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BEGIN:VEVENT
SUMMARY:Anna Fino (University of Turin)
DTSTART;VALUE=DATE-TIME:20200422T120000Z
DTEND;VALUE=DATE-TIME:20200422T130000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/1
DESCRIPTION:Title: Clo
sed $G_2$-structures\nby Anna Fino (University of Turin) as part of Vi
rtual seminar on geometry with symmetries\n\n\nAbstract\nI will review kno
wn examples of compact 7-manifolds admitting a closed $G_2$-structure. Mor
eover\, I will discuss some results on the behaviour of the Laplacian $G_2
$-flow starting from a closed $G_2$-structure whose induced metric satisfi
es suitable extra conditions.\n
LOCATION:https://researchseminars.org/talk/VSGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART;VALUE=DATE-TIME:20200506T150000Z
DTEND;VALUE=DATE-TIME:20200506T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/2
DESCRIPTION:Title: Tor
us actions and positive curvature\nby Lee Kennard (Syracuse University
) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nIn
the 1930s\, H. Hopf conjectured that an even-dimensional Riemannian manif
old with positive sectional curvature has positive Euler characteristic. I
n joint work with M. Wiemeler and B. Wilking\, this is confirmed in the sp
ecial case where the isometry group has rank at least five. Previous resul
ts of this form required the rank to grow to infinity as a function of the
manifold dimension. The main new tool is a structural result for represen
tations of tori with the special property that all isotropy groups are con
nected. Such representations are surprisingly rigid\, and we analyze them
using only elementary techniques.\n
LOCATION:https://researchseminars.org/talk/VSGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Mendes (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20200520T230000Z
DTEND;VALUE=DATE-TIME:20200520T235900Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/3
DESCRIPTION:Title: The
isometry group of spherical quotients\nby Ricardo Mendes (University
of Oklahoma) as part of Virtual seminar on geometry with symmetries\n\n\nA
bstract\nA special class of Alexandrov metric spaces are the quotients $X=
S^n/G$ of the round spheres by isometric actions of compact subgroups $G$
of $O(n+1)$. We will consider the question of how to compute the isometry
group of such $X$\, the main result being that every element in the identi
ty component of $\\operatorname{Isom}(X)$ lifts to a $G$-equivariant isome
try of the sphere. The proof relies on a pair of important results about t
he "smooth structure" of $X$.\n
LOCATION:https://researchseminars.org/talk/VSGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilka Agricola (University of Marburg)
DTSTART;VALUE=DATE-TIME:20200603T120000Z
DTEND;VALUE=DATE-TIME:20200603T130000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/4
DESCRIPTION:Title: Gen
eralizations of 3-Sasakian manifolds and skew torsion\nby Ilka Agricol
a (University of Marburg) as part of Virtual seminar on geometry with symm
etries\n\n\nAbstract\nWe define and investigate new classes of almost 3-co
ntact metric manifolds\, with two guiding ideas in mind: first\, what geom
etric objects are best suited for capturing the key properties of almost 3
-contact metric manifolds\, and second\, the newly defined classes should
admit `good' metric connections with skew torsion with interesting applica
tions: these include a well-behaved metric cone\, the existence of a gener
alized Killing spinor\, and remarkable curvature properties. This is joint
work with\nGiulia Dileo (Bari) and Leander Stecker (Marburg).\n
LOCATION:https://researchseminars.org/talk/VSGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Nikolayevsky (La Trobe University)
DTSTART;VALUE=DATE-TIME:20200701T230000Z
DTEND;VALUE=DATE-TIME:20200701T235900Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/5
DESCRIPTION:Title: Ein
stein extensions of Riemannian manifolds\nby Yuri Nikolayevsky (La Tro
be University) as part of Virtual seminar on geometry with symmetries\n\n\
nAbstract\nGiven a Riemannian space $N$ of dimension $n$ and a field $D$ o
f symmetric endomorphisms on $N$\, we define the extension $M$ of $N$ by $
D$ to be the Riemannian manifold of dimension $n+1$ obtained from $N$ by a
construction similar to extending a Lie group by a derivation of its Lie
algebra. We find the conditions on $N$ and $D$ for $M$ to be Einstein\, an
d then study various classes of Einstein extensions so obtained. It turns
