BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Anna Fino (University of Turin)
DTSTART:20200422T120000Z
DTEND:20200422T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/1
DESCRIPTION:Title: Closed $G_2$-structures\nby Anna Fino (University of Turin) as par
t of Virtual seminar on geometry with symmetries\n\n\nAbstract\nI will rev
iew known examples of compact 7-manifolds admitting a closed $G_2$-structu
re. Moreover\, I will discuss some results on the behaviour of the Laplaci
an $G_2$-flow starting from a closed $G_2$-structure whose induced metric
satisfies suitable extra conditions.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART:20200506T150000Z
DTEND:20200506T160000Z
DTSTAMP:20260404T111001Z
UID:VSGS/2
DESCRIPTION:Title: Torus actions and positive curvature\nby Lee Kennard (Syracuse Uni
versity) as part of Virtual seminar on geometry with symmetries\n\n\nAbstr
act\nIn the 1930s\, H. Hopf conjectured that an even-dimensional Riemannia
n manifold with positive sectional curvature has positive Euler characteri
stic. In joint work with M. Wiemeler and B. Wilking\, this is confirmed in
the special case where the isometry group has rank at least five. Previou
s results 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 r
epresentations of tori with the special property that all isotropy groups
are connected. Such representations are surprisingly rigid\, and we analyz
e them using only elementary techniques.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Mendes (University of Oklahoma)
DTSTART:20200520T230000Z
DTEND:20200520T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/3
DESCRIPTION:Title: The isometry group of spherical quotients\nby Ricardo Mendes (Univ
ersity of Oklahoma) as part of Virtual seminar on geometry with symmetries
\n\n\nAbstract\nA special class of Alexandrov metric spaces are the quotie
nts $X=S^n/G$ of the round spheres by isometric actions of compact subgrou
ps $G$ of $O(n+1)$. We will consider the question of how to compute the is
ometry group of such $X$\, the main result being that every element in the
identity component of $\\operatorname{Isom}(X)$ lifts to a $G$-equivarian
t isometry of the sphere. The proof relies on a pair of important results
about the "smooth structure" of $X$.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilka Agricola (University of Marburg)
DTSTART:20200603T120000Z
DTEND:20200603T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/4
DESCRIPTION:Title: Generalizations of 3-Sasakian manifolds and skew torsion\nby Ilka
Agricola (University of Marburg) as part of Virtual seminar on geometry wi
th symmetries\n\n\nAbstract\nWe define and investigate new classes of almo
st 3-contact metric manifolds\, with two guiding ideas in mind: first\, wh
at geometric objects are best suited for capturing the key properties of a
lmost 3-contact metric manifolds\, and second\, the newly defined classes
should admit `good' metric connections with skew torsion with interesting
applications: these include a well-behaved metric cone\, the existence of
a generalized Killing spinor\, and remarkable curvature properties. This i
s joint work with\nGiulia Dileo (Bari) and Leander Stecker (Marburg).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Nikolayevsky (La Trobe University)
DTSTART:20200701T230000Z
DTEND:20200701T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/5
DESCRIPTION:Title: Einstein extensions of Riemannian manifolds\nby Yuri Nikolayevsky
(La Trobe University) as part of Virtual seminar on geometry with symmetri
es\n\n\nAbstract\nGiven a Riemannian space $N$ of dimension $n$ and a fiel
d $D$ of 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 i
ts Lie algebra. We find the conditions on $N$ and $D$ for $M$ to be Einste
in\, and then study various classes of Einstein extensions so obtained. It
turns out that several remarkable phenomena and properties which were obs
erved in the homogeneous case are still present in the Riemannian case. Th
is is a joint work with D. Alekseevsky.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Wink (UCLA)
DTSTART:20200617T150000Z
DTEND:20200617T160000Z
DTSTAMP:20260404T111001Z
UID:VSGS/6
DESCRIPTION:Title: New Curvature Conditions for the Bochner Technique\nby Matthias Wi
nk (UCLA) as part of Virtual seminar on geometry with symmetries\n\n\nAbst
ract\nThe Bochner Technique has established itself as a powerful tool in G
eometry\, 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 case for manifolds with $\\lceil \\frac{n}{2} \\rceil$-positive curvat
ure operators. We will see that this is a consequence of a general vanishi
ng 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 curva
ture operator. This talk is based on joint work with Peter Petersen.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kerin (NUI Galway)
DTSTART:20200730T180000Z
DTEND:20200730T190000Z
DTSTAMP:20260404T111001Z
UID:VSGS/7
DESCRIPTION:Title: A pot-pourri of non-negatively curved 7-manifolds\nby Martin Kerin
(NUI Galway) as part of Virtual seminar on geometry with symmetries\n\n\n
Abstract\nManifolds with non-negative sectional curvature are rare and dif
ficult to find\, with interesting topological phenomena traditionally bein
g restricted by a dearth of methods of construction. In this talk\, I wil
l describe a large family of seven-dimensional manifolds with non-negative
curvature\, leading to examples of exotic diffeomorphism types\, non-stan
dard homotopy types and fake versions of familiar friends. This is based o
n joint work with Sebastian Goette and Krishnan Shankar.\n\nMartin Kerin's
talk was originally announced on July 15th\, but it had to be canceled by
technical reasons. The current talk is hosted in CUNY Geometric Analysis
Seminar\, and co-sponsored by the Virtual seminar of geometry with symmetr
ies.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gavin Ball (Université du Québec à Montréal)
DTSTART:20200729T150000Z
DTEND:20200729T160000Z
DTSTAMP:20260404T111001Z
UID:VSGS/8
DESCRIPTION:Title: Quadratic closed G2-structures\nby Gavin Ball (Université du Qué
bec à Montréal) as part of Virtual seminar on geometry with symmetries\n
\n\nAbstract\nI will talk about closed G2-structures satisfying the quadra
tic condition\, a second-order PDE system introduced by Bryant involving a
parameter. For particular special values of the parameter\, the quadratic
condition is equivalent to the Einstein equation\, the extremally Ricci-p
inched (ERP) condition\, and the eigenform condition. I will describe my r
ecent existence and classification results about these structures\, includ
ing the first example of a complete inhomogeneous ERP G2-structure\, a new
compact ERP G2-structure\, and the first examples of solutions to this PD
E system for certain values of the parameter. If time permits\, I will des
cribe a related construction of complete inhomogeneous gradient solitons f
or the G2 Laplacian flow.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Siffert (University of Münster)
DTSTART:20200826T120000Z
DTEND:20200826T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/9
DESCRIPTION:Title: Construction of explicit $p$-harmonic functions\nby Anna Siffert (
University of Münster) as part of Virtual seminar on geometry with symmet
ries\n\n\nAbstract\nThe study of $p$-harmonic functions on Riemannian mani
folds has invoked the interest of mathematicians and physicists for nearly
two centuries. Applications within physics can for example be found in co
ntinuum mechanics\, elasticity theory\, as well as two-dimensional hydrody
namics problems involving Stokes ows of incompressible Newtonian fluids.\n
\nIn my talk I will focus on the construction of explicit $p$-harmonic fun
ctions on rank-one Lie groups of Iwasawa type. This joint wok with Sigmund
ur Gudmundsson and Marko Sobak.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Lauret (Universidad Nacional de Córdoba)
DTSTART:20200812T230000Z
DTEND:20200812T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/10
DESCRIPTION:Title: Prescribing Ricci curvature on homogeneous manifolds\nby Jorge La
uret (Universidad Nacional de Córdoba) as part of Virtual seminar on geom
etry with symmetries\n\n\nAbstract\nGiven a symmetric 2-tensor $T$ on a ma
nifold $M$\, it is a classical problem in Riemannian geometry to ask about
the existence (and uniqueness) of a metric $g$ on $M$ such that $\\textr
m{Ric}(g) = T$ (see e.g. [Besse\,Chap.5]). Assuming that $M$ is a homoge
neous manifold\, we will consider in the talk the $G$-invariant version of
the problem\, where $G$ is a (unimodular\, not necessarily compact) Lie g
roup acting transitively on $M$. \n\nAfter an overview of results and que
stions\, we will give a formula for the differential $d\\textrm{Ric}$ of t
he function $\\textrm{Ric}$ at a $G$-invariant metric $g$\, which is preci
sely the Lichnerowicz Laplacian acting on $G$-invariant symmetric 2-tensor
s. The formula is in terms of the moment map for the variety of Lie algeb
ras. \n\nAs an application\, we will consider the concept of Ricci local
invertibility 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 equivale
nt to the existence of a $G$-invariant solution $g'$ to the Prescribed Ric
ci Problem $\\textrm{Ric}(g') = cT$ (for some $c>0$)\, for any $G$-invar
iant $T$ sufficiently close to $\\textrm{Ric}(g)$. Our main result is tha
t any irreducible naturally reductive metric on $M$ with respect to $G$ is
Ricci locally invertible. \n\nThis is joint work in progress with C
ynthia Will.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Ovando (Universidad Nacional de Rosario)
DTSTART:20200916T150000Z
DTEND:20200916T160000Z
DTSTAMP:20260404T111001Z
UID:VSGS/11
DESCRIPTION:Title: First integrals of the geodesic flow on nilpotent Lie groups of step
at most three\nby Gabriela Ovando (Universidad Nacional de Rosario) as
part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nIn thi
s talk we would like to consider the question of integrability of the geod
esic flow on nilmanifolds. We start with nilpotent Lie groups\, mostly of
step two and three\, equipped with a left-invariant metric. We show some a
lgebraic relations when studying functions in involution and we obtain exp
licit examples in low dimensions. Some examples of Liouville integrability
in compact 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://stable.researchseminars.org/talk/VSGS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramiro Lafuente (The University of Queensland)
DTSTART:20200930T230000Z
DTEND:20200930T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/12
DESCRIPTION:Title: Homogeneous Einstein metrics via a cohomogeneity-one approach\nby
Ramiro Lafuente (The University of Queensland) as part of Virtual seminar
on geometry with symmetries\n\n\nAbstract\nWe establish non-existence res
ults on non-compact homogeneous Einstein manifolds. The key idea in the pr
oof is to consider non-transitive group actions on these spaces (more prec
isely\, actions with cohomogeneity one)\, and to find geometric monotone q
uantities for the ODE that results from writing the Einstein equation in s
uch a setting. As an application\, we show that homogeneous Einstein metri
cs on Euclidean spaces are Einstein solvmanifolds. This is joint work with
C. Böhm.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnan Shankar (University of Oklahoma)
DTSTART:20200715T120000Z
DTEND:20200715T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/13
DESCRIPTION:Title: Highly connected 7-manifolds\, non-negative curvature and the linking
form\nby Krishnan Shankar (University of Oklahoma) as part of Virtual
seminar on geometry with symmetries\n\nAbstract: TBA\n\nThe original anno
uncement of this talk included Martin Kerin (NUI Galway\, Ireland) as the
speaker. For technical reasons during the transmission\, it was decided th
at Martin Kerin's coauthor Krishnan Shankar replace him giving a talk on t
he same subject as the original one. The organizers thank Ravi Shankar for
his help in this urgent moment.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Raffero (Università degli Studi di Torino)
DTSTART:20201014T120000Z
DTEND:20201014T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/14
DESCRIPTION:Title: Symmetries of closed G2-structures\nby Alberto Raffero (Universit
à degli Studi di Torino) as part of Virtual seminar on geometry with symm
etries\n\n\nAbstract\nIn this talk I will consider 7-manifolds endowed wit
h a closed G2-structure and having a large symmetry group. In the compact
case\, I will discuss the properties of the full automorphism group of a c
losed G2-structure\, showing how they impose strong constraints on the con
struction of homogeneous and cohomogeneity one examples. In the non-compac
t case\, I will first give a brief overview of known examples and then I w
ill describe the classification of 7-manifolds with a closed G2-structure
that are homogeneous under the action of a reductive Lie group. This is jo
int work with F. Podestà\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Bettiol (Lehman College\, CUNY)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260404T111001Z
UID:VSGS/15
DESCRIPTION:Title: Minimal spheres in ellipsoids\nby Renato Bettiol (Lehman College\
, CUNY) as part of Virtual seminar on geometry with symmetries\n\n\nAbstra
ct\nIn 1987\, Yau posed the question of whether all minimal 2-spheres in a
3-dimensional ellipsoid inside $\\mathbb R^4$ are planar\, i.e.\, determi
ned by the intersection with a hyperplane. While this is the case if the e
llipsoid is nearly round\, Haslhofer and Ketover have recently shown the e
xistence of an embedded non-planar minimal 2-sphere in sufficiently elonga
ted ellipsoids\, with min-max methods. Using bifurcation theory and the sy
mmetries that arise if at least two semi-axes coincide\, we show the exist
ence of arbitrarily many distinct embedded non-planar minimal 2-spheres in
sufficiently elongated ellipsoids of revolution. This is based on joint w
ork with P. Piccione.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sammy Sbiti (University of Pennsylvania)
DTSTART:20201111T220000Z
DTEND:20201111T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/16
DESCRIPTION:Title: On the Ricci Flow of Homogeneous Metrics on Spheres\nby Sammy Sbi
ti (University of Pennsylvania) as part of Virtual seminar on geometry wit
h symmetries\n\n\nAbstract\nWe study the Ricci flow of homogeneous metrics
on spheres. We determine their forward behavior and also classify ancient
solutions. In doing so we exhibit a new one-parameter family of ancient s
olutions on spheres.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Otiman (Roma Tre University)
DTSTART:20201125T160000Z
DTEND:20201125T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/17
DESCRIPTION:Title: Special non-Kähler metrics on solvmanifolds\nby Alexandra Otiman
(Roma Tre University) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nWe discuss old and new results about the existence of s
pecial Hermitian metrics (locally conformally Kähler\, balanced\, pluricl
osed) on complex nilmanifolds and on Oeljeklaus-Toma manifolds. This latte
r class represents a generalization of Inoue-Bombieri surfaces in arbitrar
y complex dimension and its construction\, based on algebraic number theor
y\, will allow us to give a numerical interpretation of the existence of s
everal Hermitian metrics of special type.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timothy Buttsworth (The University of Queensland)
DTSTART:20201209T220000Z
DTEND:20201209T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/18
DESCRIPTION:Title: The prescribed Ricci curvature problem on manifolds with large symmet
ry groups\nby Timothy Buttsworth (The University of Queensland) as par
t of Virtual seminar on geometry with symmetries\n\n\nAbstract\nThe prescr
ibed Ricci curvature problem continues to be of fundamental interest in Ri
emannian geometry. In this talk\, I will describe some classical results o
n this topic\, as well as some more recent results that have been achieved
with homogeneous and cohomogeneity-one assumptions.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masoumeh Zarei (Universität Augsburg)
DTSTART:20210113T160000Z
DTEND:20210113T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/19
DESCRIPTION:Title: Torus actions on 4-dimensional Alexandrov spaces\nby Masoumeh Zar
ei (Universität Augsburg) as part of Virtual seminar on geometry with sym
metries\n\n\nAbstract\nEquivariant classification of $T^2$-actions on smoo
th closed orientable 4-dimensional manifolds was obtained by Orlik and Ray
mond in 70's. In particular\, they showed that the smooth classification i
