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BEGIN:VEVENT
SUMMARY:Wolfgang Ziller (University of Pennsylvania)
DTSTART:20210209T140000Z
DTEND:20210209T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/1
DESCRIPTION:Title: A variational approach to prescribing the Ricci tensor
\nby Wolfgang Ziller (University of Pennsylvania) as part of Irish Geometr
y Seminar\n\n\nAbstract\nWe discuss the question of which tensors T can be
the Ricci tensor of a metric\, i.e. Ric(g)=T or Ric(g)=cT for some c. So
lutions can be viewed as the critical points of a modified scalar\ncurvatu
re functional and we examine the global behavior of this functional in the
case of homogeneous spaces. This is joint work with Artem Pulemotov.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McKay (University College Cork)
DTSTART:20210302T140000Z
DTEND:20210302T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/2
DESCRIPTION:Title: Locally homogeneous complex analytic geometric structures<
/a>\nby Ben McKay (University College Cork) as part of Irish Geometry Semi
nar\n\n\nAbstract\nI will present a conjecture on the classification of ho
lomorphic locally homogeneous geometric structures (modelled on complex fl
ag varieties) on smooth projective varieties. I will give an outline of wh
at we know so far.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kilian (University College Cork)
DTSTART:20210413T130000Z
DTEND:20210413T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/3
DESCRIPTION:Title: Integrable systems methods for constant mean curvature sur
faces\nby Martin Kilian (University College Cork) as part of Irish Geo
metry Seminar\n\n\nAbstract\nI will survey some of the recent progress mad
e in developing the theory of constant mean curvature surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Galaz-García (Durham University)
DTSTART:20210323T140000Z
DTEND:20210323T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/4
DESCRIPTION:Title: Geometry and topology of collapsed three-dimensional Alexa
ndrov spaces\nby Fernando Galaz-García (Durham University) as part of
Irish Geometry Seminar\n\n\nAbstract\nIn Riemannian geometry\, collapse i
mposes strong geometric and topological restrictions on the spaces on whic
h it occurs. In the case of Alexandrov spaces\, which are metric generaliz
ations of complete Riemannian manifolds with a uniform lower sectional cur
vature bound\, collapse is fairly well understood in dimension three. In t
his talk\, I will discuss the geometry and topology of three-dimensional A
lexandrov spaces and focus on those which are sufficiently collapsed. Whe
n such spaces are irreducible\, they are modeled on one of the eight three
-dimensional dimensional Thurston geometries\, excluding the hyperbolic on
e. This extends a result of Shioya and Yamaguchi\, originally formulated f
or Riemannian manifolds\, to the Alexandrov setting. (Joint work with Luis
Guijarro and Jesús Núñez-Zimbrón).\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Siffert (WWU Münster)
DTSTART:20210216T140000Z
DTEND:20210216T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/5
DESCRIPTION:Title: Construction of explicit p-harmonic functions\nby Anna
Siffert (WWU Münster) as part of Irish Geometry Seminar\n\n\nAbstract\nT
he study of p-harmonic functions on Riemannian manifolds has invoked the i
nterest of mathematicians and physicists for nearly two centuries. Applica
tions within physics can for example be found in continuum mechanics\, ela
sticity theory\, as well as two-dimensional hydrodynamics problems involvi
ng Stokes flows of incompressible Newtonian fluids.\n\nIn my talk I will f
ocus on the construction of explicit p-harmonic functions on rank-one Lie
groups of Iwasawa type. This joint wok with Sigmundur Gudmundsson and Mark
o Sobak.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wermelinger (University of Fribourg)
DTSTART:20210309T140000Z
DTEND:20210309T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/6
DESCRIPTION:Title: On the moduli space of positive Ricci metrics on 15-dimens
ional manifolds\nby Jonathan Wermelinger (University of Fribourg) as p
art of Irish Geometry Seminar\n\n\nAbstract\nIn this talk\, I am going to
show that the moduli spaces of positive Ricci curvature metrics on the tot
al spaces of $S^7$-bundles over $S^8$ which are rational homology spheres
have infinitely many path components. Furthermore\, when this total space
is a homotopy 15-sphere (called a Shimada sphere)\, we consider the involu
tion induced by fiberwise antipodal maps. The quotients are homotopy equiv
alent to $RP^{15}$ and we will study their diffeomorphism classification i
n order to prove some results on their moduli space of positive Ricci curv
ature metrics as well.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART:20210406T130000Z
