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BEGIN:VEVENT
SUMMARY:Wolfgang Ziller (University of Pennsylvania)
DTSTART;VALUE=DATE-TIME:20210209T140000Z
DTEND;VALUE=DATE-TIME:20210209T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/1
DESCRIPTION:Title: A variational approach to prescribing the Ricci tensor\nby Wo
lfgang Ziller (University of Pennsylvania) as part of Irish Geometry Semin
ar\n\n\nAbstract\nWe discuss the question of which tensors T can be the Ri
cci tensor of a metric\, i.e. Ric(g)=T or Ric(g)=cT for some c. Solutions
can be viewed as the critical points of a modified scalar\ncurvature func
tional and we examine the global behavior of this functional in the case o
f homogeneous spaces. This is joint work with Artem Pulemotov.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McKay (University College Cork)
DTSTART;VALUE=DATE-TIME:20210302T140000Z
DTEND;VALUE=DATE-TIME:20210302T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/2
DESCRIPTION:Title: Locally homogeneous complex analytic geometric structures\nby
Ben McKay (University College Cork) as part of Irish Geometry Seminar\n\n
\nAbstract\nI will present a conjecture on the classification of holomorph
ic locally homogeneous geometric structures (modelled on complex flag vari
eties) on smooth projective varieties. I will give an outline of what we k
now so far.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Kilian (University College Cork)
DTSTART;VALUE=DATE-TIME:20210413T130000Z
DTEND;VALUE=DATE-TIME:20210413T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/3
DESCRIPTION:Title: Integrable systems methods for constant mean curvature surfaces\nby Martin Kilian (University College Cork) as part of Irish Geometry S
eminar\n\n\nAbstract\nI will survey some of the recent progress made in de
veloping the theory of constant mean curvature surfaces.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Galaz-García (Durham University)
DTSTART;VALUE=DATE-TIME:20210323T140000Z
DTEND;VALUE=DATE-TIME:20210323T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/4
DESCRIPTION:Title: Geometry and topology of collapsed three-dimensional Alexandrov s
paces\nby Fernando Galaz-García (Durham University) as part of Irish
Geometry Seminar\n\n\nAbstract\nIn Riemannian geometry\, collapse imposes
strong geometric and topological restrictions on the spaces on which it oc
curs. In the case of Alexandrov spaces\, which are metric generalizations
of complete Riemannian manifolds with a uniform lower sectional curvature
bound\, collapse is fairly well understood in dimension three. In this tal
k\, I will discuss the geometry and topology of three-dimensional Alexandr
ov spaces and focus on those which are sufficiently collapsed. When such
spaces are irreducible\, they are modeled on one of the eight three-dimens
ional dimensional Thurston geometries\, excluding the hyperbolic one. This
extends a result of Shioya and Yamaguchi\, originally formulated for Riem
annian manifolds\, to the Alexandrov setting. (Joint work with Luis Guijar
ro and Jesús Núñez-Zimbrón).\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Siffert (WWU Münster)
DTSTART;VALUE=DATE-TIME:20210216T140000Z
DTEND;VALUE=DATE-TIME:20210216T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/5
DESCRIPTION:Title: Construction of explicit p-harmonic functions\nby Anna Siffer
t (WWU Münster) as part of Irish Geometry Seminar\n\n\nAbstract\nThe stud
y of p-harmonic functions on Riemannian manifolds has invoked the interest
of mathematicians and physicists for nearly two centuries. Applications w
ithin physics can for example be found in continuum mechanics\, elasticity
theory\, as well as two-dimensional hydrodynamics problems involving Stok
es flows of incompressible Newtonian fluids.\n\nIn my talk I will focus on
the construction of explicit p-harmonic functions on rank-one Lie groups
of Iwasawa type. This joint wok with Sigmundur Gudmundsson and Marko Sobak
.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Wermelinger (University of Fribourg)
DTSTART;VALUE=DATE-TIME:20210309T140000Z
DTEND;VALUE=DATE-TIME:20210309T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/6
DESCRIPTION:Title: On the moduli space of positive Ricci metrics on 15-dimensional m
anifolds\nby Jonathan Wermelinger (University of Fribourg) as part of
Irish Geometry Seminar\n\n\nAbstract\nIn this talk\, I am going to show th
at the moduli spaces of positive Ricci curvature metrics on the total spac
es of $S^7$-bundles over $S^8$ which are rational homology spheres have in
finitely many path components. Furthermore\, when this total space is a ho
motopy 15-sphere (called a Shimada sphere)\, we consider the involution in
duced by fiberwise antipodal maps. The quotients are homotopy equivalent t
o $RP^{15}$ and we will study their diffeomorphism classification in order
to prove some results on their moduli space of positive Ricci curvature m
etrics as well.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:No talk
DTSTART;VALUE=DATE-TIME:20210406T130000Z
DTEND;VALUE=DATE-TIME:20210406T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/7
DESCRIPTION:Title: No talk\nby No talk as part of Irish Geometry Seminar\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Masoumeh Zarei (Universität Augsburg)
DTSTART;VALUE=DATE-TIME:20210316T140000Z
DTEND;VALUE=DATE-TIME:20210316T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/8
DESCRIPTION:Title: Alexandrov spaces\, symmetry and positive curvature\nby Masou
