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BEGIN:VEVENT
SUMMARY:Henrique Sa Earp (Unicamp)
DTSTART;VALUE=DATE-TIME:20200424T170000Z
DTEND;VALUE=DATE-TIME:20200424T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/1
DESCRIPTION:Title: Harmonic flow of geometric structures\nby Henrique Sa Earp
(Unicamp) as part of Geometry Webinar AmSur /AmSul\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adrian Andrada (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20200522T170000Z
DTEND;VALUE=DATE-TIME:20200522T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/2
DESCRIPTION:Title: Abelian almost contact structures and connections with skew-sym
metric torsion\nby Adrian Andrada (Universidad Nacional de Córdoba) a
s part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nAbelian complex str
uctures on Lie groups have proved to be very useful in several areas of di
fferential and complex geometry. In particular\, an abelian hypercomplex s
tructure on a Lie group G (that is\, a pair of anticommuting abelian compl
ex structures)\, together with a compatible inner product\, gives rise to
an invariant hyperKähler with torsion (HKT) structure on G. This means th
at G admits a (unique) metric connection with skew-symmetric torsion (call
ed the Bismut connection) which parallelizes the hypercomplex structure. \
nIn this talk we move to the odd-dimensional case and we introduce the not
ion of abelian almost contact structures on Lie groups. We study their pro
perties and their relations with compatible metrics. Next we consider almo
st 3-contact Lie groups where each almost contact structure is abelian. We
study their main properties and we give their classification in dimension
7. After adding compatible Riemannian metrics\, we study the existence of
a certain type of metric connections with skew symmetric torsion\, introd
uced recently by Agricola and Dileo and called canonical connections. We p
rovide examples of such groups in each dimension 4n+3 and show that they a
dmit co-compact discrete subgroups\, which give rise to compact almost 3-c
ontact metric manifolds equipped with canonical connections.\n\nTo partici
pate in the webinar\, please request the link to geodif@unicamp.br with su
bject "Webinar AmSur".\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Ambrozio (University of Warwick)
DTSTART;VALUE=DATE-TIME:20200528T170000Z
DTEND;VALUE=DATE-TIME:20200528T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/3
DESCRIPTION:Title: Systolic inequalities for minimal projective planes in Riemanni
an projective spaces\nby Lucas Ambrozio (University of Warwick) as par
t of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nThe word "systole" is co
mmonly used in Geometry to denote the infimum of the length of homotopica
lly non-trivial loops in a compact Riemmanian manifold M. In a generalised
sense\, we may use it also to refer to the infimum of the k-dimensional v
olume of a class of k-dimensional submanifolds that represent some non-tri
vial topology of M. In this talk\, we will discuss some inequalities compa
ring the systole to other geometric invariants\, e.g. the total volume of
M. After reviewing in details the celebrated inequality of Pu regarding th
e systole of Riemannian projective planes\, we will discuss its generalisa
tions to higher dimensions. This is joint work with Rafael Montezuma.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Alexander Cruz Morales (Universidad Nacional de Colombia)
DTSTART;VALUE=DATE-TIME:20200605T170000Z
DTEND;VALUE=DATE-TIME:20200605T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/4
DESCRIPTION:Title: On integrality for Frobenius manifolds\nby John Alexander C
ruz Morales (Universidad Nacional de Colombia) as part of Geometry Webinar
AmSur /AmSul\n\n\nAbstract\nWe will revisit the computations of Stokes ma
trices for tt*-structures done by Cecotti and Vafa in the 90's in the cont
ext of Frobenius manifolds and the so-called monodromy identity. We will
argue that those cases provide examples of non-commutative Hodge structure
s of exponential type in the sense of Katzarkov\, Kontsevich and Pantev.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mircea Petrache (Pontificia Universidad Católica de Chile)
DTSTART;VALUE=DATE-TIME:20200611T170000Z
DTEND;VALUE=DATE-TIME:20200611T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/5
DESCRIPTION:Title: Uniform measures of dimension 1\nby Mircea Petrache (Pontif
icia Universidad Católica de Chile) as part of Geometry Webinar AmSur /Am
Sul\n\n\nAbstract\nIn his fundamental 1987 paper on the geometry of measur
es\, Preiss posed the problem of classifying uniform measures in d-dimensi
onal Euclidean space\, a question at the interface of measure theory and d
ifferential geometry.\n\n A uniform measure is a positive measure such th
at for all $r>0$\, all balls of radius $r$ with center in the support of t
he measure\, are given equal masses.\n It was proved by Kirchheim-Preiss t
hat a uniform measure in $\\mathbb{R}^d$ is a multiple of the k-dimensiona
l Hausdorff measure restricted to a k-dimensional analytic variety. This e
stablishes the link to differential geometry. An important class of unifor
m measures are G-invariant measures\, for G any subgroup of isometries of
Euclidean space. These are called homogeneous measures. Intriguing example
s of non-homogeneous uniform measures do exist (the surface area of the 3D
cone $x^2=y^2+w^2+z^2$ in $\\mathbb{R}^4$ is one)\, but they are not well
understood\, making Preiss' classification question is still widely open.
\n\n After a historical survey\, I will describe a recent joint paper with
Paul Laurain\, about uniform measures of dimension 1 in d-dimensional Euc
lidean space: we prove by a direct approach that these are all given by at
most countable unions of congruent helices or of congruent toric knots. I
n particular\, 1-dimensional uniform measures with connected support are h
omogeneous.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviana del Barco (Université Paris-Sud)
DTSTART;VALUE=DATE-TIME:20200619T170000Z
DTEND;VALUE=DATE-TIME:20200619T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/6
DESCRIPTION:Title: (Purely) coclosed G$_2$-structures on 2-step nilmanifolds\n
by Viviana del Barco (Université Paris-Sud) as part of Geometry Webinar A
mSur /AmSul\n\n\nAbstract\nIn Riemannian geometry\, simply connected nilpo
tent Lie groups endowed with left-invariant metrics\, and their compact qu
otients\, have been the source of valuable examples in the field. This m
otivated several authors to study\, in particular\, left-invariant G$_2$-
structures on 7-dimensional nilpotent Lie groups. These structures could a
lso be induced to the associated compact quotients\, also known as {\\em n
ilmanifolds}.\n\nLeft-invariant torsion free G$_2$-structures\, that is\,
defined by a simultaneously closed and coclosed positive $3$-form\, do not
exist on nilpotent Lie groups. But relaxations of this condition have bee
n the subject of study on nilmanifolds lately. One of them are coclosed G$
_2$-structures\, for which the defining $3$-form verifies $d \\star_{\\var
phi}\\varphi=0$\, and more specifically\, purely coclosed structures\, wh
ich are defined as those which are coclosed and satisfy $\\varphi\\wedge d
\\varphi=0$. \n\nIn this talk\, there will be presented recent classifica
tion results regarding left-invariant coclosed and purely coclosed G$_2$-
structures on 2-step nilpotent Lie groups. Our techniques exploit the corr
espondence between left-invariant tensors on the Lie group and their linea
r analogues at the Lie algebra level.\nIn particular\, left-invariant G$_2
$-structures on a Lie group will be seen as alternating trilinear forms de
fined on the Lie algebra. The coclosed condition now refers to the Cheval
ley-Eilenberg differential of the Lie algebra.\nWe also rely on the partic
ular Lie algebraic structure of metric 2-step nilpotent Lie algebras.\n\nO
ur goals are twofold. On the one hand we give the isomorphism classes of 2
-step nilpotent Lie algebras admitting purely coclosed G$_2$-structures. T
he analogous result for coclosed structures was obtained by Bagaglini\, Fe
rn\\'andez and Fino [Forum Math. 2018]. \n\nOn the other hand\, we focus o
n the question of {\\em which metrics} on these Lie algebras can be induce
d by a coclosed or purely coclosed structure. We show that any left-invar
iant metric is induced by a coclosed structure\, whereas every Lie algebra
admitting purely coclosed structures admits metrics which are not induced
by any such a structure. In the way of proving these results we obtain a
method to construct purely coclosed G$_2$-structures. As a consequence\, w
e obtain new examples of compact nilmanifolds carrying purely coclosed G$
_2$-structures.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Petrucio Cavalcante (Universidade Federal de Alagoas)
DTSTART;VALUE=DATE-TIME:20200625T170000Z
DTEND;VALUE=DATE-TIME:20200625T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/7
DESCRIPTION:Title: Gap theorems for free-boundary submanifolds\nby Marcos Petr
ucio Cavalcante (Universidade Federal de Alagoas) as part of Geometry Webi
nar AmSur /AmSul\n\n\nAbstract\nLet $M^n$ be a compact $n$-dimensional man
ifold minimally immersed in a unit sphere $S^{n+k}$ and let denote by $|A|
^2$ the squared norm of its second fundamental form. It follows from the f
amous Simons pinching theorem that if $|A|^2\\leq \\frac{n}{2-\\frac{1}{k}
}$\, then either $|A|^2=0$ or $|A|^2=\\frac{n}{2-\\frac{1}{k}}$. The subma
nifolds on which $|A|^2=\\frac{n}{2-\\frac{1}{k}}$ were characterized by L
