BEGIN:VCALENDAR
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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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
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:20240624T062307Z
UID:VSGS/28
DESCRIPTION:Title: Co
homogeneity one quaternionic Kähler manifolds\nby Daniël Thung (Univ
ersität Hamburg) as part of Virtual seminar on geometry with symmetries\n
\n\nAbstract\nThe study of quaternionic Kähler geometry has long been ham
pered by a lack of examples. However\, a construction known as the c-map h
as recently made it possible to construct many complete examples of negati
ve scalar curvature. Moreover\, the quaternionic Kähler manifolds that ar
ise from the c-map admit a one-parameter deformation through complete quat
ernionic Kähler manifolds. In this talk\, I will describe the (deformed)
c-map in detail and show how to use it to construct interesting cohomogene
ity one quaternionic Kähler manifolds\, focusing on a series of examples
which arise as deformations of quaternionic Kähler symmetric spaces. This
is joint work with Vicente Cortés\, Markus Röser\, and Arpan Saha.\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:20240624T062307Z
UID:VSGS/29
DESCRIPTION:Title: SK
T and Kähler-like metrics on complex manifolds\nby Nicoletta Tardini
(Università di Parma) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nSeveral special non-Kähler Hermitian metrics can be in
troduced on complex manifolds. Among them\, SKT metrics deserve particular
attention. They can be defined on a complex manifold by saying that the t
orsion of the Bismut connection associated to the metric is closed. These
metrics always exist on compact complex surfaces but the situation in high
er dimension is very different. We will discuss several properties concern
ing these metrics also in relation with the Bismut connection having Kähl
er-like curvature. Since this last property on nilmanifolds will force the
complex structure to be abelian\, we will also discuss the relation betwe
en SKT metrics and abelian complex structures on unimodular Lie algebras.\
nThese are joint works with Anna Fino and Luigi Vezzoni.\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:20240624T062307Z
UID:VSGS/30
DESCRIPTION:Title: Al
most isotropy-maximal manifolds of non-negative curvature\nby Catherin
e Searle (Wichita State University) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nWe extend the equivariant classification r
esults of Escher and Searle for closed\, simply connected\, non-negativel
y curved Riemannian n-manifolds admitting isometric isotropy-maximal toru
s actions to the class of such manifolds admitting isometric strictly almo
st isotropy-maximal torus actions. In particular\, we prove that such man
ifolds are equivariantly diffeomorphic to the free\, linear quotient by a
torus of a product of spheres of dimensions greater than or equal to three
.\n\nThis is joint work with Z. Dong and C. Escher.\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:20240624T062307Z
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 (McDaniel College)
DTSTART;VALUE=DATE-TIME:20210825T160000Z
DTEND;VALUE=DATE-TIME:20210825T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/32
DESCRIPTION:Title: Sy
mmetry groups of solvmanifolds\nby Jonathan Epstein (McDaniel College)
as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nAlt
hough it is generally difficult to determine the full isometry group of a
solvmanifold $S$\, partial knowledge of its symmetries can yield useful in
formation. For example\, the existence of a maximally symmetric metric is
related to the existence of extensions of the Lie algebra $\\mathfrak{s}$
of $S$ which admit a nontrivial Levi decomposition. Motivated by this\, we
describe the decompositions $\\mathfrak{s} = \\mathfrak{s}_1 \\ltimes \\m
athfrak{s}_2$ which yield such extensions and develop a procedure for dete
rmining their existence. When the step-size of the nilradical of $\\mathfr
ak{s}$ is bounded\, we use the representation theory of real semisimple Li
e algebras to describe the structure of such extensions. This is joint wor
k with Michael Jablonski.\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:20240624T062307Z
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:20240624T062307Z
UID:VSGS/34
DESCRIPTION:Title: Ri
gidity of Homogeneous Gradient Soliton Metrics and Related Equations\n
by Peter Petersen (UCLA) as part of Virtual seminar on geometry with symme
tries\n\n\nAbstract\nThis is joint work with Will Wylie. The goal is to cl
assify\, if possible\, the homogeneous geometric solitons. Here a geometri
c soliton is the soliton for a geometric flow. The Ricci flow is the most
prominent example of such a flow\, but there are many others where the Ric
ci tensor is replaced with some other tensor that depends in a natural way
on the Riemannian structure. We will also consider some more general prob
lems showing that our techniques can be used for other geometric problems.
\n
LOCATION:https://researchseminars.org/talk/VSGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20211006T220000Z
DTEND;VALUE=DATE-TIME:20211006T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/35
DESCRIPTION:Title: In
variant theory without groups\nby Marco Radeschi (University of Notre
Dame) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract
\nGiven an orthogonal representation of a Lie group $G$ on a Euclidean vec
tor space $V$\, Invariant Theory studies the algebra of $G$-invariant poly
nomials on $V$. This setting can be generalized by replacing the represent
ation $G$ with a foliation $F$ on $V$\, with equidistant leaves. In this c
ase\, one can study the algebra of polynomials that are constant along the
se fibers - effectively producing an Invariant Theory\, but without groups
. In this talk we will discuss a surprising relation between the geometry
of the foliation and the corresponding algebra\, including recent joint wo
rk in progress with Ricardo Mendes and Samuel Lin\, showing how to estimat
e volume and diameter of the quotient $V/F$ using the algebra.\n
LOCATION:https://researchseminars.org/talk/VSGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviana del Barco (Universidade Estadual de Campinas)
DTSTART;VALUE=DATE-TIME:20211117T160000Z
DTEND;VALUE=DATE-TIME:20211117T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/36
DESCRIPTION:Title: Un
iqueness of ad-invariant metrics\nby Viviana del Barco (Universidade E
stadual de Campinas) as part of Virtual seminar on geometry with symmetrie
s\n\n\nAbstract\nAn ad-invariant metric on a Lie algebra is a nondegenerat
e symmetric bilinear form for which inner derivations are skew-symmetric.
These are the algebraic counterparts of bi-invariant metrics on Lie groups
.\n\nIt is known that a positive definite ad-invariant metric can only be
defined on compact semisimple Lie algebras\, direct sum with an abelian fa
ctor. On compact simple Lie algebras\, every ad-invariant metric is a mult
iple of the Killing form which\, in addition\, is invariant under the Lie
algebra automorphisms.\n\nIn the pseudo-Riemannian context ad-invariant me
trics appear on more general Lie algebras such as semisimple (non-compact)
\, or solvable. For non-semisimple Lie algebras\, the orbit space of ad-in
variant metrics under the action of the automorphism group has not been sy
stematically described yet.\n\nIn this talk\, we will discuss characterist
ics of Lie algebras possessing a unique ad-invariant metric up to automorp
hisms (and sign). In particular\, we will introduce the concept of "solita
ry" metrics on Lie algebras\, which aims to encode the property of being a
unique ad-invariant metric. As we will see\, this is actually a property
of a Lie algebra rather than of the metric itself.\n\nThis characterizatio
n of uniqueness allowed us to show that Lie algebras admitting a unique ad
-invariant metric are necessarily solvable. In addition\, we show that man
y low dimensional Lie algebras carrying ad-invariant metrics are solitary.