meh Zarei (Universität Augsburg) as part of Irish Geometry Seminar\n\n\nA
bstract\nAlexandrov spaces are a generalization of Riemannian manifolds wi
th a lower curvature bound. It is then natural to ask to what extent 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 q
uestion in the context of cohomogeneity one actions on positively curved A
lexandrov spaces. I will explain some obstructions to the existence of an
invariant metric of positive curvature on a cohomogeneity one Alexandrov s
pace\, and then I will give a classification of closed simply-connected co
homogeneity one Alexandrov spaces with positive curvature in dimensions at
most 6. This is an ongoing project with Fernando Galaz-García.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claude LeBrun (Stony Brook University)
DTSTART;VALUE=DATE-TIME:20210223T133000Z
DTEND;VALUE=DATE-TIME:20210223T143000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/9
DESCRIPTION:Title: Einstein Metrics\, Conformal Curvature\, and Anti-Holomorphic Inv
olutions\nby Claude LeBrun (Stony Brook University) as part of Irish G
eometry Seminar\n\n\nAbstract\nIn the theory of Einstein manifolds\, dim
ension 4 occupies a Janus-like position\, being both the lowest dimension
in which Einstein metrics needn't have constant sectional curvature\, and
the largest dimension in which one can sometimes completely describe all
Einstein metrics on a fixed compact manifold. In this talk\, I will descr
ibe the complete classification of compact oriented Einstein 4-manifolds o
n which the determinant of the self-dual Weyl curvature is everywhere posi
tive. Up to diffeomorphism\, there are exactly 15 manifolds that admit suc
h Einstein metrics\, and on each of these 4-manifolds\, these metrics swee
p out exactly one connected component of the Einstein moduli space.\n\n***
Note the early start this week***\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joel Fine (Université Libre de Bruxelles)
DTSTART;VALUE=DATE-TIME:20210329T140000Z
DTEND;VALUE=DATE-TIME:20210329T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/10
DESCRIPTION:Title: Knots\, minimal surfaces and J-holomorphic curves\nby Joel F
ine (Université Libre de Bruxelles) as part of Irish Geometry Seminar\n\n
\nAbstract\nThe asymptotic Plateau problem is as follows: given a submanif
old K in the n-sphere\, is there a minimal submanifold in (n+1)-dimensiona
l hyperbolic space whose ideal boundary is K? I will explain how solving t
his problem when K is a knot or link in the 3-sphere leads to a knot invar
iant: the number of genus g minimal surfaces filling K depends on K only u
p to isotopy. This count of minimal surfaces is actually an example of a G
romov-Witten type invariant: minimal surfaces in H^4 lift to J-holomorphic
curves in the twistor space. It is possible to combine these counts of mi
nimal surfaces into a single polynomial invariant of the link. To finish\,
I will explain a conjecture\, that this “minimal surface polynomial”
is in fact the HOMFLYPT polynomial of the bounding link K. The HOMFLYPT po
lynomial is easy to calculate from a diagram of the link\; the conjecture
would then mean this simple combinatorial calculation gives existence resu
lts 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://researchseminars.org/talk/IrishGeomSeminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Harvey (Swansea University)
DTSTART;VALUE=DATE-TIME:20210420T130000Z
DTEND;VALUE=DATE-TIME:20210420T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/11
DESCRIPTION:Title: Estimating the reach of a submanifold\nby John Harvey (Swans
ea University) as part of Irish Geometry Seminar\n\n\nAbstract\nThe reach
is an important geometric invariant of submanifolds of Euclidean space. It
is a real-valued global invariant incorporating information about the sec
ond fundamental form of the embedding and the location of the first critic
al point of the distance from the submanifold. In the subject of geometric
inference – estimating the geometry from samples of points drawn from t
he manifold - the reach plays a crucial role. I will give a new method of
estimating the reach of a submanifold\, developed jointly with Clément Be
renfeld\, Marc Hoffmann and Krishnan Shankar. This results in improved con
vergence rates\, but a minimax optimal estimator remains to be found.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renato G. Bettiol (CUNY)
DTSTART;VALUE=DATE-TIME:20210427T130000Z
DTEND;VALUE=DATE-TIME:20210427T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/12
DESCRIPTION:Title: Geography of pinched 4-manifolds\nby Renato G. Bettiol (CUNY
) as part of Irish Geometry Seminar\n\n\nAbstract\nIt is widely expected t
hat a simply connected closed 4-dimensional Riemannian manifold with posit
ive sectional curvature must be homeomorphic to the 4-sphere or the comple
x projective plane. Using a new take on classical techniques\, we prove th
is to be the case if M is $\\delta$-pinched with $\\delta=\\frac{1}{1+3\\s
qrt3}\\cong 0.161$\, that is\, if all sectional curvatures of M lie in the
interval $[\\delta\,1]$. We also give new restrictions on the “geograph
y problem” of realizing Euler characteristics and signatures on 4-manifo
lds under any (positive or negative) pinching assumption. The main tools u
sed are convex algebro-geometric and optimization insights on sets of pinc
hed curvature operators. This is based on joint work with M. Kummer and R.