s equivalent to the topological classification. In this talk\, I present a
n equivariant classification of isometric $T^2$-actions on closed\, orient
able\, four-dimensional Alexandrov spaces\, which generalizes the equivari
ant classification of Orlik and Raymond. Moreover\, we show that such Alex
androv spaces are equivariantly homeomorphic to 4-dimensional Riemannian o
rbifolds with isometric $T^2$-actions. This is joint work with Diego Corro
and Jesús Núñez-Zimbrón.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Z. Lin (Dartmouth College)
DTSTART:20210127T190000Z
DTEND:20210127T200000Z
DTSTAMP:20260404T111001Z
UID:VSGS/20
DESCRIPTION:Title: Geometric Structure and the Laplace Spectrum\nby Samuel Z. Lin (D
artmouth College) as part of Virtual seminar on geometry with symmetries\n
\n\nAbstract\nThe Laplace spectrum of a compact Riemannian manifold is def
ined to be the set of positive eigenvalues of the associated Laplace opera
tor. Inverse spectral geometry is the study of how this set of analytic da
ta relates to the underlying geometry of the manifold.\n\nA (compact) geom
etric structure is defined to be a compact Riemannian manifold equipped wi
th a locally homogeneous metric. Geometric structures played an important
role in the study of two and three-dimensional geometry and topology. In d
imension two\, the only geometric structures are those of constant curvatu
re. Furthermore\, Berger showed that they are determined up to local isome
tries by their Laplace spectra.\n\nIn this work\, we study the following q
uestion: “To what extend are the three-dimensional geometric structures
determined by their Laplace spectra?” Among other results\, we provide s
trong evidence that the local geometry of a three-dimensional geometric st
ructure is determined by its Laplace spectrum\, which is in stark contrast
with results in higher dimensions. This is a joint work with Ben Schmidt
(Michigan State University) and Craig Sutton (Dartmouth College).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Changliang Wang (Tongji University)
DTSTART:20210224T090000Z
DTEND:20210224T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/21
DESCRIPTION:Title: The linear instability of some families of Einstein metrics\nby C
hangliang Wang (Tongji University) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nI will report some works on the linear stab
ility question of Einstein metrics. We proved the linear instability of so
me Einstein metrics with positive scalar curvature\, including some famili
es of Riemannian manifolds with real Killing spinors\, and low-dimensional
homogeneous Einstein spaces. The talk is based on joint works with McKenz
ie Wang and Uwe Semmelmann.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina M Arroyo (Universidad Nacional de Córdoba)
DTSTART:20210210T220000Z
DTEND:20210210T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/22
DESCRIPTION:Title: On the signature of the Ricci curvature on nilmanifolds\nby Romin
a M Arroyo (Universidad Nacional de Córdoba) as part of Virtual seminar o
n geometry with symmetries\n\n\nAbstract\nA classical problem in Riemannia
n geometry is to determine the possible signatures of the Ricci curvature
on a given space. The aim of this talk is to present the problem in the s
etting of nilpotent Lie groups with left-invariant metrics\, and to give a
complete answer of the problem in this case.\n\nThis is joint work with R
amiro Lafuente (The University of Queensland).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosa Sena-Dias (Instituto Superior Tecnico)
DTSTART:20210310T160000Z
DTEND:20210310T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/23
DESCRIPTION:Title: Minimal Lagrangian tori in toric manifolds\nby Rosa Sena-Dias (In
stituto Superior Tecnico) as part of Virtual seminar on geometry with symm
etries\n\n\nAbstract\nMinimal submanifolds were first introduced and studi
ed in the 18th century. They are the object of a great deal of interest no
wadays as they play an important role in Riemannian Geometry\, Mathematica
l Physics and have many applications. Still\, there are surprisingly few c
oncrete examples of such submanifolds apart from the obvious ones. \n\nIn
this talk we want to discuss examples of minimal Lagrangian tori in toric
manifolds. They come from exploiting the toric symmetry through the use o
f what Palais called the ''Principle of Symmetric Criticality''. We will g
ive background\, discuss examples and if time permits talk about open prob
lems.\n\nThis is joint work with Gonçalo Oliveira.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfang Ziller (University of Pennsylvania)
DTSTART:20210324T190000Z
DTEND:20210324T200000Z
DTSTAMP:20260404T111001Z
UID:VSGS/24
DESCRIPTION:Title: A variational approach to prescribing the Ricci tensor\nby Wolfan
g Ziller (University of Pennsylvania) as part of Virtual seminar on geomet
ry 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 so
me c. Solutions can be viewed as the critical points of a modified scalar
curvature functional and we examine the global behavior of this functional
in the case of homogeneous spaces. This is joint work with Artem Pulemoto
v.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiayin Pan (University of California-Santa Barbara)
DTSTART:20210407T220000Z
DTEND:20210407T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/25
DESCRIPTION:Title: Nonnegative Ricci curvature\, escape rate\, and virtual abelianness\nby Jiayin Pan (University of California-Santa Barbara) as part of Virt
ual seminar on geometry with symmetries\n\n\nAbstract\nA consequence of Ch
eeger-Gromoll splitting theorem states that for any open manifold $(M\,x)$
of nonnegative Ricci curvature\, if all the minimal geodesic loops at $x$
that represent 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 loops to escape from any bounded sets. In this talk\, we introduce a
quantity\, escape rate\, to measure how fast these loops escape. Then we
prove that if the escape rate is less than some positive constant $\\epsil
on(n)$\, which only depends on the dimension $n$\, then $\\pi_1(M\,x)$ is
virtually abelian. The main tools are equivariant Gromov-Hausdorff converg
ence and Cheeger-Colding theory on Ricci limit spaces.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Galaz-García (Durham University)
DTSTART:20210421T160000Z
DTEND:20210421T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/26
DESCRIPTION:Title: Geometry and Topology of collapsed three-dimensional Alexandrov Space
s\nby Fernando Galaz-García (Durham University) as part of Virtual se
minar on geometry with symmetries\n\n\nAbstract\nIn Riemannian geometry\,
collapse imposes strong geometric and topological restrictions on the spac
es on which it occurs. In the case of Alexandrov spaces\, which are metric
generalizations of complete Riemannian manifolds with a uniform lower sec
tional curvature bound\, collapse is fairly well understood in dimension t
hree. In this talk\, I will discuss the geometry and topology of three-dim
ensional Alexandrov spaces and focus on those which are sufficiently colla
psed. When such spaces are irreducible\, they are modeled on one of the e
ight three-dimensional dimensional Thurston geometries\, excluding the hyp
erbolic one. This extends a result of Shioya and Yamaguchi\, originally fo
rmulated for Riemannian manifolds\, to the Alexandrov setting. We will br
iefly discuss how spaces with circle actions enter the picture. (Joint wor
k with Luis Guijarro and Jesús Núñez-Zimbrón).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Madnick (National Center for Theoretical Sciences)
DTSTART:20210505T090000Z
DTEND:20210505T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/27
DESCRIPTION:Title: The Second Variation of Holomorphic Curves in the 6-Sphere\nby Je
sse Madnick (National Center for Theoretical Sciences) as part of Virtual
seminar on geometry with symmetries\n\n\nAbstract\nThe 6-sphere is the onl
y $n$-sphere with $n > 2$ that admits an almost-complex structure. Equipp
ing the round 6-sphere with its standard ($G_2$-invariant) almost-complex
structure\, the holomorphic curves in $S^6$ are minimal surfaces\, and pla
y an important role in $G_2$-geometry. These surfaces exist in abundance:
by a remarkable theorem of Bryant\, extended by Rowland\, every closed Ri
emann surface may be conformally embedded in $S^6$ as a holomorphic curve
of "null-torsion."\n\nWhile holomorphic curves in $S^6$ are area-minimizin
g to first order\, they are not area-minimizing to second order. This fai
lure is encoded by the spectrum of the Jacobi operator\, which contains in
formation such as the Morse index and nullity. For closed\, null-torsion
holomorphic curves of low genus\, we explicitly compute the multiplicity o
f the first Jacobi eigenvalue. Moreover\, for all genera\, we give a simp
le lower bound for the nullity in terms of the area and genus. Time permi
tting\, we will also outline some recent results in the setting of holomor
phic curves with boundary.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniël Thung (Universität Hamburg)
DTSTART:20210616T160000Z
DTEND:20210616T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/28
DESCRIPTION:Title: Cohomogeneity one quaternionic Kähler manifolds\nby Daniël Thun
g (Universität Hamburg) as part of Virtual seminar on geometry with symme
tries\n\n\nAbstract\nThe study of quaternionic Kähler geometry has long b
een hampered by a lack of examples. However\, a construction known as the
c-map has recently made it possible to construct many complete examples of
negative scalar curvature. Moreover\, the quaternionic Kähler manifolds
that arise from the c-map admit a one-parameter deformation through comple
te quaternionic Kähler manifolds. In this talk\, I will describe the (def
ormed) c-map in detail and show how to use it to construct interesting coh
omogeneity one quaternionic Kähler manifolds\, focusing on a series of ex
amples which arise as deformations of quaternionic Kähler symmetric space
s. This is joint work with Vicente Cortés\, Markus Röser\, and Arpan Sah
a.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicoletta Tardini (Università di Parma)
DTSTART:20210630T090000Z
DTEND:20210630T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/29
DESCRIPTION:Title: SKT and Kähler-like metrics on complex manifolds\nby Nicoletta T
ardini (Università di Parma) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nSeveral special non-Kähler Hermitian metrics ca
n be introduced on complex manifolds. Among them\, SKT metrics deserve par
ticular attention. They can be defined on a complex manifold by saying tha
t the torsion of the Bismut connection associated to the metric is closed.
These metrics always exist on compact complex surfaces but the situation
in higher dimension is very different. We will discuss several properties
concerning these metrics also in relation with the Bismut connection havin
g Kähler-like curvature. Since this last property on nilmanifolds will fo
rce the complex structure to be abelian\, we will also discuss the relatio
n between SKT metrics and abelian complex structures on unimodular Lie alg
ebras.\nThese are joint works with Anna Fino and Luigi Vezzoni.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Catherine Searle (Wichita State University)
DTSTART:20210811T220000Z
DTEND:20210811T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/30
DESCRIPTION:Title: Almost isotropy-maximal manifolds of non-negative curvature\nby C
atherine Searle (Wichita State University) as part of Virtual seminar on g
eometry with symmetries\n\n\nAbstract\nWe extend the equivariant classific
ation results of Escher and Searle for closed\, simply connected\, non-ne
gatively curved Riemannian n-manifolds admitting isometric isotropy-maxim
al torus actions to the class of such manifolds admitting isometric strict
ly almost isotropy-maximal torus actions. In particular\, we prove that s
uch manifolds are equivariantly diffeomorphic to the free\, linear quotien
t by a torus of a product of spheres of dimensions greater than or equal t
o three.\n\nThis is joint work with Z. Dong and C. Escher.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (National Autonomous University of Mexico)
DTSTART:20210519T160000Z
DTEND:20210519T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/31
DESCRIPTION:Title: Upper bound on the revised first Betti number and torus stability for
RCD spaces\nby Raquel Perales (National Autonomous University of Mexi
co) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\n
Gromov and Gallot showed in the past century that for a fixed dimension n
there exists a positive number $\\varepsilon(n)$ so that any $n$-dimension
al riemannian manifold satisfying $Ric_g \\textrm{diam}(M\,g)^2 \\geq -\\v
arepsilon(n)$ has first Betti number smaller than or equal to $n$. Furthe
rmore\, by Cheeger-Colding if the first Betti number equals $n$ then $M$ i
s bi-Hölder homeomorphic to a flat torus. This part is the corresponding
stability statement to the rigidity result proven by Bochner\, namely\, c
losed riemannian manifolds with nonnegative Ricci curvature and first Bett
i number equal to their dimension has to be a torus. \n\nThe proof of Grom
ov and Cheeger-Colding results rely on finding an appropriate subgroup of
the abelianized fundamental group to pass to a nice covering space of $M$
and then study the geometry of the covering. In this talk we will genera
lize these results to the case of $RCD(K\,N)$ spaces\, which is the synthe
tic notion of a riemannian manifold satisfying $Ric \\geq K$ and $dim \\l
eq N$. This class of spaces include ricci limit spaces and Alexandrov spac
es. \n\n Joint work with I. Mondello and A. Mondino.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Epstein (McDaniel College)
DTSTART:20210825T160000Z
DTEND:20210825T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/32
DESCRIPTION:Title: Symmetry groups of solvmanifolds\nby Jonathan Epstein (McDaniel C
ollege) as part of Virtual seminar on geometry with symmetries\n\n\nAbstra
ct\nAlthough it is generally difficult to determine the full isometry grou
p of a solvmanifold $S$\, partial knowledge of its symmetries can yield us
eful information. For example\, the existence of a maximally symmetric met
ric is related to the existence of extensions of the Lie algebra $\\mathfr
ak{s}$ of $S$ which admit a nontrivial Levi decomposition. Motivated by th
is\, we describe the decompositions $\\mathfrak{s} = \\mathfrak{s}_1 \\lti
mes \\mathfrak{s}_2$ which yield such extensions and develop a procedure f
or determining their existence. When the step-size of the nilradical of $\
\mathfrak{s}$ is bounded\, we use the representation theory of real semisi
mple Lie algebras to describe the structure of such extensions. This is jo
int work with Michael Jablonski.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henrique N. Sá Earp (University of Campinas (Unicamp))
DTSTART:20210728T160000Z
DTEND:20210728T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/33
DESCRIPTION:Title: Harmonic $\\rm{Sp}(2)$-invariant $\\rm{G}_2$-structures on the $7$-sp
here\nby Henrique N. Sá Earp (University of Campinas (Unicamp)) as pa
rt of Virtual seminar on geometry with symmetries\n\n\nAbstract\nWe descri
be the $10$-dimensional space of $\\rm{Sp}(2)$-invariant $\\rm{G}_2$-struc
tures on the homogeneous $7$-sphere $\\mathbb{S}^7=\\mathrm{Sp}(2)/\\rm{Sp
}(1)$ as $\\Omega_+^3(\\mathbb{S}^7)^{\\mathrm{Sp}(2)}\\simeq \\mathbb{R}^
+ \\times\\rm{Gl}^+(3\,\\mathbb{R})$. \n In those terms\, we formulate
a general Ansatz for $\\rm{G}_2$-structures\, which realises representativ
es in each of the $7$ possible isometric classes of homogeneous $\\rm{G}_2
$-structures.\n Moreover\, the well-known nearly parallel ${round}$ an
d ${squashed}$ metrics occur naturally as opposite poles in an $\\mathbb{S
}^3$-family\, the equator of which is a new $\\mathbb{S}^2$-family of cocl
osed $\\rm{G}_2$-structures satisfying the harmonicity condition $\\mathr
m{div}\\\; T=0$. \n We show general existence of harmonic representativ
es of $\\rm{G}_2$-structures in each isometric class through explicit solu
tions of the associated flow and describe the qualitative behaviour of the
flow. We study the stability of the Dirichlet gradient flow near these cr
itical points\, showing explicit examples of degenerate and nondegenerate
local maxima and minima\, at various regimes of the general Ansatz. Finall
y\, for metrics outside of the Ansatz\, we identify families of harmonic $
\\rm{G}_2$-structures\, prove long-time existence of the flow and study th
e stability properties of some well-chosen examples.\n\nJoint work with E.