\n\nTime permitting\, generalizations of the solitary conditions will be d
iscussed.\n\nThe talk is based on joint works with Diego Conti and Federic
o A. Rossi (Milano Bicocca).\n
LOCATION:https://researchseminars.org/talk/VSGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Böhm (University of Münster)
DTSTART;VALUE=DATE-TIME:20210908T160000Z
DTEND;VALUE=DATE-TIME:20210908T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/37
DESCRIPTION:Title: No
n-compact Einstein manifolds with symmetry\nby Christoph Böhm (Univer
sity of Münster) as part of Virtual seminar on geometry with symmetries\n
\n\nAbstract\nFor Einstein manifolds with negative scalar curvature admitt
ing an isometric action\nof a Lie group $G$ with compact\, smooth orbit sp
ace\, we show the following rigidity result: The\nnilradical $N$ of $G$ ac
ts polarly\, and the $N$-orbits can be extended to minimal Einstein subman
ifolds.\n\nAs an application\, we prove the Alekseevskii conjecture. This
is joint work with R. Lafuente.\n
LOCATION:https://researchseminars.org/talk/VSGS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Panagiotis Souris (University of Patras)
DTSTART;VALUE=DATE-TIME:20211103T090000Z
DTEND;VALUE=DATE-TIME:20211103T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/38
DESCRIPTION:Title: Ri
emannian geodesic orbit manifolds: An overview and some recent results
\nby Nikolaos Panagiotis Souris (University of Patras) as part of Virtual
seminar on geometry with symmetries\n\n\nAbstract\nA homogeneous Riemannia
n manifold is called geodesic orbit if all geodesics are orbits of one-par
ameter groups of isometries\, or equivalently\, integral curves of Killing
vector fields. Well-known examples include symmetric\, weakly symmetric a
nd naturally reductive manifolds\, yet a complete classification of geodes
ic orbit manifolds remains open. In this talk\, we firstly review basic a
spects of the study of geodesic orbit manifolds. Further\, we focus on com
pact Lie groups\, and we discuss recent results on Einstein Lie groups tha
t \nare not geodesic orbit manifolds.\n
LOCATION:https://researchseminars.org/talk/VSGS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Pacini (University of Torino)
DTSTART;VALUE=DATE-TIME:20211020T160000Z
DTEND;VALUE=DATE-TIME:20211020T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/39
DESCRIPTION:Title: Ri
cci curvature\, the convexity of volume and minimal Lagrangian submanifold
s\nby Tommaso Pacini (University of Torino) as part of Virtual seminar
on geometry with symmetries\n\n\nAbstract\nThere exist various classical
relationships between Ricci curvature and volume. We will show that\, in t
oric Kaehler geometry\, the relationship is particularly strong: the sign
of the Ricci curvature corresponds to convexity properties of the volume f
unctional. As an application\, we will discuss existence/uniqueness result
s for minimal Lagrangian submanifolds.\n\nWe will emphasize the fact that\
, although these topics are Riemannian/symplectic\, the ideas used in the
proofs are complex-theoretic.\n\nMore generally\, we will discuss analogou
s results in the wider context of group compactifications.\n
LOCATION:https://researchseminars.org/talk/VSGS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommy Murphy (Cal State Fullerton)
DTSTART;VALUE=DATE-TIME:20211201T230000Z
DTEND;VALUE=DATE-TIME:20211201T235900Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/41
DESCRIPTION:Title: Ri
gidity of $SU(n)$-type symmetric spaces\nby Tommy Murphy (Cal State Fu
llerton) as part of Virtual seminar on geometry with symmetries\n\n\nAbstr
act\nI show the biinvariant metric on $SU(2n+1)$ is isolated in the moduli
space of Einstein metrics\, even though it admits infinitesimal deformati
ons. This gives a non-K\\”ahler\, non-product example of this phenomenon
adding to the famous example of $\\mathbb{CP}^{2n}\\times \\mathbb{CP}^1$
found by Koiso. Time permitting\, I will also survey further application
s of our techniques to questions concerning solitonic rigidity and the sta
bility of Ricci flow. This is joint work with W. Batat\, S.J. Hall and J.
Waldron.\n
LOCATION:https://researchseminars.org/talk/VSGS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Deré (KU Leuven Kulak)
DTSTART;VALUE=DATE-TIME:20220223T160000Z
DTEND;VALUE=DATE-TIME:20220223T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/43
DESCRIPTION:Title: Si
mply transitive NIL-affine actions of solvable Lie groups\nby Jonas De
ré (KU Leuven Kulak) as part of Virtual seminar on geometry with symmetri
es\n\n\nAbstract\nAlthough not every $1$-connected solvable Lie group $G$
admits a simply transitive action via affine maps on $\\mathbb{R}^n$\, it
is known that such an action exists if one replaces $\\mathbb{R}^n$ by a s
uitable nilpotent Lie group $N$\, depending on $G$. However\, not much is
known about which pairs of Lie groups $(G\,N)$ admit such an action\, wher
e ideally you only need information about the Lie algebras corresponding t
o $G$ and $N$. The most-studied case is when $G$ is assumed to be nilpoten
t\, then the existence of a simply transitive action is related to the not
ion of complete pre-Lie algebra structures.\n\nIn recent work with Marcos
Origlia\, we showed how this problem is related to the semisimple splittin
g of the Lie algebra corresponding to $G$. Our characterization not only a
llows us to check whether a given action is simply transitive\, but also w
hether a simply transitive action exists given the Lie groups $G$ and $N$.
As a consequence\, we list the possibilities for such actions up to dimen
sion $4$.\n
LOCATION:https://researchseminars.org/talk/VSGS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeong Hyeong Park (Sungkyunkwan University)
DTSTART;VALUE=DATE-TIME:20220309T120000Z
DTEND;VALUE=DATE-TIME:20220309T130000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/44
DESCRIPTION:Title: Re
cent progress on harmonic manifolds\nby Jeong Hyeong Park (Sungkyunkwa
n University) as part of Virtual seminar on geometry with symmetries\n\n\n
Abstract\nA Riemannian manifold (M\, g) is harmonic if there exists a nonc
onstant radial harmonic function in a punctured neighborhood for any point
\, or equivalently if a volume density function centered at a point depend
s only on the distance from the center. There are many other characterizat
ions of harmonic spaces. For example\, it is known that (M\, g) is a harmo
nic space if and only if every sufficiently small geodesic sphere has cons
tant mean curvature. Szabo proved that in a harmonic space\, the volume of
the intersection of two geodesic balls of small radii depends only on the
radii and the distance between the centers.\nIn this talk\, we classify h
armonic spaces by using the asymptotic series of the density function and
eigenvalues of the Jacobi operator\, and characterize harmonic spaces in t
erms of the radial eigenspaces of the Laplacian. We discuss our recent pro
gress on harmonic spaces. (This is joint work with P. Gilkey)\n
LOCATION:https://researchseminars.org/talk/VSGS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Domínguez Vázquez (University of Santiago de Compostela)
DTSTART;VALUE=DATE-TIME:20220126T160000Z
DTEND;VALUE=DATE-TIME:20220126T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/45
DESCRIPTION:Title: Co
homogeneity one actions on symmetric spaces of noncompact type\nby Mig
uel Domínguez Vázquez (University of Santiago de Compostela) as part of
Virtual seminar on geometry with symmetries\n\n\nAbstract\nThe classificat
ion of cohomogeneity one actions (up to orbit equivalence) on real hyperbo
lic spaces is known since Cartan's investigation of isoparametric hypersur
faces in the late 1930s. The analogous classification for the other rank o
ne symmetric spaces of noncompact type was only concluded very recently. F
or higher rank\, several partial results have been obtained by Berndt and
Tamaru\, but complete classifications are only known for some rank two irr
educible spaces.\n\nIn this talk I will report on a joint work in progress
with J. Carlos Díaz-Ramos and Tomás Otero-Casal where we provide a new
structural result for cohomogeneity one actions on symmetric spaces of non
compact type and arbitrary rank. This allows us to derive the classificati
on on the spaces SL(n\,R)/SO(n) and to reduce the problem on a reducible s
pace to the classification on each one of its factors.\n
LOCATION:https://researchseminars.org/talk/VSGS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Streets (University of California\, Irvine)
DTSTART;VALUE=DATE-TIME:20220209T220000Z
DTEND;VALUE=DATE-TIME:20220209T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/46
DESCRIPTION:Title: Ge
neralized Ricci Flow\nby Jeffrey Streets (University of California\, I
rvine) as part of Virtual seminar on geometry with symmetries\n\n\nAbstrac
t\nThe generalized Ricci Flow is a natural extension of the Ricci Flow equ
ation which incorporates torsion. In this talk I will describe recent glob
al existence and convergence results\, and their application to problems i
n complex geometry.\n
LOCATION:https://researchseminars.org/talk/VSGS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Megan Kerr (Wellesley College)
DTSTART;VALUE=DATE-TIME:20220323T160000Z
DTEND;VALUE=DATE-TIME:20220323T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/47
DESCRIPTION:Title: Su
bmanifolds of Noncompact Homogeneous Spaces with Special Curvature Propert
ies\nby Megan Kerr (Wellesley College) as part of Virtual seminar on g
eometry with symmetries\n\n\nAbstract\nThe Ricci curvature form of a subma
nifold is not\, in general\, the restriction of the Ricci curvature of the
ambient space. Therefore\, classes of manifolds and submanifolds where th
e Ricci curvatures are aligned are very special. Indeed\, Tamaru exploited
this idea in the setting of noncompact symmetric spaces to construct new
examples of Einstein solvmanifolds via special subalgebras. We characteriz
e the largest category in which Tamaru's construction can be extended\, id
entifying two crucial algebraic/metric conditions. We explore a new class
of solvmanifolds defined by Kac-Moody algebras that are generalizations of
symmetric spaces for which our crucial extra conditions hold. And further
more\, in current work in progress\, we investigate other metric propertie
s of these spaces.\n\nThis is joint work with Tracy Payne.\n
LOCATION:https://researchseminars.org/talk/VSGS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hisashi Kasuya (Osaka Univ.)