DTEND:20210406T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/7
DESCRIPTION:Title: No talk\nby No talk as part of Irish Geometry Seminar\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masoumeh Zarei (Universität Augsburg)
DTSTART:20210316T140000Z
DTEND:20210316T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/8
DESCRIPTION:Title: Alexandrov spaces\, symmetry and positive curvature\nb
y Masoumeh Zarei (Universität Augsburg) as part of Irish Geometry Seminar
\n\n\nAbstract\nAlexandrov spaces are a generalization of Riemannian manif
olds with a lower curvature bound. It is then natural to ask to what exte
nt one can generalize the basic results of the Riemannian manifolds with a
lower curvature bound to Alexandrov spaces. In this talk\, I will explore
this question in the context of cohomogeneity one actions on positively c
urved Alexandrov spaces. I will explain some obstructions to the existence
of an invariant metric of positive curvature on a cohomogeneity one Alexa
ndrov space\, and then I will give a classification of closed simply-conne
cted cohomogeneity one Alexandrov spaces with positive curvature in dimens
ions at most 6. This is an ongoing project with Fernando Galaz-García.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claude LeBrun (Stony Brook University)
DTSTART:20210223T133000Z
DTEND:20210223T143000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/9
DESCRIPTION:Title: Einstein Metrics\, Conformal Curvature\, and Anti-Holomorp
hic Involutions\nby Claude LeBrun (Stony Brook University) as part of
Irish Geometry Seminar\n\n\nAbstract\nIn the theory of Einstein manifolds
\, dimension 4 occupies a Janus-like position\, being both the lowest dim
ension in which Einstein metrics needn't have constant sectional curvature
\, and the largest dimension in which one can sometimes completely descri
be all Einstein metrics on a fixed compact manifold. In this talk\, I wil
l describe the complete classification of compact oriented Einstein 4-mani
folds on which the determinant of the self-dual Weyl curvature is everywhe
re positive. Up to diffeomorphism\, there are exactly 15 manifolds that ad
mit such Einstein metrics\, and on each of these 4-manifolds\, these metri
cs sweep out exactly one connected component of the Einstein moduli space.
\n\n***Note the early start this week***\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Fine (Université Libre de Bruxelles)
DTSTART:20210329T140000Z
DTEND:20210329T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/10
DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby
Joel Fine (Université Libre de Bruxelles) as part of Irish Geometry Semi
nar\n\n\nAbstract\nThe asymptotic Plateau problem is as follows: given a s
ubmanifold K in the n-sphere\, is there a minimal submanifold in (n+1)-dim
ensional hyperbolic space whose ideal boundary is K? I will explain how so
lving this problem when K is a knot or link in the 3-sphere leads to a kno
t invariant: the number of genus g minimal surfaces filling K depends on K
only up to isotopy. This count of minimal surfaces is actually an example
of a Gromov-Witten type invariant: minimal surfaces in H^4 lift to J-holo
morphic curves in the twistor space. It is possible to combine these count
s of minimal surfaces into a single polynomial invariant of the link. To f
inish\, I will explain a conjecture\, that this “minimal surface polynom
ial” is in fact the HOMFLYPT polynomial of the bounding link K. The HOMF
LYPT polynomial is easy to calculate from a diagram of the link\; the conj
ecture would then mean this simple combinatorial calculation gives existen
ce results for minimal surfaces in H^4 filling K. This is joint work with
Marcelo Alves.\n\n***Note the exceptional day and time***\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harvey (Swansea University)
DTSTART:20210420T130000Z
DTEND:20210420T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/11
DESCRIPTION:Title: Estimating the reach of a submanifold\nby John Harvey
(Swansea University) as part of Irish Geometry Seminar\n\n\nAbstract\nThe
reach is an important geometric invariant of submanifolds of Euclidean sp
ace. It is a real-valued global invariant incorporating information about
the second fundamental form of the embedding and the location of the first
critical point of the distance from the submanifold. In the subject of ge
ometric inference – estimating the geometry from samples of points drawn
from the manifold - the reach plays a crucial role. I will give a new met
hod of estimating the reach of a submanifold\, developed jointly with Clé
ment Berenfeld\, Marc Hoffmann and Krishnan Shankar. This results in impro
ved convergence rates\, but a minimax optimal estimator remains to be foun
d.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato G. Bettiol (CUNY)