out that several remarkable phenomena and properties which were observed i
n the homogeneous case are still present in the Riemannian case. This is a
joint work with D. Alekseevsky.\n
LOCATION:https://researchseminars.org/talk/VSGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Wink (UCLA)
DTSTART;VALUE=DATE-TIME:20200617T150000Z
DTEND;VALUE=DATE-TIME:20200617T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/6
DESCRIPTION:Title: New
Curvature Conditions for the Bochner Technique\nby Matthias Wink (UCL
A) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nT
he Bochner Technique has established itself as a powerful tool in Geometry
\, e.g.\\ D.~Meyer used it to show that the Betti numbers $b_p$ of compact
$n$-dimensional manifolds with positive curvature operators vanish for $0
< p < n$. In this talk I will explain that this is more generally the cas
e for manifolds with $\\lceil \\frac{n}{2} \\rceil$-positive curvature ope
rators. We will see that this is a consequence of a general vanishing and
estimation theorem for the $p$-th Betti number for manifolds with a lower
bound on the average of the lowest $(n-p)$ eigenvalues of the curvature op
erator. This talk is based on joint work with Peter Petersen.\n
LOCATION:https://researchseminars.org/talk/VSGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kerin (NUI Galway)
DTSTART;VALUE=DATE-TIME:20200730T180000Z
DTEND;VALUE=DATE-TIME:20200730T190000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/7
DESCRIPTION:Title: A p
ot-pourri of non-negatively curved 7-manifolds\nby Martin Kerin (NUI G
alway) as part of Virtual seminar on geometry with symmetries\n\n\nAbstrac
t\nManifolds with non-negative sectional curvature are rare and difficult
to find\, with interesting topological phenomena traditionally being restr
icted by a dearth of methods of construction. In this talk\, I will descr
ibe a large family of seven-dimensional manifolds with non-negative curvat
ure\, leading to examples of exotic diffeomorphism types\, non-standard ho
motopy types and fake versions of familiar friends. This is based on joint
work with Sebastian Goette and Krishnan Shankar.\n\nMartin Kerin's talk w
as originally announced on July 15th\, but it had to be canceled by techni
cal reasons. The current talk is hosted in CUNY Geometric Analysis Seminar
\, and co-sponsored by the Virtual seminar of geometry with symmetries.\n
LOCATION:https://researchseminars.org/talk/VSGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gavin Ball (Université du Québec à Montréal)
DTSTART;VALUE=DATE-TIME:20200729T150000Z
DTEND;VALUE=DATE-TIME:20200729T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/8
DESCRIPTION:Title: Qua
dratic closed G2-structures\nby Gavin Ball (Université du Québec à
Montréal) as part of Virtual seminar on geometry with symmetries\n\n\nAbs
tract\nI will talk about closed G2-structures satisfying the quadratic con
dition\, a second-order PDE system introduced by Bryant involving a parame
ter. For particular special values of the parameter\, the quadratic condit
ion is equivalent to the Einstein equation\, the extremally Ricci-pinched
(ERP) condition\, and the eigenform condition. I will describe my recent e
xistence and classification results about these structures\, including the
first example of a complete inhomogeneous ERP G2-structure\, a new compac
t ERP G2-structure\, and the first examples of solutions to this PDE syste
m for certain values of the parameter. If time permits\, I will describe a
related construction of complete inhomogeneous gradient solitons for the
G2 Laplacian flow.\n
LOCATION:https://researchseminars.org/talk/VSGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Siffert (University of Münster)
DTSTART;VALUE=DATE-TIME:20200826T120000Z
DTEND;VALUE=DATE-TIME:20200826T130000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/9
DESCRIPTION:Title: Con
struction of explicit $p$-harmonic functions\nby Anna Siffert (Univers
ity of Münster) as part of Virtual seminar on geometry with symmetries\n\
n\nAbstract\nThe study of $p$-harmonic functions on Riemannian manifolds h
as invoked the interest of mathematicians and physicists for nearly two ce
nturies. Applications within physics can for example be found in continuum
mechanics\, elasticity theory\, as well as two-dimensional hydrodynamics
problems involving Stokes ows of incompressible Newtonian fluids.\n\nIn my
talk I will focus on the construction of explicit $p$-harmonic functions