DTSTART;VALUE=DATE-TIME:20220406T090000Z
DTEND;VALUE=DATE-TIME:20220406T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/48
DESCRIPTION:Title: Do
uble sided actions and non-invariant complex structures on compact Lie gr
oups\nby Hisashi Kasuya (Osaka Univ.) as part of Virtual seminar on ge
ometry with symmetries\n\n\nAbstract\nIt is known that every compact Lie g
roup of even dimension admits left-invariant complex structures. The purpo
se of this talk is to study "non-invariant" complex structures on semisim
ple compact Lie groups. \nThe main idea of this study is "mixing" the left
action and right action.\n\nThis is joint work with Hiroaki Ishida (Kago
shima Univ.)\n
LOCATION:https://researchseminars.org/talk/VSGS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Vezzoni (Università di Torino)
DTSTART;VALUE=DATE-TIME:20220420T160000Z
DTEND;VALUE=DATE-TIME:20220420T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/49
DESCRIPTION:Title: Th
e Calabi-Yau problem in HKT Geometry\nby Luigi Vezzoni (Università di
Torino) as part of Virtual seminar on geometry with symmetries\n\n\nAbstr
act\nHKT Geometry (HyperKahler with torsion Geometry) is the Geometry of h
yperHermitian manifolds equipped with a nondegenerate $\\partial$-closed (
2\,0)-form $\\Omega$. \nThe talk will focus on the seek of special HKT met
rics and on a conjecture of Alesker and Verbisky about the existence of a
balanced HKT metric on a compact HKT ${\\rm SL}(n\,\\mathbb{H})$-manifold.
Some new advances about the conjecture will be described.\n
LOCATION:https://researchseminars.org/talk/VSGS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schmidt (Michigan State University)
DTSTART;VALUE=DATE-TIME:20220504T220000Z
DTEND;VALUE=DATE-TIME:20220504T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/50
DESCRIPTION:Title: Pr
eserve one\, preserve all.\nby Benjamin Schmidt (Michigan State Univer
sity) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract
\nLet $(\\mathbb{E}^n\,d)$ denote $n$-dimensional Euclidean space.\n\nA st
riking theorem due to Beckman and Quarles asserts that if $n \\geq 2$ and
if $f:\\mathbb{E}^n \\rightarrow \\mathbb{E}^n$ is a function satisfying $
d(f(x)\,f(y))=1$ whenever $d(x\,y)=1$\, then $f$ is necessarily an isometr
y. I will discuss a conjecture\, formulated in collaborative work with Me
era Mainkar\, that motions of Riemannian manifolds preserving a sufficient
ly small distance are necessarily isometries. I will present examples and
supporting results to highlight the role of convexity in this rigidity ph
enomenon.\n
LOCATION:https://researchseminars.org/talk/VSGS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Corro (Karlsruher Institut für Technologie)
DTSTART;VALUE=DATE-TIME:20220921T090000Z
DTEND;VALUE=DATE-TIME:20220921T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/51
DESCRIPTION:Title: Sy
mmetry preserving solutions to the Yamabe Problem\nby Diego Corro (Kar
lsruher Institut für Technologie) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nThe Yamabe problem ask whether we can find
for a given smoooth Riemannian manifold a representative with constant sca
lar curvature in the conformal class of the given Riemannian metric. In th
is talk we consider such a problem under the extra constrain of preserving
symmetry. Namely I present that\, under mild geometry conditions\, we can
find solutions to the Yamabe problem which will also respect the symmetry
structure given by a singular Riemannian foliation. Singular Riemannian
foliations are generalizations of group actions by isometries and fiber bu
ndles.\n\nIn other words given a smooth Riemannian manifold with a smooth
Riemannian foliation\, we can find a conformal representative of the metri
c\, such that it has prescribed scalar curvature and the partition of the
manifold by the leafs\, is again a singular Rieamnnian foliation.\n
LOCATION:https://researchseminars.org/talk/VSGS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uwe Semmelmann (University of Stuttgart)
DTSTART;VALUE=DATE-TIME:20220518T160000Z
DTEND;VALUE=DATE-TIME:20220518T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/52
DESCRIPTION:Title: St
ability of the non–Symmetric space E7/PSO(8)\nby Uwe Semmelmann (Uni
versity of Stuttgart) as part of Virtual seminar on geometry with symmetri
es\n\n\nAbstract\nIn my talk I will present a new result on the stability
of Einstein metrics obtained in a recent preprint with Paul Schwahn and Gr
egor Weingart. There we prove that the normal metric on the homogeneous sp
ace E7/PSO(8) is stable with respect to the Einstein-Hilbert action\, ther
eby exhibiting\nthe first known example of a non-symmetric metric of posit
ive scalar curvature with this property.\n
LOCATION:https://researchseminars.org/talk/VSGS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thibaut Delcroix (University of Montpellier)
DTSTART;VALUE=DATE-TIME:20220615T160000Z
DTEND;VALUE=DATE-TIME:20220615T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/54
DESCRIPTION:Title: Ya
u-Tian-Donaldson conjecture for cohomogeneity one manifolds\nby Thibau
t Delcroix (University of Montpellier) as part of Virtual seminar on geome
try with symmetries\n\n\nAbstract\nThe Yau-Tian-Donaldson conjecture conce
rns the equivalence between existence of Kähler metrics with constant sca
lar curvature on a polarized complex manifold\, and an algebro-geometric K
-stability condition. It has been solved in the case of anticanonically po
larized manifolds by Chen-Donaldson-Sun\, and in the case of toric surface
s by Donaldson. In both cases\, a condition weaker than the expected K-sta
bility suffices\, and in the toric case\, Donaldson translates the K-stabi
lity into a convex polytope geometry problem.\nIn this talk\, I will prese
nt progress on the Yau-Tian-Donaldson conjecture for spherical varieties\,
and in particular\, a resolution of this conjecture in the case of polari
zed manifolds of cohomogeneity one.\n
LOCATION:https://researchseminars.org/talk/VSGS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anusha Krishnan (University of Münster)
DTSTART;VALUE=DATE-TIME:20220601T090000Z
DTEND;VALUE=DATE-TIME:20220601T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/55
DESCRIPTION:Title: Po
sitive sectional curvature and Ricci flow\nby Anusha Krishnan (Univers
ity of Münster) as part of Virtual seminar on geometry with symmetries\n\
n\nAbstract\nThe preservation of positive curvature conditions under the R
icci flow has been an important ingredient in applications of the flow to
solving problems in geometry and topology. Works by Hamilton and others e
stablished that certain positive curvature conditions are preserved under
the flow\, culminating in Wilking's unified\, Lie algebraic approach to pr
oving invariance of positive curvature conditions. Yet\, some questions r
emain. In this talk\, we describe $\\sec > 0$ metrics on $S^4$ and $\\mat
hbb{C}P^2$\, which evolve under the Ricci flow to metrics with sectional c
urvature of mixed sign. The setting is that of metrics invariant under a
Lie group action of cohomogeneity one. This is joint work with Renato Bet
tiol.\n
LOCATION:https://researchseminars.org/talk/VSGS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Origlia (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20220629T220000Z
DTEND;VALUE=DATE-TIME:20220629T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/56
DESCRIPTION:Title: Co
nformal Killing Yano $2$-forms on Lie groups\nby Marcos Origlia (Unive
rsidad Nacional de Córdoba) as part of Virtual seminar on geometry with s
ymmetries\n\n\nAbstract\nA differential $p$-form $\\eta$ on a $n$-dimensio
nal Riemannian manifold $(M\,g)$ is called Conformal Killing Yano (CKY for
short) if it satisfies for any vector field $X$ the following equation\n$
$\\nabla_X \\eta=\\dfrac{1}{p+1}\\iota_X\\mathrm{d}\\eta-\\dfrac{1}{n-p+1
}X^*\\wedge \\mathrm{d}^*\\eta\,$$\nwhere $X^*$ is the dual 1-form of $X$\
, $\\mathrm{d}^*$ is the codifferential\, $\\nabla$ is the Levi-Civita co
nnection associated to $g$ and $\\iota_X$ is the interior product with $X$
. If $\\eta$ is coclosed ($\\mathrm d^*\\eta=0$) then $\\eta$ is said to b
e a Killing-Yano $p$-form (KY for short).\n\nWe study left invariant Conf
ormal Killing Yano $2$-forms on Lie groups endowed with a left invariant m
etric. We determine\, up to isometry\, all $5$-dimensional metric Lie alge
bras under certain conditions\, admitting a CKY $2$-form. Moreover\, a cha
racterization of all possible CKY tensors on those metric Lie algebras is
exhibited.\n
LOCATION:https://researchseminars.org/talk/VSGS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Lai (Stanford University)
DTSTART;VALUE=DATE-TIME:20221026T220000Z
DTEND;VALUE=DATE-TIME:20221026T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/58
DESCRIPTION:Title: O(
2)-symmetry of 3D steady gradient Ricci solitons\nby Yi Lai (Stanford
University) as part of Virtual seminar on geometry with symmetries\n\n\nAb
stract\nFor any 3D steady gradient Ricci soliton with positive curvature\,