DTSTART:20210427T130000Z
DTEND:20210427T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/12
DESCRIPTION:Title: Geography of pinched 4-manifolds\nby Renato G. Bettio
l (CUNY) as part of Irish Geometry Seminar\n\n\nAbstract\nIt is widely exp
ected that a simply connected closed 4-dimensional Riemannian manifold wit
h positive sectional curvature must be homeomorphic to the 4-sphere or the
complex projective plane. Using a new take on classical techniques\, we p
rove this to be the case if M is $\\delta$-pinched with $\\delta=\\frac{1}
{1+3\\sqrt3}\\cong 0.161$\, that is\, if all sectional curvatures of M lie
in the interval $[\\delta\,1]$. We also give new restrictions on the “g
eography problem” of realizing Euler characteristics and signatures on 4
-manifolds under any (positive or negative) pinching assumption. The main
tools used are convex algebro-geometric and optimization insights on sets
of pinched curvature operators. This is based on joint work with M. Kummer
and R. Mendes.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolyn Gordon (Dartmouth College)
DTSTART:20210504T130000Z
DTEND:20210504T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/13
DESCRIPTION:Title: Infinitesimal Maximal Symmetry of Homogeneous Expanding R
icci Solitons\nby Carolyn Gordon (Dartmouth College) as part of Irish
Geometry Seminar\n\n\nAbstract\nA left-invariant Riemannian metric on a Li
e group G is said to be maximally symmetric if its isometry group contains
a copy of the isometry group of every other left-invariant Riemannian met
ric on G. Left-invariant Einstein metrics on simply-connected solvable
Lie groups are always maximally symmetric. We introduce a weaker notion
of infinitesimal maximal symmetry and show that left-invariant Ricci solit
on metrics on simply-connected solvable Lie groups are always infinitesima
lly maximally symmetric but not always maximally symmetric. We also discu
ss the general question of existence of maximally symmetric and infinitesi
mally maximally symmetric metrics.\n\nThis is joint work with Michael Jabl
onski.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason DeVito (University of Tennessee)
DTSTART:20210928T130000Z
DTEND:20210928T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/14
DESCRIPTION:Title: Double disk-bundles\nby Jason DeVito (University of T
ennessee) as part of Irish Geometry Seminar\n\n\nAbstract\nA double disk-b
undle is any manifold obtained by gluing the total spaces of two disk-bund
les together by a diffeomorphism. While the definition may seem quite arb
itrary\, we will show that\, in fact\, double disk-bundles arise in divers
e locations throughout geometry. We will also discuss the double soul con
jecture\, and its potential consequences\, including the classification of
Riemannian manifolds of non-negative sectional curvature under certain to
pological restrictions. This is partly joint work with Fernando Galaz-Gar
cía and Martin Kerin.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Heslin (Florida State University)
DTSTART:20211019T130000Z
DTEND:20211019T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/15
DESCRIPTION:Title: A geometric framework for ideal hydrodynamics\nby Pat
rick Heslin (Florida State University) as part of Irish Geometry Seminar\n
\n\nAbstract\nV. Arnold observed in his seminal paper that solutions of th
e Euler equations for ideal fluid motion can be viewed as geodesics of a c
ertain right-invariant metric on the group of volume-preserving diffeomorp
hisms (known as volumorphisms)\, $D_\\mu(M)$. In their celebrated paper Eb
in and Marsden provided the formulation of the above in the $H^s$ Sobolev
setting. Here they proved that the space of $H^s$ volumorphisms can be giv
en the structure of a smooth\, infinite dimensional Hilbert manifold. They
illustrated that\, when equipped with a right-invariant $L^2$ metric\, th
e geodesic equation on this manifold is a smooth ordinary differential equ
ation. They then applied the classic iteration method of Picard to obtain
existence\, uniqueness and smooth dependence on initial conditions. In par
ticular\, the last property allows one to define a smooth exponential map
on $D^s_\\mu(M)$ in analogy with the classical construction in finite dime
nsional Riemannian geometry. Hence\, the work of Arnold\, Ebin and Marsden
allows one to explore the problem of ideal fluid motion armed with tools
from Riemannian geometry. In this talk I will present some results about t
he behaviour of geodesics on these manifolds and translate them to regular
ity properties of solutions to the Euler equations.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anusha Mangala Krishnan (Universität Münster)
DTSTART:20211116T140000Z
DTEND:20211116T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/16