Loubeau\, A. Moreno and J. Saavedra.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Petersen (UCLA)
DTSTART:20210602T220000Z
DTEND:20210602T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/34
DESCRIPTION:Title: Rigidity of Homogeneous Gradient Soliton Metrics and Related Equation
s\nby Peter Petersen (UCLA) as part of Virtual seminar on geometry wit
h symmetries\n\n\nAbstract\nThis is joint work with Will Wylie. The goal i
s to classify\, if possible\, the homogeneous geometric solitons. Here a g
eometric soliton is the soliton for a geometric flow. The Ricci flow is th
e most prominent example of such a flow\, but there are many others where
the Ricci tensor is replaced with some other tensor that depends in a natu
ral way on the Riemannian structure. We will also consider some more gener
al problems showing that our techniques can be used for other geometric pr
oblems.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART:20211006T220000Z
DTEND:20211006T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/35
DESCRIPTION:Title: Invariant theory without groups\nby Marco Radeschi (University of
Notre Dame) as part of Virtual seminar on geometry with symmetries\n\n\nA
bstract\nGiven an orthogonal representation of a Lie group $G$ on a Euclid
ean vector space $V$\, Invariant Theory studies the algebra of $G$-invaria
nt polynomials on $V$. This setting can be generalized by replacing the re
presentation $G$ with a foliation $F$ on $V$\, with equidistant leaves. In
this case\, one can study the algebra of polynomials that are constant al
ong these fibers - effectively producing an Invariant Theory\, but without
groups. In this talk we will discuss a surprising relation between the ge
ometry of the foliation and the corresponding algebra\, including recent j
oint work in progress with Ricardo Mendes and Samuel Lin\, showing how to
estimate volume and diameter of the quotient $V/F$ using the algebra.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviana del Barco (Universidade Estadual de Campinas)
DTSTART:20211117T160000Z
DTEND:20211117T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/36
DESCRIPTION:Title: Uniqueness of ad-invariant metrics\nby Viviana del Barco (Univers
idade Estadual de Campinas) as part of Virtual seminar on geometry with sy
mmetries\n\n\nAbstract\nAn ad-invariant metric on a Lie algebra is a nonde
generate symmetric bilinear form for which inner derivations are skew-symm
etric. These are the algebraic counterparts of bi-invariant metrics on Lie
groups.\n\nIt is known that a positive definite ad-invariant metric can o
nly be defined on compact semisimple Lie algebras\, direct sum with an abe
lian factor. On compact simple Lie algebras\, every ad-invariant metric is
a multiple of the Killing form which\, in addition\, is invariant under t
he Lie algebra automorphisms.\n\nIn the pseudo-Riemannian context ad-invar
iant metrics appear on more general Lie algebras such as semisimple (non-c
ompact)\, or solvable. For non-semisimple Lie algebras\, the orbit space o
f ad-invariant metrics under the action of the automorphism group has not
been systematically described yet.\n\nIn this talk\, we will discuss chara
cteristics of Lie algebras possessing a unique ad-invariant metric up to a
utomorphisms (and sign). In particular\, we will introduce the concept of
"solitary" 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 pr
operty of a Lie algebra rather than of the metric itself.\n\nThis characte
rization of uniqueness allowed us to show that Lie algebras admitting a un
ique ad-invariant metric are necessarily solvable. In addition\, we show t
hat many low dimensional Lie algebras carrying ad-invariant metrics are so
litary.\n\nTime permitting\, generalizations of the solitary conditions wi
ll be discussed.\n\nThe talk is based on joint works with Diego Conti and
Federico A. Rossi (Milano Bicocca).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Böhm (University of Münster)
DTSTART:20210908T160000Z
DTEND:20210908T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/37
DESCRIPTION:Title: Non-compact Einstein manifolds with symmetry\nby Christoph Böhm
(University of Münster) as part of Virtual seminar on geometry with symme
tries\n\n\nAbstract\nFor Einstein manifolds with negative scalar curvature
admitting an isometric action\nof a Lie group $G$ with compact\, smooth o
rbit space\, we show the following rigidity result: The\nnilradical $N$ of
$G$ acts polarly\, and the $N$-orbits can be extended to minimal Einstein
submanifolds.\n\nAs an application\, we prove the Alekseevskii conjecture
. This is joint work with R. Lafuente.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolaos Panagiotis Souris (University of Patras)
DTSTART:20211103T090000Z
DTEND:20211103T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/38
DESCRIPTION:Title: Riemannian geodesic orbit manifolds: An overview and some recent resu
lts\nby Nikolaos Panagiotis Souris (University of Patras) as part of V
irtual seminar on geometry with symmetries\n\n\nAbstract\nA homogeneous Ri
emannian manifold is called geodesic orbit if all geodesics are orbits of
one-parameter groups of isometries\, or equivalently\, integral curves of
Killing vector fields. Well-known examples include symmetric\, weakly symm
etric and naturally reductive manifolds\, yet a complete classification of
geodesic orbit manifolds remains open. In this talk\, we firstly review
basic aspects of the study of geodesic orbit manifolds. Further\, we focus
on compact Lie groups\, and we discuss recent results on Einstein Lie gro
ups that \nare not geodesic orbit manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Pacini (University of Torino)
DTSTART:20211020T160000Z
DTEND:20211020T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/39
DESCRIPTION:Title: Ricci curvature\, the convexity of volume and minimal Lagrangian subm
anifolds\nby Tommaso Pacini (University of Torino) as part of Virtual
seminar on geometry with symmetries\n\n\nAbstract\nThere exist various cla
ssical relationships between Ricci curvature and volume. We will show that
\, in toric Kaehler geometry\, the relationship is particularly strong: th
e sign of the Ricci curvature corresponds to convexity properties of the v
olume functional. As an application\, we will discuss existence/uniqueness
results for minimal Lagrangian submanifolds.\n\nWe will emphasize the fac
t that\, although these topics are Riemannian/symplectic\, the ideas used
in the proofs are complex-theoretic.\n\nMore generally\, we will discuss a
nalogous results in the wider context of group compactifications.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommy Murphy (Cal State Fullerton)
DTSTART:20211201T230000Z
DTEND:20211201T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/41
DESCRIPTION:Title: Rigidity of $SU(n)$-type symmetric spaces\nby Tommy Murphy (Cal S
tate Fullerton) as part of Virtual seminar on geometry with symmetries\n\n
\nAbstract\nI show the biinvariant metric on $SU(2n+1)$ is isolated in the
moduli space of Einstein metrics\, even though it admits infinitesimal de
formations. This gives a non-K\\”ahler\, non-product example of this phe
nomenon adding to the famous example of $\\mathbb{CP}^{2n}\\times \\mathbb
{CP}^1$ found by Koiso. Time permitting\, I will also survey further appl
ications of our techniques to questions concerning solitonic rigidity and
the stability of Ricci flow. This is joint work with W. Batat\, S.J. Hall
and J. Waldron.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Deré (KU Leuven Kulak)
DTSTART:20220223T160000Z
DTEND:20220223T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/43
DESCRIPTION:Title: Simply transitive NIL-affine actions of solvable Lie groups\nby J
onas Deré (KU Leuven Kulak) as part of Virtual seminar on geometry with s
ymmetries\n\n\nAbstract\nAlthough not every $1$-connected solvable Lie gro
up $G$ 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 suitable nilpotent Lie group $N$\, depending on $G$. However\, not m
uch is known about which pairs of Lie groups $(G\,N)$ admit such an action
\, where ideally you only need information about the Lie algebras correspo
nding to $G$ and $N$. The most-studied case is when $G$ is assumed to be n
ilpotent\, then the existence of a simply transitive action is related to
the notion of complete pre-Lie algebra structures.\n\nIn recent work with
Marcos Origlia\, we showed how this problem is related to the semisimple s
plitting of the Lie algebra corresponding to $G$. Our characterization not
only allows us to check whether a given action is simply transitive\, but
also whether a simply transitive action exists given the Lie groups $G$ a
nd $N$. As a consequence\, we list the possibilities for such actions up t
o dimension $4$.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeong Hyeong Park (Sungkyunkwan University)
DTSTART:20220309T120000Z
DTEND:20220309T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/44
DESCRIPTION:Title: Recent progress on harmonic manifolds\nby Jeong Hyeong Park (Sung
kyunkwan University) as part of Virtual seminar on geometry with symmetrie
s\n\n\nAbstract\nA Riemannian manifold (M\, g) is harmonic if there exists
a nonconstant radial harmonic function in a punctured neighborhood for an
y point\, or equivalently if a volume density function centered at a point
depends only on the distance from the center. There are many other charac
terizations of harmonic spaces. For example\, it is known that (M\, g) is
a harmonic space if and only if every sufficiently small geodesic sphere h
as constant mean curvature. Szabo proved that in a harmonic space\, the vo
lume 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 cla
ssify harmonic spaces by using the asymptotic series of the density functi
on and eigenvalues of the Jacobi operator\, and characterize harmonic spac
es in terms of the radial eigenspaces of the Laplacian. We discuss our rec
ent progress on harmonic spaces. (This is joint work with P. Gilkey)\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Domínguez Vázquez (University of Santiago de Compostela)
DTSTART:20220126T160000Z
DTEND:20220126T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/45
DESCRIPTION:Title: Cohomogeneity one actions on symmetric spaces of noncompact type\
nby Miguel Domínguez Vázquez (University of Santiago de Compostela) as p
art of Virtual seminar on geometry with symmetries\n\n\nAbstract\nThe clas
sification of cohomogeneity one actions (up to orbit equivalence) on real
hyperbolic spaces is known since Cartan's investigation of isoparametric h
ypersurfaces in the late 1930s. The analogous classification for the other
rank one symmetric spaces of noncompact type was only concluded very rece
ntly. For higher rank\, several partial results have been obtained by Bern
dt and Tamaru\, but complete classifications are only known for some rank
two irreducible spaces.\n\nIn this talk I will report on a joint work in p
rogress with J. Carlos Díaz-Ramos and Tomás Otero-Casal where we provide
a new structural result for cohomogeneity one actions on symmetric spaces
of noncompact type and arbitrary rank. This allows us to derive the class
ification on the spaces SL(n\,R)/SO(n) and to reduce the problem on a redu
cible space to the classification on each one of its factors.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jeffrey Streets (University of California\, Irvine)
DTSTART:20220209T220000Z
DTEND:20220209T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/46
DESCRIPTION:Title: Generalized Ricci Flow\nby Jeffrey Streets (University of Califor
nia\, Irvine) as part of Virtual seminar on geometry with symmetries\n\n\n
Abstract\nThe generalized Ricci Flow is a natural extension of the Ricci F
low equation which incorporates torsion. In this talk I will describe rece
nt global existence and convergence results\, and their application to pro
blems in complex geometry.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Megan Kerr (Wellesley College)
DTSTART:20220323T160000Z
DTEND:20220323T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/47
DESCRIPTION:Title: Submanifolds of Noncompact Homogeneous Spaces with Special Curvature
Properties\nby Megan Kerr (Wellesley College) as part of Virtual semin
ar on geometry with symmetries\n\n\nAbstract\nThe Ricci curvature form of
a submanifold is not\, in general\, the restriction of the Ricci curvature
of the ambient space. Therefore\, classes of manifolds and submanifolds w
here the Ricci curvatures are aligned are very special. Indeed\, Tamaru ex
ploited this idea in the setting of noncompact symmetric spaces to constru
ct new examples of Einstein solvmanifolds via special subalgebras. We char
acterize the largest category in which Tamaru's construction can be extend
ed\, identifying two crucial algebraic/metric conditions. We explore a new
class of solvmanifolds defined by Kac-Moody algebras that are generalizat
ions of symmetric spaces for which our crucial extra conditions hold. And
furthermore\, in current work in progress\, we investigate other metric pr
operties of these spaces.\n\nThis is joint work with Tracy Payne.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hisashi Kasuya (Osaka Univ.)