we prove that it must be isometric to the Bryant soliton if it is asympto
tic to a ray. Otherwise\, it is asymptotic to a sector and hence a flying
wing. We show that all 3D flying wings are O(2)-symmetric. Therefore\, all
3D steady gradient Ricci solitons are O(2)-symmetric.\n
LOCATION:https://researchseminars.org/talk/VSGS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Sanmartin-Lopez (Universidad Politécnica de Madrid)
DTSTART;VALUE=DATE-TIME:20220907T090000Z
DTEND;VALUE=DATE-TIME:20220907T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/59
DESCRIPTION:Title: Is
oparametric hypersurfaces in symmetric spaces of non-compact type and high
er rank\nby Victor Sanmartin-Lopez (Universidad Politécnica de Madrid
) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nA
hypersurface is said to be isoparametric if it and its nearby equidistant
hypersurfaces have constant mean curvature. In this talk\, we will see exa
mples of these objects in the context of symmetric spaces together with so
me classification results. After that\, we will construct infinitely many
new examples of isoparametric hypersurfaces with novel properties in symme
tric spaces of non-compact type and rank greater than two.\n
LOCATION:https://researchseminars.org/talk/VSGS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guofang Wei (University of California\, Santa Barbara)
DTSTART;VALUE=DATE-TIME:20221012T160000Z
DTEND;VALUE=DATE-TIME:20221012T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/60
DESCRIPTION:Title: Si
ngular Weyl's law with Ricci curvature bounded below\nby Guofang Wei (
University of California\, Santa Barbara) as part of Virtual seminar on ge
ometry with symmetries\n\n\nAbstract\nWeyl's law describes the asymptotic
behavior of eigenvalues of the Laplace Beltrami operator. Its study has a
long history and is important in mathematics and physics. In a joint work
with J. Pan (GAFA 2022)\, using equivariant convergence\, we constructed
first examples of Ricci limit spaces with symmetry whose Hausdorff dimensi
on may not be an integer and the Hausdorff dim of the singular set is bigg
er than the Hausdorff dim of the regular set. With in-depth study of metri
c and measure of the examples\, and the delicate analysis of the heat kern
els\, in a very recent joint work with X. Dai\, S. Honda\, J. Pan we show
the surprising results that for compact RCD(K\,N)/Ricci limit spaces\, Wey
l's law may not hold for any power\, and in the case when power law holds\
, it is in terms of the Hausdorff measure of the singular set instead of t
he regular set.\n
LOCATION:https://researchseminars.org/talk/VSGS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Sutton (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20230125T160000Z
DTEND;VALUE=DATE-TIME:20230125T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/61
DESCRIPTION:Title: Ge
neric properties of Laplace eigenfunctions in the presence of torus action
s\nby Craig Sutton (Dartmouth College) as part of Virtual seminar on g
eometry with symmetries\n\n\nAbstract\nA result of Uhlenbeck (1976) states
that for a generic Riemannian metric $g$ on a closed manifold $M$ of dime
nsion at least two the real eigenspaces of the associated Laplace operator
$\\Delta_g$ are each one-dimensional and the nodal set (i.e.\, zero set)
of any $\\Delta_g$-eigenfunction is a smooth hypersurface. Now\, let $T$ b
e a non-trivial torus acting freely on a closed manifold $M$ with $\\dim M
> \\dim T$. We demonstrate that a generic $T$-invariant metric $g$ on $M$
has the following properties: (1) the real $\\Delta_g$-eigenspaces are ir
reducible representations of $T$ and\, consequently\, are of dimension one
or two\, and (2) the nodal set of any $\\Delta_g$-eigenfunction is a smoo
th hypersurface. The first of these statements is a mathematically rigorou
s instance of the belief in quantum mechanics that non-irreducible eigensp
aces are ``accidental degeneracies.'' \n\nRegarding the second statement\,
in the event the non-trivial quotient $B = M/T$ satisfies a certain topol
ogical condition\, we show that\, for a generic $T$-invariant metric $g$\,
any orthonormal basis $\\langle \\phi_j \\rangle$ consisting of $\\Delta_
g$-eigenfunctions possesses a density-one subsequence $\\langle \\phi_{j_k
}\\rangle$ where the nodal set of each $\\phi_{j_k}$ is a smooth hypersurf
ace dividing $M$ into exactly two nodal domains\, the minimal possible num
ber of nodal domains for a non-constant eigenfunction. This observation st
ands in stark contrast to the expected behavior of the nodal count in the
presence of an ergodic geodesic flow\, where examples suggest one should a
nticipate the nodal count associated to a ``typical'' sequence of orthogon
al Laplace eigenfunctions will approach infinity. \n\nThis is joint work w
ith Donato Cianci (GEICO)\, Chris Judge (Indiana) and Samuel Lin (Oklahoma
).\n
LOCATION:https://researchseminars.org/talk/VSGS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Kollross (University of Stuttgart)
DTSTART;VALUE=DATE-TIME:20221123T090000Z
DTEND;VALUE=DATE-TIME:20221123T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/62
DESCRIPTION:Title: To
tally geodesic submanifolds in exceptional symmetric spaces\nby Andrea
s Kollross (University of Stuttgart) as part of Virtual seminar on geometr
y with symmetries\n\n\nAbstract\nJoint work with Alberto Rodríguez-Vázqu
ez. I will speak about our recent paper where we classify maximal totally
geodesic subspaces in exceptional Riemannian symmetric spaces. Since the m
aximal subspaces containing flat factors have been classified by Berndt an
d Olmos\, it suffices to find the semisimple ones. We show that these corr
espond to subalgebras in the Lie algebra of the isometry group which are m
aximal among the semisimple subalgebras without compact ideals. To find al
l such subalgebras of simple real Lie algebras\, we use earlier classifica
tion results by Dynkin\, de Graaf-Marrani and Komrakov.\n
LOCATION:https://researchseminars.org/talk/VSGS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McFeely Jackson Goodman
DTSTART;VALUE=DATE-TIME:20221207T160000Z
DTEND;VALUE=DATE-TIME:20221207T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/63
DESCRIPTION:Title: Cu
rvature Operators\, Laplacians\, and Rational Cobordism\nby McFeely Ja
ckson Goodman as part of Virtual seminar on geometry with symmetries\n\n\n
Abstract\nWe give new conditions on positivity of certain linear combinati
ons of eigenvalues of the curvature operator of a Riemannian manifold whic
h imply the vanishing of the indices of Dirac operators twisted with geome
tric vector bundles. The vanishing indices in turn have topological impli
cations in terms of the Pontryagin classes\, rational cobordism type\, and
Witten genus of the manifolds. To prove our results we generalize new me
thods developed by Petersen and Wink to apply the Bochner technique to Lap
lacians on geometric vector bundles.\n
LOCATION:https://researchseminars.org/talk/VSGS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucia Martin Merchan (University of Waterloo)
DTSTART;VALUE=DATE-TIME:20230222T220000Z
DTEND;VALUE=DATE-TIME:20230222T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/64
DESCRIPTION:Title: To
pological properties of closed $\\mathrm{G}_2$ manifolds through compact q
uotients of Lie groups\nby Lucia Martin Merchan (University of Waterlo
o) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nA
$\\mathrm{G}_2$ structure on a 7-dimensional Riemannian manifold $(M\,g)$
is determined by a stable of 3-form $\\varphi$. It is said to be closed i
f $d\\varphi=0$ and torsion-free if $\\varphi$ is parallel. The purpose of
this talk is to discuss two problems where compact quotients of Lie group
s are useful for understanding topological properties of compact closed $\
\mathrm{G}_2$ manifolds that don´t admit any torsion-free $\\mathrm{G}_2$
structure. More precisely\, these problems are related to the open questi
ons: Are simply connected compact closed $\\mathrm{G}_2$ manifolds almost
formal? Could a compact closed $\\mathrm{G}_2$ manifold have third Betti n
umber $b_3=0$?\n\nUsing compact quotients of Lie groups\, we first outline
the construction of a manifold admitting a closed $\\mathrm{G}_2$ structu
re that is not almost formal and has first Betti number $b_1=1$. Later\, w
e show that there aren´t invariant exact $\\mathrm{G}_2$ structures on co
mpact quotients of Lie groups. The last result is joint work with Anna Fin
o and Alberto Raffero.\n
LOCATION:https://researchseminars.org/talk/VSGS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason DeVito (The University of Tennessee at Martin)
DTSTART;VALUE=DATE-TIME:20230208T160000Z
DTEND;VALUE=DATE-TIME:20230208T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/65
DESCRIPTION:Title: Th
e non-simply connected double soul conjecture\nby Jason DeVito (The Un
iversity of Tennessee at Martin) as part of Virtual seminar on geometry wi
th symmetries\n\n\nAbstract\nCheeger and Gromoll's Soul theorem asserts th