on rank-one Lie groups of Iwasawa type. This joint wok with Sigmundur Gudm
undsson and Marko Sobak.\n
LOCATION:https://researchseminars.org/talk/VSGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Lauret (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20200812T230000Z
DTEND;VALUE=DATE-TIME:20200812T235900Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/10
DESCRIPTION:Title: Pr
escribing Ricci curvature on homogeneous manifolds\nby Jorge Lauret (U
niversidad Nacional de Córdoba) as part of Virtual seminar on geometry wi
th symmetries\n\n\nAbstract\nGiven a symmetric 2-tensor $T$ on a manifold
$M$\, it is a classical problem in Riemannian geometry to ask about the ex
istence (and uniqueness) of a metric $g$ on $M$ such that $\\textrm{Ric}(
g) = T$ (see e.g. [Besse\,Chap.5]). Assuming that $M$ is a homogeneous m
anifold\, we will consider in the talk the $G$-invariant version of the pr
oblem\, where $G$ is a (unimodular\, not necessarily compact) Lie group ac
ting transitively on $M$. \n\nAfter an overview of results and questions\
, we will give a formula for the differential $d\\textrm{Ric}$ of the func
tion $\\textrm{Ric}$ at a $G$-invariant metric $g$\, which is precisely th
e Lichnerowicz Laplacian acting on $G$-invariant symmetric 2-tensors. The
formula is in terms of the moment map for the variety of Lie algebras. \
n\nAs an application\, we will consider the concept of Ricci local inverti
bility for a metric $g$\, i.e.\, when the kernel of $d\\textrm{Ric}$ at $g
$ consists only of the subspace generated by $g$. This is equivalent to t
he existence of a $G$-invariant solution $g'$ to the Prescribed Ricci Prob
lem $\\textrm{Ric}(g') = cT$ (for some $c>0$)\, for any $G$-invariant $T
$ sufficiently close to $\\textrm{Ric}(g)$. Our main result is that any i
rreducible naturally reductive metric on $M$ with respect to $G$ is Ricci
locally invertible. \n\nThis is joint work in progress with Cynthia
Will.\n
LOCATION:https://researchseminars.org/talk/VSGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Ovando (Universidad Nacional de Rosario)
DTSTART;VALUE=DATE-TIME:20200916T150000Z
DTEND;VALUE=DATE-TIME:20200916T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/11
DESCRIPTION:Title: Fi
rst integrals of the geodesic flow on nilpotent Lie groups of step at most
three\nby Gabriela Ovando (Universidad Nacional de Rosario) as part o
f Virtual seminar on geometry with symmetries\n\n\nAbstract\nIn this talk
we would like to consider the question of integrability of the geodesic fl
ow on nilmanifolds. We start with nilpotent Lie groups\, mostly of step tw
o and three\, equipped with a left-invariant metric. We show some algebrai
c relations when studying functions in involution and we obtain explicit e
xamples in low dimensions. Some examples of Liouville integrability in com
pact quotients will be shown.\n\nNotice that the schedule has been shifted
one week forward\, with Ovando's seminar three weeks after Siffert's.\n
LOCATION:https://researchseminars.org/talk/VSGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramiro Lafuente (The University of Queensland)
DTSTART;VALUE=DATE-TIME:20200930T230000Z
DTEND;VALUE=DATE-TIME:20200930T235900Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/12
DESCRIPTION:Title: Ho
mogeneous Einstein metrics via a cohomogeneity-one approach\nby Ramiro
Lafuente (The University of Queensland) as part of Virtual seminar on geo
metry with symmetries\n\n\nAbstract\nWe establish non-existence results on
non-compact homogeneous Einstein manifolds. The key idea in the proof is
to consider non-transitive group actions on these spaces (more precisely\,
actions with cohomogeneity one)\, and to find geometric monotone quantiti
es for the ODE that results from writing the Einstein equation in such a s
etting. As an application\, we show that homogeneous Einstein metrics on E
uclidean spaces are Einstein solvmanifolds. This is joint work with C. Bö
hm.\n
LOCATION:https://researchseminars.org/talk/VSGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnan Shankar (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20200715T120000Z
DTEND;VALUE=DATE-TIME:20200715T130000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/13
DESCRIPTION:Title: Hi
ghly connected 7-manifolds\, non-negative curvature and the linking form\nby Krishnan Shankar (University of Oklahoma) as part of Virtual semina
r on geometry with symmetries\n\nAbstract: TBA\n\nThe original announcemen