DTSTART:20220406T090000Z
DTEND:20220406T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/48
DESCRIPTION:Title: Double sided actions and non-invariant complex structures on compact
Lie groups\nby Hisashi Kasuya (Osaka Univ.) as part of Virtual semina
r on geometry with symmetries\n\n\nAbstract\nIt is known that every compac
t Lie group of even dimension admits left-invariant complex structures. Th
e purpose of this talk is to study "non-invariant" complex structures on
semisimple compact Lie groups. \nThe main idea of this study is "mixing" t
he left action and right action.\n\nThis is joint work with Hiroaki Ishid
a (Kagoshima Univ.)\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Vezzoni (Università di Torino)
DTSTART:20220420T160000Z
DTEND:20220420T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/49
DESCRIPTION:Title: The Calabi-Yau problem in HKT Geometry\nby Luigi Vezzoni (Univers
ità di Torino) as part of Virtual seminar on geometry with symmetries\n\n
\nAbstract\nHKT Geometry (HyperKahler with torsion Geometry) is the Geomet
ry of hyperHermitian manifolds equipped with a nondegenerate $\\partial$-c
losed (2\,0)-form $\\Omega$. \nThe talk will focus on the seek of special
HKT metrics and on a conjecture of Alesker and Verbisky about the existenc
e of a balanced HKT metric on a compact HKT ${\\rm SL}(n\,\\mathbb{H})$-ma
nifold. Some new advances about the conjecture will be described.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Schmidt (Michigan State University)
DTSTART:20220504T220000Z
DTEND:20220504T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/50
DESCRIPTION:Title: Preserve one\, preserve all.\nby Benjamin Schmidt (Michigan State
University) as part of Virtual seminar on geometry with symmetries\n\n\nA
bstract\nLet $(\\mathbb{E}^n\,d)$ denote $n$-dimensional Euclidean space.\
n\nA striking 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 satis
fying $d(f(x)\,f(y))=1$ whenever $d(x\,y)=1$\, then $f$ is necessarily an
isometry. I will discuss a conjecture\, formulated in collaborative work
with Meera Mainkar\, that motions of Riemannian manifolds preserving a suf
ficiently small distance are necessarily isometries. I will present examp
les and supporting results to highlight the role of convexity in this rigi
dity phenomenon.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego Corro (Karlsruher Institut für Technologie)
DTSTART:20220921T090000Z
DTEND:20220921T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/51
DESCRIPTION:Title: Symmetry preserving solutions to the Yamabe Problem\nby Diego Cor
ro (Karlsruher Institut für Technologie) as part of Virtual seminar on ge
ometry with symmetries\n\n\nAbstract\nThe Yamabe problem ask whether we ca
n find for a given smoooth Riemannian manifold a representative with const
ant scalar curvature in the conformal class of the given Riemannian metric
. In this talk we consider such a problem under the extra constrain of pre
serving symmetry. Namely I present that\, under mild geometry conditions\,
we can find solutions to the Yamabe problem which will also respect the s
ymmetry structure given by a singular Riemannian foliation. Singular Riem
annian foliations are generalizations of group actions by isometries and f
iber bundles.\n\nIn other words given a smooth Riemannian manifold with a
smooth Riemannian foliation\, we can find a conformal representative of th
e metric\, 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://stable.researchseminars.org/talk/VSGS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uwe Semmelmann (University of Stuttgart)
DTSTART:20220518T160000Z
DTEND:20220518T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/52
DESCRIPTION:Title: Stability of the non–Symmetric space E7/PSO(8)\nby Uwe Semmelma
nn (University of Stuttgart) as part of Virtual seminar on geometry with s
ymmetries\n\n\nAbstract\nIn my talk I will present a new result on the sta
bility of Einstein metrics obtained in a recent preprint with Paul Schwahn
and Gregor Weingart. There we prove that the normal metric on the homogen
eous space E7/PSO(8) is stable with respect to the Einstein-Hilbert action
\, thereby exhibiting\nthe first known example of a non-symmetric metric o
f positive scalar curvature with this property.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thibaut Delcroix (University of Montpellier)
DTSTART:20220615T160000Z
DTEND:20220615T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/54
DESCRIPTION:Title: Yau-Tian-Donaldson conjecture for cohomogeneity one manifolds\nby
Thibaut Delcroix (University of Montpellier) as part of Virtual seminar o
n geometry with symmetries\n\n\nAbstract\nThe Yau-Tian-Donaldson conjectur
e concerns the equivalence between existence of Kähler metrics with const
ant scalar curvature on a polarized complex manifold\, and an algebro-geom
etric K-stability condition. It has been solved in the case of anticanonic
ally polarized manifolds by Chen-Donaldson-Sun\, and in the case of toric
surfaces by Donaldson. In both cases\, a condition weaker than the expecte
d K-stability suffices\, and in the toric case\, Donaldson translates the
K-stability into a convex polytope geometry problem.\nIn this talk\, I wil
l present progress on the Yau-Tian-Donaldson conjecture for spherical vari
eties\, and in particular\, a resolution of this conjecture in the case of
polarized manifolds of cohomogeneity one.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anusha Krishnan (University of Münster)
DTSTART:20220601T090000Z
DTEND:20220601T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/55
DESCRIPTION:Title: Positive sectional curvature and Ricci flow\nby Anusha Krishnan (
University of Münster) as part of Virtual seminar on geometry with symmet
ries\n\n\nAbstract\nThe preservation of positive curvature conditions unde
r the Ricci flow has been an important ingredient in applications of the f
low to solving problems in geometry and topology. Works by Hamilton and o
thers established that certain positive curvature conditions are preserved
under the flow\, culminating in Wilking's unified\, Lie algebraic approac
h to proving invariance of positive curvature conditions. Yet\, some ques
tions remain. In this talk\, we describe $\\sec > 0$ metrics on $S^4$ and
$\\mathbb{C}P^2$\, which evolve under the Ricci flow to metrics with sect
ional curvature of mixed sign. The setting is that of metrics invariant u
nder a Lie group action of cohomogeneity one. This is joint work with Ren
ato Bettiol.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Origlia (Universidad Nacional de Córdoba)
DTSTART:20220629T220000Z
DTEND:20220629T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/56
DESCRIPTION:Title: Conformal Killing Yano $2$-forms on Lie groups\nby Marcos Origlia
(Universidad Nacional de Córdoba) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nA differential $p$-form $\\eta$ on a $n$-d
imensional Riemannian manifold $(M\,g)$ is called Conformal Killing Yano (
CKY for short) if it satisfies for any vector field $X$ the following equa
tion\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-Ci
vita connection associated to $g$ and $\\iota_X$ is the interior product w
ith $X$. If $\\eta$ is coclosed ($\\mathrm d^*\\eta=0$) then $\\eta$ is sa
id to be a Killing-Yano $p$-form (KY for short).\n\nWe study left invaria
nt Conformal Killing Yano $2$-forms on Lie groups endowed with a left inva
riant metric. We determine\, up to isometry\, all $5$-dimensional metric L
ie algebras under certain conditions\, admitting a CKY $2$-form. Moreover\
, a characterization of all possible CKY tensors on those metric Lie algeb
ras is exhibited.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yi Lai (Stanford University)
DTSTART:20221026T220000Z
DTEND:20221026T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/58
DESCRIPTION:Title: O(2)-symmetry of 3D steady gradient Ricci solitons\nby Yi Lai (St
anford University) as part of Virtual seminar on geometry with symmetries\
n\n\nAbstract\nFor any 3D steady gradient Ricci soliton with positive curv
ature\, we prove that it must be isometric to the Bryant soliton if it is
asymptotic 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. Therefor
e\, all 3D steady gradient Ricci solitons are O(2)-symmetric.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Sanmartin-Lopez (Universidad Politécnica de Madrid)
DTSTART:20220907T090000Z
DTEND:20220907T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/59
DESCRIPTION:Title: Isoparametric hypersurfaces in symmetric spaces of non-compact type a
nd higher rank\nby Victor Sanmartin-Lopez (Universidad Politécnica de
Madrid) as part of Virtual seminar on geometry with symmetries\n\n\nAbstr
act\nA hypersurface is said to be isoparametric if it and its nearby equid
istant hypersurfaces have constant mean curvature. In this talk\, we will
see examples of these objects in the context of symmetric spaces together
with some classification results. After that\, we will construct infinitel
y many new examples of isoparametric hypersurfaces with novel properties i
n symmetric spaces of non-compact type and rank greater than two.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guofang Wei (University of California\, Santa Barbara)
DTSTART:20221012T160000Z
DTEND:20221012T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/60
DESCRIPTION:Title: Singular Weyl's law with Ricci curvature bounded below\nby Guofan
g Wei (University of California\, Santa Barbara) as part of Virtual semina
r on geometry with symmetries\n\n\nAbstract\nWeyl's law describes the asym
ptotic behavior of eigenvalues of the Laplace Beltrami operator. Its study
has a long history and is important in mathematics and physics. In a joi
nt work with J. Pan (GAFA 2022)\, using equivariant convergence\, we const
ructed first examples of Ricci limit spaces with symmetry whose Hausdorff
dimension may not be an integer and the Hausdorff dim of the singular set
is bigger than the Hausdorff dim of the regular set. With in-depth study o
f metric and measure of the examples\, and the delicate analysis of the he
at kernels\, in a very recent joint work with X. Dai\, S. Honda\, J. Pan w
e show the surprising results that for compact RCD(K\,N)/Ricci limit space
s\, Weyl'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 inste
ad of the regular set.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Craig Sutton (Dartmouth College)
DTSTART:20230125T160000Z
DTEND:20230125T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/61
DESCRIPTION:Title: Generic properties of Laplace eigenfunctions in the presence of torus
actions\nby Craig Sutton (Dartmouth College) as part of Virtual semin
ar on geometry with symmetries\n\n\nAbstract\nA result of Uhlenbeck (1976)
states that for a generic Riemannian metric $g$ on a closed manifold $M$
of dimension at least two the real eigenspaces of the associated Laplace o
perator $\\Delta_g$ are each one-dimensional and the nodal set (i.e.\, zer
o set) of any $\\Delta_g$-eigenfunction is a smooth hypersurface. Now\, le
t $T$ be 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 irreducible representations of $T$ and\, consequently\, are of dimens
ion one or two\, and (2) the nodal set of any $\\Delta_g$-eigenfunction is
a smooth hypersurface. The first of these statements is a mathematically
rigorous instance of the belief in quantum mechanics that non-irreducible
eigenspaces are ``accidental degeneracies.'' \n\nRegarding the second stat
ement\, in the event the non-trivial quotient $B = M/T$ satisfies a certai
n topological condition\, we show that\, for a generic $T$-invariant metri
c $g$\, any orthonormal basis $\\langle \\phi_j \\rangle$ consisting of $\
\Delta_g$-eigenfunctions possesses a density-one subsequence $\\langle \\p
hi_{j_k}\\rangle$ where the nodal set of each $\\phi_{j_k}$ is a smooth hy
persurface dividing $M$ into exactly two nodal domains\, the minimal possi
ble number of nodal domains for a non-constant eigenfunction. This observa
tion stands in stark contrast to the expected behavior of the nodal count
in the presence of an ergodic geodesic flow\, where examples suggest one s
hould anticipate the nodal count associated to a ``typical'' sequence of o
rthogonal Laplace eigenfunctions will approach infinity. \n\nThis is joint
work with Donato Cianci (GEICO)\, Chris Judge (Indiana) and Samuel Lin (O
klahoma).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Kollross (University of Stuttgart)
DTSTART:20221123T090000Z
DTEND:20221123T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/62
DESCRIPTION:Title: Totally geodesic submanifolds in exceptional symmetric spaces\nby
Andreas Kollross (University of Stuttgart) as part of Virtual seminar on
geometry with symmetries\n\n\nAbstract\nJoint work with Alberto Rodríguez
-Vázquez. I will speak about our recent paper where we classify maximal t
otally geodesic subspaces in exceptional Riemannian symmetric spaces. Sinc
e the maximal subspaces containing flat factors have been classified by Be
rndt and Olmos\, it suffices to find the semisimple ones. We show that the
se correspond to subalgebras in the Lie algebra of the isometry group whic
h are maximal among the semisimple subalgebras without compact ideals. To
find all such subalgebras of simple real Lie algebras\, we use earlier cla
ssification results by Dynkin\, de Graaf-Marrani and Komrakov.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McFeely Jackson Goodman
DTSTART:20221207T160000Z
DTEND:20221207T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/63
DESCRIPTION:Title: Curvature Operators\, Laplacians\, and Rational Cobordism\nby McF
eely Jackson Goodman as part of Virtual seminar on geometry with symmetrie
s\n\n\nAbstract\nWe give new conditions on positivity of certain linear co
mbinations of eigenvalues of the curvature operator of a Riemannian manifo
ld which imply the vanishing of the indices of Dirac operators twisted wit
h geometric vector bundles. The vanishing indices in turn have topologica
l implications in terms of the Pontryagin classes\, rational cobordism typ
e\, and Witten genus of the manifolds. To prove our results we generalize
new methods developed by Petersen and Wink to apply the Bochner technique
to Laplacians on geometric vector bundles.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucia Martin Merchan (University of Waterloo)
DTSTART:20230222T220000Z
DTEND:20230222T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/64
DESCRIPTION:Title: Topological properties of closed $\\mathrm{G}_2$ manifolds through co
mpact quotients of Lie groups\nby Lucia Martin Merchan (University of
Waterloo) as part of Virtual seminar on geometry with symmetries\n\n\nAbst
ract\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 c
losed if $d\\varphi=0$ and torsion-free if $\\varphi$ is parallel. The pur
pose of this talk is to discuss two problems where compact quotients of Li
e groups are useful for understanding topological properties of compact cl
osed $\\mathrm{G}_2$ manifolds that don´t admit any torsion-free $\\mathr
m{G}_2$ structure. More precisely\, these problems are related to the open
questions: Are simply connected compact closed $\\mathrm{G}_2$ manifolds
almost formal? Could a compact closed $\\mathrm{G}_2$ manifold have third
Betti number $b_3=0$?\n\nUsing compact quotients of Lie groups\, we first
outline the construction of a manifold admitting a closed $\\mathrm{G}_2$
structure that is not almost formal and has first Betti number $b_1=1$. La
ter\, we show that there aren´t invariant exact $\\mathrm{G}_2$ structure
s on compact quotients of Lie groups. The last result is joint work with A
nna Fino and Alberto Raffero.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason DeVito (The University of Tennessee at Martin)
DTSTART:20230208T160000Z
DTEND:20230208T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/65
DESCRIPTION:Title: The non-simply connected double soul conjecture\nby Jason DeVito
(The University of Tennessee at Martin) as part of Virtual seminar on geom
etry with symmetries\n\n\nAbstract\nCheeger and Gromoll's Soul theorem ass
erts that a complete non-compact Riemannian manifold of non-negative secti
onal curvature has the structure of a vector bundle over a closed totally
geodesic submanifold. The double soul conjecture (DSC) predicts an analog
ous structure on every closed simply connected Riemannian manifold of non-
negative sectional curvature: it should decompose as a union of two disk
bundles (possible of different ranks).\n\nIf one relaxes the hypothesis of
the DSC to allow non-simply connected manifolds\, then previously only a
single counterexample was known. We will discuss two new infinite familie
s of counterexamples\, one positively curved and the other flat. In addit
ion\, all of our counterexamples are so-called biquotients\, quotients of
Riemannian homogeneous spaces by free isometric actions. We will also in
vestigate the biquotient structure on the flat examples\, finding that\, i
n contrast with the homogeneous case\, they do not support a biquotient st
ructure induced from a connected Lie group.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hemangi Madhusudan Shah (Harish-Chandra Research Institute)
DTSTART:20230308T090000Z
DTEND:20230308T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/66
DESCRIPTION:Title: Some Solitons on Homogeneous Almost $\\alpha$-Cosymplectic 3-Manifold
s and Harmonic Manifolds\nby Hemangi Madhusudan Shah (Harish-Chandra R
esearch Institute) as part of Virtual seminar on geometry with symmetries\
n\n\nAbstract\nWe investigate the nature of Einstein solitons\, whether it
is steady\, shrinking or expanding on almost alpha-cosymplectic 3-manifol
ds. We also prove that a simply connected homogeneous almost $\\alpha$-cos
ymplectic 3-manifold\, admitting a contact Einstein soliton\, is an unimod
ular semidirect product Lie group. Finally\, we show that a harmonic manif