at a complete non-compact Riemannian manifold of non-negative sectional cu
rvature has the structure of a vector bundle over a closed totally geodesi
c submanifold. The double soul conjecture (DSC) predicts an analogous str
ucture on every closed simply connected Riemannian manifold of non-negativ
e sectional curvature: it should decompose as a union of two disk bundles
(possible of different ranks).\n\nIf one relaxes the hypothesis of the DS
C to allow non-simply connected manifolds\, then previously only a single
counterexample was known. We will discuss two new infinite families of co
unterexamples\, one positively curved and the other flat. In addition\, a
ll of our counterexamples are so-called biquotients\, quotients of Riemann
ian homogeneous spaces by free isometric actions. We will also investiga
te the biquotient structure on the flat examples\, finding that\, in contr
ast with the homogeneous case\, they do not support a biquotient structure
induced from a connected Lie group.\n
LOCATION:https://researchseminars.org/talk/VSGS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hemangi Madhusudan Shah (Harish-Chandra Research Institute)
DTSTART;VALUE=DATE-TIME:20230308T090000Z
DTEND;VALUE=DATE-TIME:20230308T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/66
DESCRIPTION:Title: So
me Solitons on Homogeneous Almost $\\alpha$-Cosymplectic 3-Manifolds and H
armonic Manifolds\nby Hemangi Madhusudan Shah (Harish-Chandra Research
Institute) as part of Virtual seminar on geometry with symmetries\n\n\nAb
stract\nWe investigate the nature of Einstein solitons\, whether it is ste
ady\, shrinking or expanding on almost alpha-cosymplectic 3-manifolds. We
also prove that a simply connected homogeneous almost $\\alpha$-cosymplect
ic 3-manifold\, admitting a contact Einstein soliton\, is an unimodular se
midirect product Lie group. Finally\, we show that a harmonic manifold adm
its a non-trivial Ricci soliton if and only if it is flat. Thus we show t
hat rank one symmetric spaces of compact as well as non-compact type are s
table under a Ricci soliton. In particular\, we obtain a strengthening of
Theorem 1 and Theorem 2 of the paper on the Stability of symmetric spaces
of noncompact type under Ricci flow\, by R. Balmer.\n
LOCATION:https://researchseminars.org/talk/VSGS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yurii G. Nikonorov (Southern Mathematical Institute of the Vladika
vkaz Scientific Center of the Russian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20230322T160000Z
DTEND;VALUE=DATE-TIME:20230322T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/67
DESCRIPTION:Title: Fi
nite homogeneous metric spaces with special properties\nby Yurii G. Ni
konorov (Southern Mathematical Institute of the Vladikavkaz Scientific Cen
ter of the Russian Academy of Sciences) as part of Virtual seminar on geom
etry with symmetries\n\n\nAbstract\nThis talk is devoted to some recent re
sults on finite homogeneous metric spaces obtained in joint papers with Pr
of. V.N. Berestovskii. Every finite homogeneous metric subspace of an Eucl
idean space represents the vertex set of a compact convex polytope with th
e isometry group that is transitive on the set of vertices\, moreover\, al
l these vertices lie on some sphere. Consequently\, the study of such subs
ets is closely related to the theory of convex polytopes in Euclidean spac
es.\n\nThe main subject of discussion is the classification of regular and
semiregular polytopes in Euclidean spaces by whether or not their vertex
sets have the normal homogeneity property or the Clifford - Wolf homogenei
ty property.\nThe normal homogeneity and the Clifford - Wolf homogeneity d
escribe more stronger properties than the homogeneity. Therefore\, it is q
uite natural to check the presence of these properties for the vertex sets
of regular and semiregular polytopes.\n\nIn the second part of the talk\,
we consider the $m$-point homogeneity property and the point homogeneity
degree for finite metric spaces. Among main results\, there is a classific
ation of polyhedra with all edges of equal length and with 2-point homogen
eous vertex sets.\n\nThe most recent results and still unsolved problems i
n this topic will also be discussed.\n
LOCATION:https://researchseminars.org/talk/VSGS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Tolcachier (National University of Córdoba)
DTSTART;VALUE=DATE-TIME:20230405T220000Z
DTEND;VALUE=DATE-TIME:20230405T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/69
DESCRIPTION:Title: Sp
ecial Hermitian structures on products of Sasakian manifolds\nby Aleja
ndro Tolcachier (National University of Córdoba) as part of Virtual semin
ar on geometry with symmetries\n\n\nAbstract\nIt is known that the product
of two Sasakian manifolds carries a 2-parameter family of Hermitian struc
tures $(J_{a\,b}\,g_{a\,b})$. In this talk we will investigate when these
Hermitian structures are locally conformally Kähler\, balanced\, strong K
ähler with torsion\, Gauduchon or $k$-Gauduchon ($k≥2$). Moreover\, we
will study the Bismut connection associated to $(J_{a\,b}\,g_{a\,b})$ and
we will provide formulas for the associated Bismut-Ricci tensor $\\operato
rname{Ric}^B$ and the Bismut-Ricci form $\\rho^B$. We will show that these
tensors vanish if and only if each Sasakian factor is $\\eta$-Einstein wi
th appropriate constants and we will also exhibit some examples fulfilling
these conditions\, thus providing new examples of Calabi-Yau with torsion
manifolds. This talk is based in a recent joint work with my PhD advisor
Adrián Andrada.\n
LOCATION:https://researchseminars.org/talk/VSGS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Salamon (King's College London)
DTSTART;VALUE=DATE-TIME:20230503T160000Z
DTEND;VALUE=DATE-TIME:20230503T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/70
DESCRIPTION:Title: Th
e flag manifold $SU(3)/T^2$ and its subvarieties\nby Simon Salamon (Ki
ng's College London) as part of Virtual seminar on geometry with symmetrie
s\n\n\nAbstract\nThis talk will emphasize symmetries inherent in studying
the geometry of the complex 3-dimensional flag manifold\, in particular\,
those arising from the special Hermitian structure of $\\C^3$. It will be
based mainly on joint work with A. Altavilla\, E. Ballico\, and M.C. Bramb
illa on the behaviour of algebraic curves and surfaces in the flag manifol
d with respect to its (non-holomorphic) twistor projection to the complex
projective plane.\n
LOCATION:https://researchseminars.org/talk/VSGS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Nienhaus (WWU Münster)
DTSTART;VALUE=DATE-TIME:20230614T090000Z
DTEND;VALUE=DATE-TIME:20230614T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/71
DESCRIPTION:Title: Ei
nstein metrics on spheres of even dimension\nby Jan Nienhaus (WWU Mün
ster) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract
\nThe first non-round Einstein metrics on spheres were described in 1973 b
y Jensen in dimensions 4n+3 (n > 0). For the next 25 years it remained an
open problem whether the same could be done in even dimensions. This quest
ion was settled in 1998 when C. Böhm constructed infinite families of Ein
stein metrics on all Spheres of dimension between 5 and 9\, in particular
on $S^6$ and $S^8$. \n\nOver the last 25 years\, all spheres of odd dimens
ion (at least 5) have been shown to admit non-round Einstein metrics\, but
there have been no new developments in even dimensions above 8\, leaving
open to speculation the question of whether non-uniqueness of the round me
tric is a low-dimensional phenomenon or to be expected in all dimensions.\
n\nI will give an overview of the methods used to construct non-round Eins
tein metrics\, which we recently used to construct three new Einstein metr
ics on $S^{10}$.\n\n\n\nThis is joint work with Matthias Wink\n
LOCATION:https://researchseminars.org/talk/VSGS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Geatti (Universita' di Roma Tor Vergata)
DTSTART;VALUE=DATE-TIME:20230913T160000Z
DTEND;VALUE=DATE-TIME:20230913T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/72
DESCRIPTION:Title: Ge
ometry of Hermitian symmetric spaces under the action of a maximal unipote
nt group.\nby Laura Geatti (Universita' di Roma Tor Vergata) as part o
f Virtual seminar on geometry with symmetries\n\n\nAbstract\nGiven a compl
ex manifold $M$ with a Lie group $G$ action by holomorphic transformatio
ns\, \nit is of interest to understand associated invariant objects l
ike the invariant Stein subdomains and the invariant plurisubharmoni
c functions.\n\nA classical example of this framework is given by tube d
omains in complex Euclidean space\, where $M={\\bf C}^n$ and $G={\\bf R}^
n$ acts by translations. \n\nAn ${\\bf R}^n$-invariant domain $D={\\bf R
}^n+i\\Omega$ in ${\\bf C}^n$ is Stein if and only if its base $\\Omega$
is geometrically convex (Bochner's tube theorem). Moreover an ${\\bf R}^
n$-invariant function on a Stein tube domain $D$ is plurisubharmonic if an
d only if its restriction to $\\Omega$ is convex. \n\n\n In this talk\, we