t of this talk included Martin Kerin (NUI Galway\, Ireland) as the speaker
. For technical reasons during the transmission\, it was decided that Mart
in Kerin's coauthor Krishnan Shankar replace him giving a talk on the same
subject as the original one. The organizers thank Ravi Shankar for his he
lp in this urgent moment.\n
LOCATION:https://researchseminars.org/talk/VSGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Raffero (Università degli Studi di Torino)
DTSTART;VALUE=DATE-TIME:20201014T120000Z
DTEND;VALUE=DATE-TIME:20201014T130000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/14
DESCRIPTION:Title: Sy
mmetries of closed G2-structures\nby Alberto Raffero (Università degl
i Studi di Torino) as part of Virtual seminar on geometry with symmetries\
n\n\nAbstract\nIn this talk I will consider 7-manifolds endowed with a clo
sed G2-structure and having a large symmetry group. In the compact case\,
I will discuss the properties of the full automorphism group of a closed G
2-structure\, showing how they impose strong constraints on the constructi
on of homogeneous and cohomogeneity one examples. In the non-compact case\
, I will first give a brief overview of known examples and then I will des
cribe the classification of 7-manifolds with a closed G2-structure that ar
e homogeneous under the action of a reductive Lie group. This is joint wor
k with F. Podestà\n
LOCATION:https://researchseminars.org/talk/VSGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Bettiol (Lehman College\, CUNY)
DTSTART;VALUE=DATE-TIME:20201028T150000Z
DTEND;VALUE=DATE-TIME:20201028T160000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/15
DESCRIPTION:Title: Mi
nimal spheres in ellipsoids\nby Renato Bettiol (Lehman College\, CUNY)
as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nIn
1987\, Yau posed the question of whether all minimal 2-spheres in a 3-dime
nsional ellipsoid inside $\\mathbb R^4$ are planar\, i.e.\, determined by
the intersection with a hyperplane. While this is the case if the ellipsoi
d is nearly round\, Haslhofer and Ketover have recently shown the existenc
e of an embedded non-planar minimal 2-sphere in sufficiently elongated ell
ipsoids\, with min-max methods. Using bifurcation theory and the symmetrie
s that arise if at least two semi-axes coincide\, we show the existence of
arbitrarily many distinct embedded non-planar minimal 2-spheres in suffic
iently elongated ellipsoids of revolution. This is based on joint work wit
h P. Piccione.\n
LOCATION:https://researchseminars.org/talk/VSGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sammy Sbiti (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20201111T220000Z
DTEND;VALUE=DATE-TIME:20201111T230000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/16
DESCRIPTION:Title: On
the Ricci Flow of Homogeneous Metrics on Spheres\nby Sammy Sbiti (Uni
versity of Pennsylvania) as part of Virtual seminar on geometry with symme
tries\n\n\nAbstract\nWe study the Ricci flow of homogeneous metrics on sph
eres. We determine their forward behavior and also classify ancient soluti
ons. In doing so we exhibit a new one-parameter family of ancient solution
s on spheres.\n
LOCATION:https://researchseminars.org/talk/VSGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Otiman (Roma Tre University)
DTSTART;VALUE=DATE-TIME:20201125T160000Z
DTEND;VALUE=DATE-TIME:20201125T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/17
DESCRIPTION:Title: Sp
ecial non-Kähler metrics on solvmanifolds\nby Alexandra Otiman (Roma
Tre University) as part of Virtual seminar on geometry with symmetries\n\n
\nAbstract\nWe discuss old and new results about the existence of special
Hermitian metrics (locally conformally Kähler\, balanced\, pluriclosed) o
n complex nilmanifolds and on Oeljeklaus-Toma manifolds. This latter class
represents a generalization of Inoue-Bombieri surfaces in arbitrary compl
ex dimension and its construction\, based on algebraic number theory\, wil
l allow us to give a numerical interpretation of the existence of several
Hermitian metrics of special type.\n
LOCATION:https://researchseminars.org/talk/VSGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Buttsworth (The University of Queensland)
DTSTART;VALUE=DATE-TIME:20201209T220000Z
DTEND;VALUE=DATE-TIME:20201209T230000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/18
DESCRIPTION:Title: Th
e prescribed Ricci curvature problem on manifolds with large symmetry grou