awson (when $k=1$) and by Chern-do Carmo-Kobayashi (for any $k$). \n\nThes
e important results say that there exists a gap in the space of minimal su
bmanifolds in $S^{n+k}$ in terms of the length of their second fundamental
forms and their dimensions. \n\nLatter\, Lawson and Simons proved a topol
ogical gap result without making any assumption on the mean curvature of t
he submanifold. Namely\, they proved that if $M^n$ is a compact submanifol
d in $S^{n+k}$ such that $|A|^2\\leq \\min\\{p(n-p)\, 2\\sqrt{p(n-p)}\\}$\
, then for any finitely generated Abelian group $G$\, $H_p(M\;G)=0$. In pa
rticular\, if $|A|^2< \\min\\{n-1\, 2\\sqrt{n-1}\\}$\, then $M$ is a homot
opy sphere. \n\nIt is well known that free-boundary minimal submanifolds i
n the unit ball share similar properties as compact minimal submanifolds i
n the round sphere. For instance\, Ambrozio and Nunes obtained a geometric
gap type theorem for free-boundary minimal surfaces $M$ in the Euclidean
unit $3$-ball $B^3$. They proved that if $|A|^2(x)\\langle x\, N(x)\\rangl
e^2\\leq 2$\, where $N(x)$ is the unit normal vector at $x\\in M$\, then
$M$ is either the equatorial disk or the critical catenoid. \n\nIn the fir
st part of this talk\, I will present a generalization of Ambrozio and Nun
es theorem for constant mean curvature surfaces. Precisely\, if the tracel
ess second fundamental form $\\phi$ of a free-boundary CMC surface $B^3$ s
atisfies $|\\phi|^2(x)\\langle x\, N(x)\\rangle^2\\leq (2+H\\langle x\, N
(x)\\rangle )^2/2$ then $M$ is either a spherical cap or a portion of a De
launay surface. This is joint work with Barbosa and Pereira.\n\nIn the sec
ond part\, I will present a topological gap theorem for free-boundary subm
anifolds in the unit ball. More precisely\, if $|\\phi|^2\\leq \\frac{np}{
n-p}$\, then the $p$-th cohomology group of $M$ with real coefficients van
ishes. In particular\, if $|\\phi|^2\\leq \\frac{n}{n-1}$\, then $M$ has o
nly one boundary component. This is joint work with Mendes and Vitório.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Umberto Hryniewicz (RWTH Aachen University)
DTSTART;VALUE=DATE-TIME:20200703T170000Z
DTEND;VALUE=DATE-TIME:20200703T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/9
DESCRIPTION:Title: Pseudo-holomorphic curves and applications to geodesic flows\nby Umberto Hryniewicz (RWTH Aachen University) as part of Geometry Web
inar AmSur /AmSul\n\n\nAbstract\nThis talk is intended to survey applicati
ons of pseudo-holomorphic curves to Reeb ows in dimension three\, with an
eye towards geometry. For the geometer the interest stems from the fact th
at geodesic \nflows are particular examples of Reeb flows. I will discuss
characterizations of lens spaces\, existence/non-existence of closed geode
sics with a given knot type under pinching conditions on the curvature\, s
harp systolic inequalities\, existence of elliptic dynamics (in relation t
o an old conjecture of Poincaré)\, and generalizations of Birkhoff's annu
lar global surface of section for positively curved 2-spheres.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Lauret (Universidad Nacional del Sur)
DTSTART;VALUE=DATE-TIME:20200709T170000Z
DTEND;VALUE=DATE-TIME:20200709T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/10
DESCRIPTION:Title: Diameter and Laplace eigenvalue estimates for homogeneous Riem
annian manifolds\nby Emilio Lauret (Universidad Nacional del Sur) as p
art of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nGiven $G$ a compact Li
e group and $K$ a closed subgroup of it\, we will study whether the functi
onal $\\lambda_1(G/K\,g) \\textrm{diam}(G/K\,g)^2$ is bounded by above amo
ng $G$-invariant metrics $g$ on the (compact) homogeneous space $G/K$. Her
e\, $\\textrm{diam}(G/K\,g)$ and $\\lambda_1(G/K\,g)$ denote the diameter
and the smallest positive eigenvalue of the Laplace-Beltrami operator asso
ciated to $(G/K\,g)$.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregorio Pacelli (Universidade Federal do Ceará)
DTSTART;VALUE=DATE-TIME:20200717T170000Z
DTEND;VALUE=DATE-TIME:20200717T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/11
DESCRIPTION:Title: A stochastic half-space theorem for minimal surfaces of $\\mat
hbb{R}^{3}$.\nby Gregorio Pacelli (Universidade Federal do Ceará) as
part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nI will talk about a s
tochastic half-space theorem for minimal surfaces of $\\mathbb{R}^{3}$ .
More precisely\; Thm. $\\Sigma$ be a complete minimal surface with bounded
curvature in $\\mathbb{R}^{3}$ and $M$ be a complete\, parabolic (recurr
ent) minimal surface immersed in $\\mathbb{R}^{3}$. Then $\\Sigma \\cap M
\\neq \\emptyset$ unless they are parallel planes. \nThis is a work in pro
gress with Luquesio Jorge and Leandro Pessoa.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina Arroyo (Universidad Nacional Cordoba)
DTSTART;VALUE=DATE-TIME:20200723T170000Z
DTEND;VALUE=DATE-TIME:20200723T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/12
DESCRIPTION:Title: The prescribed Ricci curvature problem for naturally reductive
metrics on simple Lie groups\nby Romina Arroyo (Universidad Nacional
Cordoba) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nOne of th
e most important challenges of Riemannian geometry is to understand the Ri
cci curvature tensor. An interesting open problem related with it is to fi
nd a Riemannian metric whose Ricci curvature is prescribed\, that is\, a R
iemannian metric $g$ and a real number $c>0$ satisfying\n\\[\n\\operatorna
me{Ric} (g) = c T\,\n\\]\nfor some 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 withi
n the class of naturally reductive metrics when $M$ is a simple Lie group\
, and present recently obtained results in this setting. \n\nThis talk is
based on joint works with Mark Gould (The University of Queensland) Artem
Pulemotov (The University of Queensland) and Wolfgang Ziller (University o
f Pennsylvania).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Perales (Unam)
DTSTART;VALUE=DATE-TIME:20200731T170000Z
DTEND;VALUE=DATE-TIME:20200731T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/13
DESCRIPTION:Title: Convergence of manifolds under volume convergence and uniform
diameter and tensor bounds\nby Raquel Perales (Unam) as part of Geomet
ry Webinar AmSur /AmSul\n\n\nAbstract\nBased on join work with Allen-Sorma
ni and Cabrera Pacheco-Ketterer. Given a Riemannian manifold $M$ and a pai
r of Riemannian tensors $g_0 \\leq g_j$ on $M$ it follows that $vol(M)\\l
eq vol_j(M)$. Furthermore\, the volumes are equal if and only if $g_0=g_j
$.\n\nIn this talk I will show that for a sequence of Riemannian metrics $
g_j$ defined on $M$ that satisfy \n$g_0\\leq g_j$\, $diam (M_j) \\leq D$ a
nd $vol(M_j)\\to vol(M_0)$ then $(M\,g_j)$ converge to $(M\,g_0)$ in the v
olume preserving intrinsic flat sense. I will present examples demonstrat
ing that under these conditions we do not necessarily obtain smooth\, $C^0
$ or Gromov-Hausdorff convergence.\n\nFurthermore\, this result can be app
lied to show the stability of graphical tori.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolau S. Aiex (Auckland)
DTSTART;VALUE=DATE-TIME:20200806T170000Z
DTEND;VALUE=DATE-TIME:20200806T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/14
DESCRIPTION:Title: Compactness of free boundary CMC surfaces\nby Nicolau S. A
iex (Auckland) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nWe
will talk about the compactness of the space of CMC surfaces on ambient ma
nifolds with positive Ricci curvature and convex boundary. We characterize
compactness based on geometric information on the surface. This is ana
logous to a result of Fraser-Li on free boundary minimal surfaces\, howeve
r\, the lack of a Steklov eigenvalue lower bound makes the proof fairly di
fferent. The proof is an adaptation of White's proof of the compactness of
stationary surfaces of parametric elliptic functionals. This is a joint w
ork with Han Hong.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo R. Longa (USP)
DTSTART;VALUE=DATE-TIME:20200814T170000Z
DTEND;VALUE=DATE-TIME:20200814T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/15
DESCRIPTION:Title: Sharp systolic inequalities for $3$-manifolds with boundary\nby Eduardo R. Longa (USP) as part of Geometry Webinar AmSur /AmSul\n\n\
nAbstract\nSystolic Geometry dates back to the late 1940s\, with the work
of Loewner and his student\, Pu. This branch of differential geometry rec
eived more attention after the seminal work of Gromov\, where he proved h
is famous systolic inequality and introduced many important concepts. In t
his talk I will recall the notion of systole and present some sharp systol
ic inequalities for free boundary surfaces in $3$-manifolds.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Pons (UNAB)
DTSTART;VALUE=DATE-TIME:20200820T170000Z
DTEND;VALUE=DATE-TIME:20200820T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/16
DESCRIPTION:Title: Non Canonical Metrics on Diff($S^1$)\nby Daniel Pons (UNAB
) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nWe review some o
f V.I. Arnold’s ideas on diffeomorphism groups on manifolds. When the un
derlying manifold is the circle\, we study the geometry of such a group en
dowed with some metrics.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lotay (University of Oxford)
DTSTART;VALUE=DATE-TIME:20200903T170000Z
DTEND;VALUE=DATE-TIME:20200903T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/17
DESCRIPTION:Title: Deformed G2-instantons\nby Jason Lotay (University of Oxfo
rd) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nDeformed G2-in
stantons are special connections occurring in G2 geometry in 7 dimensions.
