewon Park (Yale University)
DTSTART;VALUE=DATE-TIME:20230323T201500Z
DTEND;VALUE=DATE-TIME:20230323T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/78
DESCRIPTION:Title: A Compactness Theorem for Rotationally Symmetric Riemannia
n Manifolds with Positive Scalar Curvature\nby Jiewon Park (Yale Unive
rsity) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 64
96.\n\nAbstract\nIt is a conjecture of Gromov and Sormani that sequences o
f compact Riemannian manifolds with nonnegative scalar curvature and area
of minimal surfaces bounded below should have subsequences which converge
in the intrinsic flat sense to limit spaces which have nonnegative general
ized scalar curvature and Euclidean tangent cones almost everywhere. In th
is talk I will present a joint work with Wenchuan Tian and Changliang Wang
\, where we proved this conjecture for rotationally symmetric manifolds.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Mendes (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20230316T201500Z
DTEND;VALUE=DATE-TIME:20230316T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/79
DESCRIPTION:Title: A Weyl Law for singular Riemannian foliations\nby Rica
rdo Mendes (University of Oklahoma) as part of CUNY Geometric Analysis Sem
inar\n\nLecture held in GC 6496.\n\nAbstract\nA classic version of the Wey
l Law describes the asymptotic behavior of the eigenvalues of the Laplace
operator on a closed Riemannian manifold $M$ in terms of its dimension and
volume. In the 1970's\, Donnelly and Bruenning--Heintze established a ver
sion when a compact group $G$ acts on $M$ by isometries: the rate of growt
h of eigenvalues associated to $G$-invariant eigenfunctions is controlled
by the dimension and volume of the orbit space $M/G$. I will describe a ge
neralization where the decomposition of $M$ into $G$-orbits is replaced wi
th a singular Riemannian foliation. This is based on joint work-in-progres
s with Marco Radeschi and Samuel Lin.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lawrence Mouillé
DTSTART;VALUE=DATE-TIME:20230223T211500Z
DTEND;VALUE=DATE-TIME:20230223T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/80
DESCRIPTION:Title: Positive intermediate Ricci curvature with maximal symmetr
y rank\nby Lawrence Mouillé as part of CUNY Geometric Analysis Semina
r\n\nLecture held in GC 6496.\n\nAbstract\nPositive $k$th-intermediate Ric
ci curvature is a condition on an $n$-manifold that interpolates between p
ositive sectional curvature ($k = 1$) and positive Ricci curvature ($k = n
- 1$). In a foundational result for the study of closed manifolds with po
sitive sectional curvature and large isometry group\, Grove and Searle cla
ssified 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 thi
s rigidity result to manifolds with positive 2nd-intermediate Ricci curvat
ure. The exceptional cases are dimension 4\, in which we rule out several
candidates using a Frankel-type argument\, and dimension 6\, in which it i
s known that a product of 3-spheres admits a metric with positive 2nd-inte
rmediate Ricci curvature and maximal symmetry rank. This talk is based on
joint work with Lee Kennard.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART;VALUE=DATE-TIME:20230420T201500Z
DTEND;VALUE=DATE-TIME:20230420T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/81
DESCRIPTION:Title: Minimal Surfaces in Hyperbolic 3-manifolds\nby Baris C
oskunuzer (UT Dallas) as part of CUNY Geometric Analysis Seminar\n\n\nAbst
ract\nIn this talk\, we will show the existence of smoothly embedded close
d minimal surfaces in infinite volume hyperbolic 3-manifolds. The talk wil
l be non-technical\, and accessible to graduate students.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Florian Johne (Columbia University)
DTSTART;VALUE=DATE-TIME:20230216T211500Z
DTEND;VALUE=DATE-TIME:20230216T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/82
DESCRIPTION:Title: A generalization of Geroch's conjecture\nby Florian Jo