ps\nby Timothy Buttsworth (The University of Queensland) as part of Vi
rtual seminar on geometry with symmetries\n\n\nAbstract\nThe prescribed Ri
cci curvature problem continues to be of fundamental interest in Riemannia
n geometry. In this talk\, I will describe some classical results on this
topic\, as well as some more recent results that have been achieved with h
omogeneous and cohomogeneity-one assumptions.\n
LOCATION:https://researchseminars.org/talk/VSGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masoumeh Zarei (Universität Augsburg)
DTSTART;VALUE=DATE-TIME:20210113T160000Z
DTEND;VALUE=DATE-TIME:20210113T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/19
DESCRIPTION:Title: To
rus actions on 4-dimensional Alexandrov spaces\nby Masoumeh Zarei (Uni
versität Augsburg) as part of Virtual seminar on geometry with symmetries
\n\n\nAbstract\nEquivariant classification of $T^2$-actions on smooth clos
ed orientable 4-dimensional manifolds was obtained by Orlik and Raymond in
70's. In particular\, they showed that the smooth classification is equiv
alent to the topological classification. In this talk\, I present an equiv
ariant classification of isometric $T^2$-actions on closed\, orientable\,
four-dimensional Alexandrov spaces\, which generalizes the equivariant cla
ssification of Orlik and Raymond. Moreover\, we show that such Alexandrov
spaces are equivariantly homeomorphic to 4-dimensional Riemannian orbifold
s with isometric $T^2$-actions. This is joint work with Diego Corro and Je
sús Núñez-Zimbrón.\n
LOCATION:https://researchseminars.org/talk/VSGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Z. Lin (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20210127T190000Z
DTEND;VALUE=DATE-TIME:20210127T200000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/20
DESCRIPTION:Title: Ge
ometric Structure and the Laplace Spectrum\nby Samuel Z. Lin (Dartmout
h College) as part of Virtual seminar on geometry with symmetries\n\n\nAbs
tract\nThe Laplace spectrum of a compact Riemannian manifold is defined to
be the set of positive eigenvalues of the associated Laplace operator. In
verse spectral geometry is the study of how this set of analytic data rela
tes to the underlying geometry of the manifold.\n\nA (compact) geometric s
tructure is defined to be a compact Riemannian manifold equipped with a lo
cally homogeneous metric. Geometric structures played an important role in
the study of two and three-dimensional geometry and topology. In dimensio
n two\, the only geometric structures are those of constant curvature. Fur
thermore\, Berger showed that they are determined up to local isometries b
y their Laplace spectra.\n\nIn this work\, we study the following question
: “To what extend are the three-dimensional geometric structures determi
ned by their Laplace spectra?” Among other results\, we provide strong e
vidence that the local geometry of a three-dimensional geometric structure
is determined by its Laplace spectrum\, which is in stark contrast with r
esults in higher dimensions. This is a joint work with Ben Schmidt (Michig
an State University) and Craig Sutton (Dartmouth College).\n
LOCATION:https://researchseminars.org/talk/VSGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changliang Wang (Tongji University)
DTSTART;VALUE=DATE-TIME:20210224T090000Z
DTEND;VALUE=DATE-TIME:20210224T100000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/21
DESCRIPTION:Title: Th
e linear instability of some families of Einstein metrics\nby Changlia
ng Wang (Tongji University) as part of Virtual seminar on geometry with sy
mmetries\n\n\nAbstract\nI will report some works on the linear stability q
uestion of Einstein metrics. We proved the linear instability of some Eins
tein metrics with positive scalar curvature\, including some families of R
iemannian manifolds with real Killing spinors\, and low-dimensional homoge
neous Einstein spaces. The talk is based on joint works with McKenzie Wang
and Uwe Semmelmann.\n
LOCATION:https://researchseminars.org/talk/VSGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina M Arroyo (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20210210T220000Z
DTEND;VALUE=DATE-TIME:20210210T230000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/22
DESCRIPTION:Title: On
the signature of the Ricci curvature on nilmanifolds\nby Romina M Arr
oyo (Universidad Nacional de Córdoba) as part of Virtual seminar on geome
try with symmetries\n\n\nAbstract\nA classical problem in Riemannian geome