They arise as "mirrors" to certain calibrated cycles\, providing an analo
gue to deformed Hermitian-Yang-Mills connections\, and are critical points
of Chern-Simons-type functional. I will describe an elementary constructi
on of the first non-trivial examples of deformed G2-instantons\, and their
relation to 3-Sasakian geometry\, nearly parallel G2-structures\, isometr
ic G2-structures\, obstructions in deformation theory\, the topology of th
e moduli space\, and the Chern-Simons-type functional.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizabeth Gasparim (Universidad de Norte)
DTSTART;VALUE=DATE-TIME:20200911T170000Z
DTEND;VALUE=DATE-TIME:20200911T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/18
DESCRIPTION:Title: Graft surgeries\nby Elizabeth Gasparim (Universidad de Nor
te) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nI will explain
the new concepts of graft surgeries which allow us to modify surfaces\,
Calabi-Yau threefolds and vector bundles over them\, producing a variet
y of ways to describe local characteristic classes. In particular\, we ge
neralize the construction of conifold transition presented by Smith-Thomas
-Yau.This is joint work with Bruno Suzuki\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lino Grama (Universidade Estadual de Campinas)
DTSTART;VALUE=DATE-TIME:20200917T170000Z
DTEND;VALUE=DATE-TIME:20200917T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/19
DESCRIPTION:Title: Invariant Einstein metrics on real flag manifolds\nby Lino
Grama (Universidade Estadual de Campinas) as part of Geometry Webinar AmS
ur /AmSul\n\n\nAbstract\nIn this talk we will discuss the classification o
f invariant Einstein metrics on real flag manifolds associated to simple a
nd non-compact split real forms of complex classical Lie algebras whose is
otropy representation decomposes into two or three irreducible sub-represe
ntations. We also discuss some phenomena in real flag manifolds that can n
ot happen in complex flag manifolds. This includes the non-existence of in
variant Einstein metric and examples of non-diagonal Einstein metrics. Thi
s is a joint work with Brian Grajales\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Garcia-Fernandez (Universidad Autónoma de Madrid)
DTSTART;VALUE=DATE-TIME:20200925T170000Z
DTEND;VALUE=DATE-TIME:20200925T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/20
DESCRIPTION:Title: Generalized Ricci flow\nby Mario Garcia-Fernandez (Univers
idad Autónoma de Madrid) as part of Geometry Webinar AmSur /AmSul\n\n\nAb
stract\nThe generalized Ricci flow equation is a geometric evolution\nequa
tion which has recently emerged from investigations into\nmathematical phy
sics\, Hitchin’s generalized geometry program\, and\ncomplex geometry. T
he generalized Ricci flow can regarded as a tool for\nconstructing canonic
al metrics in generalized geometry and complex\nnon-Kähler geometry\, and
extends the fundamental Hamilton/Perelman\ntheory of Ricci flow. In this
talk I will give an introduction to this\ntopic\, with a special emphasis
on examples and geometric aspects of the\ntheory. Based on joint work with
Jeffrey Streets (UC Irvine)\,\narXiv:2008.07004.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariel Saez (Pontificia Universidad Católica de Chile)
DTSTART;VALUE=DATE-TIME:20201001T170000Z
DTEND;VALUE=DATE-TIME:20201001T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/21
DESCRIPTION:Title: Short-time existence for the network flow\nby Mariel Saez
(Pontificia Universidad Católica de Chile) as part of Geometry Webinar Am
Sur /AmSul\n\n\nAbstract\nThe network flow is a system of parabolic differ
ential equations that describes the motion of a family of curves in which
each of them evolves under curve-shortening flow. This problem arises natu
rally in physical phenomena and its solutions present a rich variety of be
haviors. \n\nThe goal of this talk is to describe some properties of this
geometric flow and to discuss an alternative proof of short-time existence
for non-regular initial conditions. The methods of our proof are based on
techniques of geometric microlocal analysis that have been used to unders
tand parabolic problems on spaces with conic singularities. This is joint
work with Jorge Lira\, Rafe Mazzeo\, and Alessandra Pluda.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Struchiner (Universidade de São Paulo)
DTSTART;VALUE=DATE-TIME:20201009T170000Z
DTEND;VALUE=DATE-TIME:20201009T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/22
DESCRIPTION:Title: Singular Riemannian Foliations and Lie Groupoids\nby Ivan
Struchiner (Universidade de São Paulo) as part of Geometry Webinar AmSur
/AmSul\n\n\nAbstract\nI will discuss the problem of obtaining a "Holonomy
Groupoid" for a singular Riemannian foliation (SRF). Throughout the talk I
will try to explain why we want to obtain such a Lie groupoid by stating
results which are valid for regular foliations and how they can be obtaine
d from the Holonomy groupoid of the foliation. Although we do not yet know
how to associate a holonomy groupoid to any SRF\, we can obtain the holon
omy groupoid of the linearization of the SRF in a tubular neighbourhood of
(the closure of) a leaf. I will explain this construction.\n\nI will not
assume that the audience has prior knowledge of Singular Riemannian Foliat
ions or of Lie Groupoids and will try to make the talk accessible to a bro
ad audience.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fadel (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20201015T170000Z
DTEND;VALUE=DATE-TIME:20201015T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/23
DESCRIPTION:Title: The asymptotic geometry of G$_2$-monopoles\nby Daniel Fade
l (Universidade Federal Fluminense) as part of Geometry Webinar AmSur /AmS
ul\n\n\nAbstract\nG$_2$-geometry is a very rich and vast subject in Differ
ential Geometry which has been seeing a \nlot of progress in the last two
decades. There are by now very powerful methods that produce millions of e
xamples of G$_2$ holonomy metrics on the compact setting\n and infinitely
many on the non-compact setting. Besides these fruitful advances\, at pres
ent\, there is no systematic understanding of these metrics. In fact\, a v
ery\n important problem in G$_2$-geometry is to develop methods to disting
uish G$_2$-manifolds. One approach intended at producing invariants of G$_
2$-manifolds is by means\n of higher dimensional gauge theory. G$_2$-monop
oles are solutions to a first order nonlinear PDE for pairs consisting of
a connection on a principal bundle over \na noncompact G$_2$-manifold and
a section of the associated adjoint bundle. They arise as the dimensional
reduction of the higher dimensional Spin$(7)$-instanton\n equation\, and a
re special critical points of an intermediate energy functional related to
the Yang-Mills-Higgs energy.\n\nDonaldson-Segal (2009) suggested that one
possible approach to produce an enumerative invariant of (noncompact) G$_
2$-manifolds is by considering a ``count" of G$_2$-monopoles\n and this sh
ould be related to conjectural invariants ``counting" rigid coassociate (c
odimension 3 and calibrated) cycles. Oliveira (2014) started the study of
G$_2$-monopoles\n providing the first concrete non-trivial examples and gi
ving evidence supporting the Donaldson-Segal program by finding families o
f G$_2$-monopoles parametrized by a\n positive real number\, called the ma
ss\, which in the limit when such parameter goes to infinity concentrate a
long a compact coassociative submanifold. In this talk I \nwill explain so
me recent results\, obtained in collaboration with Ákos Nagy and Gonçalo
Oliveira\, which show that the asymptotic behavior satisfied by the examp
les \nare in fact general phenomena which follows from natural assumptions
such as the finiteness of the intermediate energy. This is a very much ne
eded development in \norder to produce a satisfactory moduli theory and ma
king progress towards a rigorous definition of the putative invariant. Tim
e permitting\, I will mention some \ninteresting open problems and possibl
e future directions in this theory.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (Università di Torino)
DTSTART;VALUE=DATE-TIME:20201023T170000Z
DTEND;VALUE=DATE-TIME:20201023T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/24
DESCRIPTION:Title: Balanced metrics and the Hull-Strominger system\nby Anna F
ino (Università di Torino) as part of Geometry Webinar AmSur /AmSul\n\n\n
Abstract\nA Hermitian metric on a complex manifold is balanced if its fund
amental form is co-closed. An important tool for the study of balanced man
ifolds is the Hull-Strominger system. \nIn the talk I will review so
me general results about balanced metrics and present new smooth solu
tions to the Hull-Strominger system\, showing that the Fu-Yau solution on
torus bundles over K3 surfaces can be generalized to torus bundles over K
3 orbifolds. The talk is based on a joint work with G. Grantcharov and L
. Vezzoni.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Álvaro Krüger Ramos (Universidade Federal do Rio Grande do Sul)
DTSTART;VALUE=DATE-TIME:20201029T170000Z
DTEND;VALUE=DATE-TIME:20201029T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/25
DESCRIPTION:Title: Existence and non existence of complete area minimizing surfac
es in $\\mathbb{E}(-1\,\\tau)$.\nby Álvaro Krüger Ramos (Universidad
e Federal do Rio Grande do Sul) as part of Geometry Webinar AmSur /AmSul\n
\n\nAbstract\nRecall that $\\mathbb{E}(-1\,\\tau)$ is a homogeneous space
with four-dimensional isometry group which is given by the total space of
a fibration over $\\mathbb{H}^2$ with bundle curvature $\\tau$. Given a fi
nite collection of simple closed curves in $\\partial_{\\infty}|mathbb{E}(
-1\,\\tau)$\, we provide sufficient conditions on $\\Gamma$ so that there
exists an area minimizing surface $\\Sigma$ in $\\mathbb{E}(-1\,\\tau)$ wi
th asymptotic boundary $\\Gamma$. We also present necessary conditions for
such a surface $\\Sigma$ to exist. This is joint work with P. Klaser and
A. Menezes.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asun Jiménez (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20201106T170000Z
DTEND;VALUE=DATE-TIME:20201106T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/26