hne (Columbia University) as part of CUNY Geometric Analysis Seminar\n\nLe
cture held in 6496.\n\nAbstract\nClosed manifolds with topology $N = M \\t
imes S^1$ do not admit metrics of positive Ricci curvature by the theorem
of Bonnet-Myers\, while the the resolution of the Geroch conjecture implie
s that the torus $T^n$ does not admit a metric of positive scalar curvatur
e. In this talk we explain a non-existence result for metrics of positive
m-intermediate curvature (a notion of curvature reducing to Ricci curvatu
re for $m = 1$\, and scalar curvature for $m = n-1$) on closed manifolds w
ith topology $N^n = M^{n-m} \\times T^m$ for $n \\leq 7$. Our proof uses
minimization of weighted areas\, the associated stability inequality\, and
delicate estimates on the second fundamental form. This is joint work wit
h Simon Brendle and Sven Hirsch\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hunter Stufflebeam (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20230309T211500Z
DTEND;VALUE=DATE-TIME:20230309T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/83
DESCRIPTION:Title: Stability of Convex Disks\nby Hunter Stufflebeam (Univ
ersity of Pennsylvania) as part of CUNY Geometric Analysis Seminar\n\nLect
ure held in GC 6496.\n\nAbstract\nWe prove that topological disks with pos
itive curvature and strictly convex boundary of large length are close to
round spherical caps of constant boundary curvature in the Gromov-Hausdorf
f and Sormani-Wenger Intrinsic Flat senses. This proves stability for a th
eorem of F. Hang and X. Wang.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eris Runa (Gran Sasso Science Institute\, L’Aquila)
DTSTART;VALUE=DATE-TIME:20230216T223000Z
DTEND;VALUE=DATE-TIME:20230216T233000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/85
DESCRIPTION:Title: Energy driven pattern formation for local/non-local system
s\nby Eris Runa (Gran Sasso Science Institute\, L’Aquila) as part of
CUNY Geometric Analysis Seminar\n\n\nAbstract\nIn this talk we will consi
der a class of local/nonlocal interaction functionals motivated by the phy
sics literature. The functionals contain a local term which penalizes inte
rfaces\, and a non-local term which favors oscillations. The equilibrium b
etween these two terms is expected to result in\nthe emergence of pattern
formation. We will show that minimizers are periodic stripes and in partic
ular that the functional exhibits the phenomenon of symmetry breaking.\n\n
This talk is presented jointly with the Nonlinear Analysis and PDEs Semina
r.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jackson Goodman (UC Berkeley)
DTSTART;VALUE=DATE-TIME:20230330T201500Z
DTEND;VALUE=DATE-TIME:20230330T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
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\nAbs
tract\nWe give new conditions on positivity of certain linear combinations
of eigenvalues of the curvature operator of a Riemannian manifold which i
mply the vanishing of the indices of Dirac operators twisted with bundles
of tensors. The vanishing indices in turn have topological implications in
terms of the Pontryagin classes\, rational cobordism type\, and Witten ge
nus of the manifolds. To prove our results we generalize new methods devel
oped by Petersen and Wink to apply the Bochner technique to Laplacians on
bundles of tensors. This is joint work with Renato Bettiol.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Lejmi (Bronx Community College)
DTSTART;VALUE=DATE-TIME:20230309T223000Z
DTEND;VALUE=DATE-TIME:20230309T233000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/87
DESCRIPTION:Title: Special metrics in almost-Hermitian geometry\nby Mehdi
Lejmi (Bronx Community College) as part of CUNY Geometric Analysis Semina
r\n\nLecture held in GC 6496.\n\nAbstract\nIn this talk\, we discuss the e
xistence of some canonical metrics on compact almost-Hermitian manifolds.