present a generalization of the above results in the setting of a Herm
itian symmetric space of the non-compact type $G/K$ under the action of
a maximal unipotent subgroup $N\\subset G$. \nAs a by-product we obtain
all $N$-invariant potentials of the Bergman metric of $G/K$ in a Lie theor
etical fashion and an explicit formula for the moment maps $\\mu\\colon
G/K\\to {\\mathfrak n}^*$ associated to such potentials.\n\n \nThis is wo
rk in collaboration with Andrea Iannuzzi.\n
LOCATION:https://researchseminars.org/talk/VSGS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mary Sandoval (Trinity College)
DTSTART;VALUE=DATE-TIME:20230517T220000Z
DTEND;VALUE=DATE-TIME:20230517T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/73
DESCRIPTION:Title: De
tecting Orbifold Singularities via the Orbifold Length Spectra\nby Mar
y Sandoval (Trinity College) as part of Virtual seminar on geometry with s
ymmetries\n\n\nAbstract\nIn this talk\, we will consider the geodesic flow
on a compact Riemannian orbifold $\\mathcal{O}$. Assuming the set of clos
ed geodesics on the orbifold is non-empty\, we consider the following ques
tion: Is it possible to detect orbifold singularities via the length spec
trum of $\\mathcal{O}$ and the length spectrum of the associated orthonorm
al frame bundle of the orbifold? The answer is a qualifed yes\, provided t
hat the closed geodesic flow on $\\mathcal{O}$ intersects with the singula
r set of the orbifold\, and the non-trivial isotropy group of the singular
ity ``closes up" the geodesic. Assuming these conditions are satisfied\, w
e consider a second question: Given a singularity on a closed geodesic\, w
hat aspects of the isotropy group can be determined by the dynamics of the
geodesic flow for closed geodesics that pass through the singularity? Par
tial results to this second question will be discussed. The proofs will us
e some recent results from the spectral theory of leaf spaces of regular a
nd singular Riemannian foliations.\n
LOCATION:https://researchseminars.org/talk/VSGS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Schwahn (University of Stuttgart)
DTSTART;VALUE=DATE-TIME:20230531T160000Z
DTEND;VALUE=DATE-TIME:20230531T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/74
DESCRIPTION:Title: Th
e Lichnerowicz Laplacian on normal homogeneous spaces\nby Paul Schwahn
(University of Stuttgart) as part of Virtual seminar on geometry with sym
metries\n\n\nAbstract\nThe Lichnerowicz Laplacian $\\Delta_L$ is an intere
sting differential operator on Riemannian manifolds\, generalizing the Hod
ge-de Rham Laplacian on differential forms to tensors of arbitrary type. I
t features prominently in the study of the linear stability of Einstein me
trics.\n\nNormal homogeneous spaces are a natural setting in which Casimir
operators occur. In the 80s\, Koiso studied the stability of symmetric sp
aces of compact type\, utilizing the coincidence of $\\Delta_L$ with a Cas
imir operator. Motivated by his and also the $G$-stability results of Laur
et-Lauret-Will\, we generalize Koiso's strategy to general normal homogene
ous spaces.\n\nUltimately this approach is sufficient to provide many new
non-symmetric examples of stable Einstein manifolds of positive scalar cur
vature.\n
LOCATION:https://researchseminars.org/talk/VSGS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Olmos (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20230628T160000Z
DTEND;VALUE=DATE-TIME:20230628T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/75
DESCRIPTION:Title: Ho
pf fibrations and totally geodesic submanifolds\nby Carlos Olmos (Univ
ersidad Nacional de Córdoba) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nA Hopf-Berger sphere of factor $\\tau$ is the
total space of a Hopf fibration such that the Riemannian metric is rescal
ed by a factor $\\tau\\neq 1$ in the directions of the fibers. If the Hop
f fibration is the complex one\, a Hopf-Berger sphere of $\\tau <1$ is the
usual Berger sphere. Any Hopf-Berger sphere may be regarded as a geodesi
c sphere $\\mathsf{S}_t^m(o)\\subset\\bar M$ of radius $t$ of a rank one s
ymmetric space of non-constant curvature ($\\bar M$ is compact if and only
if $\\tau <1$). A Hopf-Berger sphere has positive curvature if and only
if $\\tau <4/3$. A standard totally geodesic submanifold of $\\mathsf{S}_t
^m(o)$ is obtained as the intersection of the geodesic sphere with a total
ly geodesic submanifold of $\\bar M$ that contains the center $o$. In this
talk we will refer to our recent classification of totally geodesic subma
nifolds of Hopf-Berger spheres. In particular\, for quaternionic and octo
nionic fibrations\, non-standard totally geodesic spheres with the same di
mension of the fiber appear\, for $\\tau <1/2$. Moreover\, there are tot
ally geodesic $\\mathbb RP^2$\, and $\\mathbb RP^3$ (under some restricti
ons on $\\tau$\, the dimension\, and the type of the fibration). On the
one hand\, as a consequence of the connectedness principle of Wilking\, t
here does not exist a totally geodesic $\\mathbb RP^4$ in a space of po
sitive curvature which diffeomorphic to the sphere $S^7$. On the other h
and\, we construct an example of a totally geodesic $\\mathbb RP^2$ in a H
opf-Berger sphere of dimension $7$ and positive curvature. Could there exi
st a totally geodesic $\\mathbb RP^3$ in a space of positive curvature whi
ch diffeomorphic to $S^7$?.\n\nThis talk is based on a joint work with Al
berto Rodríguez-Vázquez.\n
LOCATION:https://researchseminars.org/talk/VSGS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Thompson (The University of Queensland)
DTSTART;VALUE=DATE-TIME:20230712T220000Z
DTEND;VALUE=DATE-TIME:20230712T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/76
DESCRIPTION:Title: Ne
w examples of Ricci solitons with non-compact symmetry\nby Adam Thomps
on (The University of Queensland) as part of Virtual seminar on geometry w
ith symmetries\n\n\nAbstract\nThere are many examples of Ricci solitons th
at are constructed using the following ansatz: the soliton admits a cohomo
geneity one group action by a compact Lie group. On the other hand\, there
are very few examples of cohomogeneity one Ricci solitons where the group
acting is non-compact. In fact\, all known examples of inhomogeneous Ricc
i solitons with non-compact symmetry have either abelian symmetry or speci
al holonomy. We will discuss our construction of new examples of complete
cohomogeneity one gradient Ricci solitons where the group action is by a n
on-compact solvable Lie group\, many of which do not have special holonomy
.\n
LOCATION:https://researchseminars.org/talk/VSGS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonardo Cavenaghi (State University of Campinas)
DTSTART;VALUE=DATE-TIME:20230726T160000Z
DTEND;VALUE=DATE-TIME:20230726T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/77
DESCRIPTION:Title: Th
e complete dynamics description of positively curved metrics in the Wallac
h flag manifold $\\mathrm{SU}(3)/\\mathrm{T}^2$ and other homogeneous spac
es\nby Leonardo Cavenaghi (State University of Campinas) as part of Vi
rtual seminar on geometry with symmetries\n\n\nAbstract\nThe family of inv
ariant Riemannian manifolds in the Wallach flag manifold $\\mathrm{SU}(3)/
\\mathrm{T}^2$ is described by three parameters $(x\,y\,z)$ of positive re
al numbers. By restricting such a family of metrics in the tetrahedron $\\
mathcal{T}:= x+y+z = 1$\, we show how to describe all regions $\\mathcal R
\\subset \\mathcal T$ admitting metrics with curvature properties varying
from positive sectional curvature to positive scalar curvature\, includin
g positive intermediate curvature notion's. We study the dynamics of such
regions under the projected Ricci flow in the plane $(x\,y)$\, concluding
sign curvature maintenance and escaping. We stress how this approach can b
e generalized to several other homogeneous spaces and can be helpful to di
scuss the moduli space of bundles associated with the principal bundle $\\
mathrm{T}^2\\hookrightarrow \\mathrm{SU}(3) \\rightarrow \\mathrm{SU}(3)/\
\mathrm{T}^2$.\n\nThis work is done in collaboration with Lino Grama\, Ric
ardo M. Martins and Douglas D. Novaes\n
LOCATION:https://researchseminars.org/talk/VSGS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fangyang Zheng (Chongqing Normal University)
DTSTART;VALUE=DATE-TIME:20231108T090000Z
DTEND;VALUE=DATE-TIME:20231108T100000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/78
DESCRIPTION:Title: Wh
en will the Chern connection of a Hermitian manifold have parallel torsion
and curvature?\nby Fangyang Zheng (Chongqing Normal University) as pa
rt of Virtual seminar on geometry with symmetries\n\n\nAbstract\nThis talk
is a based on joint work with Prof. Lei Ni at UCSD. We consider a special
type of compact\, locally homogeneous Hermitian manifolds\, where Chern c
onnection is Ambrose-Singer\, namely having parallel torsion and curvature
. We will also discuss the Bismut case\, where some partial answers were o