DESCRIPTION:Title: Isolated singularities of Elliptic Linear Weingarten graphs\nby Asun Jiménez (Universidade Federal Fluminense) as part of Geometry
Webinar AmSur /AmSul\n\n\nAbstract\nIn this talk we will study isolated si
ngularities of graphs whose mean and Gaussian curvature satisfy the ellipt
ic linear relation $2\\alpha H+\\beta K=1$\, $\\alpha^2+\\beta>0$. This fa
mily of surfaces includes convex and non-convex singular surfaces and also
cusp-type surfaces. We determine in which cases the singularity is in fac
t removable\, and classify non-removable isolated singularities in terms o
f regular analytic strictly convex curves in $S^2$. This is a joint work w
ith João P. dos Santos.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Amelia Salazar (Universidade Federal Fluminense)
DTSTART;VALUE=DATE-TIME:20201120T170000Z
DTEND;VALUE=DATE-TIME:20201120T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/27
DESCRIPTION:Title: Fundamentals of Lie theory for groupoids and algebroids\nb
y María Amelia Salazar (Universidade Federal Fluminense) as part of Geome
try Webinar AmSur /AmSul\n\n\nAbstract\nThe foundation of Lie theory is Li
e's three theorems that provide a construction of the Lie algebra associat
ed to any Lie group\; the converses of Lie's theorems provide an integrati
on\, i.e. a mechanism for constructing a Lie group out of a Lie algebra. T
he Lie theory for groupoids and algebroids has many analogous results to t
hose for Lie groups and Lie algebras\, however\, it differs in important r
espects: one of these aspects is that there are Lie algebroids which do no
t admit any integration by a Lie groupoid. In joint work with Cabrera and
Marcut\, we showed that the non-integrability issue can be overcome by con
sidering local Lie groupoids instead. In this talk I will explain a constr
uction of a local Lie groupoid integrating a given Lie algebroid and I wil
l point out the similarities with the classical theory for Lie groups and
Lie algebras.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matheus Vieira (Universidade Federal do Espírito Santo)
DTSTART;VALUE=DATE-TIME:20201112T170000Z
DTEND;VALUE=DATE-TIME:20201112T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/28
DESCRIPTION:Title: Biharmonic hypersurfaces in hemispheres\nby Matheus Vieira
(Universidade Federal do Espírito Santo) as part of Geometry Webinar AmS
ur /AmSul\n\n\nAbstract\nWe consider the Balmuş -Montaldo-Oniciuc's conje
cture in the case of hemispheres. We prove that a compact non-minimal biha
rmonic hypersurface in a hemisphere of $S^{n+1}$ must be the small hypersp
here $S^n(1/\\sqrt{2})$\, provided that $n^2-H^2$ does not change sign.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Piccione (Universidade de São Paulo)
DTSTART;VALUE=DATE-TIME:20201126T170000Z
DTEND;VALUE=DATE-TIME:20201126T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/29
DESCRIPTION:Title: Minimal spheres in ellipsoids\nby Paolo Piccione (Universi
dade de São Paulo) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract
\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.\, determin
ed by the intersection with a hyperplane. While this is the case if the el
lipsoid is nearly round\, Haslhofer and Ketover have recently shown the ex
istence of an embedded non-planar minimal 2-sphere in sufficiently elongat
ed ellipsoids\, with min-max methods. Using bifurcation theory and the sym
metries that arise in the case where at least two semi-axes coincide\, we
show the existence of arbitrarily many distinct embedded non-planar minima
l 2-spheres in sufficiently elongated ellipsoids of revolution. This is ba
sed on joint work with R. G. Bettiol..\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simon Salamon (King's College London)
DTSTART;VALUE=DATE-TIME:20201204T170000Z
DTEND;VALUE=DATE-TIME:20201204T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/30
DESCRIPTION:Title: Lie groups and special holonomy\nby Simon Salamon (King's
College London) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nI
shall describe the geometry underlying known examples of explicit metrics
with holonomy $\\mathrm{SU}(2)$ (dimension 4) and $\\mathrm{G}_2$ (dimensi
on 7)\, arising from the action of both nilpotent and simple Lie groups.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudio Gorodski (USP)
DTSTART;VALUE=DATE-TIME:20220325T170000Z
DTEND;VALUE=DATE-TIME:20220325T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/31
DESCRIPTION:Title: A diameter gap for isometric quotients of the unit sphere\
nby Claudio Gorodski (USP) as part of Geometry Webinar AmSur /AmSul\n\n\nA
bstract\nWe will explain our proof of the existence of $\\epsilon>0$ such
that\nevery quotient of the unit sphere $S^n$ ($n\\geq2$)\nby a isometric
group action has diameter zero or at least\n$\\epsilon$. The novelty is th
e independence of $\\epsilon$ from~$n$.\nThe classification of finite simp
le groups is used in the proof.\n\n(Joint work with C. Lange\, A. Lytchak
and R. A. E. Mendes.)\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina M. Arroyo (UNC)
DTSTART;VALUE=DATE-TIME:20220408T170000Z
DTEND;VALUE=DATE-TIME:20220408T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/33
DESCRIPTION:Title: SKT structures on nilmanifolds\nby Romina M. Arroyo (UNC)
as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nA $J$-Hermitian me
tric $g$ on a complex manifold $(M\,J)$ is called strong Kähler with tors
ion (SKT for short) if its $2$-fundamental form $\\omega:=g(J\\cdot\,\\cdo
t)$ satisfies $\\partial \\bar \\partial \\omega =0$. \n\nThe aim of this
talk is to discuss the existence of invariant SKT structures on nilmanifol
ds. We will prove that any nilmanifold admitting an invariant SKT structur
e is either a torus or $2$-step nilpotent\, and we will provide examples o
f invariant SKT structures on $2$-step nilmanifolds in arbitrary dimension
s. \n\nThis talk is based on a joint work with Marina Nicolini.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sueli I. R. Costa (University of Campinas - Brazil)
DTSTART;VALUE=DATE-TIME:20220506T170000Z
DTEND;VALUE=DATE-TIME:20220506T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/34
DESCRIPTION:Title: Geometry and information\nby Sueli I. R. Costa (University
of Campinas - Brazil) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstr
act\nIn this talk it will be presented an introduction and some recent dev
elopments in two topics of Geometry we have been working which have applic
ations in Communications: Lattices and Information Geometry. Lattices are
discrete additive subgroups of the n-dimensional Euclidean space and have
been used in coding for reliability and security in transmissions through
different channels. Currently Lattice based cryptography is one of the ma
in subareas of the so called Post-quantum Cryptography. Information Geomet
ry is devoted to the study of statistical manifolds of probability distri
butions by considering different metrics and divergence measures and have
been used in several applications related to data analysis. We will appro
ach here particularly the space of multivariate normal distributions with
the Fisher metric and some applications.\n\nSome References:\n- S. Amari\,
Information Geometry and Its Applications. Springer\, 2016. \n- S. I. R.
Costa et al\, “Lattices Applied to Coding for Reliable and Secure\nComm
unications” Springer\, 2017 \n- S. I. R. Costa\, S. A. Santos\, J. A .
Strapasson\, Fisher information distance: A geometrical reading” Discre
te Applied Mathematics\, 197\, 59-69 (2015)\n- J. Pinele \, J. Strapasson
\, S. I. R. Costa\, The Fisher–Rao Distance between Multivariate betwee
n Multivariate Normal Distributions: Special Cases\, Bounds and Applicatio
ns\, Entropy 2020\, 22\, 404\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shubham Dwivedi (Humboldt University\, Berlin)
DTSTART;VALUE=DATE-TIME:20220520T170000Z
DTEND;VALUE=DATE-TIME:20220520T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/35
DESCRIPTION:Title: Associative submanifolds in Joyce's generalised Kummer constru
ction\nby Shubham Dwivedi (Humboldt University\, Berlin) as part of Ge
ometry Webinar AmSur /AmSul\n\n\nAbstract\nAssociative submanifolds are sp
ecial 3-dimensional manifolds in $\\mathrm{G_2}$ manifolds which are 7-dim
ensional. They are examples of calibrated submanifolds and there is a rese
arch programme that attempts to count them in order to define numerical in
variants of $\\mathrm{G_2}$ manifolds\, similar to Gromov-Witten invariant
s. However the scarcity of examples of associative submanifolds makes it
difficult to work out the details of this programme. In the talk I will ex
plain how to construct associatives in $\\mathrm{G_2}$ manifolds construct
ed by Joyce\, whose existence had previously been predicted by physicists
. The talk is based on a joint work with Daniel Platt (King's College Lond
on) and Thomas Walpuski (Humboldt University\, Berlin).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eder Moraes Correa (UFMG/Unicamp)
DTSTART;VALUE=DATE-TIME:20220701T170000Z
DTEND;VALUE=DATE-TIME:20220701T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/36
DESCRIPTION:Title: Levi-Civita Ricci-flat metrics on compact Hermitian Weyl-Einst
ein manifolds\nby Eder Moraes Correa (UFMG/Unicamp) as part of Geometr
y Webinar AmSur /AmSul\n\n\nAbstract\nAs shown in [2]\, the first Aeppli-C
hern class of a compact Hermitian manifold can be represented by its first
Levi-Civita Ricci curvature. From this\, a natural question to ask (inspi
red by the Calabi-Yau theorem [3]) is the following: On a compact complex
manifold with vanishing first Aeppli-Chern class\, does there exist a smoo
th Levi-Civita Ricci-flat Hermitian metric? In general\, it is particularl
y challenging to solve the Levi-Civita Ricci-flat equation\, since there a
re non-elliptic terms involved in the underlying PDE problem. In this talk
\, we will investigate the above question in the setting of compact Hermit
ian Weyl-Einstein manifolds. The main purpose is to show that every compac
t Hermitian Weyl-Einstein manifold admits a Levi-Civita Ricci-flat Hermiti
an metric [1]. This result generalizes previous constructions on Hopf mani
folds [2].\n\n\n[1] Correa\, E. M.\; Levi-Civita Ricci-flat metrics on non
-Kähler Calabi-Yau manifolds\, arxiv:2204.04824v3 (2022).\n\n[2] Liu\, K.