For example\, we study an analogue of the Yamabe problem in Hermitian geom
etry. We also discuss Einstein-like metrics in Hermitian geometry.\n\nThis
talk is presented jointly with the Nonlinear Analysis and PDEs Seminar.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Sweeney (Stony Brook)
DTSTART;VALUE=DATE-TIME:20230511T201500Z
DTEND;VALUE=DATE-TIME:20230511T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/88
DESCRIPTION:Title: Examples for Scalar Sphere Stability\nby Paul Sweeney
(Stony Brook) as part of CUNY Geometric Analysis Seminar\n\n\nAbstract\nTw
o different ways scalar curvature can characterize the sphere are describe
d by the rigidity theorems of Llarull and of Marques-Neves. Associated wit
h these rigidity theorems are two stability conjectures. In this talk\, we
will produce examples related to these stability conjectures. The first s
et of examples demonstrates the necessity of including a condition on the
minimum area of all minimal surfaces to prevent bubbling along the sequenc
e. The second set of examples are sequences that do not converge in the Gr
omov-Hausdorff sense but do converge in the volume-preserving intrinsic fl
at sense. In order to construct such sequences\, we improve the Gromov-Law
son tunnel construction so that one can attach wells and tunnels to a mani
fold with scalar curvature bounded below and only decrease the scalar curv
ature by an arbitrarily small amount. This allows a generalization of othe
r examples that use tunnels such as the sewing construction of Basilio\, D
odziuk\, and Sormani\, and the construction due to Basilio\, Kazaras\, and
Sormani of an intrinsic flat limit with no geodesics.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Mira (Universidad Politecnica de Cartagena)
DTSTART;VALUE=DATE-TIME:20230420T213000Z
DTEND;VALUE=DATE-TIME:20230420T223000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/89
DESCRIPTION:Title: Minimal annuli with free boundary in the unit ball\nby
Pablo Mira (Universidad Politecnica de Cartagena) as part of CUNY Geometr
ic Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn this 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 than the c
ritical 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 discus
s several open problems. We will also show how our method produces embedde
d capillary minimal annuli in the unit ball that are not rotational\, thus
solving a problem by Wente (1995). Joint work with Isabel Fernandez and L
aurent Hauswirth.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Wang (Stony Brook)
DTSTART;VALUE=DATE-TIME:20230427T201500Z
DTEND;VALUE=DATE-TIME:20230427T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/90
DESCRIPTION:Title: Topology of complete $3$-manifolds with uniformly positive
scalar curvature\nby Jian Wang (Stony Brook) as part of CUNY Geometri
c Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nA well-known q
uestion posed by S.T. Yau is how to classify 3-manifolds admitting a comp
lete metric with (uniformly) positive scalar curvature up to diffeomorphis
m. It was resolved by G.Perelman for closed $3$-manifolds. However\, the n
on-compact case is complicated. In this talk\, I will give a complete topo
logical characterization for complete open $3$-manifolds with uniformly po
sitive scalar curvature. Furthermore\, we will talk about its generalizati
on for $3$-manifolds with boundaries.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niels Moller (University of Copenhagen)
DTSTART;VALUE=DATE-TIME:20230921T201500Z
DTEND;VALUE=DATE-TIME:20230921T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/91
DESCRIPTION:Title: Rigidity of the grim reaper cylinder as a collapsed self-t
ranslating soliton\nby Niels Moller (University of Copenhagen) as part
of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstrac
t\nMean curvature flow self-translating solitons are minimal hypersurfaces
for a certain incomplete conformal background metric\, and are among the
possible singularity models for the flow. In the collapsed case\, they are
confined to slabs in space. The simplest non-trivial such example\, the g
rim reaper curve $\\Gamma$ in $\\mathbb{R}^2$\, has been known since 1956\
, as an explicit ODE-solution\, which also easily gave its uniqueness.\n\n
We consider here the case of surfaces\, where the rigidity result for $\\G
amma\\times\\mathbb{R}$ that we'll show is:\nThe grim reaper cylinder is t
he unique (up to rigid motions) finite entropy unit speed self-translating
surface which has width equal to $\\pi$ and is bounded from below. (Joint
w/ Impera & Rimoldi.)\n\nTime permitting\, we'll also discuss recent uniq
ueness results in the collapsed simply-connected low entropy case (joint w
/ Gama & Martín)\, using Morse theory and nodal set techniques\, which ex
tend Chini's classification.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sven Hirsch (IAS)
DTSTART;VALUE=DATE-TIME:20230914T201500Z
DTEND;VALUE=DATE-TIME:20230914T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/93
DESCRIPTION:Title: Hawking mass monotonicity for initial data sets\nby Sv
en Hirsch (IAS) as part of CUNY Geometric Analysis Seminar\n\nLecture held
in GC 6496.\n\nAbstract\nAn interesting feature of General Relativity is