Mendes.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carolyn Gordon (Dartmouth College)
DTSTART;VALUE=DATE-TIME:20210504T130000Z
DTEND;VALUE=DATE-TIME:20210504T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/13
DESCRIPTION:Title: Infinitesimal Maximal Symmetry of Homogeneous Expanding Ricci So
litons\nby Carolyn Gordon (Dartmouth College) as part of Irish Geometr
y Seminar\n\n\nAbstract\nA left-invariant Riemannian metric on a Lie 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 metric on
G. Left-invariant Einstein metrics on simply-connected solvable Lie gro
ups are always maximally symmetric. We introduce a weaker notion of infi
nitesimal maximal symmetry and show that left-invariant Ricci soliton metr
ics on simply-connected solvable Lie groups are always infinitesimally max
imally symmetric but not always maximally symmetric. We also discuss the
general question of existence of maximally symmetric and infinitesimally m
aximally symmetric metrics.\n\nThis is joint work with Michael Jablonski.\
n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason DeVito (University of Tennessee)
DTSTART;VALUE=DATE-TIME:20210928T130000Z
DTEND;VALUE=DATE-TIME:20210928T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/14
DESCRIPTION:Title: Double disk-bundles\nby Jason DeVito (University of Tennesse
e) as part of Irish Geometry Seminar\n\n\nAbstract\nA double disk-bundle i
s any manifold obtained by gluing the total spaces of two disk-bundles tog
ether by a diffeomorphism. While the definition may seem quite arbitrary\
, we will show that\, in fact\, double disk-bundles arise in diverse locat
ions throughout geometry. We will also discuss the double soul conjecture
\, and its potential consequences\, including the classification of Rieman
nian manifolds of non-negative sectional curvature under certain topologic
al restrictions. This is partly joint work with Fernando Galaz-García an
d Martin Kerin.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Heslin (Florida State University)
DTSTART;VALUE=DATE-TIME:20211019T130000Z
DTEND;VALUE=DATE-TIME:20211019T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/15
DESCRIPTION:Title: A geometric framework for ideal hydrodynamics\nby Patrick He
slin (Florida State University) as part of Irish Geometry Seminar\n\n\nAbs
tract\nV. Arnold observed in his seminal paper that solutions of the Euler
equations for ideal fluid motion can be viewed as geodesics of a certain
right-invariant metric on the group of volume-preserving diffeomorphisms (
known as volumorphisms)\, $D_\\mu(M)$. In their celebrated paper Ebin 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 given the
structure of a smooth\, infinite dimensional Hilbert manifold. They illust
rated that\, when equipped with a right-invariant $L^2$ metric\, the geode
sic equation on this manifold is a smooth ordinary differential equation.