\; Yang\, X.\; Ricci curvatures on Hermitian manifolds\, Trans. Amer. Math
. Soc. 369 (2017)\, no. 7\, 5157-5196.\n\n[3] Yau\, S.-T.\; On the Ricci c
urvature of a compact Kähler manifold and the complex Monge-Ampère equat
ion. I\, Comm. Pure Appl. Math. 31 (1978)\, no. 3\, 339-411. MR480350.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Moreno (Unicamp)
DTSTART;VALUE=DATE-TIME:20220422T170000Z
DTEND;VALUE=DATE-TIME:20220422T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/37
DESCRIPTION:Title: Invariant $G_2$-structures with free-divergence torsion tensor
\nby Andrés Moreno (Unicamp) as part of Geometry Webinar AmSur /AmSul
\n\n\nAbstract\nA $G_2$-structure with free divergence torsion can be inte
rpreted as a critical point of the energy functional\, restricted to its i
sometric class. Hence\, it represents the better $G_2$-structure in a give
n family. These kinds of $G_2$-structures are an alternative for the study
of $G_2$-geometry\, in cases when the torsion free problem is either triv
ial or obstructed. In general\, there are some known classes of $G_2$-stru
ctures with free-divergence torsion\, namely closed and nearly parallel $G
_2$-structures. In this talk\, we are going to present some unknown classe
s of invariant $G_2$-structures with free divergence torsion\, specificall
y in the context of the 7-sphere and of the solvable Lie groups with a cod
imension-one Abelian normal subgroup.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gonçalo Oliveira (UFF)
DTSTART;VALUE=DATE-TIME:20220603T170000Z
DTEND;VALUE=DATE-TIME:20220603T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/38
DESCRIPTION:Title: Special Lagrangians and Lagrangian mean curvature flow\nby
Gonçalo Oliveira (UFF) as part of Geometry Webinar AmSur /AmSul\n\n\nAbs
tract\n(joint work with Jason Lotay) Richard Thomas and Shing-Tung-Yau pro
posed two conjectures on the existence of special Lagrangian submanifolds
and on the use of Lagrangian mean curvature flow to find them. In this tal
k\, I will report on joint work with Jason Lotay to prove these on certain
symmetric hyperKahler 4-manifolds. If time permits I may also comment on
our work in progress to tackle more refined conjectures of Dominic Joyce r
egarding the existence of Bridgeland stability conditions on Fukaya catego
ries and their interplay with Lagrangian mean curvature flow.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis J. Alías (Murcia)
DTSTART;VALUE=DATE-TIME:20220617T170000Z
DTEND;VALUE=DATE-TIME:20220617T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/39
DESCRIPTION:Title: Mean curvature flow solitons in warped product spaces\nby
Luis J. Alías (Murcia) as part of Geometry Webinar AmSur /AmSul\n\n\nAbst
ract\nIn this lecture we establish a natural framework for the study of me
an curvature flow solitons in warped product spaces. Our approach allows u
s to identify some natural geometric quantities that satisfy elliptic equa
tions or differential inequalities in a simple and manageable form for whi
ch the machinery of weak maximum principles is valid. The latter is one of
the main tools we apply to derive several new characterizations and rigid
ity results for MCFS that extend to our general setting known properties\,
for instance\, in Euclidean space. Besides\, as in Euclidean space\, MCFS
are also stationary immersions for a weighted volume functional. Under th
is point of view\, we are able to find geometric conditions for finiteness
of the index and some characterizations of stable solitons. \n\nThe resul
ts of this lecture have been obtained in collaboration with Jorge H. de Li
ra\, from Universidade Federal do Ceará\, and Marco Rigoli\, from Univers
ità degli Study di Milano\, and they can be found in the following papers
:\n\n[1] Luis J. Alías\, Jorge H. de Lira and Marco Rigoli\, Mean curvatu
re flow solitons in the presence of conformal vector fields\, The Journal
of Geometric Analysis 30 (2020)\, 1466-1529.\n\n[2] Luis J. Alías\, Jorge
H. de Lira and Marco Rigoli\, Stability of mean curvature flow solitons i
n warped product spaces. To appear in Revista Matemática Complutense (202
2).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Struchiner (USP)
DTSTART;VALUE=DATE-TIME:20220909T170000Z
DTEND;VALUE=DATE-TIME:20220909T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/40
DESCRIPTION:Title: Lie groupoids and singular Riemannian foliations\nby Ivan
Struchiner (USP) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nI
will discuss some aspects of the interplay between Lie groupoids and sing
ular Riemannian foliations. To each singular Riemannian foliation we assoc
iate a linear holonomy groupoid to a neighbourhood of each leaf. This grou
poid is a dense subgroupoid of a proper Lie groupoid. On the other hand\,
Lie groupoids with compatible metrics give rise to singular Riemannian fol
iations. We discuss how far these groupoids are from being a dense subgrou
poid of a proper Lie groupoid.\n\nThe talk will be based on joint work wit
h Marcos Alexandrino\, Marcelo Inagaki and Mateus de Melo.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregorio Pacelli Bessa (UFC)
DTSTART;VALUE=DATE-TIME:20220729T170000Z
DTEND;VALUE=DATE-TIME:20220729T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/41
DESCRIPTION:Title: On the mean exit time of cylindrically bounded submanifolds of
$N\\times \\mathbb{R}$ with bounded mean curvature.\nby Gregorio Pace
lli Bessa (UFC) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nWe
show that the global mean exit time of cylindrically bounded submanifolds
of $N\\times \\mathbb{R}$ is finite\, where the sectional curvature $K_N\
\leq b\\leq 0$.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Ambrozio (IMPA)
DTSTART;VALUE=DATE-TIME:20220819T170000Z
DTEND;VALUE=DATE-TIME:20220819T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/42
DESCRIPTION:Title: Zoll-like metrics in minimal surface theory\nby Lucas Ambr
ozio (IMPA) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\na Zoll
metric is a Riemannian metric g on a manifold such that all of its geodes
ics are periodic and have the same finite fundamental period. In particula
r\, (M\,g) is a compact manifold such that each tangent one-dimensional su
bspace of each one of its points is tangent to some closed geodesic. Since
periodic geodesics are not only periodic orbits of a flow\, but also clos
ed curves that are critical points of the length functional\, the notion o
f Zoll metrics admits natural generalisations in the context of minimal su
bmanifold theory\, that is\, the theory of critical points of the area fun
ctional. In this talk\, based on joint work with F. Codá (Princeton) and
A. Neves (UChicago)\, I will discuss why these new\, generalised notions s
eem relevant to me beyond its obvious geometric appeal\, and discuss two d
ifferent methods to obtain infinitely many such examples on spheres\, with
perhaps unexpected properties.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luis Florit (IMPA)
DTSTART;VALUE=DATE-TIME:20220826T170000Z
DTEND;VALUE=DATE-TIME:20220826T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/43
DESCRIPTION:Title: A Nash type theorem and extrinsic surgeries for positive scala
r curvature\nby Luis Florit (IMPA) as part of Geometry Webinar AmSur /
AmSul\n\n\nAbstract\nAs shown by Gromov-Lawson and Stolz the only obstruct
ion to the existence of positive scalar curvature metrics on closed simply
connected manifolds in dimensions at least five appears on spin manifolds
\, and is given by the non-vanishing of the α-genus of Hitchin.\n\nWhen u
nobstructed we shall realise a positive scalar curvature metric by an imme
rsion into Euclidean space whose dimension is uniformly close to the class
ical Whitney upper bound for smooth immersions\, and it is in fact equal
to the Whitney bound in most dimensions. Our main tool is an extrinsic cou
nterpart of the well-known Gromov-Lawson surgery procedure for constructin
g positive scalar curvature metrics.\n\nThis is a joint work with B. Hanke
published in Commun. Contemp. Math. 2022.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Garcia-Fernández (Universidad Autónoma de Madrid and ICMAT
)
DTSTART;VALUE=DATE-TIME:20220923T170000Z
DTEND;VALUE=DATE-TIME:20220923T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/44
DESCRIPTION:Title: Non-Kähler Calabi-Yau geometry and pluriclosed flow\nby M
ario Garcia-Fernández (Universidad Autónoma de Madrid and ICMAT) as part
of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn this talk I will overv
iew joint work with J. Jordan and J. Streets\, in arXiv:2106.13716\, about
Hermitian\, pluriclosed metrics with vanishing Bismut-Ricci form. These m
etrics give a natural extension of Calabi-Yau metrics to the setting of co
mplex\, non-Kählermanifolds\, and arise independently in mathematical phy
sics. We reinterpret this condition in terms of the Hermitian-Einstein equ
ation on an associated holomorphic Courant algebroid\, and thus refer to s
olutions as Bismut Hermitian-Einstein. This implies Mumford-Takemoto slope
stability obstructions\, and using these we exhibit infinitely many topol
ogically distinct complex manifolds in every dimension with vanishing firs
t Chern class which do not admit Bismut Hermitian-Einstein metrics. This r
eformulation also leads to a new description of pluriclosed flow\, as intr
oduced by Streets and Tian\, implying new global existence results. In par
ticular\, on all complex non-Kähler surfaces of nonnegative Kodaira dimen
sion. On complex manifolds which admit Bismut-flat metrics we show global
existence and convergence of pluriclosed flow to a Bismut-flat metric.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guillermo Henry (UBA)
DTSTART;VALUE=DATE-TIME:20221104T170000Z
DTEND;VALUE=DATE-TIME:20221104T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/46
DESCRIPTION:Title: Isoparametric foliations and solutions of Yamabe type equation
s on manifolds with boundary.\nby Guillermo Henry (UBA) as part of Geo
metry Webinar AmSur /AmSul\n\n\nAbstract\nA foliation such that their regu
lar leaves are parallel CMC hypersurfaces is called isoparametric. In th
is talk we are going to discuss some results on the existence of solutions
of the Yamabe equation on compact Riemannian manifolds with boundary indu
ced these type of foliations. Joint work with Juan Zuccotti.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raquel Villacampa (CUD- Zaragoza)
DTSTART;VALUE=DATE-TIME:20221118T170000Z
DTEND;VALUE=DATE-TIME:20221118T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/47
DESCRIPTION:Title: Nilmanifolds: examples and counterexamples in geometry and top
ology\nby Raquel Villacampa (CUD- Zaragoza) as part of Geometry Webina
r AmSur /AmSul\n\n\nAbstract\nNilmanifolds are a special type of different
iable compact manifolds defined as the quotient of a nilpotent\, simply co
nnected Lie group by a lattice.\n\nSince Thurston used them in 1976 to sho
w an example of a compact complex symplectic manifold being non-Kähler\,
many other topological and geometrical questions have been answered using
nilmanifolds. In this talk we will show some of these problems such as th
e holonomy of certain metric connections\, deformations of structures or s
pectral sequences.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilka Agricola (Marburg)
DTSTART;VALUE=DATE-TIME:20221209T170000Z
DTEND;VALUE=DATE-TIME:20221209T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/48
DESCRIPTION:Title: On the geometry and the curvature of 3-(α\, δ)-Sasaki manifo
lds\nby Ilka Agricola (Marburg) as part of Geometry Webinar AmSur /AmS
ul\n\n\nAbstract\nWe consider $3$-$(\\alpha\, \\delta)$-Sasaki manifolds\,
generalizing the classic 3-Sasaki case. We show\nhow these are closely re
lated to various types of quaternionic Kähler orbifolds via connections\n
with skew-torsion and a canonical submersion. Making use of this relation
we discuss curvature operators and show that in dimension 7 many such mani
folds have strongly positive curvature. Joint work with Giulia Dileo (Bari
) and Leander Stecker (Hamburg).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Origlia (CONICET)
DTSTART;VALUE=DATE-TIME:20221021T170000Z
DTEND;VALUE=DATE-TIME:20221021T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/49
DESCRIPTION:Title: Conformal Killing Yano $2$-forms on Lie groups\nby Marcos