the presence of singularities which can occur in even the simplest example
s such as the Schwarzschild spacetime. However\, in this case the singular
ity is cloaked behind the event horizon of the black hole which has been c
onjectured to be generically the case. To analyze this so-called Cosmic Ce
nsorship Conjecture\, Roger Penrose proposed in 1973 a test which involves
Hawking's area theorem\, the final state conjecture and a geometric inequ
ality on initial data sets $(M\,g\,k)$. For $k=0$ this so-called Penrose i
nequality has been proven by Gerhard Huisken and Tom Ilmanen via inverse m
ean curvature flow and by Hubert Bray using the conformal flow\, but in ge
neral the question is wide open. We will present several approaches to gen
eralize the Hawking mass monotonicity formula to arbitrary initial data se
ts including a new one based on double null foliations. For this purpose\,
we start with recalling spacetime harmonic functions and their applicatio
ns which have been introduced together with Demetre Kazaras and Marcus Khu
ri in the context of the spacetime positive mass theorem.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Nikolayevsky (La Trobe University)
DTSTART;VALUE=DATE-TIME:20230907T201500Z
DTEND;VALUE=DATE-TIME:20230907T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/94
DESCRIPTION:Title: Einstein hypersurfaces in irreducible symmetric spaces
\nby Yuri Nikolayevsky (La Trobe University) as part of CUNY Geometric Ana
lysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn this talk\, I wi
ll present the results of a joint paper of Jeong Hyeong Park and myself in
which we give a classification of Einstein hypersurfaces in irreducible s
ymmetric spaces. The main theorem states that there are three classes of s
uch hypersurfaces\, belonging to three different geometries: homogeneous g
eometry (for Einstein hypersurfaces in noncompact symmetric spaces)\, Lege
ndrian geometry (Einstein hypersurfaces in SU(3)/SO(3) and affine geometry
(Einstein hypersurfaces in SL(3)/SO(3)).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Tony (WWU Muenster)
DTSTART;VALUE=DATE-TIME:20231130T211500Z
DTEND;VALUE=DATE-TIME:20231130T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/95
DESCRIPTION:Title: Scalar curvature comparison geometry and the higher mappin
g degree\nby Thomas Tony (WWU Muenster) as part of CUNY Geometric Anal
ysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nLlarull proved in th
e late '90s that the round $n$-sphere is area-extremal in the sense that o
ne cannot increase the scalar curvature and the metric simultaneously. Goe
tte and Semmelmann generalized Llarull's work and proved an extremality an
d rigidity statement for area-non-increasing spin maps $f\\colon M\\to N$
of non-zero $\\hat{A}$-degree between two closed connected oriented Rieman
nian manifolds.\n\nIn this talk\, I will extend this classical result to m
aps between not necessarily orientable manifolds and replace the topologic
al condition on the $\\hat{A}$-degree with a less restrictive condition in
volving the so-called higher mapping degree. For that purpose\, I will fir
st present an index formula connecting the higher mapping degree and the E
uler characteristic of $N$ with the index of a certain Dirac operator line
ar over a $\\mathrm{C}^\\ast$-algebra. Second\, I will use this index form
ula to show that the topological assumptions\, together with our extremal
geometric situation\, give rise to a family of almost constant sections th
at can be used to deduce the extremality and rigidity statements.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brian Harvie (National Taiwan University)
DTSTART;VALUE=DATE-TIME:20231116T211500Z
DTEND;VALUE=DATE-TIME:20231116T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/96
DESCRIPTION:Title: The equality case of the static Minkowski inequality and a
pplications\nby Brian Harvie (National Taiwan University) as part of C
UNY Geometric Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nAs
ymptotically flat static spaces are Riemannian manifolds that correspond t
o static vacuum spacetimes in general relativity. The most important examp
le is the Schwarzschild space\, a rotationally symmetric Riemannian manifo
ld corresponding to the Schwarzschild spacetime. A number of important que
stions about the uniqueness of the Schwarzschild spacetime may be posed as
rigidity questions for AF static spaces. These include the famous static
black hole uniqueness theorems of Israel and Bunting/Masood-ul-Alam as wel
l as the more recent uniqueness theorems for static spacetimes containing
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 static space
s. Like the Minkowski inequality for convex hypersurfaces in Euclidean spa
ce\, this inequality gives a bound from below on the total mean curvature
of the boundary of the manifold. First\, I will characterize rigidity with
in this inequality\, showing under suitable boundary assumptions that the
equality is achieved only by rotationally symmetric regions of Schwarzschi
ld space. As an application\, I will show uniqueness of suitably-defined s
tatic metric extensions for the Bartnik data of Schwarzschild coordinate s