try is to determine the possible signatures of the Ricci curvature on a gi
ven space. The aim of this talk is to present the problem in the setting
of nilpotent Lie groups with left-invariant metrics\, and to give a comple
te answer of the problem in this case.\n\nThis is joint work with Ramiro L
afuente (The University of Queensland).\n
LOCATION:https://researchseminars.org/talk/VSGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosa Sena-Dias (Instituto Superior Tecnico)
DTSTART;VALUE=DATE-TIME:20210310T160000Z
DTEND;VALUE=DATE-TIME:20210310T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/23
DESCRIPTION:Title: Mi
nimal Lagrangian tori in toric manifolds\nby Rosa Sena-Dias (Instituto
Superior Tecnico) as part of Virtual seminar on geometry with symmetries\
n\n\nAbstract\nMinimal submanifolds were first introduced and studied in t
he 18th century. They are the object of a great deal of interest nowadays
as they play an important role in Riemannian Geometry\, Mathematical Physi
cs and have many applications. Still\, there are surprisingly few concrete
examples of such submanifolds apart from the obvious ones. \n\nIn this t
alk we want to discuss examples of minimal Lagrangian tori in toric manifo
lds. They come from exploiting the toric symmetry through the use of what
Palais called the ''Principle of Symmetric Criticality''. We will give bac
kground\, discuss examples and if time permits talk about open problems.\n
\nThis is joint work with Gonçalo Oliveira.\n
LOCATION:https://researchseminars.org/talk/VSGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfang Ziller (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20210324T190000Z
DTEND;VALUE=DATE-TIME:20210324T200000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/24
DESCRIPTION:Title: A
variational approach to prescribing the Ricci tensor\nby Wolfang Zille
r (University of Pennsylvania) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nWe discuss the question of which tensors T can
be the Ricci tensor of a metric\, i.e. Ric(g)=T or Ric(g)=cT for some c. S
olutions can be viewed as the critical points of a modified scalar curvatu
re functional and we examine the global behavior of this functional in the
case of homogeneous spaces. This is joint work with Artem Pulemotov.\n
LOCATION:https://researchseminars.org/talk/VSGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiayin Pan (University of California-Santa Barbara)
DTSTART;VALUE=DATE-TIME:20210407T220000Z
DTEND;VALUE=DATE-TIME:20210407T230000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/25
DESCRIPTION:Title: No
nnegative Ricci curvature\, escape rate\, and virtual abelianness\nby
Jiayin Pan (University of California-Santa Barbara) as part of Virtual sem
inar on geometry with symmetries\n\n\nAbstract\nA consequence of Cheeger-G
romoll splitting theorem states that for any open manifold $(M\,x)$ of non
negative Ricci curvature\, if all the minimal geodesic loops at $x$ that r
epresent elements of $\\pi_1(M\,x)$ are contained in a bounded set\, then
$\\pi_1(M\,x)$ is virtually abelian. However\, it is prevalent for these l
oops to escape from any bounded sets. In this talk\, we introduce a quanti
ty\, escape rate\, to measure how fast these loops escape. Then we prove t
hat if the escape rate is less than some positive constant $\\epsilon(n)$\
, which only depends on the dimension $n$\, then $\\pi_1(M\,x)$ is virtual
ly abelian. The main tools are equivariant Gromov-Hausdorff convergence an
d Cheeger-Colding theory on Ricci limit spaces.\n
LOCATION:https://researchseminars.org/talk/VSGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Galaz-García (Durham University)
DTSTART;VALUE=DATE-TIME:20210421T160000Z
DTEND;VALUE=DATE-TIME:20210421T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/26
DESCRIPTION:Title: Ge
ometry and Topology of collapsed three-dimensional Alexandrov Spaces\n
by Fernando Galaz-García (Durham University) as part of Virtual seminar o
n geometry with symmetries\n\n\nAbstract\nIn Riemannian geometry\, collaps
e imposes strong geometric and topological restrictions on the spaces on w
hich it occurs. In the case of Alexandrov spaces\, which are metric genera
lizations of complete Riemannian manifolds with a uniform lower sectional
curvature bound\, collapse is fairly well understood in dimension three. I
n this talk\, I will discuss the geometry and topology of three-dimensiona
l Alexandrov spaces and focus on those which are sufficiently collapsed.