They then applied the classic iteration method of Picard to obtain existen
ce\, uniqueness and smooth dependence on initial conditions. In particular
\, the last property allows one to define a smooth exponential map on $D^s
_\\mu(M)$ in analogy with the classical construction in finite dimensional
Riemannian geometry. Hence\, the work of Arnold\, Ebin and Marsden allows
one to explore the problem of ideal fluid motion armed with tools from Ri
emannian geometry. In this talk I will present some results about the beha
viour of geodesics on these manifolds and translate them to regularity pro
perties of solutions to the Euler equations.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anusha Mangala Krishnan (Universität Münster)
DTSTART;VALUE=DATE-TIME:20211116T140000Z
DTEND;VALUE=DATE-TIME:20211116T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/16
DESCRIPTION:Title: Positive sectional curvature and Ricci flow\nby Anusha Manga
la Krishnan (Universität Münster) as part of Irish Geometry Seminar\n\n\
nAbstract\nThe preservation of positive curvature conditions under the Ric
ci flow has been an important ingredient in applications of the flow to so
lving problems in geometry and topology. Works by Hamilton and others est
ablished that certain positive curvature conditions are preserved under th
e flow\, culminating in Wilking's unified\, Lie algebraic approach to prov
ing invariance of positive curvature conditions. Yet\, some questions rem
ain. In this talk\, we describe $\\sec > 0$ initial metrics on $S^4$\, wh
ere the condition of $\\sec > 0$ is not preserved under the Ricci flow. P
reviously\, examples of such behaviour were known for $\\sec \\geq 0$\, an
d for $\\sec > 0$ in dimension 6 and above. This is joint work with Renat
o Bettiol.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Huettemann (Queen's University Belfast)
DTSTART;VALUE=DATE-TIME:20211130T140000Z
DTEND;VALUE=DATE-TIME:20211130T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/17
DESCRIPTION:Title: On algebraic K -theory and its applications\nby Thomas Huett
emann (Queen's University Belfast) as part of Irish Geometry Seminar\n\n\n
Abstract\nThis will be an overview talk\, starting with the classical\nlow
er algebraic K-groups of a ring. I will report on various\napplications of
the constructions in algebra\, topology and geometry (eg\,\nfiniteness ob
structions\, classification of h-cobordisms with Whitehead\ntorsion\, find
ing obstructions to extending vector bundles). Time\npermitting I will ske
tch some general splitting results relating to\nprojective spaces and Laur
ent polynomial extensions\, respectively.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brendan Guilfoyle (Munster Technological University)
DTSTART;VALUE=DATE-TIME:20211005T130000Z
DTEND;VALUE=DATE-TIME:20211005T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/18
DESCRIPTION:Title: The Toponogov conjecture on complete surfaces\nby Brendan Gu
ilfoyle (Munster Technological University) as part of Irish Geometry Semin
ar\n\n\nAbstract\nA conjecture of Toponogov states that a complete convex
plane P embedded in Euclidean 3-space must have $\\inf |\\kappa_1 - \\kapp
a_2|=0$. Thus\, there must be an umbilic point on P\, albeit at infinity.
\n\nIn this talk I will sketch the proof of this conjecture for smooth sur
faces (in collaboration with Wilhelm Klingenberg). The first step of the p
roof involves studying an associated Riemann-Hilbert boundary value proble
m and showing that it is Fredholm regular for any counterexample to the co
njecture. Then mean curvature flow with boundary supplies enough solutions
to show that the problem cannot be Fredholm regular\, thus establishing t
he non-existence of a counterexample.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART;VALUE=DATE-TIME:20210921T130000Z
DTEND;VALUE=DATE-TIME:20210921T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/19
DESCRIPTION:Title: Regular matroids and Riemannian manifolds\nby Lee Kennard (S
yracuse University) as part of Irish Geometry Seminar\n\n\nAbstract\nIn jo
int work with Michael Wiemeler and Burkhard Wilking at the University of M
uenster\, we are investigating torus representations having the special pr
operty that all isotropy groups are connected. I will discuss the connecti
on to matroid theory\, how this connection helps us prove structural resul
ts for torus representations\, and some applications in the Grove Symmetry
Program.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramiro Lafuente (University of Queensland)
DTSTART;VALUE=DATE-TIME:20211026T130000Z
DTEND;VALUE=DATE-TIME:20211026T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/20
DESCRIPTION:Title: Non-compact Einstein manifolds with symmetry\nby Ramiro Lafu
ente (University of Queensland) as part of Irish Geometry Seminar\n\n\nAbs
tract\nIn this talk we will discuss recent joint work in collaboration wit
h Christoph Böhm in which we obtain structure results for non-compact Ein
stein manifolds admitting a cocompact isometric action of a connected Lie
group. As an application\, we prove the Alekseevskii conjecture (1975): an
y connected homogeneous Einstein space of negative scalar curvature is dif