DESCRIPTION:Title: Positive sectional curvature and Ricci flow\nby Anush
a Mangala Krishnan (Universität Münster) as part of Irish Geometry Semin
ar\n\n\nAbstract\nThe preservation of positive curvature conditions under
the Ricci flow has been an important ingredient in applications of the flo
w to solving problems in geometry and topology. Works by Hamilton and oth
ers established that certain positive curvature conditions are preserved u
nder the flow\, culminating in Wilking's unified\, Lie algebraic approach
to proving invariance of positive curvature conditions. Yet\, some questi
ons remain. In this talk\, we describe $\\sec > 0$ initial metrics on $S^
4$\, where the condition of $\\sec > 0$ is not preserved under the Ricci f
low. Previously\, examples of such behaviour were known for $\\sec \\geq
0$\, and for $\\sec > 0$ in dimension 6 and above. This is joint work wit
h Renato Bettiol.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Huettemann (Queen's University Belfast)
DTSTART:20211130T140000Z
DTEND:20211130T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/17
DESCRIPTION:Title: On algebraic K -theory and its applications\nby Thoma
s Huettemann (Queen's University Belfast) as part of Irish Geometry Semina
r\n\n\nAbstract\nThis will be an overview talk\, starting with the classic
al\nlower algebraic K-groups of a ring. I will report on various\napplicat
ions of the constructions in algebra\, topology and geometry (eg\,\nfinite
ness obstructions\, classification of h-cobordisms with Whitehead\ntorsion
\, finding obstructions to extending vector bundles). Time\npermitting I w
ill sketch some general splitting results relating to\nprojective spaces a
nd Laurent polynomial extensions\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Guilfoyle (Munster Technological University)
DTSTART:20211005T130000Z
DTEND:20211005T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/18
DESCRIPTION:Title: The Toponogov conjecture on complete surfaces\nby Bre
ndan Guilfoyle (Munster Technological University) as part of Irish Geometr
y Seminar\n\n\nAbstract\nA conjecture of Toponogov states that a complete
convex plane P embedded in Euclidean 3-space must have $\\inf |\\kappa_1 -
\\kappa_2|=0$. Thus\, there must be an umbilic point on P\, albeit at inf
inity. \n\nIn this talk I will sketch the proof of this conjecture for smo
oth surfaces (in collaboration with Wilhelm Klingenberg). The first step o
f the proof involves studying an associated Riemann-Hilbert boundary value
problem and showing that it is Fredholm regular for any counterexample to
the conjecture. Then mean curvature flow with boundary supplies enough so
lutions to show that the problem cannot be Fredholm regular\, thus establi
shing the non-existence of a counterexample.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART:20210921T130000Z
DTEND:20210921T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/19
DESCRIPTION:Title: Regular matroids and Riemannian manifolds\nby Lee Ken
nard (Syracuse University) as part of Irish Geometry Seminar\n\n\nAbstract
\nIn joint work with Michael Wiemeler and Burkhard Wilking at the Universi
ty of Muenster\, we are investigating torus representations having the spe
cial property that all isotropy groups are connected. I will discuss the c
onnection to matroid theory\, how this connection helps us prove structura
l results for torus representations\, and some applications in the Grove S
ymmetry Program.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramiro Lafuente (University of Queensland)
DTSTART:20211026T130000Z
DTEND:20211026T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/20
DESCRIPTION:Title: Non-compact Einstein manifolds with symmetry\nby Rami
ro Lafuente (University of Queensland) as part of Irish Geometry Seminar\n
\n\nAbstract\nIn this talk we will discuss recent joint work in collaborat
ion with Christoph Böhm in which we obtain structure results for non-comp
act Einstein manifolds admitting a cocompact isometric action of a connect
ed Lie group. As an application\, we prove the Alekseevskii conjecture (19
75): any connected homogeneous Einstein space of negative scalar curvature
is diffeomorphic to a Euclidean space.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Tyrell (University of Texas\, Dallas)
DTSTART:20211123T140000Z
DTEND:20211123T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/21
DESCRIPTION:Title: Renormalized Area for 4-dimensional Minimal Hypersurfaces
of a Poincaré-Einstein Space\nby Aaron Tyrell (University of Texas\,
Dallas) as part of Irish Geometry Seminar\n\n\nAbstract\nIn 1999 Graham a
nd Witten showed that one can define a notion of renormalized area for pro
perly embedded minimal submanifolds of Poincaré-Einstein spaces. For even