When such spaces are irreducible\, they are modeled on one of the eight th
ree-dimensional dimensional Thurston geometries\, excluding the hyperbolic
one. This extends a result of Shioya and Yamaguchi\, originally formulate
d for Riemannian manifolds\, to the Alexandrov setting. We will briefly d
iscuss how spaces with circle actions enter the picture. (Joint work with
Luis Guijarro and Jesús Núñez-Zimbrón).\n
LOCATION:https://researchseminars.org/talk/VSGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Madnick (National Center for Theoretical Sciences)
DTSTART;VALUE=DATE-TIME:20210505T090000Z
DTEND;VALUE=DATE-TIME:20210505T100000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/27
DESCRIPTION:Title: Th
e Second Variation of Holomorphic Curves in the 6-Sphere\nby Jesse Mad
nick (National Center for Theoretical Sciences) as part of Virtual seminar
on geometry with symmetries\n\n\nAbstract\nThe 6-sphere is the only $n$-s
phere with $n > 2$ that admits an almost-complex structure. Equipping the
round 6-sphere with its standard ($G_2$-invariant) almost-complex structu
re\, the holomorphic curves in $S^6$ are minimal surfaces\, and play an im
portant role in $G_2$-geometry. These surfaces exist in abundance: by a r
emarkable theorem of Bryant\, extended by Rowland\, every closed Riemann s
urface may be conformally embedded in $S^6$ as a holomorphic curve of "nul
l-torsion."\n\nWhile holomorphic curves in $S^6$ are area-minimizing to fi
rst order\, they are not area-minimizing to second order. This failure is
encoded by the spectrum of the Jacobi operator\, which contains informati
on such as the Morse index and nullity. For closed\, null-torsion holomor
phic curves of low genus\, we explicitly compute the multiplicity of the f
irst Jacobi eigenvalue. Moreover\, for all genera\, we give a simple lowe
r bound for the nullity in terms of the area and genus. Time permitting\,
we will also outline some recent results in the setting of holomorphic cu
rves with boundary.\n
LOCATION:https://researchseminars.org/talk/VSGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniël Thung (Universität Hamburg)
DTSTART;VALUE=DATE-TIME:20210616T160000Z
DTEND;VALUE=DATE-TIME:20210616T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/28
DESCRIPTION:by Daniël Thung (Universität Hamburg) as part of Virtual sem
inar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicoletta Tardini (Università di Parma)
DTSTART;VALUE=DATE-TIME:20210630T090000Z
DTEND;VALUE=DATE-TIME:20210630T100000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/29
DESCRIPTION:by Nicoletta Tardini (Università di Parma) as part of Virtual
seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Searle (Wichita State University)
DTSTART;VALUE=DATE-TIME:20210811T220000Z
DTEND;VALUE=DATE-TIME:20210811T230000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/30
DESCRIPTION:by Catherine Searle (Wichita State University) as part of Virt
ual seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (National Autonomous University of Mexico)
DTSTART;VALUE=DATE-TIME:20210519T160000Z
DTEND;VALUE=DATE-TIME:20210519T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/31
DESCRIPTION:Title: Up
per bound on the revised first Betti number and torus stability for RCD sp
aces\nby Raquel Perales (National Autonomous University of Mexico) as
part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nGromov
and Gallot showed in the past century that for a fixed dimension n there e
xists a positive number $\\varepsilon(n)$ so that any $n$-dimensional riem
annian manifold satisfying $Ric_g \\textrm{diam}(M\,g)^2 \\geq -\\varepsil
on(n)$ has first Betti number smaller than or equal to $n$. Furthermore\,
by Cheeger-Colding if the first Betti number equals $n$ then $M$ is bi-H
ölder homeomorphic to a flat torus. This part is the corresponding stabi
lity statement to the rigidity result proven by Bochner\, namely\, closed
riemannian manifolds with nonnegative Ricci curvature and first Betti numb
er equal to their dimension has to be a torus. \n\nThe proof of Gromov and
Cheeger-Colding results rely on finding an appropriate subgroup of the ab
elianized fundamental group to pass to a nice covering space of $M$ and th
en study the geometry of the covering. In this talk we will generalize t
hese results to the case of $RCD(K\,N)$ spaces\, which is the synthetic no
tion of a riemannian manifold satisfying $Ric \\geq K$ and $dim \\leq N$.