Origlia (CONICET) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\n
A differential $p$-form $\\eta$ on a $n$-dimensional Riemannian manifold $
(M\,g)$ is called Conformal Killing Yano (CKY for short) if it satisfies f
or any vector field $X$ the following equation\n\\[ \\nabla_X \\eta=\\dfr
ac{1}{p+1}\\iota_X\\mathrm{d}\\eta-\\dfrac{1}{n-p+1}X^*\\wedge \\mathrm{d}
^*\\eta\,\n\\]\nwhere $X^*$ is the dual 1-form of $X$\, $\\mathrm{d}^*$ i
s the codifferential\, $\\nabla$ is the Levi-Civita connection associated
to $g$ and $\\iota_X$ is the interior product with $X$. If $\\eta$ is cocl
osed ($\\mathrm d^*\\eta=0$) then $\\eta$ is said to be a Killing-Yano $p
$-form (KY for short).\n\nWe study left invariant Conformal Killing Yano $
2$-forms on Lie groups endowed with a left invariant metric. We determine\
, up to isometry\, all $5$-dimensional metric Lie algebras under certain c
onditions\, admitting a CKY $2$-form. Moreover\, a characterization of all
possible CKY tensors on those metric Lie algebras is exhibited.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Da Rong Cheng (University of Miami)
DTSTART;VALUE=DATE-TIME:20230512T170000Z
DTEND;VALUE=DATE-TIME:20230512T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/50
DESCRIPTION:Title: Existence of free boundary constant mean curvature disks\n
by Da Rong Cheng (University of Miami) as part of Geometry Webinar AmSur /
AmSul\n\n\nAbstract\nGiven a surface S in R3\, a classical problem is to f
ind disk-type surfaces with prescribed constant mean curvature whose bound
ary meets S orthogonally. When S is diffeomorphic to a sphere\, direct min
imization could lead to trivial solutions and hence min-max constructions
are needed. Among the earliest such constructions is the work of Struwe\,
who produced the desired free boundary CMC disks for almost every mean cur
vature value up to that of the smallest round sphere enclosing S. In a pre
vious joint work with Xin Zhou (Cornell)\, we combined Struwe's method wit
h other techniques to obtain an analogous result for CMC 2-spheres in Riem
annian 3-spheres and were able to remove the "almost every" restriction in
the presence of positive ambient curvature. In this talk\, I will report
on more recent progress where the ideas in that work are applied back to t
he free boundary problem to refine and improve Struwe's result.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Dileo (Univesity of Bari)
DTSTART;VALUE=DATE-TIME:20230623T170000Z
DTEND;VALUE=DATE-TIME:20230623T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/51
DESCRIPTION:Title: Special classes of transversely Kähler almost contact metric
manifolds\nby Giulia Dileo (Univesity of Bari) as part of Geometry Web
inar AmSur /AmSul\n\n\nAbstract\nI will discuss some special classes of al
most contact metric manifolds $(M\,\\varphi\,\\xi\,\\eta\,g)$ such that th
e structure $(\\varphi\,g)$ is projectable along the 1-dimensional foliati
on generated by $\\xi$\, and the transverse geometry is given by a Kähle
r structure. I will focus on quasi-Sasakian manifolds and the new class of
anti-quasi-Sasakian manifolds. In this case\, the transverse geometry is
given by a Kähler structure endowed with a closed 2-form of type (2\,0)\,
as for instance hyperkähler structures. I will describe examples of anti
-quasi-Sasakian manifolds\, including compact nilmanifolds and principal c
ircle bundles\, investigate Riemannian curvature properties\, and the exis
tence of connections with torsion preserving the structure. This is a join
t work with Dario Di Pinto (Bari).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yang-Hui He (London Institute\, Royal Institution & Merton College
\, Oxford University)
DTSTART;VALUE=DATE-TIME:20230526T170000Z
DTEND;VALUE=DATE-TIME:20230526T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/52
DESCRIPTION:Title: Universes as BigData: Physics\, Geometry and Machine-Learning
\nby Yang-Hui He (London Institute\, Royal Institution & Merton Colleg
e\, Oxford University) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstr
act\nThe search for the Theory of Everything has led to superstring theory
\, which then led physics\, first to algebraic/differential geometry/topol
ogy\, and then to computational geometry\, and now to data science.\nWith
a concrete playground of the geometric landscape\, accumulated by the coll
aboration of physicists\, mathematicians and computer scientists over the
last 4 decades\, we show how the latest techniques in machine-learning can
help explore problems of interest to theoretical physics and to pure math
ematics.\nAt the core of our programme is the question: how can AI help us
with mathematics?\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Laura Barberis (UNC)
DTSTART;VALUE=DATE-TIME:20230609T170000Z
DTEND;VALUE=DATE-TIME:20230609T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/53
DESCRIPTION:Title: Complex structures on $2$-step nilpotent Lie algebras\nby
Maria Laura Barberis (UNC) as part of Geometry Webinar AmSur /AmSul\n\n\nA
bstract\nThere is a notion of nilpotent complex structures on nilpotent Li
e algebras introduced by Cordero-Fernández-Gray-Ugarte (2000). Not every
complex structure on a nilpotent Lie algebra $\\mathfrak{n}$ is nilpotent\
, but when $\\mathfrak{n}$ is $2$-step nilpotent any complex structure on
$\\mathfrak{n}$ is nilpotent of step either $2$ or $3$ (a fact proved by
J. Zhang in 2022). The class of nilpotent complex structures of step $2$ s
trictly contains the space of abelian and bi-invariant complex structures
on a $2$-step nilpotent Lie algebra. In this work in progress\, we obtain
a characterization of the $2$-step nilpotent Lie algebras whose correspond
ing Lie groups admit a left invariant complex structure. We consider separ
ately the cases when the complex structure is nilpotent of step $2$ or $3$
. Some applications of our results to Hermitian geometry are discussed\, f
or instance\, it turns out that the $2$-step nilpotent Lie algebras constr
ucted by Tamaru from Hermitian symmetric spaces admit pluriclosed (or SKT)
metrics. We also show that abelian complex structures are frequent on nat
urally reductive $2$-step nilmanifolds\, while it is known (Del Barco-Moro
ianu) that these do not admit orthogonal bi-invariant complex structures.\
n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos Olmos (UNC)
DTSTART;VALUE=DATE-TIME:20230317T170000Z
DTEND;VALUE=DATE-TIME:20230317T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/54
DESCRIPTION:Title: Totally geodesic submanifolds of Hopf-Berger spheres\nby C
arlos Olmos (UNC) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\n
A Hopf-Berger sphere of factor $\\tau$ is a sphere which is the total spa
ce of a Hopf fibration and such that the Riemannian metric is rescaled by
a factor $\\tau\\neq 1$ in the directions of the fibers. A Hopf-Berger sph
ere is the usual {\\it Berger sphere} for the complex Hopf fibration. A H
opf-Berger sphere may be regarded as a geodesic sphere $\\mathsf{S}_t^m(o)
\\subset\\bar M$ of radius $t$ of a rank one symmetric space of non-consta
nt curvature ($\\bar M$ is compact if and only if $\\tau <1$). A Hopf-Ber
ger sphere has positive curvature if and only if $\\tau <4/3$. A standard
totally geodesic submanifold of $\\mathsf{S}_t^m(o)$ is obtained as the in
tersection of the geodesic sphere with a totally geodesic submanifold of $
\\bar M$. We will speak about the classification of totally geodesic subm
anifolds of Hopf-Berger spheres. In particular\, for quaternionic and oc
tonionic fibrations\, non-standard totally geodesic spheres with the same
dimension of the fiber appear\, for $\\tau <1/2$. Moreover\, there are to
tally geodesic $\\mathbb RP^2$\, and $\\mathbb RP^3$ (with some restricti
ons on $\\tau$\, the dimension and the type of the fibration). On the on
e hand\, as a consequence of the connectedness principle of Wilking\, the
re does not exist a totally geodesic $\\mathbb RP^4$ in a space of posi
tive curvature which diffeomorphic to the sphere $S^7$. On the other han
d\, we construct an example of a totally geodesic $\\mathbb RP^2$ in a Hop
f-Berger sphere of dimension $7$ and positive curvature. Natural question:
could there exist a totally geodesic $\\mathbb RP^3$ in a space of positi
ve curvature which diffeomorphic to $S^7$?.\n\nThis talk is related to a
joint work with Alberto Rodríguez-Vázquez.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ruy Tojeiro (ICMC-USP (São Carlos))
DTSTART;VALUE=DATE-TIME:20230331T170000Z
DTEND;VALUE=DATE-TIME:20230331T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/55
DESCRIPTION:Title: Infinitesimally Bonnet bendable hypersurfaces\nby Ruy Toje
iro (ICMC-USP (São Carlos)) as part of Geometry Webinar AmSur /AmSul\n\n\
nAbstract\nThe classical Bonnet problem is to classify all immersions $f\
\colon\\\,M^2\\to\\R^3$ into Euclidean three-space that are not determined
\,\nup to a rigid motion\, by their induced metric and mean curvature func
tion.\nThe natural extension of Bonnet problem for Euclidean hypersurface
s of dimension $n\\geq 3$ was studied by Kokubu. In this talk we report o
n joint work with M. Jimenez\, in which we investigate an infinitesimal ve
rsion of Bonnet problem for hypersurfaces with dimension $n\\geq 3$ of any
space form\, namely\, we classify the hypersurfaces $f\\colon M^n\\to\\Q_
c^{n+1}$\, $n\\geq 3$\, of any space form $\\Q_c^{n+1}$ of constant curvat
ure $c$\, for which there exists a (non-trivial) one-parameter family of i
mmersions $f_t\\colon M^n\\to\\Q_c^{n+1}$\, with $f_0=f$\, whose induced
metrics $g_t$ and mean curvature functions $H_t$ coincide ``up to the firs
t order"\, that is\, $\\partial/\\partial t|_{t=0}g_t=0=\\partial/\\partia
l t|_{t=0}H_t.$\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lino Grama (Unicamp)
DTSTART;VALUE=DATE-TIME:20230414T170000Z
DTEND;VALUE=DATE-TIME:20230414T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/56
DESCRIPTION:Title: Kähler-like scalar curvature on homogeneous spaces\nby Li
no Grama (Unicamp) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\
nIn this talk\, we will discuss the curvature properties of invariant almo
st Hermitian geometry on generalized flag manifolds. Specifically\, we wil
l focus on the "Kähler-like scalar curvature metric" - that is\, almost H
ermitian structures $(g\,J)$ satisfying $s=2s_C$\, where $s$ is the Rieman
nian scalar curvature and $s_C$ is the Chern scalar curvature. We will pro
vide a classification of such metrics on generalized flag manifolds whose
isotropy representation decomposes into two or three irreducible component
s. This is a joint work with A. Oliveira.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fadel (IMPA)
DTSTART;VALUE=DATE-TIME:20230428T170000Z
DTEND;VALUE=DATE-TIME:20230428T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/57
DESCRIPTION:Title: On the harmonic flow of geometric structures\nby Daniel Fa
del (IMPA) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn this
talk\, I will report on recent results of an ongoing collaboration with
Éric Loubeau\, Andrés Moreno and Henrique Sá Earp on the study of the h
armonic flow of $H$-structures. This is the negative gradient flow of a na
tural Dirichlet-type energy functional on an isometric class of $H$-struct
ures on a closed Riemannian $n$-manifold\, where $H$ is the stabilizer in
$\\mathrm{SO}(n)$ of a finite collection of tensors in $\\mathbb{R}^n$. Us
ing general Bianchi-type identities of $H$-structures\, we are able to pro
ve monotonicity formulas for scale-invariant local versions of the energy\
, similar to the classic formulas proved by Struwe and Chen (1988-89) in t
he theory of harmonic map heat flow. We then deduce a general epsilon-regu
larity result along the harmonic flow and\, more importantly\, we get long
-time existence and finite-time singularity results in parallel to the cla
ssical results proved by Chen-Ding (1990) in harmonic map theory. In parti
cular\, we show that if the energy of the initial $H$-structure is small e
nough\, depending on the $C^0$-norm of its torsion\, then the harmonic flo
w exists for all time and converges to a torsion-free $H$-structure. Moreo
ver\, we prove that the harmonic flow of $H$-structures develops a finite
time singularity if the initial energy is sufficiently small but there is
no torsion-free $H$-structure in the homotopy class of the initial $H$-str