feomorphic to a Euclidean space.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aaron Tyrell (University of Texas\, Dallas)
DTSTART;VALUE=DATE-TIME:20211123T140000Z
DTEND;VALUE=DATE-TIME:20211123T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/21
DESCRIPTION:Title: Renormalized Area for 4-dimensional Minimal Hypersurfaces of a P
oincaré-Einstein Space\nby Aaron Tyrell (University of Texas\, Dallas
) as part of Irish Geometry Seminar\n\n\nAbstract\nIn 1999 Graham and Witt
en showed that one can define a notion of renormalized area for properly e
mbedded minimal submanifolds of Poincaré-Einstein spaces. For even-dimens
ional submanifolds\, this quantity is an invariant of the ambient metric a
nd the submanifold. In 2008 Alexakis and Mazzeo wrote a paper on this quan
tity for surfaces in a 3-dimensional PE manifold\, getting an explicit for
mula and studying its functional properties. We will look at a formula fo
r the renormalized area of a minimal hypersurface of a 5-dimensional Poinc
aré-Einstein space.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nadine Große (Universität Freiburg)
DTSTART;VALUE=DATE-TIME:20211207T140000Z
DTEND;VALUE=DATE-TIME:20211207T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/22
DESCRIPTION:Title: On the space of metrics with invertible Dirac operator\nby N
adine Große (Universität Freiburg) as part of Irish Geometry Seminar\n\n
\nAbstract\nAmmann\, Dahl and Humbert showed that the property that a mani
fold admits a metric with invertible Dirac operator persists under the rig
ht surgeries. That is the Dirac-counterpart of the Gromov-Lawson construct
ion on the question of existence of postive scalar curvature\nmetrics and
has also implications on this question. We consider now the question wheth
er we can also obtain a homotopy equivalence statement for spaces of metri
cs with invertible Dirac operator under surgery in the spirit of the posit
ive scalar curvature result by Chernysh/Walsh. This is joint work with N.
Pederzani.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina Arroyo (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20211109T140000Z
DTEND;VALUE=DATE-TIME:20211109T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/24
DESCRIPTION:Title: The prescribed Ricci curvature problem for naturally reductive m
etrics on simple Lie groups\nby Romina Arroyo (Universidad Nacional de
Córdoba) as part of Irish Geometry Seminar\n\n\nAbstract\nA classical pr
oblem in geometric analysis is to find a Riemannian metric whose Ricci cur
vature is prescribed\, that is\, a Riemannian metric $g$ and a real number
$c>0$ satisfying\n\\[\n\\operatorname{Ric} (g) = c T\,\n\\]\nfor some fix
ed symmetric $(0\, 2)$-tensor field $T$ on a manifold $M\,$ where $\\opera
torname{Ric} (g)$ denotes the Ricci curvature of $g.$\n\nThe aim of this t
alk is to discuss this problem within the class of naturally reductive met
rics 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 (The Unive
rsity of Queensland)\, Artem Pulemotov (The University of Queensland) and
Wolfgang Ziller (University of Pennsylvania).\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Radeschi (University of Notre Dame)
DTSTART;VALUE=DATE-TIME:20211012T130000Z
DTEND;VALUE=DATE-TIME:20211012T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/25
DESCRIPTION:Title: Invariant theory without groups\nby Marco Radeschi (Universi
ty of Notre Dame) as part of Irish Geometry Seminar\n\n\nAbstract\nGiven a
n orthogonal representation of a Lie group G on a Euclidean vector space V
\, Invariant Theory studies the representation via the algebra of G-invari
ant polynomials on V. This setting can be generalized by replacing the rep
resentation G with a foliation F on V\, with equidistant leaves. In this c
ase\, one can study the algebra of polynomials that are constant along the
se leaves - effectively producing an Invariant Theory\, but without groups
involved. In this talk we will discuss a surprising relation between the
geometry of the foliation and the corresponding algebra\, including recent
joint work in progress with Ricardo Mendes and Samuel Lin\, showing how t
o estimate volume and diameter of the quotient V/F using the algebra.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Lauret (Universidad Nacional del Sur)
DTSTART;VALUE=DATE-TIME:20211102T140000Z
DTEND;VALUE=DATE-TIME:20211102T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/26
DESCRIPTION:Title: On the smallest positive Laplace eigenvalue of a homogeneous CRO
SS\nby Emilio Lauret (Universidad Nacional del Sur) as part of Irish G
eometry Seminar\n\n\nAbstract\nWe will show an explicit expression for the
lowest positive eigenvalue of the Laplace-Beltrami operator associated to
any homogeneous metric on the underlying manifold of a CROSS (a compact r
ank one symmetric space.\n\nAs a first consequence\, we will show that the
Laplace spectrum distinguishes any metric among the space of homogeneous
metrics on CROSSes. Furthermore\, we will study the local rigidity of hom
ogeneous metrics on CROSSes as solutions of the Yamabe problem. If time p
ermits\, we will localize in an explicit way the set of resonant radii of