-dimensional submanifolds\, this quantity is an invariant of the ambient m
etric and the submanifold. In 2008 Alexakis and Mazzeo wrote a paper on th
is quantity for surfaces in a 3-dimensional PE manifold\, getting an expli
cit formula and studying its functional properties. We will look at a for
mula for the renormalized area of a minimal hypersurface of a 5-dimensiona
l Poincaré-Einstein space.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadine Große (Universität Freiburg)
DTSTART:20211207T140000Z
DTEND:20211207T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/22
DESCRIPTION:Title: On the space of metrics with invertible Dirac operator\nby Nadine Große (Universität Freiburg) as part of Irish Geometry Semi
nar\n\n\nAbstract\nAmmann\, Dahl and Humbert showed that the property that
a manifold admits a metric with invertible Dirac operator persists under
the right surgeries. That is the Dirac-counterpart of the Gromov-Lawson co
nstruction on the question of existence of postive scalar curvature\nmetri
cs and has also implications on this question. We consider now the questio
n whether we can also obtain a homotopy equivalence statement for spaces o
f metrics with invertible Dirac operator under surgery in the spirit of th
e positive scalar curvature result by Chernysh/Walsh. This is joint work w
ith N. Pederzani.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina Arroyo (Universidad Nacional de Córdoba)
DTSTART:20211109T140000Z
DTEND:20211109T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/24
DESCRIPTION:Title: The prescribed Ricci curvature problem for naturally redu
ctive metrics on simple Lie groups\nby Romina Arroyo (Universidad Naci
onal de Córdoba) as part of Irish Geometry Seminar\n\n\nAbstract\nA class
ical problem in geometric analysis is to find a Riemannian metric whose Ri
cci curvature is prescribed\, that is\, a Riemannian metric $g$ and a real
number $c>0$ satisfying\n\\[\n\\operatorname{Ric} (g) = c T\,\n\\]\nfor s
ome fixed symmetric $(0\, 2)$-tensor field $T$ on a manifold $M\,$ where $
\\operatorname{Ric} (g)$ denotes the Ricci curvature of $g.$\n\nThe aim of
this talk is to discuss this problem within the class of naturally reduct
ive metrics when $M$ is a simple Lie group\, and present obtained results
in this setting. \n\nThis talk is based on joint works with Mark Gould (Th
e University of Queensland)\, Artem Pulemotov (The University of Queenslan
d) and Wolfgang Ziller (University of Pennsylvania).\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART:20211012T130000Z
DTEND:20211012T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/25
DESCRIPTION:Title: Invariant theory without groups\nby Marco Radeschi (U
niversity of Notre Dame) as part of Irish Geometry Seminar\n\n\nAbstract\n
Given an orthogonal representation of a Lie group G on a Euclidean vector
space V\, Invariant Theory studies the representation via the algebra of G
-invariant polynomials on V. This setting can be generalized by replacing
the representation 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 leaves - effectively producing an Invariant Theory\, but without
groups involved. In this talk we will discuss a surprising relation betwe
en the geometry of the foliation and the corresponding algebra\, including
recent joint work in progress with Ricardo Mendes and Samuel Lin\, showin
g how to estimate volume and diameter of the quotient V/F using the algebr
a.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Lauret (Universidad Nacional del Sur)
DTSTART:20211102T140000Z
DTEND:20211102T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/26
DESCRIPTION:Title: On the smallest positive Laplace eigenvalue of a homogene
ous CROSS\nby Emilio Lauret (Universidad Nacional del Sur) as part of
Irish Geometry Seminar\n\n\nAbstract\nWe will show an explicit expression
for the lowest positive eigenvalue of the Laplace-Beltrami operator associ
ated to any homogeneous metric on the underlying manifold of a CROSS (a co
mpact rank one symmetric space.\n\nAs a first consequence\, we will show t
hat the Laplace spectrum distinguishes any metric among the space of homog
eneous metrics on CROSSes. Furthermore\, we will study the local rigidity
of homogeneous metrics on CROSSes as solutions of the Yamabe problem. If
time permits\, we will localize in an explicit way the set of resonant ra
dii of geodesic spheres on CROSSes endowed with certain homogeneous metric
s.\n\nThis is joint work with Renato Bettiol and Paolo Piccione.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Wink (WWU Münster)
DTSTART:20220201T140000Z
DTEND:20220201T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/27
DESCRIPTION:Title: Generalizations of Tachibana's theorem\nby Matthias W
ink (WWU Münster) as part of Irish Geometry Seminar\n\n\nAbstract\nA famo