pheres. This talk is based on joint work with Ye-Kai Wang of NYCU.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfgang Ziller (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20231026T201500Z
DTEND;VALUE=DATE-TIME:20231026T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/97
DESCRIPTION:Title: Hypersurfaces with constant Ricci curvature\nby Wolfga
ng Ziller (University of Pennsylvania) as part of CUNY Geometric Analysis
Seminar\n\nLecture held in GC 6496.\n\nAbstract\nWe will talk about a clas
sification of hypersurfaces in $S^4(1)$ and $H^4$ with the property that t
he eigenvalues of the Ricci curvature are constant (and hence the curvatur
e tensor is “constant"). They can be described as the embedding of a sur
face\, which is algebraic (with singularities).\n \nThis is joint work wit
h Robert Bryant and Luis Florit.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Skorobogatova (Princeton University)
DTSTART;VALUE=DATE-TIME:20231109T211500Z
DTEND;VALUE=DATE-TIME:20231109T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/98
DESCRIPTION:Title: Higher codimension area-minimizers: structure of singulari
ties and uniqueness of tangent cones\nby Anna Skorobogatova (Princeton
University) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6496.\n\nAbstract\nThe problem of determining the size and structure o
f the interior singular set of area-minimizing surfaces has been studied t
horoughly in a number of different frameworks\, with many ground-breaking
contributions. In the framework of integral currents\, when the codimensio
n of the surface is higher than 1\, the presence of singular points with f
lat tangent cones creates an obstruction to easily understanding the inter
ior singularities. Little progress has been made in full generality since
Almgren’s celebrated $(m-2)$-Hausdorff dimension bound on the singular s
et for an $m$-dimensional area-minimizing integral current\, which was sin
ce revisited and simplified by De Lellis and Spadaro.\n\nIn this talk I wi
ll discuss recent joint works with Camillo De Lellis and Paul Minter\, whe
re 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://researchseminars.org/talk/CUNY_GeometricAnalysis/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jingbo Wan (Columbia University)
DTSTART;VALUE=DATE-TIME:20230928T201500Z
DTEND;VALUE=DATE-TIME:20230928T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/99
DESCRIPTION:Title: Rigidity of contracting maps using harmonic map heat flow<
/a>\nby Jingbo Wan (Columbia University) as part of CUNY Geometric Analysi
s Seminar\n\nLecture held in GC 6496.\n\nAbstract\nIn this talk\, we are g
oing to consider the rigidity of map between positively curved closed mani
folds\, which is motivated by the recent work of Tsai-Tsui-Wang. We show t
hat distance non-increasing map between complex projective spaces is eithe
r an isometry or homotopically trivial. The rigidity result also holds on
a wider class of manifolds with positive curvature and weaker contracting
property on the map in between distance non-increasing and area non-increa
sing. 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-C
hun Lee in CUHK.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Santiago Cordero Misteli (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20231019T201500Z
DTEND;VALUE=DATE-TIME:20231019T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/100
DESCRIPTION:Title: Morse index bounds for free boundary minimal hypersurface
s through covering arguments\nby Santiago Cordero Misteli (Stony Brook
University) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6496.\n\nAbstract\nHow complicated can a minimal surface be? This ques
tion has led to interesting discoveries about the relationships between va
rious notions of complexity. In this context\, an important open question
is the Schoen conjecture\, which roughly says that the Morse index dominat
es the topology. This conjecture has been established in certain cases und
er some assumptions on the ambient curvature. In 2019\, Antoine Song intro
duced a novel approach to prove a similar bound on the Betti numbers in te
rms of the Morse index. This new proof doesn't impose any ambient curvatur
e assumptions but requires a control on the area. In this talk I will expl
ain joint work with Giada Franz\, where we generalize Song's approach to p
rove a similar statement for free boundary minimal hypersurfaces.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dongyeong Ko (Rutgers University)
DTSTART;VALUE=DATE-TIME:20231012T201500Z
DTEND;VALUE=DATE-TIME:20231012T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/102
DESCRIPTION:Title: Capillary and Free boundary embedded geodesics on Riemann
ian 2-disks with a strictly convex boundary\nby Dongyeong Ko (Rutgers
University) as part of CUNY Geometric Analysis Seminar\n\nLecture held in
GC 6496.\n\nAbstract\nThe existence of embedded geodesics on surfaces is a
foundational problem. I will explain the existence of two capillary embed
ded geodesics on Riemannian 2-disks with a strictly convex boundary with a
certain condition via a multi-parameter min-max construction. I will then
explain the existence of two free boundary embedded geodesics on Riemanni