old admits a non-trivial Ricci soliton if and only if it is flat. Thus we
show that rank one symmetric spaces of compact as well as non-compact typ
e are stable under a Ricci soliton. In particular\, we obtain a strengthen
ing 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://stable.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:20230322T160000Z
DTEND:20230322T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/67
DESCRIPTION:Title: Finite homogeneous metric spaces with special properties\nby Yuri
i G. Nikonorov (Southern Mathematical Institute of the Vladikavkaz Scienti
fic Center of the Russian Academy of Sciences) as part of Virtual seminar
on geometry with symmetries\n\n\nAbstract\nThis talk is devoted to some re
cent results on finite homogeneous metric spaces obtained in joint papers
with Prof. V.N. Berestovskii. Every finite homogeneous metric subspace of
an Euclidean space represents the vertex set of a compact convex polytope
with the isometry group that is transitive on the set of vertices\, moreov
er\, all these vertices lie on some sphere. Consequently\, the study of su
ch subsets is closely related to the theory of convex polytopes in Euclide
an spaces.\n\nThe main subject of discussion is the classification of regu
lar and semiregular polytopes in Euclidean spaces by whether or not their
vertex sets have the normal homogeneity property or the Clifford - Wolf ho
mogeneity property.\nThe normal homogeneity and the Clifford - Wolf homoge
neity describe more stronger properties than the homogeneity. Therefore\,
it is quite natural to check the presence of these properties for the vert
ex sets of regular and semiregular polytopes.\n\nIn the second part of the
talk\, we consider the $m$-point homogeneity property and the point homog
eneity degree for finite metric spaces. Among main results\, there is a cl
assification of polyhedra with all edges of equal length and with 2-point
homogeneous vertex sets.\n\nThe most recent results and still unsolved pro
blems in this topic will also be discussed.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Tolcachier (National University of Córdoba)
DTSTART:20230405T220000Z
DTEND:20230405T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/69
DESCRIPTION:Title: Special Hermitian structures on products of Sasakian manifolds\nb
y Alejandro Tolcachier (National University of Córdoba) as part of Virtua
l seminar on geometry with symmetries\n\n\nAbstract\nIt is known that the
product of two Sasakian manifolds carries a 2-parameter family of Hermitia
n structures $(J_{a\,b}\,g_{a\,b})$. In this talk we will investigate when
these Hermitian structures are locally conformally Kähler\, balanced\, s
trong Kähler with torsion\, Gauduchon or $k$-Gauduchon ($k≥2$). Moreove
r\, 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 $\\
operatorname{Ric}^B$ and the Bismut-Ricci form $\\rho^B$. We will show tha
t these tensors vanish if and only if each Sasakian factor is $\\eta$-Eins
tein with appropriate constants and we will also exhibit some examples ful
filling these conditions\, thus providing new examples of Calabi-Yau with
torsion manifolds. This talk is based in a recent joint work with my PhD a
dvisor Adrián Andrada.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Salamon (King's College London)
DTSTART:20230503T160000Z
DTEND:20230503T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/70
DESCRIPTION:Title: The flag manifold $SU(3)/T^2$ and its subvarieties\nby Simon Sala
mon (King's College London) as part of Virtual seminar on geometry with sy
mmetries\n\n\nAbstract\nThis talk will emphasize symmetries inherent in st
udying the geometry of the complex 3-dimensional flag manifold\, in partic
ular\, those arising from the special Hermitian structure of $\\C^3$. It w
ill be based mainly on joint work with A. Altavilla\, E. Ballico\, and M.C
. Brambilla on the behaviour of algebraic curves and surfaces in the flag
manifold with respect to its (non-holomorphic) twistor projection to the c
omplex projective plane.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jan Nienhaus (WWU Münster)
DTSTART:20230614T090000Z
DTEND:20230614T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/71
DESCRIPTION:Title: Einstein metrics on spheres of even dimension\nby Jan Nienhaus (W
WU Münster) as part of Virtual seminar on geometry with symmetries\n\n\nA
bstract\nThe first non-round Einstein metrics on spheres were described in
1973 by Jensen in dimensions 4n+3 (n > 0). For the next 25 years it remai
ned an open problem whether the same could be done in even dimensions. Thi
s question was settled in 1998 when C. Böhm constructed infinite families
of Einstein metrics on all Spheres of dimension between 5 and 9\, in part
icular on $S^6$ and $S^8$. \n\nOver the last 25 years\, all spheres of odd
dimension (at least 5) have been shown to admit non-round Einstein metric
s\, but there have been no new developments in even dimensions above 8\, l
eaving open to speculation the question of whether non-uniqueness of the r
ound metric is a low-dimensional phenomenon or to be expected in all dimen
sions.\n\nI will give an overview of the methods used to construct non-rou
nd Einstein metrics\, which we recently used to construct three new Einste
in metrics on $S^{10}$.\n\n\n\nThis is joint work with Matthias Wink\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Geatti (Universita' di Roma Tor Vergata)
DTSTART:20230913T160000Z
DTEND:20230913T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/72
DESCRIPTION:Title: Geometry of Hermitian symmetric spaces under the action of a maximal
unipotent group.\nby Laura Geatti (Universita' di Roma Tor Vergata) as
part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nGiven
a complex manifold $M$ with a Lie group $G$ action by holomorphic transf
ormations\, \nit is of interest to understand associated invariant ob
jects like the invariant Stein subdomains and the invariant plurisub
harmonic functions.\n\nA classical example of this framework is given by
tube domains 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 $\\O
mega$ is geometrically convex (Bochner's tube theorem). Moreover an ${\
\bf R}^n$-invariant function on a Stein tube domain $D$ is plurisubharmoni
c if and only if its restriction to $\\Omega$ is convex. \n\n\n In this ta
lk\, we present a generalization of the above results in the setting of
a Hermitian symmetric space of the non-compact type $G/K$ under the act
ion 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 Li
e theoretical fashion and an explicit formula for the moment maps $\\mu\
\colon G/K\\to {\\mathfrak n}^*$ associated to such potentials.\n\n \nThis
is work in collaboration with Andrea Iannuzzi.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mary Sandoval (Trinity College)
DTSTART:20230517T220000Z
DTEND:20230517T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/73
DESCRIPTION:Title: Detecting Orbifold Singularities via the Orbifold Length Spectra\
nby Mary Sandoval (Trinity College) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nIn this talk\, we will consider the geodes
ic flow on a compact Riemannian orbifold $\\mathcal{O}$. Assuming the set
of closed geodesics on the orbifold is non-empty\, we consider the followi
ng question: Is it possible to detect orbifold singularities via the leng
th spectrum of $\\mathcal{O}$ and the length spectrum of the associated or
thonormal frame bundle of the orbifold? The answer is a qualifed yes\, pro
vided that the closed geodesic flow on $\\mathcal{O}$ intersects with the
singular set of the orbifold\, and the non-trivial isotropy group of the s
ingularity ``closes up" the geodesic. Assuming these conditions are satisf
ied\, we consider a second question: Given a singularity on a closed geode
sic\, what aspects of the isotropy group can be determined by the dynamics
of the geodesic flow for closed geodesics that pass through the singulari
ty? Partial results to this second question will be discussed. The proofs
will use some recent results from the spectral theory of leaf spaces of re
gular and singular Riemannian foliations.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Schwahn (University of Stuttgart)
DTSTART:20230531T160000Z
DTEND:20230531T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/74
DESCRIPTION:Title: The Lichnerowicz Laplacian on normal homogeneous spaces\nby Paul
Schwahn (University of Stuttgart) as part of Virtual seminar on geometry w
ith symmetries\n\n\nAbstract\nThe Lichnerowicz Laplacian $\\Delta_L$ is an
interesting differential operator on Riemannian manifolds\, generalizing
the Hodge-de Rham Laplacian on differential forms to tensors of arbitrary
type. It features prominently in the study of the linear stability of Eins
tein metrics.\n\nNormal homogeneous spaces are a natural setting in which
Casimir operators occur. In the 80s\, Koiso studied the stability of symme
tric spaces of compact type\, utilizing the coincidence of $\\Delta_L$ wit
h a Casimir operator. Motivated by his and also the $G$-stability results
of Lauret-Lauret-Will\, we generalize Koiso's strategy to general normal h
omogeneous spaces.\n\nUltimately this approach is sufficient to provide ma
ny new non-symmetric examples of stable Einstein manifolds of positive sca
lar curvature.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Olmos (Universidad Nacional de Córdoba)
DTSTART:20230628T160000Z
DTEND:20230628T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/75
DESCRIPTION:Title: Hopf fibrations and totally geodesic submanifolds\nby Carlos Olmo
s (Universidad Nacional de Córdoba) as part of Virtual seminar on geometr
y with symmetries\n\n\nAbstract\nA Hopf-Berger sphere of factor $\\tau$ i
s the total space of a Hopf fibration such that the Riemannian metric is
rescaled by a factor $\\tau\\neq 1$ in the directions of the fibers. If
the Hopf 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
geodesic sphere $\\mathsf{S}_t^m(o)\\subset\\bar M$ of radius $t$ of a ran
k one symmetric space of non-constant curvature ($\\bar M$ is compact if a
nd only if $\\tau <1$). A Hopf-Berger sphere has positive curvature if an
d only if $\\tau <4/3$. A standard totally geodesic submanifold of $\\math
sf{S}_t^m(o)$ is obtained as the intersection of the geodesic sphere with
a totally geodesic submanifold of $\\bar M$ that contains the center $o$.
In this talk we will refer to our recent classification of totally geodesi
c submanifolds of Hopf-Berger spheres. In particular\, for quaternionic a
nd octonionic fibrations\, non-standard totally geodesic spheres with the
same dimension of the fiber appear\, for $\\tau <1/2$. Moreover\, there a
re totally geodesic $\\mathbb RP^2$\, and $\\mathbb RP^3$ (under some re
strictions on $\\tau$\, the dimension\, and the type of the fibration).
On the one hand\, as a consequence of the connectedness principle of Wilki
ng\, there does not exist a totally geodesic $\\mathbb RP^4$ in a space
of positive curvature which diffeomorphic to the sphere $S^7$. On the
other hand\, we construct an example of a totally geodesic $\\mathbb RP^2$
in a Hopf-Berger sphere of dimension $7$ and positive curvature. Could th
ere exist a totally geodesic $\\mathbb RP^3$ in a space of positive curvat
ure which diffeomorphic to $S^7$?.\n\nThis talk is based on a joint work
with Alberto Rodríguez-Vázquez.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Thompson (The University of Queensland)
DTSTART:20230712T220000Z
DTEND:20230712T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/76
DESCRIPTION:Title: New examples of Ricci solitons with non-compact symmetry\nby Adam
Thompson (The University of Queensland) as part of Virtual seminar on geo
metry with symmetries\n\n\nAbstract\nThere are many examples of Ricci soli
tons that are constructed using the following ansatz: the soliton admits a
cohomogeneity one group action by a compact Lie group. On the other hand\
, there are very few examples of cohomogeneity one Ricci solitons where th
e group acting is non-compact. In fact\, all known examples of inhomogeneo
us Ricci solitons with non-compact symmetry have either abelian symmetry o
r special holonomy. We will discuss our construction of new examples of co
mplete cohomogeneity one gradient Ricci solitons where the group action is
by a non-compact solvable Lie group\, many of which do not have special h
olonomy.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonardo Cavenaghi (State University of Campinas)
DTSTART:20230726T160000Z
DTEND:20230726T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/77
DESCRIPTION:Title: The complete dynamics description of positively curved metrics in the
Wallach flag manifold $\\mathrm{SU}(3)/\\mathrm{T}^2$ and other homogeneo
us spaces\nby Leonardo Cavenaghi (State University of Campinas) as par
t of Virtual seminar on geometry with symmetries\n\n\nAbstract\nThe family
of invariant Riemannian manifolds in the Wallach flag manifold $\\mathrm{
SU}(3)/\\mathrm{T}^2$ is described by three parameters $(x\,y\,z)$ of posi
tive real numbers. By restricting such a family of metrics in the tetrahed
ron $\\mathcal{T}:= x+y+z = 1$\, we show how to describe all regions $\\ma
thcal R \\subset \\mathcal T$ admitting metrics with curvature properties
varying from positive sectional curvature to positive scalar curvature\, i
ncluding positive intermediate curvature notion's. We study the dynamics o
f such regions under the projected Ricci flow in the plane $(x\,y)$\, conc
luding sign curvature maintenance and escaping. We stress how this approac
h can be generalized to several other homogeneous spaces and can be helpfu
l to discuss the moduli space of bundles associated with the principal bun
dle $\\mathrm{T}^2\\hookrightarrow \\mathrm{SU}(3) \\rightarrow \\mathrm{S
U}(3)/\\mathrm{T}^2$.\n\nThis work is done in collaboration with Lino Gram
a\, Ricardo M. Martins and Douglas D. Novaes\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fangyang Zheng (Chongqing Normal University)
DTSTART:20231108T090000Z
DTEND:20231108T100000Z
DTSTAMP:20260404T111001Z
UID:VSGS/78
DESCRIPTION:Title: When will the Chern connection of a Hermitian manifold have parallel
torsion and curvature?\nby Fangyang Zheng (Chongqing Normal University
) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nTh
is 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 connection is Ambrose-Singer\, namely having parallel torsion and cu
rvature. We will also discuss the Bismut case\, where some partial answers
were obtained and some open questions were proposed.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Eastwood (University of Adelaide)
DTSTART:20231011T220000Z
DTEND:20231011T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/79
DESCRIPTION:Title: The range of the double fibration transform\nby Michael Eastwood
(University of Adelaide) as part of Virtual seminar on geometry with symme
tries\n\n\nAbstract\nOn and off\, for the past 20 years or so\, Joe Wolf a
nd I had been working on this transform. The input is the Dolbeault cohomo
logy of certain homogeneous vector bundles and the output is solutions of
certain invariant systems of partial differential equations. Perhaps we ha
d bitten off more than we could chew. Some cases are straightforward. Othe
rs are unreasonably awkward. I’ll talk about our long draft article\, es
pecially its motivation and what still needs to be done.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julieth Saavedra (University of Ceará)
DTSTART:20231025T160000Z
DTEND:20231025T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/80
DESCRIPTION:Title: Laplacian coflow of G_2-structures: Review and open questions.\nb
y Julieth Saavedra (University of Ceará) as part of Virtual seminar on ge
ometry with symmetries\n\n\nAbstract\nGeometric flows involving $G_2$-stru
ctures have proven to be valuable tools in the study of $G_2$-geometry. So
me examples of the Laplacian coflow of $G_2$-structures have been develope
d on contact Calabi-Yau manifolds and Abelian Lie groups. In this flow on
contact Calabi-Yau manifolds\, it was shown that it exhibits a singularity
\, leading to metric and volume collapse. Additionally\, we will explore s
ome results obtained from the almost Abelian Lie groups in the Laplacian c
oflow\, revealing that the solution converges to a torsion-free $G_2$-stru
cture.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART:20231206T160000Z
DTEND:20231206T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/81
DESCRIPTION:Title: Torus actions with connected isotropy groups\nby Lee Kennard (Syr
acuse University) as part of Virtual seminar on geometry with symmetries\n
\n\nAbstract\nRecent work with Michael Wiemeler and Burkhard Wilking analy
zes torus representations all of whose isotropy groups are connected. An i
mportant structure result is a splitting theorem\, which states that the r
epresentation splits as a product after passing to the induced action on a
suitable fixed-point set. More recently\, we found a connection between t
hese representations and combinatorial objects called regular matroids\, a
nd we applied work of Seymour to classify torus representations with conne
cted isotropy groups. As an application\, we prove new obstructions to the
existence of Riemannian metrics with positive sectional curvature and lar
ge symmetry. In some cases\, the assumption on the torus rank is independe
nt of the manifold dimension.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anusha M. Krishnan (University of Münster)
DTSTART:20240117T160000Z
DTEND:20240117T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/82
DESCRIPTION:Title: Toral symmetries of homogeneous collapsed ancient Ricci flows\nby
Anusha M. Krishnan (University of Münster) as part of Virtual seminar on
geometry with symmetries\n\n\nAbstract\nRicci flow solutions that are def
ined for all negative times\, are called ancient\, and have a special sign
ificance since they arise as blowup limits at singularities of the flow.