ucture. Finally\, based on the analogous work of He-Li (2021) for almost c
omplex structures\, we give a general construction of examples where the l
ater finite-time singularity result applies on the flat $n$-torus\, provid
ed the $n$-th homotopy group of the quotient $\\mathrm{SO}(n)/H$ is non-tr
ivial\; e.g. when $n=7$ and $H=\\mathrm{G}_2$\, or when $n=8$ and $H=\\mat
hrm{Spin}(7)$.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Salvai (FAMAF\, Universidad Nacional de Córdoba\, Argentin
a)
DTSTART;VALUE=DATE-TIME:20230811T170000Z
DTEND;VALUE=DATE-TIME:20230811T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/58
DESCRIPTION:Title: Maximal vorticity of sections of the orthonormal frame bundle
via calibrations\nby Marcos Salvai (FAMAF\, Universidad Nacional de C
órdoba\, Argentina) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstrac
t\nLet M be an oriented three dimensional Riemannian manifold. We define
a notion of vorticity of local sections of the bundle SO(M) -> M of all
its positively oriented orthonormal tangent frames. When M is a space fo
rm\, we relate the concept to a suitable invariant split pseudo-Riemannian
metric on Iso_o (M) equiv SO(M): A local section has positive vorticity i
f and only if it determines a space-like submanifold. In the Euclidean cas
e we find explicit homologically volume maximizing sections using a split
special Lagrangian calibration. We introduce the concept of optimal vortic
ity and give an optimal screwed global section for the three-sphere. We pr
ove that it is also homologically volume maximizing (now using a common on
e-point split calibration). Besides\, we show that no optimal section can
exist in the Euclidean and hyperbolic cases.\n\nM. Salvai\, A split specia
l Lagrangian calibration associated with frame vorticity\, accepted for pu
blication in Adv. Calc. Var.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mauro Subils (UN Rosario)
DTSTART;VALUE=DATE-TIME:20230825T170000Z
DTEND;VALUE=DATE-TIME:20230825T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/59
DESCRIPTION:Title: Magnetic trajectories on the Heisenberg group of dimension thr
ee\nby Mauro Subils (UN Rosario) as part of Geometry Webinar AmSur /Am
Sul\n\n\nAbstract\nA magnetic trajectory is a curve $\\gamma$ on a Rieman
nian manifold $(M\, g)$ satisfying the equation:\n$$\\nabla_{\\gamma'}{\\g
amma'}= q F\\gamma'$$\nwhere $\\nabla$ is the corresponding Levi-Civita
connection and $F$ is a skew-symmetric $(1\,1)$-tensor such that the cor
responding 2-form $g(F\\cdot \,\\cdot)$ is closed.\n\nIn this talk we are
going to describe all magnetic trajectories on the Heisenberg Lie group of
dimension three $H_3$ for any invariant Lorentz force. We will write expl
icitly the magnetic equations and show that the solutions are described by
Jacobi's elliptic functions. As a consequence\, we will prove the existen
ce and characterize the periodic magnetic trajectories.\nThen we will indu
ce the Lorentz force to a compact quotient $H_3/\\Gamma$ and study the per
iodic magnetic trajectories there\, proving its existence for any energy l
evel when $F$ is non-exact. \n\nThis is a joint work with Gabriela Ovand
o (UNR).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rafael Montezuma (UFC)
DTSTART;VALUE=DATE-TIME:20230922T170000Z
DTEND;VALUE=DATE-TIME:20230922T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/63
DESCRIPTION:Title: The width of curves in Riemannian manifolds\nby Rafael Mon
tezuma (UFC) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn th
is talk we develop a Morse-Lusternik-Schnirelmann theory for the distance
between two points of a smoothly embedded circle in a complete Riemannian
manifold. This theory suggests very naturally a definition of width that g
eneralises the classical definition of the width of plane curves. Pairs of
points of the circle realising the width bound one or more minimising geo
desics that intersect the curve in special configurations. When the circle
bounds a totally convex disc\, we classify the possible configurations un
der a further geometric condition. We also present properties and characte
risations of curves that can be regarded as the Riemannian analogues of pl
ane curves of constant width. This talk is based on a joint work with Luca
s Ambrozio (IMPA) and Roney Santos (UFC).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Gaspar (Pontificia Universidad Católica de Chile)
DTSTART;VALUE=DATE-TIME:20231006T170000Z
DTEND;VALUE=DATE-TIME:20231006T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/64
DESCRIPTION:Title: Heteroclinic solutions and a Morse-theoretic approach to an Al
len-Cahn approximation of mean curvature flows\nby Pedro Gaspar (Ponti
ficia Universidad Católica de Chile) as part of Geometry Webinar AmSur /A
mSul\n\n\nAbstract\nThe Allen–Cahn equation is a semilinear parabolic pa
rtial differential equation that models phase-transition and phase-separat
ion phenomena and which provides a regularization for the mean curvature f
low (MCF)\, one of the most studied extrinsic geometric flows. \nIn this t
alk\, we employ Morse-theoretical considerations to construct eternal solu
tions of the Allen–Cahn equation that connect unstable equilibria in com
pact manifolds. We describe the space of such solutions in a round 3-spher
e under a low-energy assumption\, and indicate how these solutions could b
e used to produce geometrically interesting MCFs. This is joint work with
Jingwen Chen (University of Pennsylvania).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviana del Barco (Unicamp)
DTSTART;VALUE=DATE-TIME:20231117T170000Z
DTEND;VALUE=DATE-TIME:20231117T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/65
DESCRIPTION:Title: $G_2$-instantons on nilpotent Lie groups\nby Viviana del B
arco (Unicamp) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn
this talk we will discuss recent advancements on G$_2$-instantons on 7-dim
ensional 2-step nilpotent Lie groups endowed with a left-invariant coclose
d G$_2$-structures. I will present necessary and sufficient conditions for
the characteristic connection of the G$_2$-structure to be an instanton\,
in terms of the torsion of the G$_2$-structure\,\nthe torsion of the conn
ection and the Lie group structure. These conditions allow to show that th
e metrics corresponding to the G$_2$-instantons define a naturally reducti
ve structure on the simply connected 2-step nilpotent Lie group with left-
invariant Riemannian metric. This is a joint work with Andrew Clarke and A
ndrés Moreno.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rayssa Caju (Universidad de Chile)
DTSTART;VALUE=DATE-TIME:20231020T170000Z
DTEND;VALUE=DATE-TIME:20231020T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/66
DESCRIPTION:Title: Constant Q-curvature metrics\nby Rayssa Caju (Universidad
de Chile) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nOver the
past few decades\, there has been significant exploration of the interpla
y between geometry and partial differential equations. In particular\, som
e problems arising in conformal geometry\, such as\nthe classical Yamabe p
roblem\, can be reduced to the study of PDEs with critical exponent on\nma
nifolds. More recently\, the so-called Q-curvature equation\, a fourth-ord
er elliptic PDE with\ncritical exponent\, is another class of conformal eq
uations that has drawn considerable attention\nby its relation with a natu
ral concept of curvature. In this talk\, I would like to motivate these\np
roblems from a geometric and analytic perspective\, and discuss some recen
t developments in the\narea\, in particular regarding the singular Q-curva
ture problem.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Jablonski (University of Oklahoma)
DTSTART;VALUE=DATE-TIME:20231103T170000Z
DTEND;VALUE=DATE-TIME:20231103T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/67
DESCRIPTION:Title: Real semi-simple Lie algebras are determined by their Iwasawa
subalgebras.\nby Michael Jablonski (University of Oklahoma) as part of
Geometry Webinar AmSur /AmSul\n\n\nAbstract\nReal semi-simple Lie algebra
s arise naturally both algebraically\, in the study of Lie theory\, and ge
ometrically\, in the study of symmetric spaces. After recalling why these
algebras are of interest\, we will investigate their uniqueness properties
through the lens of special subalgebras\, the so-called Iwasawa subalgebr
as. While the results are algebraic\, the tools to obtain them come from t
he Riemannian geometry of solvmanifolds. We will finish the talk with a qu
ick discussion of the complex setting and how it differs from the real set
ting. This is joint work with Jon Epstein (McDaniel College).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eveline Legendre (U. Lyon)
DTSTART;VALUE=DATE-TIME:20231201T170000Z
DTEND;VALUE=DATE-TIME:20231201T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/68
DESCRIPTION:Title: The Einstein-Hilbert functional in Kähler and Sasaki geometry
\nby Eveline Legendre (U. Lyon) as part of Geometry Webinar AmSur /AmS
ul\n\n\nAbstract\nIn this talk I will present a recent joint work with Abd
ellah Lahdilli and Carlo Scarpa where\, given a polarised Kähler manifold
$(M\,L)$\, we consider the circle bundle associated to the polarization w
ith the induced transversal holomorphic structure. The space of contact st
ructures compatible with this transversal structure is naturally identifie
d with a bundle\, of infinite rank\, over the space of Kähler metrics in
the first Chern class of L. We show that the Einstein--Hilbert functional
of the associated Tanaka--Webster connections is a functional on this bund
le\, whose critical points are constant scalar curvature Sasaki structures
. In particular\, when the group of automorphisms of $(M\,L)$ is discrete\
, these critical points correspond to constant scalar curvature Kähler me
trics in the first Chern class of $L$. If time permits\, I will explain ho
w we associate a two real parameters family of these contact structures to
any ample test configuration and relate the limit\, on the central fibre\
, to a primitive of the Donaldson-Futaki invariant. As a by-product\, we s
how that the existence of cscK metrics on a polarized manifold implies K-s
emistability\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Moroianu (Paris-Saclay/CNRS)
DTSTART;VALUE=DATE-TIME:20240308T170000Z
DTEND;VALUE=DATE-TIME:20240308T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/69
DESCRIPTION:Title: Weyl structures with special holonomy on compact conformal man
ifolds\nby Andrei Moroianu (Paris-Saclay/CNRS) as part of Geometry Web
inar AmSur /AmSul\n\n\nAbstract\nWe consider compact conformal manifolds $
(M\,[g])$ endowed with a closed Weyl structure $\\nabla$\, i.e. a torsion-
free connection preserving the conformal structure\, which is locally but
not globally the Levi-Civita connection of a metric in $[g]$. Our aim is t
o classify all such structures when both $\\nabla$ and $\\nabla^g$\, the L
evi-Civita connection of $g$\, have special holonomy. In such a setting\,
$(M\,[g]\,\\nabla)$ is either flat\, or irreducible\, or carries a locally
conformally product (LCP) structure.\nSince the flat case is already comp
letely classified\, we focus on the last two cases.\nWhen $\\nabla$ has ir
reducible holonomy we prove that $(M\,g)$ is either Vaisman\, or a mapping
torus of an isometry of a compact nearly Kähler or nearly parallel $\\ma
thrm{G}_2$ manifold\, while in the LCP case we prove that $g$ is neither K
ähler nor Einstein\, thus reducible by the Berger-Simons Theorem\, and we
obtain the local classification of such structures in terms of adapted me
trics. This is joint work with Florin Belgun and Brice Flamencourt.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:João Henrique Santos de Andrade (USP)
DTSTART;VALUE=DATE-TIME:20240322T170000Z
DTEND;VALUE=DATE-TIME:20240322T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/70
DESCRIPTION:Title: Compactness of singular solutions to the GJMS equation\nby
João Henrique Santos de Andrade (USP) as part of Geometry Webinar AmSur
/AmSul\n\n\nAbstract\nWe study some compactness properties of the set of c
onformally flat singular metrics with constant positive $Q$-curvature (int
eger or fractional) on a finitely punctured sphere.\nBased on some recent
classification results\, we focus on some cases of integer $Q$-curvature.