an 2-disks with a strictly convex boundary by free boundary curve shorteni
ng flow on surfaces\, which is a free boundary analog of Grayson’s theor
em of 1989. Finally\, I will explain the Morse Index bound of such geodesi
cs.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Hanke (Universitaet Augsburg)
DTSTART;VALUE=DATE-TIME:20231207T223000Z
DTEND;VALUE=DATE-TIME:20231207T233000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/103
DESCRIPTION:Title: New developments in the scalar curvature rigidity of sphe
res\nby Bernhard Hanke (Universitaet Augsburg) as part of CUNY Geometr
ic Analysis Seminar\n\nLecture held in GC 6496.\n\nAbstract\nLower scalar
curvature bounds on spin Riemannian manifolds exhibit remarkable extremali
ty and rigidity phenomena determined by spectral properties of Dirac opera
tors. For example\, a fundamental result of Llarull states that there is n
o smooth Riemannian metric on the n-sphere which dominates the round metri
c and whose scalar curvature is greater than or equal to the scalar curvat
ure of the round metric\, except for the round metric itself. A similar re
sult holds for smooth comparison maps from spin Riemannian manifolds to ro
und spheres. \n\nAnswering questions posed by Gromov in his "Four Lecture
s"\, we generalize these results in two directions: First\, to Riemannian
metrics with regularity less than $C^1$ and Lipschitz comparison maps\, an
d second\, to spheres with two antipodal points removed. This is joint wor
k with Cecchini-Schick and with Bär-Brendle-Wang\, respectively.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ao Sun (Lehigh University)
DTSTART;VALUE=DATE-TIME:20240307T211500Z
DTEND;VALUE=DATE-TIME:20240307T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/104
DESCRIPTION:Title: Interpolation method in mean curvature flow\nby Ao Su
n (Lehigh University) as part of CUNY Geometric Analysis Seminar\n\nLectur
e held in GC 6417.\n\nAbstract\nThe interpolation method is a very powerfu
l tool to construct special solutions in geometric analysis. I will presen
t two applications in mean curvature flow: one is constructing a new genus
one self-shrinking mean curvature flow\, and another one is constructing
immortal mean curvature flow with higher multiplicity convergence. The tal
k is based on joint work with Adrian Chu (UChicago) and joint work with Ji
ngwen Chen (UPenn).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doug Stryker (Princeton University)
DTSTART;VALUE=DATE-TIME:20240314T201500Z
DTEND;VALUE=DATE-TIME:20240314T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/105
DESCRIPTION:Title: Stable minimal hypersurfaces in $\\mathbb R^5$\nby Do
ug Stryker (Princeton University) as part of CUNY Geometric Analysis Semin
ar\n\nLecture held in GC 6417.\n\nAbstract\nI will discuss why every compl
ete two-sided stable minimal hypersurface in $\\mathbb R^5$ is flat\, base
d on joint work with Otis Chodosh\, Chao Li\, and Paul Minter.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Sarnataro (Princeton University)
DTSTART;VALUE=DATE-TIME:20240314T213000Z
DTEND;VALUE=DATE-TIME:20240314T223000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/106
DESCRIPTION:Title: The Allen—Cahn equation and free boundary minimal surfa
ces\nby Lorenzo Sarnataro (Princeton University) as part of CUNY Geome
tric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nIn recent y
ears\, the combined work of Guaraco\, Hutchinson\, Tonegawa\, and Wickrama
sekera have established a min-max construction of minimal hypersurfaces in
closed Riemannian manifolds\, based on the analysis of singular limits of
sequences of solutions of the Allen—Cahn equation\, a semi-linear ellip
tic equation arising in the theory of phase transitions. In this talk\, I
will describe some recent boundary regularity results for such limit-inter
faces\, which provide the first step towards an Allen—Cahn min-max const
ruction of free boundary minimal hypersurfaces in Riemannian manifolds wit
h boundary. \nThis is based on joint work with Martin Li (CUHK) and Davide
Parise (UCSD).\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Martin (Universidad de Granada)
DTSTART;VALUE=DATE-TIME:20240418T201500Z
DTEND;VALUE=DATE-TIME:20240418T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/107
DESCRIPTION:Title: Some new examples of translating solitons for the mean cu
rvature flow: Annuloids and Delta-wings\nby Francisco Martin (Universi
dad de Granada) as part of CUNY Geometric Analysis Seminar\n\nLecture held
in GC 6417.\n\nAbstract\nIn this presentation\, we shall describe new ann
ular examples of complete translating solitons for the mean curvature flow
and how they are related to a family of translating graphs\, the Delta-wi
ngs. In addition\, we will prove some related results that answer question
s that arise naturally in this investigation. These results apply to trans
lators in general\, not just to graphs or annuli. This is a joint work wit
h David Hoffman and Brian White.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lu Wang (Yale University)
DTSTART;VALUE=DATE-TIME:20240321T201500Z
DTEND;VALUE=DATE-TIME:20240321T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/108
DESCRIPTION:Title: A mean curvature flow approach to density of minimal cone