us theorem of Tachibana says that compact Einstein manifolds with positive
curvature operators have constant curvature. In this talk we will discuss
several generalizations of this theorem. For example\, we show that it su
ffices to assume that the curvature operator\nis $\\lfloor \\frac{n-1}{2}
\\rfloor$-positive\, where $n$ is the dimension of the manifold. Time perm
itting\, we discuss analogues of Tachibana's theorem for Kähler manifolds
and quaternion Kähler manifolds. This talk is based on joint work with
Peter Petersen.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David González Álvaro (Universidad Politécnica de Madrid)
DTSTART:20220208T140000Z
DTEND:20220208T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/28
DESCRIPTION:Title: Manifolds of $Ric_k > 0$\nby David González Álvaro
(Universidad Politécnica de Madrid) as part of Irish Geometry Seminar\n\n
\nAbstract\nThe curvature conditions $Ric_k>0$ on n-dimensional manifolds
interpolate between positive sectional curvature (when k=1) and positive R
icci curvature (when k = n-1). In this talk we will review their definitio
ns and context\, and explain how to construct manifolds of $Ric_k>0$ with
k as small as possible\, based on joint work with Miguel Domínguez-Vázqu
ez and Lawrence Mouillé. Afterwards we will discuss some related open que
stions.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Poljsak (WWU Münster)
DTSTART:20220405T130000Z
DTEND:20220405T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/29
DESCRIPTION:Title: Towards Finding the Second Best Einstein Metric in Low Di
mensions\nby Kevin Poljsak (WWU Münster) as part of Irish Geometry Se
minar\n\n\nAbstract\nA metric $g$ on a simply connected manifold $M$ is ca
lled the second best Einstein metric\, if $(M\,g)$ is an Einstein manifold
with positive scalar curvature which is non isometric to the sphere and i
ts curvature operator $R$ minimizes the angle $\\sphericalangle(R(p)\, Id)
$ to the identity at each point $p \\in M$ among all Einstein manifolds wi
th the properties above. \\\\\nIn this talk we use the identity $2(\\text{
scal}/n) R = \\Delta R + 2(R^2+R^{\\#})$ that holds for all Einstein manif
olds in order to present an approach finding the second best Einstein metr
ic in dimensions $\\leq 11$.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Georgiou (Waterford IT)
DTSTART:20220412T130000Z
DTEND:20220412T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/30
DESCRIPTION:Title: Almost Paracomplex Structure on 4-manifolds\nby Nikos
Georgiou (Waterford IT) as part of Irish Geometry Seminar\n\n\nAbstract\n
In joint work with Brendan Guilfoyle at the Munster Technological Universi
ty\, we are investigating the existence or otherwise of parallel\, isometr
ic\, and anti-isometric almost paracomplex structures on a pseudo-Riemanni
an 4-manifold. These structures provide a connection between Einstein metr
ics and metrics that are locally conformally flat and scalar flat. In thi
s talk I will discuss the recent development of these structures as well a
s some applications in certain 4-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART:20220301T140000Z
DTEND:20220301T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/31
DESCRIPTION:Title: The maximal spectral gap of a hyperbolic surface\nby
Michael Magee (Durham University) as part of Irish Geometry Seminar\n\n\nA
bstract\nA hyperbolic surface is a surface with metric of constant curvatu
re -1. The spectral gap between the first two eigenvalues of the Laplacian
on a closed hyperbolic surface contains a good deal of information about
the surface\, including its connectivity\, dynamical properties of its geo
desic flow\, and error terms in geodesic counting problems. For arithmetic
hyperbolic surfaces the spectral gap is also the subject of one of the bi
ggest open problems in automorphic forms: Selberg’s eigenvalue conjectur
e.\n\nIt was an open problem from the 1970s whether there exist a sequence
of closed hyperbolic surfaces with genera tending to infinity and spectra
l gap tending to 1/4. (The value 1/4 here is the asymptotically optimal on
e.) Recently we proved that this is indeed possible. I’ll discuss the ve
ry interesting background of this problem in detail as well as some ideas
of the proof. This is joint work with Will Hide.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Dryden (Bucknell University)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/32
DESCRIPTION:Title: Applications of symmetry to certain eigenvalue bounds on
surfaces\nby Emily Dryden (Bucknell University) as part of Irish Geome
try Seminar\n\n\nAbstract\nWe study a class of eigenvalue problems for sur
faces. The question of finding meaningful upper bounds for these eigenval
ues has a long history going back to Weinstock\, who studied an isoperimet