btained and some open questions were proposed.\n
LOCATION:https://researchseminars.org/talk/VSGS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Eastwood (University of Adelaide)
DTSTART;VALUE=DATE-TIME:20231011T220000Z
DTEND;VALUE=DATE-TIME:20231011T230000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/79
DESCRIPTION:Title: Th
e range of the double fibration transform\nby Michael Eastwood (Univer
sity of Adelaide) as part of Virtual seminar on geometry with symmetries\n
\n\nAbstract\nOn and off\, for the past 20 years or so\, Joe Wolf and I ha
d been working on this transform. The input is the Dolbeault cohomology of
certain homogeneous vector bundles and the output is solutions of certain
invariant systems of partial differential equations. Perhaps we had bitte
n off more than we could chew. Some cases are straightforward. Others are
unreasonably awkward. I’ll talk about our long draft article\, especiall
y its motivation and what still needs to be done.\n
LOCATION:https://researchseminars.org/talk/VSGS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julieth Saavedra (University of Ceará)
DTSTART;VALUE=DATE-TIME:20231025T160000Z
DTEND;VALUE=DATE-TIME:20231025T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/80
DESCRIPTION:Title: La
placian coflow of G_2-structures: Review and open questions.\nby Julie
th Saavedra (University of Ceará) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nGeometric flows involving $G_2$-structures
have proven to be valuable tools in the study of $G_2$-geometry. Some exam
ples of the Laplacian coflow of $G_2$-structures have been developed on co
ntact Calabi-Yau manifolds and Abelian Lie groups. In this flow on contact
Calabi-Yau manifolds\, it was shown that it exhibits a singularity\, lead
ing to metric and volume collapse. Additionally\, we will explore some res
ults obtained from the almost Abelian Lie groups in the Laplacian coflow\,
revealing that the solution converges to a torsion-free $G_2$-structure.\
n
LOCATION:https://researchseminars.org/talk/VSGS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART;VALUE=DATE-TIME:20231206T160000Z
DTEND;VALUE=DATE-TIME:20231206T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/81
DESCRIPTION:Title: To
rus actions with connected isotropy groups\nby Lee Kennard (Syracuse U
niversity) as part of Virtual seminar on geometry with symmetries\n\n\nAbs
tract\nRecent work with Michael Wiemeler and Burkhard Wilking analyzes tor
us representations all of whose isotropy groups are connected. An importan
t structure result is a splitting theorem\, which states that the represen
tation splits as a product after passing to the induced action on a suitab
le fixed-point set. More recently\, we found a connection between these re
presentations and combinatorial objects called regular matroids\, and we a
pplied work of Seymour to classify torus representations with connected is
otropy groups. As an application\, we prove new obstructions to the existe
nce of Riemannian metrics with positive sectional curvature and large symm
etry. In some cases\, the assumption on the torus rank is independent of t
he manifold dimension.\n
LOCATION:https://researchseminars.org/talk/VSGS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anusha M. Krishnan (University of Münster)
DTSTART;VALUE=DATE-TIME:20240117T160000Z
DTEND;VALUE=DATE-TIME:20240117T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/82
DESCRIPTION:Title: To
ral symmetries of homogeneous collapsed ancient Ricci flows\nby Anusha
M. Krishnan (University of Münster) as part of Virtual seminar on geomet
ry with symmetries\n\n\nAbstract\nRicci flow solutions that are defined fo
r all negative times\, are called ancient\, and have a special significanc
e since they arise as blowup limits at singularities of the flow. Several
instances in the literature suggest that ancient solutions to the Ricci f
low have a higher degree of symmetry than initially assumed. In recent wo
rk (joint with F. Pediconi and S. Sbiti)\, we show that under certain assu
mptions\, collapsed homogeneous ancient solutions to the Ricci flow have a
dditional toral symmetry.\n
LOCATION:https://researchseminars.org/talk/VSGS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mat Langford (Australian National University)
DTSTART;VALUE=DATE-TIME:20240131T230000Z
DTEND;VALUE=DATE-TIME:20240131T235900Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/83
DESCRIPTION:Title: An
cient solutions to geometric flows with small symmetry groups\nby Mat
Langford (Australian National University) as part of Virtual seminar on ge
ometry with symmetries\n\n\nAbstract\nA useful method for the construction
of examples of proper solutions to elliptic or parabolic (geometric) part
ial differential equations involves the reduction of the equation to a sim
pler one (typically\, an algebraic equation or an ordinary differential eq
uation) via the imposition of a suitable symmetry Ansatz. I will present s
ome recent "genuinely parabolic" constructions of ancient solutions to geo
metric flows (mean curvature flow\, fully nonlinear extrinsic flows and th
e Ricci flow) which rely on (sometimes *much*) weaker symmetry Ans&au
ml\;tze. While the resulting equations are still parabolic partial differe
ntial equations\, the imposed symmetries nonetheless yield crucial simplif
ications (e.g. allowing for the exploitation of special properties of geom
etric flow equations which only hold in low space dimensions).\n
LOCATION:https://researchseminars.org/talk/VSGS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaime Santos Rodríguez (Universidad Autónoma de Madrid)
DTSTART;VALUE=DATE-TIME:20240228T160000Z
DTEND;VALUE=DATE-TIME:20240228T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/85
DESCRIPTION:Title: Sy
mmetries of Wasserstein spaces\nby Jaime Santos Rodríguez (Universida
d Autónoma de Madrid) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nLet $\\mathbb{P}_p(X)$ be the space of probability meas
ures with finite $p-$moments on a metric space $(X\,d).$ Using solutions t
o the optimal transport problem of Monge-Kantorovich it is possible to equ
ip $\\mathbb{P}_p(X)$ with a distance $\\mathbb{W}_p$ known as the $L^p-$W
asserstein distance. \n\nWith this the resulting metric space $(\\mathbb{P
}_p(X)\, \\mathbb{W}_p)$ will share many geometrical properties with the b
ase space $(X\,d)$ such as: compactness\, existence of geodesics\, and eve
n non-negative sectional curvature bounds (when $p=2$).\n\nTherefore\, a n
atural question is whether it is possible for $(\\mathbb{P}_p(X)\, \\mathb
b{W}_p)$ to be more symmetric than the original space $(X\,d).$ In this ta
lk we will first introduce the optimal transport problem\, Wasserstein spa
ces\, and some of its properties. Once this is done we will discuss some o
f the results regarding isometries in these spaces.\n
LOCATION:https://researchseminars.org/talk/VSGS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Markina (University of Bergen)
DTSTART;VALUE=DATE-TIME:20240214T140000Z
DTEND;VALUE=DATE-TIME:20240214T150000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/86
DESCRIPTION:Title: A
unified approach to extremal curves on Stiefel manifolds\nby Irina Mar
kina (University of Bergen) as part of Virtual seminar on geometry with sy
mmetries\n\n\nAbstract\nWe present a unified framework for studying extrem
al curves on real Stiefel manifolds. We start with a smooth one-parameter
family of pseudo-Riemannian metrics on a product of orthogonal groups acti
ng transitively on Stiefel manifolds. We find Euler-Langrange equations fo
r a class of extremal curves that includes geodesics with respect to diffe
rent Riemannian metrics and smooth curves of constant geodesic curvature.
For some specific values of the parameter in the family of pseudo-Riemanni
an metrics we recover certain well-known metrics used in the applied mathe
matics.\n \nThis is a joint work with K. Hueper (University of Wurzburg\,
Germany) and F. Silva Leite (University of Coimbra\, Portugal)\n
LOCATION:https://researchseminars.org/talk/VSGS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie-Amelie Lawn (Imperial College London)
DTSTART;VALUE=DATE-TIME:20240313T160000Z
DTEND;VALUE=DATE-TIME:20240313T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/87
DESCRIPTION:Title: Ge
neralized spin structures and homogeneous spaces\nby Marie-Amelie Lawn
(Imperial College London) as part of Virtual seminar on geometry with sym
metries\n\n\nAbstract\nSpin geometry is a useful tool to describe geometri
c properties of manifolds. For instance\, it is well-known that a manifold
admitting parallel spinors has to be Ricci flat. Another example is Seibe
rg-Witten theory which relies on the existence of a notion of spin structu
re on 4-manifolds. However not every manifold admits a classical spin str
ucture. In this talk we generalise this notion\, so that every manifold ad
mits a generalised spin structure. We look at obstructions for such struct
ure and study their G-equivariance in the case of homogeneous spaces G/H.