s\nby Lu Wang (Yale University) as part of CUNY Geometric Analysis Sem
inar\n\nLecture held in GC 6417.\n\nAbstract\nMinimal cones are models for
singularities in minimal submanifolds\, as well as stationary solutions t
o the mean curvature flow. In this talk\, I will explain how to utilize me
an curvature flow to yield near optimal estimates on density of topologica
lly nontrivial minimal cones. This is joint with Jacob Bernstein.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tin Yau Tsang (NYU)
DTSTART;VALUE=DATE-TIME:20240229T211500Z
DTEND;VALUE=DATE-TIME:20240229T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/109
DESCRIPTION:Title: Another aspect of Gromov's conjectures\nby Tin Yau Ts
ang (NYU) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC
6417.\n\nAbstract\nIn this talk\, we will discuss some of Gromov's conjec
tures on scalar curvature from the perspective of general relativity\, in
particular their partial solutions by the positive mass theorem.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Giorgi (Columbia University)
DTSTART;VALUE=DATE-TIME:20240215T211500Z
DTEND;VALUE=DATE-TIME:20240215T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/110
DESCRIPTION:Title: The nonlinear stability of black holes: an overview\n
by Elena Giorgi (Columbia University) as part of CUNY Geometric Analysis S
eminar\n\nLecture held in GC 6417.\n\nAbstract\nBlack holes are the most s
triking predictions of General Relativity and are by now understood to be
fundamental objects in our universe. In this colloquium talk\, I will prov
ide an overview of their mathematical properties\, in particular concernin
g 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://researchseminars.org/talk/CUNY_GeometricAnalysis/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Piccione (Universidade de Sao Paulo)
DTSTART;VALUE=DATE-TIME:20240328T201500Z
DTEND;VALUE=DATE-TIME:20240328T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/111
DESCRIPTION:Title: A multiplicity result for solutions of Yamabe-type proble
ms\nby Paolo Piccione (Universidade de Sao Paulo) as part of CUNY Geom
etric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI will dis
cuss a general nonuniqueness result for conformally variational invariants
on the universal cover of closed Riemannian manifolds whose fundamental g
roup has infinite profinite completion. This is based on works in collabor
ation with R. Bettiol\, J. H. Andrade\, J. Case and J. Wei.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Ratzkin (Universität Würzburg)
DTSTART;VALUE=DATE-TIME:20240328T213000Z
DTEND;VALUE=DATE-TIME:20240328T223000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/113
DESCRIPTION:Title: Stability estimates for the total Q-curvature functional<
/a>\nby Jesse Ratzkin (Universität Würzburg) as part of CUNY Geometric A
nalysis Seminar\n\nLecture held in GC 6417.\n\nAbstract\nI will discuss st
ability estimates for metrics close to those minimizing the total Q-curvat
ure functional on compact manifolds\, generalizing previous stability esti
mates for the classical Sobolev inequality due to Bianchi and Egnell and s
tability of minimizing Yamabe metrics\, due to Engelstein\, Neumeyer and S
polaor. Generically\, the distance to the set of minimizing metrics is con
trolled by the square of the Q-curvature deficit. We are also able to char
acterize some examples where this distance is controlled by a higher power
of the Q-curvature deficit\, and I will discuss these examples in some de
tail. This is joint work with Joāo Henrique Andrade\, Tobias König and J
uncheng Wei.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Pérez-Ayala (Princeton University)
DTSTART;VALUE=DATE-TIME:20240208T211500Z
DTEND;VALUE=DATE-TIME:20240208T221500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/114
DESCRIPTION:Title: Extremal Eigenvalues for the Paneitz Operator in 4-Dimens
ional Manifolds\nby Samuel Pérez-Ayala (Princeton University) as part
of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.\n\nAbstrac
t\nOn any closed Riemannian manifold\, we can consider the Laplace-Beltram
i operator together with its sequence of eigenvalues. As the metric is var
ied conformally\, the eigenvalues change\, leading to a natural variationa
l problem of finding conformal metrics that extremize a specific eigenvalu
e under a volume constraint. A beautiful observation by Nadirashvili says
that these special extremal metrics are in correspondence with th
e existence of harmonic maps into higher dimensional spheres. In this talk
\, I will explain a similar connection for the Paneitz operator in four ma
nifolds and conformal-harmonic maps. Additionally\, I will report in some
recent work with A.Chang and M.Gursky\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jianxiong Wang (University of Connecticut)
DTSTART;VALUE=DATE-TIME:20240418T213000Z
DTEND;VALUE=DATE-TIME:20240418T223000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/115
DESCRIPTION:Title: Higher order conformal equations on hyperbolic spaces and
the symmetry of solutions\nby Jianxiong Wang (University of Connectic
ut) as part of CUNY Geometric Analysis Seminar\n\nLecture held in GC 6417.