Several instances in the literature suggest that ancient solutions to the
Ricci flow have a higher degree of symmetry than initially assumed. In re
cent work (joint with F. Pediconi and S. Sbiti)\, we show that under certa
in assumptions\, collapsed homogeneous ancient solutions to the Ricci flow
have additional toral symmetry.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mat Langford (Australian National University)
DTSTART:20240131T230000Z
DTEND:20240131T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/83
DESCRIPTION:Title: Ancient solutions to geometric flows with small symmetry groups\n
by Mat Langford (Australian National University) as part of Virtual semina
r on geometry with symmetries\n\n\nAbstract\nA useful method for the const
ruction of examples of proper solutions to elliptic or parabolic (geometri
c) partial differential equations involves the reduction of the equation t
o a simpler one (typically\, an algebraic equation or an ordinary differen
tial equation) via the imposition of a suitable symmetry Ansatz. I will pr
esent some recent "genuinely parabolic" constructions of ancient solutions
to geometric flows (mean curvature flow\, fully nonlinear extrinsic flows
and the Ricci flow) which rely on (sometimes much) weaker symmetry
Ansä\;tze. While the resulting equations are still parabolic partial
differential equations\, the imposed symmetries nonetheless yield crucial
simplifications (e.g. allowing for the exploitation of special properties
of geometric flow equations which only hold in low space dimensions).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jaime Santos Rodríguez (Universidad Autónoma de Madrid)
DTSTART:20240228T160000Z
DTEND:20240228T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/85
DESCRIPTION:Title: Symmetries of Wasserstein spaces\nby Jaime Santos Rodríguez (Uni
versidad Autónoma de Madrid) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nLet $\\mathbb{P}_p(X)$ be the space of probabili
ty measures with finite $p-$moments on a metric space $(X\,d).$ Using solu
tions to the optimal transport problem of Monge-Kantorovich it is possible
to equip $\\mathbb{P}_p(X)$ with a distance $\\mathbb{W}_p$ known as the
$L^p-$Wasserstein distance. \n\nWith this the resulting metric space $(\\m
athbb{P}_p(X)\, \\mathbb{W}_p)$ will share many geometrical properties wit
h the base space $(X\,d)$ such as: compactness\, existence of geodesics\,
and even non-negative sectional curvature bounds (when $p=2$).\n\nTherefor
e\, a natural question is whether it is possible for $(\\mathbb{P}_p(X)\,
\\mathbb{W}_p)$ to be more symmetric than the original space $(X\,d).$ In
this talk we will first introduce the optimal transport problem\, Wasserst
ein spaces\, and some of its properties. Once this is done we will discuss
some of the results regarding isometries in these spaces.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irina Markina (University of Bergen)
DTSTART:20240214T140000Z
DTEND:20240214T150000Z
DTSTAMP:20260404T111001Z
UID:VSGS/86
DESCRIPTION:Title: A unified approach to extremal curves on Stiefel manifolds\nby Ir
ina Markina (University of Bergen) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nWe present a unified framework for studying
extremal curves on real Stiefel manifolds. We start with a smooth one-par
ameter family of pseudo-Riemannian metrics on a product of orthogonal grou
ps acting transitively on Stiefel manifolds. We find Euler-Langrange equat
ions for a class of extremal curves that includes geodesics with respect t
o different Riemannian metrics and smooth curves of constant geodesic curv
ature. For some specific values of the parameter in the family of pseudo-R
iemannian metrics we recover certain well-known metrics used in the applie
d mathematics.\n \nThis is a joint work with K. Hueper (University of Wurz
burg\, Germany) and F. Silva Leite (University of Coimbra\, Portugal)\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marie-Amelie Lawn (Imperial College London)
DTSTART:20240313T160000Z
DTEND:20240313T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/87
DESCRIPTION:Title: Generalized spin structures and homogeneous spaces\nby Marie-Amel
ie Lawn (Imperial College London) as part of Virtual seminar on geometry w
ith symmetries\n\n\nAbstract\nSpin geometry is a useful tool to describe g
eometric properties of manifolds. For instance\, it is well-known that a m
anifold admitting parallel spinors has to be Ricci flat. Another example i
s Seiberg-Witten theory which relies on the existence of a notion of spin
structure on 4-manifolds. However not every manifold admits a classical s
pin structure. In this talk we generalise this notion\, so that every mani
fold admits a generalised spin structure. We look at obstructions for such
structure and study their G-equivariance in the case of homogeneous space
s G/H. We will discuss the spheres as an example.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kyle Broder (The University of Queensland)
DTSTART:20240327T230000Z
DTEND:20240327T235900Z
DTSTAMP:20260404T111001Z
UID:VSGS/88
DESCRIPTION:Title: Invariant metrics in complex analysis and a conjecture of Kobayashi a
nd Lang\nby Kyle Broder (The University of Queensland) as part of Virt
ual seminar on geometry with symmetries\n\n\nAbstract\nA compact complex m
anifold $X$ is declared Kobayashi hyperbolic if every holomorphic map from
the complex plane into $X$ is constant. Kobayashi hyperbolic manifolds ha
ve maintained a central role in our understanding of the landscape of comp
lex manifolds since their introduction in 1967. One striking feature of co
mplex geometry is the capacity to encode this highly transcendental notion
of hyperbolicity in the coarse geometric language of distance functions t
hat are invariant under the automorphism group and decrease under holomorp
hic maps. A long-standing conjecture of Kobayashi (1970) and Lang (1986) p
redicts that a compact Kobayashi hyperbolic Kähler manifold admits a Käh
ler—Einstein metric of negative Ricci curvature. We will present the mos
t general evidence for the Kobayashi—Lang conjecture: A compact Kähler
manifold with a pluriclosed metric of negative holomorphic curvature admit
s a unique Kähler—Einstein metric of negative Ricci curvature. This res
ult is a joint work with James Stanfield and comes from the first general
improvement on the Schwarz lemma for holomorphic maps between Hermitian ma
nifolds since 1978.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Sebastián Rodríguez (Pontificia Universidad Javeriana)
DTSTART:20240424T130000Z
DTEND:20240424T140000Z
DTSTAMP:20260404T111001Z
UID:VSGS/89
DESCRIPTION:Title: Isospectrality in Symmetric Spaces\nby Juan Sebastián Rodríguez
(Pontificia Universidad Javeriana) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nFor a Riemannian manifold $(M\,g)$\, we de
fine its spectrum as the spectrum of the Laplace–Beltrami operator $\\De
lta_g$. We say that two Riemannian manifolds are isospectral if their spec
tra are equal. A fundamental problem in spectral geometry is to describe t
he isospectral class of distinguishable Riemannian manifolds.\n\nIn this t
alk\, we study two families of homogeneous metrics on the manifolds $\\mat
hrm{SO}(2n+2)/\\mathrm{U}(n+1)$ 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 research is conducted jointly with Emilio Lauret\, PhD (Universidad
Nacional del Sur\, Argentina).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dennis Wulle
DTSTART:20240410T160000Z
DTEND:20240410T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/90
DESCRIPTION:Title: Cohomogeneity one manifolds with quasipositive curvature\nby Denn
is Wulle as part of Virtual seminar on geometry with symmetries\n\n\nAbstr
act\nLet $G$ 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-dimensional. In this sense cohomogeneity one manifolds are the most s
ymmetric manifolds after homogeneous spaces\, which have a $0$-dimensional
orbit space. In this talk we will give a classification of cohomogeneity
one manifolds admitting an invariant metric with quasipositive sectional c
urvature\, except for two infinite families in dimension $7$. A Riemannian
manifold has quasipositive sectional curvature\, if it has non-negative s
ectional curvature and contains one point\, where all tangent planes have
positive sectional curvature. A similar classification in positive curvatu
re has already been obtained by Verdiani in even dimensions and Grove\, Wi
lking and Ziller in odd dimensions. Surprisingly\, our result only adds tw
o more examples to their list: an Eschenburg space and a Bazaikin space\,
which were previously known to admit metrics with quasipositive curvature.
\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesse Madnick (University of Oregon / Seton Hall University)
DTSTART:20240508T160000Z
DTEND:20240508T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/91
DESCRIPTION:Title: The Morse index of quartic minimal hypersurfaces\nby Jesse Madnic
k (University of Oregon / Seton Hall University) as part of Virtual semina
r on geometry 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-decreasing to second order. In practice\, computing the Morse index
of a given minimal hypersurface is extremely difficult\, requiring detaile
d information about the Laplace spectrum of S. Indeed\, even for the simpl
est case 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
hypersurfaces. Moreover\, we observe that their spectra contain both integ
er eigenvalues as well as (irrational) eigenvalues that are not expressibl
e in radicals. Time permitting\, we'll discuss some open problems and work
-in-progress. This is joint work with Gavin Ball (Wisconsin) and Uwe Semme
lmann (Stuttgart).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Bryant (Duke University)
DTSTART:20240605T160000Z
DTEND:20240605T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/92
DESCRIPTION:Title: Affine Bonnet surfaces\nby Robert Bryant (Duke University) as par
t of Virtual seminar on geometry with symmetries\n\n\nAbstract\nThe Bonnet
problem in Euclidean surface theory is well-known: Given a metric $g$ an
d a function $H$ on an oriented surface $M^2$\, when (and in how many ways
) can $(M\,g)$ be isometrically immersed in $\\mathbb{R}^3$ with mean curv
ature $H$? For generic data $(g\,H)$\, such an immersion does not exist a
nd\, in the case that one does exist\, it is unique up to ambient isometry
. Bonnet showed that\, aside from the famous case of surfaces of constant
mean curvature\, there is a finite-dimensional moduli space of $(g\,H)$ f
or which the space of such "Bonnet immersions" has positive dimension.\n\n
The corresponding problem in affine theory (a favorite topic of Eugenio Ca
labi) is still not completely solved. After reviewing the results on the
Euclidean problem by O. Bonnet\, J. Radon\, É. Cartan\, A. Bobenko and ot
hers\, I will give a report on affine analogs of those results. In partic
ular\, I will consider the classification of the data $(g\,H)$ for which t
he space of "affine Bonnet immersions" has positive dimension\, showing a
surprising connection with integrable systems in the case of data $(g\,H)$
for which the space of affine Bonnet immersions has the highest possible
dimension.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Pediconi (University of Florence)
DTSTART:20240522T100000Z
DTEND:20240522T110000Z
DTSTAMP:20260404T111001Z
UID:VSGS/93
DESCRIPTION:Title: A moment map for twisted-Hamiltonian vector fields on locally conform
ally Kähler manifolds\nby Francesco Pediconi (University of Florence)
as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nAcc
ording to Fujiki and Donaldson's foundational work\, the scalar curvature
of Kähler metrics arises as a moment map for an infinite-dimensional Hami
ltonian action. In this talk\, we generalize this result to the broader fr
amework of locally conformally Kähler Geometry. This is joint work with D
. Angella\, S. Calamai\, and C. Spotti.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Sáez (Pontificia Universidad Católica de Chile)
DTSTART:20240619T130000Z
DTEND:20240619T140000Z
DTSTAMP:20260404T111001Z
UID:VSGS/94
DESCRIPTION:Title: Translators for mean curvature flow\nby Mariel Sáez (Pontificia
Universidad Católica de Chile) as part of Virtual seminar on geometry wit
h symmetries\n\n\nAbstract\nIn this talk I am going to present the relevan
ce of mean curvature flow\, some self-similar solutions to this equation a
nd discuss some recent results.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Reiser (University of Fribourg)
DTSTART:20240911T160000Z
DTEND:20240911T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/95
DESCRIPTION:Title: Twisted suspensions\, torus actions\, and positive Ricci curvature\nby Philipp Reiser (University of Fribourg) as part of Virtual seminar o
n geometry with symmetries\n\n\nAbstract\nThe twisted suspension of a mani
fold can be seen as a smooth analogue of the classical suspension operatio
n for topological spaces. Its construction is motivated by the spinning op
eration in knot theory and it is obtained by surgery on a fibre of a princ
ipal circle bundle over the given manifold. In this talk I will show that
Riemannian metrics of positive Ricci curvature can be lifted along twisted
suspensions. As application we obtain first examples of simply-connected
manifolds of positive Ricci curvature with maximal symmetry rank in any di
mension\, and we obtain new examples of (rational) homology spheres with a
Riemannian metric of positive Ricci curvature.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wolfang Ziller
DTSTART:20241023T160000Z
DTEND:20241023T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/97
DESCRIPTION:Title: Curvature Homogeneous Manifolds\nby Wolfang Ziller as part of Vir
tual seminar on geometry with symmetries\n\n\nAbstract\nWe first give a su
rvey of the main known results (and open question) about manifolds whose c
urvature is the same at all points.\nWe then discuss recent joint work wi
th Luis Florit and Robert Bryant on curvature homogeneous hypersurfaces in
space forms.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeria Gutiérrez (Universidad Nacional de Córdoba)
DTSTART:20240925T120000Z
DTEND:20240925T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/98
DESCRIPTION:Title: Stability of (generalized) Einstein Metrics on aligned Homogeneous Sp
aces.\nby Valeria Gutiérrez (Universidad Nacional de Córdoba) as par
t of Virtual seminar on geometry with symmetries\n\n\nAbstract\nGiven two
standard Einstein homogeneous spaces $G_i/K$\, where each $G_i$ is a compa
ct simple Lie group and $K$ is a closed subgroup of them satisfying certai
n additional conditions\, we consider $M = G_1\\times G_2/\\Delta K$. Rece
ntly\, Lauret and Will proved the existence of a generalized Einstein metr
ic on any of these spaces. When $G_1=G_2=H$ they also studied the existenc
e and classification of $H \\times H$-invariant Einstein metrics on $M= H\
\times H/\\Delta K$.\n\nIn this talk we will discuss the definition and pr
operties of aligned homogeneous spaces with two factors\, review the resul
ts obtained by Lauret and Will and establish the dynamical stability of ge
neralized Einstein metrics as fixed points of the generalized Ricci flow o
n $M$. Additionally\, we will explore the stability relative to the Hilbe
rt action of non-diagonal Einstein metrics on $M=H\\times H/\\Delta K$ whe
n $H/K$ is an irreducible symmetric space.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Rodríguez Vázquez (Université Libre de Bruxelles)
DTSTART:20241204T120000Z
DTEND:20241204T130000Z
DTSTAMP:20260404T111001Z
UID:VSGS/99
DESCRIPTION:Title: Totally geodesic submanifolds of the homogeneous nearly Kähler 6-man
ifolds and their G2-cones\nby Alberto Rodríguez Vázquez (Université
Libre de Bruxelles) as part of Virtual seminar on geometry with symmetrie