We will discuss the spheres as an example.\n
LOCATION:https://researchseminars.org/talk/VSGS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyle Broder (The University of Queensland)
DTSTART;VALUE=DATE-TIME:20240327T230000Z
DTEND;VALUE=DATE-TIME:20240327T235900Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/88
DESCRIPTION:Title: In
variant metrics in complex analysis and a conjecture of Kobayashi and Lang
\nby Kyle Broder (The University of Queensland) as part of Virtual sem
inar on geometry with symmetries\n\n\nAbstract\nA compact complex manifold
$X$ is declared Kobayashi hyperbolic if every holomorphic map from the co
mplex plane into $X$ is constant. Kobayashi hyperbolic manifolds have main
tained a central role in our understanding of the landscape of complex man
ifolds since their introduction in 1967. One striking feature of complex g
eometry is the capacity to encode this highly transcendental notion of hyp
erbolicity in the coarse geometric language of distance functions that are
invariant under the automorphism group and decrease under holomorphic map
s. A long-standing conjecture of Kobayashi (1970) and Lang (1986) predicts
that a compact Kobayashi hyperbolic Kähler manifold admits a Kähler—E
instein metric of negative Ricci curvature. We will present the most gener
al evidence for the Kobayashi—Lang conjecture: A compact Kähler manifol
d with a pluriclosed metric of negative holomorphic curvature admits a uni
que Kähler—Einstein metric of negative Ricci curvature. This result is
a joint work with James Stanfield and comes from the first general improve
ment on the Schwarz lemma for holomorphic maps between Hermitian manifolds
since 1978.\n
LOCATION:https://researchseminars.org/talk/VSGS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Sebastián Rodríguez (Pontificia Universidad Javeriana)
DTSTART;VALUE=DATE-TIME:20240424T130000Z
DTEND;VALUE=DATE-TIME:20240424T140000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/89
DESCRIPTION:Title: Is
ospectrality in Symmetric Spaces\nby Juan Sebastián Rodríguez (Ponti
ficia Universidad Javeriana) as part of Virtual seminar on geometry with s
ymmetries\n\n\nAbstract\nFor a Riemannian manifold $(M\,g)$\, we define it
s spectrum as the spectrum of the Laplace–Beltrami operator $\\Delta_g$.
We say that two Riemannian manifolds are isospectral if their spectra are
equal. A fundamental problem in spectral geometry is to describe the isos
pectral class of distinguishable Riemannian manifolds.\n\nIn this talk\, w
e study two families of homogeneous metrics on the manifolds $\\mathrm{SO}
(2n+2)/\\mathrm{U}(n+1)$ and $\\mathrm{SU}(2n+2)/\\mathrm{Sp}(n+1)$. Using
Lie theoretical methods\, we describe the spectrum of each metric within
these families and establish results regarding spectral uniqueness. This r
esearch is conducted jointly with Emilio Lauret\, PhD (Universidad Naciona
l del Sur\, Argentina).\n
LOCATION:https://researchseminars.org/talk/VSGS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Wulle
DTSTART;VALUE=DATE-TIME:20240410T160000Z
DTEND;VALUE=DATE-TIME:20240410T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/90
DESCRIPTION:Title: Co
homogeneity one manifolds with quasipositive curvature\nby Dennis Wull
e as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nLe
t $G$ be a Lie group acting by isometries on a Riemannian manifold $(M\,g)
$. The action is of cohomogeneity one\, if the orbit space $M/G$ is one-di
mensional. In this sense cohomogeneity one manifolds are the most symmetri
c manifolds after homogeneous spaces\, which have a $0$-dimensional orbit
space. In this talk we will give a classification of cohomogeneity one man
ifolds admitting an invariant metric with quasipositive sectional curvatur
e\, except for two infinite families in dimension $7$. A Riemannian manifo
ld has quasipositive sectional curvature\, if it has non-negative sectiona
l curvature and contains one point\, where all tangent planes have positiv
e sectional curvature. A similar classification in positive curvature has
already been obtained by Verdiani in even dimensions and Grove\, Wilking a
nd Ziller in odd dimensions. Surprisingly\, our result only adds two more
examples to their list: an Eschenburg space and a Bazaikin space\, which w
ere previously known to admit metrics with quasipositive curvature.\n
LOCATION:https://researchseminars.org/talk/VSGS/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Madnick (University of Oregon / Seton Hall University)
DTSTART;VALUE=DATE-TIME:20240508T160000Z
DTEND;VALUE=DATE-TIME:20240508T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/91
DESCRIPTION:Title: Th
e Morse index of quartic minimal hypersurfaces\nby Jesse Madnick (Univ
ersity of Oregon / Seton Hall University) as part of Virtual seminar on ge
ometry with symmetries\n\n\nAbstract\nGiven a minimal hypersurface S in a
round sphere\, its Morse index is the number of variations that are area-d
ecreasing to second order. In practice\, computing the Morse index of a gi
ven minimal hypersurface is extremely difficult\, requiring detailed infor
mation about the Laplace spectrum of S. Indeed\, even for the simplest cas
e in which S is homogeneous\, the Morse index of S is not known in general
.\n\nIn this talk\, we compute the Morse index of two such minimal hypersu
rfaces. Moreover\, we observe that their spectra contain both integer eige
nvalues as well as (irrational) eigenvalues that are not expressible in ra
dicals. Time permitting\, we'll discuss some open problems and work-in-pro
gress. This is joint work with Gavin Ball (Wisconsin) and Uwe Semmelmann (
Stuttgart).\n
LOCATION:https://researchseminars.org/talk/VSGS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Bryant (Duke University)
DTSTART;VALUE=DATE-TIME:20240605T160000Z
DTEND;VALUE=DATE-TIME:20240605T170000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/92
DESCRIPTION:Title: Af
fine Bonnet surfaces\nby Robert Bryant (Duke University) as part of Vi
rtual seminar on geometry with symmetries\n\n\nAbstract\nThe Bonnet proble
m in Euclidean surface theory is well-known: Given a metric $g$ and a fun
ction $H$ on an oriented surface $M^2$\, when (and in how many ways) can $
(M\,g)$ be isometrically immersed in $\\mathbb{R}^3$ with mean curvature $
H$? For generic data $(g\,H)$\, such an immersion does not exist and\, in
the case that one does exist\, it is unique up to ambient isometry. Bonn
et showed that\, aside from the famous case of surfaces of constant mean c
urvature\, there is a finite-dimensional moduli space of $(g\,H)$ for whic
h the space of such "Bonnet immersions" has positive dimension.\n\nThe cor
responding problem in affine theory (a favorite topic of Eugenio Calabi) i
s still not completely solved. After reviewing the results on the Euclide
an problem by O. Bonnet\, J. Radon\, É. Cartan\, A. Bobenko and others\,
I will give a report on affine analogs of those results. In particular\,
I will consider the classification of the data $(g\,H)$ for which the spac
e of "affine Bonnet immersions" has positive dimension\, showing a surpris
ing connection with integrable systems in the case of data $(g\,H)$ for wh
ich the space of affine Bonnet immersions has the highest possible dimensi
on.\n
LOCATION:https://researchseminars.org/talk/VSGS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Pediconi (University of Florence)
DTSTART;VALUE=DATE-TIME:20240522T100000Z
DTEND;VALUE=DATE-TIME:20240522T110000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/93
DESCRIPTION:Title: A
moment map for twisted-Hamiltonian vector fields on locally conformally K
ähler manifolds\nby Francesco Pediconi (University of Florence) as pa
rt of Virtual seminar on geometry with symmetries\n\n\nAbstract\nAccording
to Fujiki and Donaldson's foundational work\, the scalar curvature of Kä
hler metrics arises as a moment map for an infinite-dimensional Hamiltonia
n action. In this talk\, we generalize this result to the broader framewor
k of locally conformally Kähler Geometry. This is joint work with D. Ange
lla\, S. Calamai\, and C. Spotti.\n
LOCATION:https://researchseminars.org/talk/VSGS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Sáez (Pontificia Universidad Católica de Chile)
DTSTART;VALUE=DATE-TIME:20240619T130000Z
DTEND;VALUE=DATE-TIME:20240619T140000Z
DTSTAMP;VALUE=DATE-TIME:20240624T062307Z
UID:VSGS/94
DESCRIPTION:Title: Tr
anslators for mean curvature flow\nby Mariel Sáez (Pontificia Univers
idad Católica de Chile) as part of Virtual seminar on geometry with symme
tries\n\n\nAbstract\nIn this talk I am going to present the relevance of m
ean curvature flow\, some self-similar solutions to this equation and disc
uss some recent results.\n
LOCATION:https://researchseminars.org/talk/VSGS/94/
END:VEVENT
END:VCALENDAR