geodesic spheres on CROSSes endowed with certain homogeneous metrics.\n\nT
his is joint work with Renato Bettiol and Paolo Piccione.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthias Wink (WWU Münster)
DTSTART;VALUE=DATE-TIME:20220201T140000Z
DTEND;VALUE=DATE-TIME:20220201T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/27
DESCRIPTION:Title: Generalizations of Tachibana's theorem\nby Matthias Wink (WW
U Münster) as part of Irish Geometry Seminar\n\n\nAbstract\nA famous theo
rem of Tachibana says that compact Einstein manifolds with positive curvat
ure operators have constant curvature. In this talk we will discuss severa
l generalizations of this theorem. For example\, we show that it suffices
to assume that the curvature operator\nis $\\lfloor \\frac{n-1}{2} \\rfloo
r$-positive\, where $n$ is the dimension of the manifold. Time permitting\
, we discuss analogues of Tachibana's theorem for Kähler manifolds and qu
aternion Kähler manifolds. This talk is based on joint work with Peter P
etersen.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David González Álvaro (Universidad Politécnica de Madrid)
DTSTART;VALUE=DATE-TIME:20220208T140000Z
DTEND;VALUE=DATE-TIME:20220208T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/28
DESCRIPTION:Title: Manifolds of $Ric_k > 0$\nby David González Álvaro (Univer
sidad Politécnica de Madrid) as part of Irish Geometry Seminar\n\n\nAbstr
act\nThe curvature conditions $Ric_k>0$ on n-dimensional manifolds interpo
late between positive sectional curvature (when k=1) and positive Ricci cu
rvature (when k = n-1). In this talk we will review their definitions and
context\, and explain how to construct manifolds of $Ric_k>0$ with k as sm
all as possible\, based on joint work with Miguel Domínguez-Vázquez and
Lawrence Mouillé. Afterwards we will discuss some related open questions.
\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Poljsak (WWU Münster)
DTSTART;VALUE=DATE-TIME:20220405T130000Z
DTEND;VALUE=DATE-TIME:20220405T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/29
DESCRIPTION:Title: Towards Finding the Second Best Einstein Metric in Low Dimension
s\nby Kevin Poljsak (WWU Münster) as part of Irish Geometry Seminar\n
\n\nAbstract\nA metric $g$ on a simply connected manifold $M$ is called th
e second best Einstein metric\, if $(M\,g)$ is an Einstein manifold with p
ositive scalar curvature which is non isometric to the sphere and its curv
ature operator $R$ minimizes the angle $\\sphericalangle(R(p)\, Id)$ to th
e identity at each point $p \\in M$ among all Einstein manifolds with 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 manifolds in
order to present an approach finding the second best Einstein metric in d
imensions $\\leq 11$.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikos Georgiou (Waterford IT)
DTSTART;VALUE=DATE-TIME:20220412T130000Z
DTEND;VALUE=DATE-TIME:20220412T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/30
DESCRIPTION:Title: Almost Paracomplex Structure on 4-manifolds\nby Nikos Georgi
ou (Waterford IT) as part of Irish Geometry Seminar\n\n\nAbstract\nIn join
t work with Brendan Guilfoyle at the Munster Technological University\, we
are investigating the existence or otherwise of parallel\, isometric\, an
d anti-isometric almost paracomplex structures on a pseudo-Riemannian 4-ma
nifold. These structures provide a connection between Einstein metrics and
metrics that are locally conformally flat and scalar flat. In this talk
I will discuss the recent development of these structures as well as some
applications in certain 4-manifolds.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Magee (Durham University)
DTSTART;VALUE=DATE-TIME:20220301T140000Z
DTEND;VALUE=DATE-TIME:20220301T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
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\nAbstract
\nA hyperbolic surface is a surface with metric of constant curvature -1.
The spectral gap between the first two eigenvalues of the Laplacian on a c
losed hyperbolic surface contains a good deal of information about the sur
face\, including its connectivity\, dynamical properties of its geodesic f
low\, and error terms in geodesic counting problems. For arithmetic hyperb
olic surfaces the spectral gap is also the subject of one of the biggest o
pen problems in automorphic forms: Selberg’s eigenvalue conjecture.\n\nI
t was an open problem from the 1970s whether there exist a sequence of clo
sed hyperbolic surfaces with genera tending to infinity and spectral gap t
ending to 1/4. (The value 1/4 here is the asymptotically optimal one.) Rec
ently we proved that this is indeed possible. I’ll discuss the very inte
resting background of this problem in detail as well as some ideas of the
proof. This is joint work with Will Hide.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emily Dryden (Bucknell University)
DTSTART;VALUE=DATE-TIME:20220315T140000Z
DTEND;VALUE=DATE-TIME:20220315T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/32
DESCRIPTION:Title: Applications of symmetry to certain eigenvalue bounds on surface
s\nby Emily Dryden (Bucknell University) as part of Irish Geometry Sem
inar\n\n\nAbstract\nWe study a class of eigenvalue problems for surfaces.