s\n\n\nAbstract\nI will discuss work with Juan Manuel Lorenzo Naveiro (Uni
versidade de Santiago de Compostela)\, where we classify totally geodesic
submanifolds of homogeneous nearly Kähler 6-manifolds and their G2-holono
my cones. For this\, we develop algebraic tools to study totally geodesic
submanifolds in naturally reductive homogeneous spaces and Riemannian cone
s.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Siffert (Universität Münster)
DTSTART:20241120T160000Z
DTEND:20241120T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/101
DESCRIPTION:Title: Construction of biharmonic submanifolds of cohomogeneity one manifol
ds\nby Anna Siffert (Universität Münster) as part of Virtual seminar
on geometry with symmetries\n\n\nAbstract\nWe provide a construction meth
od for biharmonic submanifolds of cohomogeneity one manifolds. In particul
ar\, we give new examples of biharmonic submanifolds and study the normal
index of these submanifolds.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:F Tripaldi (University of Leeds)
DTSTART:20241009T160000Z
DTEND:20241009T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/102
DESCRIPTION:Title: Extracting subcomplexes on nilpotent groups without relying on homog
eneous structures\nby F Tripaldi (University of Leeds) as part of Virt
ual seminar on geometry with symmetries\n\n\nAbstract\nI will present a ge
neral construction of subcomplexes on nilpotent Lie groups equipped with a
Riemannian metric. The aim is to emphasise how relying on different struc
tures (homogenous and non-homogenous ones) affects the resulting subcomple
x. \nI will then show how particular subcomplexes are better suited than o
thers depending on the geometric setting and the possible applications.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniela Di Donato (University of Pavia)
DTSTART:20250122T160000Z
DTEND:20250122T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/103
DESCRIPTION:Title: Rectifiability in Carnot groups\nby Daniela Di Donato (Universit
y of Pavia) as part of Virtual seminar on geometry with symmetries\n\n\nAb
stract\nIntrinsic regular surfaces in Carnot groups play the same role as
C^1 surfaces in Euclidean spaces. As in Euclidean spaces\, intrinsic regul
ar surfaces can be locally defined in different ways: e.g. as non critical
level sets or as continuously intrinsic differentiable graphs. The equiva
lence of these natural definitions is the problem that we are studying. Pr
ecisely our aim is to generalize some results proved by Ambrosio\, Serra C
assano\, Vittone valid in Heisenberg groups to the more general setting of
Carnot groups. This is joint work with Antonelli\, Don and Le Donne\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stuart James Hall (Newcastle University)
DTSTART:20250212T160000Z
DTEND:20250212T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/104
DESCRIPTION:Title: Rigidity to second order of compact irreducible symmetric spaces
\nby Stuart James Hall (Newcastle University) as part of Virtual seminar o
n geometry with symmetries\n\n\nAbstract\nIn the 1980s Koiso showed that o
nly 5 types of compact irreducible symmetric space admit infinitesimal Ein
stein deformations\; he also developed an obstruction to such deformations
being integrable to second order but left the calculation of this obstruc
tion on these spaces open. I will report on work of the last few years tha
t computes the obstruction on these spaces and what this says about the ri
gidity of compact irreducible symmetric spaces.\nThis is joint work with W
afaa Batat\, Thomas Murphy\, Paul Schwahn\, Uwe Semmelmann\, and James Wal
dron.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio Zamora Barrera (Oregon State University)
DTSTART:20250319T160000Z
DTEND:20250319T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/105
DESCRIPTION:Title: Topology of manifolds with almost non-negative curvature and maximal
rank and their Gromov--Hausdorff limits\nby Sergio Zamora Barrera (Or
egon State University) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nThere are many characterizations of the torus as a Riem
annian manifold. For example\, it is the only closed manifold of non-negat
ive Ricci curvature and first Betti number equal to its dimension. In this
talk we will discuss two problems: \n\n- When such characterizations are
replaced by slightly weaker hypotheses\, will we still get a torus or some
thing related? \n\n- If a space X can be approximated by something we know
is a torus\, is X necessarily a torus?\n\nWe will discuss both classical
and current results in different contexts. This includes joint work with
Xingyu Zhu.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jade Brisson (Université de Neuchâtel)
DTSTART:20250219T180000Z
DTEND:20250219T190000Z
DTSTAMP:20260404T111001Z
UID:VSGS/106
DESCRIPTION:Title: Upper bounds\, spectral ratios and spectral gaps for Steklov eigenva
lues of warped products\nby Jade Brisson (Université de Neuchâtel) a
s part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nIn th
e first part of the talk\, we investigate the Steklov spectrum of the warp
ed product $[0\,L]\\times_h \\Sigma$ equipped with the metric $dt^2+h(t)^2
g_\\Sigma$\, where $\\Sigma$ is a compact surface. We find sharp upper bou
nds for the Steklov eigenvalues in terms of the eigenvalues of the Laplaci
an on $\\Sigma$. In particular\, we apply our method to the case of metric
of revolution on the 3-dimensional ball and we obtain a sharp estimate on
the spectral gap between two consecutive Steklov eigenvalues.\n\nIn the s
econd part\, we investigate the spectral ratios as well as spectral gaps f
or higher order Steklov eigenvalues of Riemannian manifolds with revolutio
n-type metrics. This is based on joint works with Bruno Colbois and Katie
Gittins.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrico Le Donne (University of Fribourg)
DTSTART:20250903T130000Z
DTEND:20250903T140000Z
DTSTAMP:20260404T111001Z
UID:VSGS/107
DESCRIPTION:Title: Asymptotic geometry of Riemannian nilpotent groups\nby Enrico Le
Donne (University of Fribourg) as part of Virtual seminar on geometry wit
h symmetries\n\n\nAbstract\nAsymptotic cones of Riemannian nilpotent Lie g
roups are Carnot groups.\nThe volume of balls in Carnot groups grows exact
ly as a power of the radius. Heuristically\, the better the asymptotic con
e approximates a Riemannian group\, the closer to a polynomial the volume
growth becomes. I will discuss several results obtained over the last few
years in collaboration with Breuillard\, Nalon\, Nicolussi Golo\, and Ryoo
.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomoya Tatsuno (University of Oklahoma)
DTSTART:20250402T220000Z
DTEND:20250402T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/108
DESCRIPTION:Title: Sectional Curvature Pinching of Two-Step Nilmanifolds\nby Tomoya
Tatsuno (University of Oklahoma) as part of Virtual seminar on geometry w
ith symmetries\n\n\nAbstract\nNilmanifolds are homogeneous Riemannian mani
folds admitting a transitive nilpotent Lie group of isometries. By classic
al results (Wolf\, Milnor)\, nilmanifolds are always of mixed curvature. T
wo-step nilmanifolds are particularly important\, as they play a crucial r
ole in the classification of quarter-pinched homogeneous manifolds of nega
tive curvature by Eberlein and Heber. Given a two-step nilmanifold\, we st
udy its pinching constant\, which is the ratio of the minimum and maximum
of sectional curvature.\n\nA prototype of a two-step nilmanifold is the 3-
dimensional Heisenberg group (so-called Nil). In this case\, it is well kn
own that the pinching constant is -3. In this talk\, we show that for any
two-step nilmanifold\, the pinching constant lies in the compact interval
[-3\, -3/2]. We give examples of two-step nilmanifolds that achieve the bo
unds -3 and -3/2\, respectively. Moreover\, we discuss why the bounds -3 a
nd -3/2 are special in terms of rigidity.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (Università di Torino)
DTSTART:20250430T160000Z
DTEND:20250430T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/109
DESCRIPTION:Title: An overview on strong geometries with torsion (Distinguished lecture
5th anniversary)\nby Anna Fino (Università di Torino) as part of Vir
tual seminar on geometry with symmetries\n\n\nAbstract\nA strong geometry
with torsion is a Riemannian manifold carrying a metric connection \nwith
closed skew-symmetric torsion. In the seminar I will first review genera
l properties of metric connections with closed skew-symmetric torsion. \n
Then I will focus on the case of Hermitian manifolds and 7-manifolds endo
wed with a G_2-structure.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizabeth Stanhope (Lewis & Clark College)
DTSTART:20250611T160000Z
DTEND:20250611T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/110
DESCRIPTION:Title: Using Hodge spectra to detect orbifold singularities\nby Elizabe
th Stanhope (Lewis & Clark College) as part of Virtual seminar on geometry
with symmetries\n\n\nAbstract\nA Riemannian orbifold is a mildly singular
generalization of a Riemannian manifold. A fundamental question in the La
place spectral geometry of Riemannian orbifolds is whether or not a singul
ar orbifold can be isospectral to a manifold. This question is open for th
e spectrum of the Laplacian acting on functions. We will see that combinin
g information from the spectrum of the Laplacian on functions with informa
tion from the spectrum of the Hodge Laplacian on 1-forms allows us to dete
ct orbifold singularities in some cases. For example\, a singular Riemann
ian orbifold of dimension 3 or less cannot be both 0 and 1-isospectral to
a Riemannian manifold. The proof relies on the heat invariants associated
to the $p$-spectrum of the corresponding Hodge Laplacian. We will also dis
cuss a few inverse spectral results for the individual $p$-spectra themsel
ves.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karen Butt (University of Chicago)
DTSTART:20250416T160000Z
DTEND:20250416T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/111
DESCRIPTION:Title: Monotonicity of Liouville entropy along the Ricci flow\nby Karen
Butt (University of Chicago) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nWe consider the geodesic flow of a closed negati
vely curved surface. Its Liouville entropy is an invariant of the measurab
le dynamics of the flow\, which roughly captures the average exponential d
ivergence of nearby trajectories. For negatively curved surfaces of fixed
total area\, Katok proved this invariant is maximized at hyperbolic metric
s\, ie\, metrics of constant negative curvature. Our main result is that\,
in this setting\, the Liouville entropy is monotonically increasing along
the normalized Ricci flow on the space of metrics. This affirmatively ans
wers a question of Manning\, and gives a new proof of Katok’s aforementi
oned result. In addition to geometric and dynamical methods\, our proof al
so uses microlocal analysis. This is joint work with Erchenko\, Humbert\,
and Mitsutani.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesús Núñez Zimbrón (Universidad Nacional Autónoma de México
)
DTSTART:20250514T160000Z
DTEND:20250514T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/112
DESCRIPTION:Title: Cohomogeneity one RCD spaces\nby Jesús Núñez Zimbrón (Univer
sidad Nacional Autónoma de México) as part of Virtual seminar on geometr
y with symmetries\n\n\nAbstract\nI will speak about joint work with Diego
Corro and Jaime Santos in which we study RCD-spaces $(X\,d\,m)$ with group
actions by isometries preserving the reference measure $m$ and whose orbi
t space has dimension one\, i.e. cohomogeneity one actions. RCD spaces are
metric measure spaces with a notion of "Ricci curvature bounded below and
dimension bounded above". In the talk I will mention a version of the Sli
ce Theorem for cohomogeneity one spaces that we show and then use to obtai
n topological structural results analogous to those available in the smoot
h setting. I will also mention how to construct new cohomogeneity one RCD-
spaces. As an application of these results we obtain the classification of
cohomogeneity one\, "non-collapsed" RCD-spaces of dimension at most $4$.\
n
LOCATION:https://stable.researchseminars.org/talk/VSGS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elia Fusi (University of Torino)
DTSTART:20250528T100000Z
DTEND:20250528T110000Z
DTSTAMP:20260404T111001Z
UID:VSGS/113
DESCRIPTION:Title: Homogeneous generalized Ricci flow\nby Elia Fusi (University of
Torino) as part of Virtual seminar on geometry with symmetries\n\n\nAbstra
ct\nThe generalized Ricci flow is the natural analogue of the Ricci flow i
n the setting of generalized Geometry and it has a deep connection with th
e pluriclosed flow\, a geometric flow of pluriclosed Hermitian metrics.\nT
o serve as motivation for our work\, I will firstly introduce the pluriclo
sed flow and state some open questions\, finally stating the precise link
with the generalized Ricci flow. \nAfterwards\, I will focus on the study
of the homogeneous generalized Ricci flow\, discussing its long-time exist
ence on solvable Lie groups and asymptotics in the nilpotent case\, with
a special focus on the consequences for the pluriclosed flow. All such r
esults are obtained by means of a new interpretation of the generalized R
icci flow as a flow of Dorfman brackets and of the generalized Ricci cur
vature as the moment map of a suitable action on Dorfman brackets.\nThis
is a joint work with Ramiro Lafuente and James Stanfield.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommy Murphy
DTSTART:20250625T160000Z
DTEND:20250625T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/114
DESCRIPTION:Title: Riemannian 3-symmetric spaces\, their moduli\, and Ricci solitons\nby Tommy Murphy as part of Virtual seminar on geometry with symmetries\
n\n\nAbstract\nRiemannian 3-symmetric spaces are a natural generalization
of the classical symmetric spaces of Cartan. Their classification has be
en open since the pioneering work of Gray-Wolf in the sixties which focuse
d on the semisimple case. I will outline the full classification\, stressi
ng some of the more remarkable features including their rich moduli space
structure. As a by-product\, a very general construction of Ricci solitons
is presented which is of independent interest.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Goertsches (Philipps-Universität Marburg)
DTSTART:20250917T160000Z
DTEND:20250917T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/115
DESCRIPTION:Title: On torus equivariant $S^4$-bundles over $S^4$ and Petrie-type Questi
ons for GKM Manifolds\nby Oliver Goertsches (Philipps-Universität Mar
burg) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract
\nIn GKM theory one associates to certain torus actions on closed manifold
s a labelled graph which describes the induced action on the equivariant o
ne-skeleton. It can be regarded as a generalization of (quasi)toric theory
\, retaining only the one-skeleton of the orbit space polytope. In this ta
lk I will explain an interesting class of examples of GKM manifolds in dim
ension 8 with exotic behavior: it contains pairs of homotopy equivalent GK
M manifolds with different first Pontryagin class\, as well as pairs of GK
M actions on the same smooth manifold whose GKM graphs do not agree as uns
igned graphs. This is in line with previous results that show that GKM man
ifolds exhibit rigid behaviour only in dimensions up to 6.\n\nThis is join
t work with Panagiotis Konstantis and Leopold Zoller.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emmett Wyman (Binghamton University)
DTSTART:20251015T160000Z
DTEND:20251015T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/116
DESCRIPTION:Title: Spectral geometry and symmetries\nby Emmett Wyman (Binghamton Un