\n\nAbstract\nThe classification of solutions for semilinear PDEs\, as wel
l as the classification of critical points of the corresponding functional
s\, have wide applications in the study of partial differential equations
and differential geometry. The classical moving plane method and the movin
g sphere method in Euclidean space provide an effective approach to captur
ing the symmetry of solutions. In this talk\, we develop a moving sphere a
pproach for integral equations in the hyperbolic space\, to obtain the sym
metry property as well as a characterization result towards positive solut
ions for nonlinear problems involving the GJMS operators (a generalization
of the Paneitz operator). Our methods also rely on Helgason-Fourier analy
sis and Hardy-Littlewood-Sobolev inequalities on hyperbolic spaces togethe
r with a Kelvin transform.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marina Ville (CNRS\, Université Paris-Est Créteil)
DTSTART;VALUE=DATE-TIME:20240411T201500Z
DTEND;VALUE=DATE-TIME:20240411T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/116
DESCRIPTION:Title: Branched surfaces in 4-manifolds\nby Marina Ville (CN
RS\, Université Paris-Est Créteil) as part of CUNY Geometric Analysis Se
minar\n\nLecture held in GC 6417.\n\nAbstract\nIn the 1980s\, geometers st
udied the twistor degree of a surface $S$ in a 4-manifold $M$\, given by t
he sum of its tangent and normal bundles\, $TS$ and $NS$. A question arose
: if a sequence $(S_n)$ of immersed surfaces in $M$ degenerates into a bra
nched surface $S_0$\, how do the twistors degree of $S_0$ compare with tho
se of the $S_n$'s? I go back to this problem and treat it locally around a
branch point $p$ of $S_0$. It means comparing the amount of curvatures of
$TS_n$ and $NS_n$ which concentrate close to $p$ when $n$ tends to infini
ty. I approach this question with topological tools (braids) rather than a
nalytic ones and I give a few cases where an extra assumption\, either geo
metrical or topological\, allows to get some answers.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Liam Mazurowski (Cornell University)
DTSTART;VALUE=DATE-TIME:20240509T201500Z
DTEND;VALUE=DATE-TIME:20240509T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/117
DESCRIPTION:Title: Stability for the Yamabe Invariant of S^3\nby Liam Ma
zurowski (Cornell University) as part of CUNY Geometric Analysis Seminar\n
\nLecture held in GC 6417.\n\nAbstract\nThe Yamabe problem asks whether ev
ery closed Riemannian manifold admits a conformal metric with constant sca
lar curvature. The Yamabe problem has been fully resolved in the affirmati
ve by the work of Yamabe\, Trudinger\, Aubin\, and Schoen. The resolution
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 most that
of the round sphere with the same volume. Moreover\, if equality holds the
n (M^n\,g) is conformal to a round sphere. It is natural to investigate t
he stability of this inequality. In this talk\, we will show that if the t
otal scalar curvature of (S^3\,g) is close to that of the round 3-sphere w
ith the same volume\, then some metric in the conformal class of g is clos
e to round in a certain sense. This is joint work with Xuan Yao.\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Junming Xie (Rutgers University)
DTSTART;VALUE=DATE-TIME:20240912T201500Z
DTEND;VALUE=DATE-TIME:20240912T211500Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/118
DESCRIPTION:by Junming Xie (Rutgers University) as part of CUNY Geometric
Analysis Seminar\n\nLecture held in GC 6417.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernd Kawohl (University of Cologne)
DTSTART;VALUE=DATE-TIME:20240912T213000Z
DTEND;VALUE=DATE-TIME:20240912T223000Z
DTSTAMP;VALUE=DATE-TIME:20240530T031429Z
UID:CUNY_GeometricAnalysis/119
DESCRIPTION:by Bernd Kawohl (University of Cologne) as part of CUNY Geomet
ric Analysis Seminar\n\nLecture held in GC 6417.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/CUNY_GeometricAnalysis/119/
END:VEVENT
END:VCALENDAR