The question of finding meaningful upper bounds for these eigenvalues has
a long history going back to Weinstock\, who studied an isoperimetric ine
quality for a certain lowest eigenvalue of a simply-connected planar domai
n. We will explore some recent contributions to the story\, with an emphas
is on results that can be seen in pictures.\n\nJoint work with: Teresa Ari
as-Marco (Universidad de Extremadura\, Spain)\,\nCarolyn S. Gordon (Dartmo
uth College\, USA)\,\nAsma Hassannezhad (University of Bristol\, UK)\,\nAl
lie Ray (Birmingham-Southern College\, USA)\,\nElizabeth Stanhope (Lewis &
Clark College\, USA).\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Reiser (Karlsruher Institut für Technologie)
DTSTART;VALUE=DATE-TIME:20220215T140000Z
DTEND;VALUE=DATE-TIME:20220215T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/33
DESCRIPTION:Title: Generalized Surgery on Riemannian Manifolds of Positive Ricci Cu
rvature and Applications in Dimension 6\nby Philipp Reiser (Karlsruher
Institut für Technologie) as part of Irish Geometry Seminar\n\n\nAbstrac
t\nIn this talk I will review the known techniques to construct metrics of
positive Ricci curvature via surgery. These techniques go back to Sha-Yan
g and Wraith for higher surgeries and to Perelman and Burdick for connecte
d sums. I will then present a generalization of the surgery theorem of Wra
ith\, in which the surgery construction itself gets generalized. Finally\,
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 metr
ic of positive Ricci curvature. These examples are constructed as boundari
es of manifolds obtained by plumbings according to a simply-connected grap
h.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Mondino (University of Oxford)
DTSTART;VALUE=DATE-TIME:20220322T140000Z
DTEND;VALUE=DATE-TIME:20220322T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/34
DESCRIPTION:Title: Optimal Transport\, weak Laplacian bounds and minimal boundaries
in non-smooth spaces with Lower Ricci Curvature bounds\nby Andrea Mon
dino (University of Oxford) as part of Irish Geometry Seminar\n\n\nAbstrac
t\nThe goal of the seminar is to report on recent joint work with Daniele
Semola\, motivated by a question of Gromov to establish a “synthetic reg
ularity theory" for minimal surfaces in non-smooth ambient spaces. In the
setting of non-smooth spaces with lower Ricci Curvature bounds:\n\n- We es
tablish a new principle relating lower Ricci Curvature bounds to the prese
rvation of Laplacian bounds under the evolution via the Hopf-Lax semigroup
\;\n\n- We develop an intrinsic viscosity theory of Laplacian bounds and p
rove equivalence with other weak notions of Laplacian bounds\;\n\n- We pro
ve sharp Laplacian bounds on the distance function from a set (locally) mi
nimizing the perimeter: this corresponds to vanishing mean curvature in th
e smooth setting\;\n\n- We study the regularity of boundaries of sets (loc
ally) minimizing the perimeter\, obtaining sharp bounds on the Hausdorff c
o-dimension of the singular set plus content estimates and topological reg
ularity of the regular set.\nOptimal transport plays the role of underlyin
g technical tool for addressing various points.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asma Hassannezhad (University of Bristol)
DTSTART;VALUE=DATE-TIME:20220329T130000Z
DTEND;VALUE=DATE-TIME:20220329T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/35
DESCRIPTION:Title: Nodal counts for the Dirichlet-to Neumann operators with potenti
al\nby Asma Hassannezhad (University of Bristol) as part of Irish Geom
etry Seminar\n\n\nAbstract\nThe zero set of an eigenfunction is called the
nodal set and the connected components of its complement are called the N
odal domains. The well-known Courant nodal domain theorem gives an upper b
ound for the nodal count of Laplace eigenfunctions on a compact manifold.
