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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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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:20230331T090642Z
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
END:VCALENDAR