ric inequality for a certain lowest eigenvalue of a simply-connected plana
r domain. We will explore some recent contributions to the story\, with an
emphasis on results that can be seen in pictures.\n\nJoint work with: Ter
esa Arias-Marco (Universidad de Extremadura\, Spain)\,\nCarolyn S. Gordon
(Dartmouth College\, USA)\,\nAsma Hassannezhad (University of Bristol\, UK
)\,\nAllie Ray (Birmingham-Southern College\, USA)\,\nElizabeth Stanhope (
Lewis & Clark College\, USA).\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Reiser (Karlsruher Institut für Technologie)
DTSTART:20220215T140000Z
DTEND:20220215T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/33
DESCRIPTION:Title: Generalized Surgery on Riemannian Manifolds of Positive R
icci Curvature and Applications in Dimension 6\nby Philipp Reiser (Kar
lsruher Institut für Technologie) as part of Irish Geometry Seminar\n\n\n
Abstract\nIn this talk I will review the known techniques to construct met
rics of positive Ricci curvature via surgery. These techniques go back to
Sha-Yang and Wraith for higher surgeries and to Perelman and Burdick for c
onnected sums. I will then present a generalization of the surgery theorem
of Wraith\, in which the surgery construction itself gets generalized. Fi
nally\, I will discuss applications in dimension 6. Here we obtain a large
class of new examples of closed\, simply-connected 6-manifolds that admit
a metric of positive Ricci curvature. These examples are constructed as b
oundaries of manifolds obtained by plumbings according to a simply-connect
ed graph.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART:20220322T140000Z
DTEND:20220322T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/34
DESCRIPTION:Title: Optimal Transport\, weak Laplacian bounds and minimal bou
ndaries in non-smooth spaces with Lower Ricci Curvature bounds\nby And
rea Mondino (University of Oxford) as part of Irish Geometry Seminar\n\n\n
Abstract\nThe goal of the seminar is to report on recent joint work with D
aniele Semola\, motivated by a question of Gromov to establish a “synthe
tic regularity theory" for minimal surfaces in non-smooth ambient spaces.
In the setting of non-smooth spaces with lower Ricci Curvature bounds:\n\n
- We establish a new principle relating lower Ricci Curvature bounds to th
e preservation of Laplacian bounds under the evolution via the Hopf-Lax se
migroup\;\n\n- We develop an intrinsic viscosity theory of Laplacian bound
s and prove equivalence with other weak notions of Laplacian bounds\;\n\n-
We prove sharp Laplacian bounds on the distance function from a set (loca
lly) minimizing the perimeter: this corresponds to vanishing mean curvatur
e in the smooth setting\;\n\n- We study the regularity of boundaries of se
ts (locally) minimizing the perimeter\, obtaining sharp bounds on the Haus
dorff co-dimension of the singular set plus content estimates and topologi
cal regularity of the regular set.\nOptimal transport plays the role of un
derlying technical tool for addressing various points.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asma Hassannezhad (University of Bristol)
DTSTART:20220329T130000Z
DTEND:20220329T140000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/35
DESCRIPTION:Title: Nodal counts for the Dirichlet-to Neumann operators with
potential\nby Asma Hassannezhad (University of Bristol) as part of Iri
sh Geometry Seminar\n\n\nAbstract\nThe zero set of an eigenfunction is cal
led the nodal set and the connected components of its complement are calle
d the Nodal domains. The well-known Courant nodal domain theorem gives an
upper bound for the nodal count of Laplace eigenfunctions on a compact man
ifold. We consider the harmonic extension of eigenfunctions of the Dirich
let-to-Neumann operators with potential. When the potential is zero\, thes
e harmonic extensions are called the Steklov eigenfunctions. It has been k
nown that the Courant nodal domain theorem holds for Steklov eigenfunction
s. We discuss how we can get a Courant-type bound for the nodal count of t
he Dirichlet-to-Neumann operator in the presence of a potential.\n\nThis i
s joint work with David Sher.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Hanke (Universität Augsburg)
DTSTART:20220222T140000Z
DTEND:20220222T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/36
DESCRIPTION:Title: Boundary conditions for scalar curvature\nby Bernhard
Hanke (Universität Augsburg) as part of Irish Geometry Seminar\n\n\nAbst
ract\nWe show a general deformation principle for boundary conditions of m
etrics with lower scalar curvature bounds. This implies that the relaxati
on of boundary conditions often induces weak homotopy equivalences of spac
es of such metrics.\n\nCombining this with the existence of fibre bundles
over spheres whose total spaces have non-zero $\\hat{A}$-genera we constru