We consider the harmonic extension of eigenfunctions of the Dirichlet-to-
Neumann operators with potential. When the potential is zero\, these harmo
nic extensions are called the Steklov eigenfunctions. It has been known th
at the Courant nodal domain theorem holds for Steklov eigenfunctions. We d
iscuss how we can get a Courant-type bound for the nodal count of the Diri
chlet-to-Neumann operator in the presence of a potential.\n\nThis is joint
work with David Sher.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Hanke (Universität Augsburg)
DTSTART;VALUE=DATE-TIME:20220222T140000Z
DTEND;VALUE=DATE-TIME:20220222T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/36
DESCRIPTION:Title: Boundary conditions for scalar curvature\nby Bernhard Hanke
(Universität Augsburg) as part of Irish Geometry Seminar\n\n\nAbstract\nW
e show a general deformation principle for boundary conditions of metrics
with lower scalar curvature bounds. This implies that the relaxation of b
oundary conditions often induces weak homotopy equivalences of spaces of s
uch metrics.\n\nCombining this with the existence of fibre bundles over sp
heres whose total spaces have non-zero $\\hat{A}$-genera we construct comp
act manifolds for which the spaces of positive scalar curvature metrics wi
th mean convex boundaries have nontrivial higher homotopy groups. \n\nThis
is joint work with Christian Bär.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Bechtluft-Sachs (Maynooth University)
DTSTART;VALUE=DATE-TIME:20220308T140000Z
DTEND;VALUE=DATE-TIME:20220308T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/37
DESCRIPTION:Title: Linking integrals in negatively curved symmetric spaces\nby
Stefan Bechtluft-Sachs (Maynooth University) as part of Irish Geometry Sem
inar\n\n\nAbstract\nGauss' integral formula for the linking number of loop
s in Euclidean space readily generalizes to submanifolds of an oriented Ri
emannian manifold with sufficiently vanishing homology. To this end one ne
eds an inverse to the Cartan differential. In particular\, any right inver
se of the differential form Laplacian or Dirac operator yields such a link
ing kernel.\nWe will show how all this can be made almost explicit on nega
tively curved symmetric spaces (non compact rank one symmetric space) in t
erms of a solution of an ordinary differential equation.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lee Kennard (Syracuse University)
DTSTART;VALUE=DATE-TIME:20220518T144500Z
DTEND;VALUE=DATE-TIME:20220518T153000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/38
DESCRIPTION:Title: Graph systoles and torus representations\nby Lee Kennard (Sy
racuse University) as part of Irish Geometry Seminar\n\n\nAbstract\nA clas
sical graph invariant is the girth\, which is the length of the shortest c
ycle. In the presence of weights or distances assigned to the edges\, one
can similarly define the weighted girth or systole of a graph. Bollobás a
nd Szemerédi have proved asymptotic bounds on this quantity as the graph
Betti number goes to infinity. I will discuss new bounds for the case of s
mall Betti number proved recently in joint work with Michael Wiemeler and
Burkhard Wilking. This has implications for structure of torus representat
ions with connected isotropy groups and applications to the problem of cla
ssifying Riemannian manifolds with positive curvature and large isometry g
roups.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krishnan Shankar (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20220518T154500Z
DTEND;VALUE=DATE-TIME:20220518T163000Z
DTSTAMP;VALUE=DATE-TIME:20220528T191317Z
UID:IrishGeomSeminar/39
DESCRIPTION:Title: Growth competitions in non-positive curvature\nby Krishnan S
hankar (University of Oklahoma) as part of Irish Geometry Seminar\n\n\nAbs
tract\nThe notion of a growth competition between two deterministically gr
owing clusters in a complete\, non-compact metric space (or graph) was fir
st proposed by I. Benjamini and recently explored in the case of 2-dimensi
onal Euclidean and hyperbolic spaces by his student\, R. Assouline. A grow
th competition in a non-compact\, complete Riemannian manifold\, $X$\, (or
more generally a complete\, non-compact geodesic metric space) is the exi
stence of two sets\, $A_t$ (fast) and $B_t$ (slow)\, $t\\geq 0$\, that gro
w 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 curve 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\niii $\\{
B_t \\}_{t \\geq 0}$ is a parametrized family of subsets defined as\, $B_
t := \\cup_\\beta \\beta([0\,t])$\, where $\\beta(s)$ is a $1$-Lipschitz c
urve in $X$ and $\\beta (s) \\not\\in A_s$ for all $s \\in [0\,t]$. The co
llection of sets $B_t$ are the slow sets.\n\niv The limiting sets are deno
ted 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 distinc
t points $p$\, $q$ in a path connected\, complete\, geodesic metric space
$X$ and a real number $\\lambda > 1$\, there exists a unique growth compet
ition satisfying the above conditions. A basic geometric question one may
ask in this setting is: under what circumstances is the slow set\, $B_\\in
fty$\, totally bounded (surrounded) by the fast set\, $A_\\infty$\, versus
when are they both unbounded (co-existence)? The applications of this geo
metric 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 been explo
ring the above question in the setting of non-positive curvature. In this
talk we introduce growth competitions and give a preview of some results a
nd open problems.\n
LOCATION:https://researchseminars.org/talk/IrishGeomSeminar/39/
END:VEVENT
END:VCALENDAR