iversity) as part of Virtual seminar on geometry with symmetries\n\n\nAbst
ract\nWe will present two short results linking the spectrum of the Laplac
e-Beltrami operator on a compact Riemannian manifold to its Lie group of i
sometries:\n\n(1) Each manifold with a simple Laplace-Beltrami spectrum ha
s a finite isometry group. (https://arxiv.org/abs/2407.18797)\n\n(2) If a
two-dimensional drumhead "sounds the same" when struck at any two points\,
the action of the isometry group on the surface is transitive. (https://a
rxiv.org/abs/2307.06224)\n\nWe will discuss some background on Laplace-Bel
trami eigenfunctions\, give short proofs of the results\, and discuss some
further questions if time permits. This is joint work with Xing Wang\, Fe
ng Wang\, and Yakun Xi.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Klaus Kröncke (KTH Royal Institute of Technology)
DTSTART:20251029T140000Z
DTEND:20251029T150000Z
DTSTAMP:20260404T111001Z
UID:VSGS/117
DESCRIPTION:Title: On the volume-renormalized mass\nby Klaus Kröncke (KTH Royal In
stitute of Technology) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nWe give an overview on results about a new mass-like qu
antity on asymptotically hyperbolic manifolds\, which was recently introdu
ced by Dahl\, McCormick and me. The volume-renormalized mass is essentiall
y a linear combination of the ADM mass surface integral and a renormalizat
ion of the volume. It is well-defined and diffeomorphism invariant under w
eaker fall-off conditions than required to ensure that the renormalized vo
lume and the ADM mass surface integral are well-defined separately. We sho
w that our quantity can be deduced from a reduced Hamiltonian perspective
and that it is nonincreasing along CMC foliations of asymptotically Milne-
like vacuum spacetimes. We prove a positive mass theorem for orientable th
ree-manifolds which don’t contain non-separating spheres. In addition\,
we demonstrate that a Poincaré–Einstein manifold is dynamically stable
under the Ricci flow if and only if it is a local minimizer of the mass. T
his talk is based on collaborations with Mattias Dahl\, Stephen McCormick\
, Francesca Oronzio\, Alan Pinoy and Louis Yudowitz.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patric Donovan (University of New South Wales)
DTSTART:20251001T220000Z
DTEND:20251001T230000Z
DTSTAMP:20260404T111001Z
UID:VSGS/118
DESCRIPTION:Title: Bubble sheets and $\\kappa$-solutions in four-dimensional Ricci flow
\nby Patric Donovan (University of New South Wales) as part of Virtual
seminar on geometry with symmetries\n\n\nAbstract\nAs discovered by Perel
man\, the study of ancient Ricci flows which are $\\kappa$-noncollapsed is
a crucial prerequisite to understanding the singularity behaviour of more
general Ricci flows. In dimension three\, these so-called "$\\kappa$-solu
tions" have been fully classified through the groundbreaking work of Brend
le\, Daskalopoulos\, and Šešum. Their classification result can be exten
ded to higher dimensions\, but only for those Ricci flows that have unifor
mly positive isotropic curvature (PIC)\, as well as weakly-positive isotro
pic curvature of the second type (PIC2)\; it appears the classification re
sult fails with only minor modifications to the curvature assumption. Inde
ed\, with the alternative assumption of non-negative curvature operator\,
a rich variety of new examples emerge\, as recently constructed by Buttswo
rth\, Lai\, and Haslhofer\; Haslhofer himself has conjectured that this li
st of non-negatively curved $\\kappa$-solutions is now exhaustive in dimen
sion four. In this talk\, we will discuss some recent progress towards res
olving Haslhofer's conjecture\, including a compactness result for non-neg
atively curved $\\kappa$-solutions in dimension four\, and a symmetry imp
rovement result for bubble-sheet regions. This is joint work with Anusha
Krishnan and Timothy Buttsworth.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katie Gittins (Durham University)
DTSTART:20251112T160000Z
DTEND:20251112T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/119
DESCRIPTION:Title: Nodal counts for the Robin problem on Lipschitz domains.\nby Kat
ie Gittins (Durham University) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nWe consider the Courant-sharp eigenvalues of th
e Laplacian (with boundary conditions) on Euclidean domains. That is\, the
eigenvalues that have a corresponding eigenfunction which achieves the ma
ximum number of nodal domains given by Courant's theorem. We will first gi
ve an overview of previous results for the Courant-sharp Dirichlet\, Neuma
nn\, and Robin eigenvalues of the Laplacian. In particular\, Pleijel's the
orem and upper bounds for the number of Courant-sharp eigenvalues. We will
then present recent joint work with Asma Hassannezhad\, Corentin Léna\,
and David Sher which extends previous results in various directions.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato Bettiol (City University of New York)
DTSTART:20251210T190000Z
DTEND:20251210T200000Z
DTSTAMP:20260404T111001Z
UID:VSGS/120
DESCRIPTION:Title: Counting homogeneous Einstein metrics\nby Renato Bettiol (City U
niversity of New York) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nI will describe an explicit upper bound on the number o
f isolated homogeneous Einstein metrics on compact homogeneous spaces whos
e isotropy representation has no repeated irreducibles. According to a con
jecture of Böhm-Wang-Ziller\, such homogeneous spaces ought to have only
finitely many homogeneous Einstein metrics. Sufficient conditions under wh
ich this conjecture holds will also be discussed. This is joint work with
Hannah Friedman (UC Berkeley).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haotian Wu (University of Sydney)
DTSTART:20251126T230000Z
DTEND:20251127T000000Z
DTSTAMP:20260404T111001Z
UID:VSGS/121
DESCRIPTION:Title: Asymptotic behavior of unstable perturbations of the Fubini–Study
metric in Ricci flow\nby Haotian Wu (University of Sydney) as part of
Virtual seminar on geometry with symmetries\n\n\nAbstract\nThe Ricci flow
can be regarded as a dynamical system on the space of Riemannian metrics.
It is important to identify and study its fixed points\, which are general
ized Einstein metrics known as Ricci solitons. A prominent example of a Ri
cci soliton is the Fubini–Study metric on complex projective space. Krö
ncke has shown that the Fubini–Study metric is an unstable generalized s
tationary solution of Ricci flow. This raises an interesting question: Wha
t happens to Ricci flow solutions that start at arbitrarily small but unst
able perturbations of the Fubini–Study metric? In a joint work with Garf
inkle\, Isenberg and Knopf\, we carry out numerical simulations which indi
cate Ricci flow solutions originating at unstable perturbations of the Fub
ini–Study metric develop local singularities modeled by the FIK shrinkin
g soliton discovered by Feldman\, Ilmanen and Knopf.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvio Reggiani (Universidad Nacional de Rosario)
DTSTART:20260311T160000Z
DTEND:20260311T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/122
DESCRIPTION:Title: The geometry of sedenion zero divisors\nby Silvio Reggiani (Univ
ersidad Nacional de Rosario) as part of Virtual seminar on geometry with s
ymmetries\n\n\nAbstract\nThe sedenion algebra is a non-associative real al
gebra obtained from the octonions via the Cayley-Dickson construction. Its
zero divisors admit a natural description as a principal bundle over the
Stiefel manifold $V_{2\,7}$\, with total space the compact Lie group $G_2$
and fiber $S^3$\, which is similar to the Hopf fibration.\n\nIn this talk
\, we discuss some geometric aspects of this fibration. We show that the n
atural submanifold metric on the total space is isometric to a naturally r
eductive left-invariant metric on $G_2$\, yielding a Riemannian submersion
onto an exceptional symmetric space. We also consider a deformation of th
e metric on $V_{2\,7}$\, analogous to the Berger spheres\, obtaining a new
Einstein metric and a family of non-negatively curved metrics.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcus Marrocos (Universidade Federal do Amazonas)
DTSTART:20260211T160000Z
DTEND:20260211T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/123
DESCRIPTION:Title: On the generic irreducibility of the spectrum of the Laplacian on ho
mogeneous spaces.\nby Marcus Marrocos (Universidade Federal do Amazona
s) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nW
e discuss the generic irreducibility of Laplace eigenspaces on compact hom
ogeneous spaces $M=G/K$ with $G$-invariant metrics. While Uhlenbeck’s th
eorem suggests that\, for generic metrics\, Laplace eigenvalues are simple
\, $G$-invariance forces multiplicities. Since each eigenspace carries a n
atural representation of $G$\, the appropriate substitute is representatio
n-theoretic simplicity: each eigenspace should be an irreducible $G$-modul
e. Building on Schueth’s viewpoint for compact Lie groups with left-inva
riant metrics\, we present the framework developed for homogeneous spaces\
, emphasizing the results of Petrecca--Röser and the remarks in de Olivei
ra--Marrocos on real versus complex irreducibility and on structural sourc
es of eigenvalue collisions in higher rank. We conclude with a discrete an
alogue: generic spectra of weighted Laplacians on Cayley graphs.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Lenze (Karlsruhe Institute of Technology)
DTSTART:20260128T160000Z
DTEND:20260128T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/124
DESCRIPTION:Title: Rigidity of the Ebin metric\nby David Lenze (Karlsruhe Institute
of Technology) as part of Virtual seminar on geometry with symmetries\n\n
\nAbstract\nIn 1970\, Ebin introduced a natural L2-type metric on the infi
nite-dimensional space of Riemannian metrics over a given manifold. Though
the infinite dimensional geometry of this space has been extensively-stud
ied\, a new metric perspective emerged in 2013 when Clarke showed that the
completion with respect to the Ebin metric turns out to be a CAT(0) space
.\n\nRecently\, Cavallucci provided a shorter and more conceptual proof of
a strengthened result that in addition to being CAT(0) establishes the co
mpletion of the space of Riemannian metrics to depend only on the dimensio
n of the underlying manifold.\n\nAfter reviewing this recent progress\, I
will present new results providing a complete characterization of the Ebin
metric's self-isometries. Furthermore\, I will show that—in contrast to
Cavallucci's findings on the completion—the isometry class of the uncom
pleted space recovers the underlying manifold in the strongest plausible w
ay.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nazia Valiyakath (Syracuse University)
DTSTART:20260225T160000Z
DTEND:20260225T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/126
DESCRIPTION:Title: On nilpotent and solvable quasi-Einstein manifolds\nby Nazia Val
iyakath (Syracuse University) as part of Virtual seminar on geometry with
symmetries\n\n\nAbstract\nIn this talk\, I will discuss the classification
of quasi-Einstein metrics on nilpotent and unimodular solvable Lie groups
. Focusing on quasi-Einstein metrics $(M\,g\,X)$ for which the metric $g$
and the vector field $X$ are left-invariant—what we call totally left-in
variant quasi-Einstein metrics—I will first present a complete classific
ation in the nilpotent case. In particular\, I will show that a nilpotent
Lie group admits such a metric if and only if it is Heisenberg.\n\nI will
then turn to unimodular solvable Lie groups and show that the existence of
a non-flat totally left-invariant quasi-Einstein metric imposes strong st
ructural restrictions\, forcing the center of the group to be one-dimensio
nal. Under the additional assumption that the adjoint action is given by a
normal derivation\, I will describe a full classification: the Lie group
must be standard and its nilradical necessarily Heisenberg. As an applicat
ion\, I will explain why the only near-horizon geometries arising on nilma
nifolds are quotients $\\Gamma \\backslash H_n$ of the Heisenberg group.\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ricardo Mendes (The University of Oklahoma)
DTSTART:20260422T160000Z
DTEND:20260422T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/127
DESCRIPTION:by Ricardo Mendes (The University of Oklahoma) as part of Virt
ual seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomás Otero (Universität Münster)
DTSTART:20260325T160000Z
DTEND:20260325T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/128
DESCRIPTION:Title: Cohomogeneity-one actions on symmetric spaces\nby Tomás Otero (
Universität Münster) as part of Virtual seminar on geometry with symmetr
ies\n\n\nAbstract\nIn this talk\, I will report on recent developments on
the classification of cohomogeneity-one actions on symmetric spaces. The f
ocus will be on symmetric spaces of noncompact type and of "mixed type" (i
.e. those whose universal cover splits as a nontrivial product $\\widetild
e{M}=M_+\\times M_0\\times M_-$\, with $M_+$ of compact type\, $M_0$ a Euc
lidean space\, and $M_-$ of noncompact type). For the former spaces a comp
lete classification was recently obtained by Sanmartín-López and Solonen
ko. For the latter\, in an upcoming work with Ivan Solonenko and Hiroshi T
amaru\, we show that cohomogeneity-one actions split with respect to the a
forementioned decomposition\, with the only exception of a family of "diag
onal" actions (which we parameterize explicitly).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David González Álvaro (Universidad Politécnica de Madrid)
DTSTART:20260520T160000Z
DTEND:20260520T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/129
DESCRIPTION:by David González Álvaro (Universidad Politécnica de Madrid
) as part of Virtual seminar on geometry with symmetries\n\nAbstract: TBA\
n
LOCATION:https://stable.researchseminars.org/talk/VSGS/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Cristina Castro Ferreira (University of Minho)
DTSTART:20260506T160000Z
DTEND:20260506T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/130
DESCRIPTION:Title: Isometries of 3-Dimensional Semi-Riemannian Lie Groups\nby Ana C
ristina Castro Ferreira (University of Minho) as part of Virtual seminar o
n geometry with symmetries\n\n\nAbstract\nLet G be a connected\, simply co
nnected three-dimensional Lie group (unimodular\nor non-unimodular) equipp
ed with a left-invariant (Riemannian or Lorentzian) met-\nric g. By defini
tion\, the isometry group Isom(G\, g) contains G itself\, acting by left\n
translations. It turns out that\, generically\, Isom(G\, g) is actually eq
ual to G\, and the\nnatural question then becomes to classify those specia
l metrics for which this is not\nthe case. Using Lie-theoretical methods\,
we present a unified approach to obtain all\npairs (G\, g) whose full iso
metry group Isom(G\, g) has dimension greater than or\nequal to four. As a
consequence\, we determine\, for every pair (G\, g)\, up to automor-\nphi
sm and scaling\, the dimension of Isom(G\, g)\, which can be three\, four\
, or six. \n(Joint work with S. Chaib and A. Zeghib).\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christine Escher (Oregon State University)
DTSTART:20260617T160000Z
DTEND:20260617T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/132
DESCRIPTION:by Christine Escher (Oregon State University) as part of Virtu
al seminar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ines Kath (University of Greifswald)
DTSTART:20260715T160000Z
DTEND:20260715T170000Z
DTSTAMP:20260404T111001Z
UID:VSGS/133
DESCRIPTION:by Ines Kath (University of Greifswald) as part of Virtual sem
inar on geometry with symmetries\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/VSGS/133/
END:VEVENT
END:VCALENDAR