ct compact manifolds for which the spaces of positive scalar curvature met
rics with mean convex boundaries have nontrivial higher homotopy groups. \
n\nThis is joint work with Christian Bär.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Bechtluft-Sachs (Maynooth University)
DTSTART:20220308T140000Z
DTEND:20220308T150000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/37
DESCRIPTION:Title: Linking integrals in negatively curved symmetric spaces\nby Stefan Bechtluft-Sachs (Maynooth University) as part of Irish Geome
try Seminar\n\n\nAbstract\nGauss' integral formula for the linking number
of loops in Euclidean space readily generalizes to submanifolds of an orie
nted Riemannian manifold with sufficiently vanishing homology. To this end
one needs an inverse to the Cartan differential. In particular\, any righ
t inverse of the differential form Laplacian or Dirac operator yields such
a linking kernel.\nWe will show how all this can be made almost explicit
on negatively curved symmetric spaces (non compact rank one symmetric spac
e) in terms of a solution of an ordinary differential equation.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART:20220518T144500Z
DTEND:20220518T153000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/38
DESCRIPTION:Title: Graph systoles and torus representations\nby Lee Kenn
ard (Syracuse University) as part of Irish Geometry Seminar\n\n\nAbstract\
nA classical graph invariant is the girth\, which is the length of the sho
rtest cycle. In the presence of weights or distances assigned to the edges
\, one can similarly define the weighted girth or systole of a graph. Boll
obás and Szemerédi have proved asymptotic bounds on this quantity as the
graph Betti number goes to infinity. I will discuss new bounds for the ca
se of small Betti number proved recently in joint work with Michael Wiemel
er and Burkhard Wilking. This has implications for structure of torus repr
esentations with connected isotropy groups and applications to the problem
of classifying Riemannian manifolds with positive curvature and large iso
metry groups.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnan Shankar (University of Oklahoma)
DTSTART:20220518T154500Z
DTEND:20220518T163000Z
DTSTAMP:20260404T111104Z
UID:IrishGeomSeminar/39
DESCRIPTION:Title: Growth competitions in non-positive curvature\nby Kri
shnan Shankar (University of Oklahoma) as part of Irish Geometry Seminar\n
\n\nAbstract\nThe notion of a growth competition between two deterministic
ally growing clusters in a complete\, non-compact metric space (or graph)
was first proposed by I. Benjamini and recently explored in the case of 2-
dimensional Euclidean and hyperbolic spaces by his student\, R. Assouline.
A growth competition in a non-compact\, complete Riemannian manifold\, $X
$\, (or more generally a complete\, non-compact geodesic metric space) is
the existence of two sets\, $A_t$ (fast) and $B_t$ (slow)\, $t\\geq 0$\, t
hat grow from singletons according to the following simple rules:\n\ni $A_
0 = \\{ q \\}\, \\ B_0 = \\{ p \\}$ and $p \\neq q$.\n\nii $\\{ A_t \\}_{t
\\geq 0}$ is a parametrized family of subsets defined as\, $A_t := \\cup_
\\alpha \\alpha([0\,t])$\, where $\\alpha(s)$ is a $\\lambda$-Lipschitz cu
rve in $X$\, with $\\lambda > 1$ such that $\\alpha (s) \\not\\in B_s$ for
all $s \\in [0\,t]$. The collection of sets $A_t$ are the fast sets.\n\ni
ii $\\{ B_t \\}_{t \\geq 0}$ is a parametrized family of subsets defined a
s\, $B_t := \\cup_\\beta \\beta([0\,t])$\, where $\\beta(s)$ is a $1$-Lips
chitz curve in $X$ and $\\beta (s) \\not\\in A_s$ for all $s \\in [0\,t]$.
The collection of sets $B_t$ are the slow sets.\n\niv The limiting sets a
re denoted as $A_\\infty = \\cup_{t \\geq 0} A_t$ and $B_\\infty = \\cup_{
t \\geq 0} B_t$.\n\nA key result shown by Assouline is that given any two
distinct points $p$\, $q$ in a path connected\, complete\, geodesic metric
space $X$ and a real number $\\lambda > 1$\, there exists a unique growth
competition satisfying the above conditions. A basic geometric question o
ne may ask in this setting is: under what circumstances is the slow set\,
$B_\\infty$\, totally bounded (surrounded) by the fast set\, $A_\\infty$\,
versus when are they both unbounded (co-existence)? The applications of t
his geometric exploration are evident in a variety of settings (including
disease/vaccine vectors\, flow of misinformation or the control of forest
fires). In recent work with Benjamin Schmidt and Ralf Spatzier we have bee
n exploring the above question in the setting of non-positive curvature. I
n this talk we introduce growth competitions and give a preview of some re
sults and open problems.\n
LOCATION:https://stable.researchseminars.org/talk/IrishGeomSeminar/39/
END:VEVENT
END:VCALENDAR