This class of spaces include ricci limit spaces and Alexandrov spaces. \n
\n Joint work with I. Mondello and A. Mondino.\n
LOCATION:https://researchseminars.org/talk/VSGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Epstein (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20210825T160000Z
DTEND;VALUE=DATE-TIME:20210825T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/32
DESCRIPTION:by Jonathan Epstein (University of Oklahoma) as part of Virtua
l seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrique N. Sá Earp (University of Campinas (Unicamp))
DTSTART;VALUE=DATE-TIME:20210728T160000Z
DTEND;VALUE=DATE-TIME:20210728T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/33
DESCRIPTION:Title: Ha
rmonic $\\rm{Sp}(2)$-invariant $\\rm{G}_2$-structures on the $7$-sphere\nby Henrique N. Sá Earp (University of Campinas (Unicamp)) as part of V
irtual seminar on geometry with symmetries\n\n\nAbstract\nWe describe the
$10$-dimensional space of $\\rm{Sp}(2)$-invariant $\\rm{G}_2$-structures o
n the homogeneous $7$-sphere $\\mathbb{S}^7=\\mathrm{Sp}(2)/\\rm{Sp}(1)$ a
s $\\Omega_+^3(\\mathbb{S}^7)^{\\mathrm{Sp}(2)}\\simeq \\mathbb{R}^+ \\tim
es\\rm{Gl}^+(3\,\\mathbb{R})$. \n In those terms\, we formulate a gener
al Ansatz for $\\rm{G}_2$-structures\, which realises representatives in e
ach of the $7$ possible isometric classes of homogeneous $\\rm{G}_2$-struc
tures.\n Moreover\, the well-known nearly parallel ${round}$ and ${squ
ashed}$ metrics occur naturally as opposite poles in an $\\mathbb{S}^3$-fa
mily\, the equator of which is a new $\\mathbb{S}^2$-family of coclosed $
\\rm{G}_2$-structures satisfying the harmonicity condition $\\mathrm{div}\
\\; T=0$. \n We show general existence of harmonic representatives of $
\\rm{G}_2$-structures in each isometric class through explicit solutions o
f the associated flow and describe the qualitative behaviour of the flow.
We study the stability of the Dirichlet gradient flow near these critical
points\, showing explicit examples of degenerate and nondegenerate local m
axima and minima\, at various regimes of the general Ansatz. Finally\, for
metrics outside of the Ansatz\, we identify families of harmonic $\\rm{G}
_2$-structures\, prove long-time existence of the flow and study the stabi
lity properties of some well-chosen examples.\n\nJoint work with E. Loubea
u\, A. Moreno and J. Saavedra.\n
LOCATION:https://researchseminars.org/talk/VSGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Petersen (UCLA)
DTSTART;VALUE=DATE-TIME:20210602T220000Z
DTEND;VALUE=DATE-TIME:20210602T230000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/34
DESCRIPTION:by Peter Petersen (UCLA) as part of Virtual seminar on geometr
y with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20211006T160000Z
DTEND;VALUE=DATE-TIME:20211006T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/35
DESCRIPTION:by Marco Radeschi (University of Notre Dame) as part of Virtua
l seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviana del Barco (Universidade Estadual de Campinas)
DTSTART;VALUE=DATE-TIME:20210922T160000Z
DTEND;VALUE=DATE-TIME:20210922T170000Z
DTSTAMP;VALUE=DATE-TIME:20210514T192328Z
UID:VSGS/36
DESCRIPTION:by Viviana del Barco (Universidade Estadual de Campinas) as pa
rt of Virtual seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/VSGS/36/
END:VEVENT
END:VCALENDAR