We introduce a notion of necksize for these metrics in our moduli space\,
which we use to characterize compactness. More precisely\, we prove that i
f the punctures remain separated and the necksize at each puncture is boun
ded away from zero along a sequence of metrics\, then a subsequence conver
ges with respect to the Gromov-Hausdorff metric. Our proof relies on an up
per bound estimate which is proved using moving planes and a blow-up argum
ent. This is combined with a lower bound estimate which is a consequence o
f a removable singularity theorem. We also introduce a homological invaria
nt which may be of independent interest for upcoming research.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ernani Ribeiro Jr. (Universidade Federal do Ceará - UFC)
DTSTART;VALUE=DATE-TIME:20240405T170000Z
DTEND;VALUE=DATE-TIME:20240405T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/71
DESCRIPTION:Title: Rigidity of compact quasi-Einstein manifolds with boundary
\nby Ernani Ribeiro Jr. (Universidade Federal do Ceará - UFC) as part of
Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn this talk\, we discuss the
geometry of compact quasi-Einstein manifolds with boundary. This topic is
directly related to warped product Einstein metrics\, static spaces and s
mooth metric measure spaces. We show that a 3-dimensional simply connected
compact quasi-Einstein manifold with boundary and constant scalar curvatu
re must be isometric to either the standard hemisphere $S^3_{+}\,$ or the
cylinder $I\\times S^2$ with product metric. For dimension n=4\, we prove
that a 4-dimensional simply connected compact quasi-Einstein manifold with
boundary and constant scalar curvature is isometric to either the standar
d hemisphere $S^4_{+}\,$ or the cylinder $I\\times S^3$ with product metri
c\, or the product space $S^2_{+}\\times S^2$ with the doubly warped produ
ct metric. Other related results for arbitrary dimensions are also discuss
ed. This is a joint work with J. Costa and D. Zhou.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakob Stein (Unicamp)
DTSTART;VALUE=DATE-TIME:20240503T170000Z
DTEND;VALUE=DATE-TIME:20240503T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/72
DESCRIPTION:Title: Instantons on asymptotically local conical G2 metrics\nby
Jakob Stein (Unicamp) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstra
ct\nAsymptotically locally conical (ALC) metrics can be viewed as higher-d
imensional analogues of ALF gravitational instantons\, such as the Taub-NU
T metric. In the setting of special holonomy\, families of Yang-Mills inst
antons on ALC G2-metrics are expected to display some of the same features
as the families of instantons on ALF spaces\, studied recently by Cherkis
-Larrain-Hubach-Stern. We will demonstrate this relationship explicitly in
the cohomogeneity one setting\, and study the behaviour of Yang-Mills ins
tantons as the underlying geometry varies in a one-parameter family. This
talk features two ongoing joint works\, one with Matt Turner\, and one wi
th Lorenzo Foscolo and Calum Ross.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Gorginyan (IMPA)
DTSTART;VALUE=DATE-TIME:20240517T170000Z
DTEND;VALUE=DATE-TIME:20240517T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/73
DESCRIPTION:Title: Quaternionic-solvable hypercomplex nilmanifolds\nby Yulia
Gorginyan (IMPA) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nA
hypercomplex structure on a Lie algebra is a triple of complex structures
I\, J\, and K satisfying the quaternionic relations. A quaternionic-solva
ble Lie algebra is a Lie algebra\, admitting a finite filtration by quater
nionic-invariant subalgebras\, such that each successive quotient is abeli
an. We will discuss the quaternionic-solvable hypercomplex structures on a
nilpotent Lie algebra and hypercomplex nilmanifolds\, corresponding to th
em.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Vittone (UNRosario)
DTSTART;VALUE=DATE-TIME:20240531T170000Z
DTEND;VALUE=DATE-TIME:20240531T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/74
DESCRIPTION:Title: Nullity and Symmetry in homogeneous Spaces\nby Francisco V
ittone (UNRosario) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\
nIn any Riemannian manifold one can define two natural subspaces of each t
angent space. The first is given by the nullity of the curvature tensor\,
and the second is given by the parallel Killing vector fields at a point (
transvections). In a homogeneous spaces\, both subspaces allow to define i
nvariant distributions\, called the nullity distribution and the distribut
ion of symmetry\, which are related to each other. We present some recent
works which study the restrictions that the existence of nullity imposes i
n the Lie algebra of the whole isometry group of a Riemannian homogeneous
space and its relation to the distribution of symmetry. We finally introdu
ce some work in progress on the extension of these concepts to Lorentzian
homogeneous spaces.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yamile Godoy (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20240614T170000Z
DTEND;VALUE=DATE-TIME:20240614T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/75
DESCRIPTION:Title: Tangent ray foliations and outer billiards\nby Yamile Godo
y (Universidad Nacional de Córdoba) as part of Geometry Webinar AmSur /Am
Sul\n\nInteractive livestream: https://meet.google.com/nzd-idoy-zej\nView-
only livestream: https://meet.google.com/nzd-idoy-zej\n\nAbstract\nGiven a
smooth closed strictly convex curve $\\gamma$ in the plane and a point $x
$ outside of $\\gamma$\, there are two tangent lines to $\\gamma$ throug
h $x$\; choose one of them consistently\, say\, the right one from the vie
wpoint of $x$\, and the outer billiard map $B$ is defined by reflecting $
x$ about the point of tangency. We observe that the good definition and th
e injectivity of the plane outer billiard map is a consequence of the fact
that the tangent rays associated to both tangent vectors to $\\gamma$ det
ermine foliations of the exterior of the curve. \n\nIn this talk\, we w
ill present the results obtained from a generalization of the problem of d
efining outer billiards in higher dimensions. Let $v$ be a smooth unit ve
ctor field on a complete\, umbilic (but not totally geodesic) hypersurface
$N$ in a space form\; for example on the unit sphere $S^{2k-1} \\subset \
\mathbb{R}^{2k}$\, or on a horosphere in hyperbolic space. We give necessa
ry and sufficient conditions on $v$ for the rays with initial velocities $
v$ (and $-v$) to foliate the exterior $U$ of $N$. We find and explore rela
tionships among these vector fields and geodesic vector fields on $N$. Whe
n the rays corresponding to each of $\\pm v$ foliate $U$\, $v$ induces an
outer billiard map whose billiard table is $U$. We describe the unit vecto
r fields on $N$ whose associated outer billiard map is volume preserving.\
n\nThis is a joint work with Michael Harrison (Institute for Advanced Stud
y\, Princeton) and Marcos Salvai (UNC\, Argentina).\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/75/
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Tolcachier (UNCordoba)
DTSTART;VALUE=DATE-TIME:20240419T170000Z
DTEND;VALUE=DATE-TIME:20240419T180000Z
DTSTAMP;VALUE=DATE-TIME:20240614T063408Z
UID:AmSurAmSulGeometry/76
DESCRIPTION:Title: Complex solvmanifolds with holomorphically trivial canonical b
undle\nby Alejandro Tolcachier (UNCordoba) as part of Geometry Webinar
AmSur /AmSul\n\n\nAbstract\nThe canonical bundle of a complex manifold $(
M\,J)$\, with $\\operatorname{dim}_{\\mathbb{C}} M=n$\, is defined as the
$n$-th exterior power of its holomorphic tangent bundle and it is a holomo
rphic line bundle over $M$. Complex manifolds with holomorphically trivial
canonical bundle are important in differential\, complex\, and algebraic
geometry and also have relations with theoretical physics. It is well know
n that every nilmanifold $\\Gamma\\backslash G$ equipped with an invariant
complex structure has (holomorphically) trivial canonical bundle\, due to
the existence of an invariant \n (holomorphic) trivializing section. For
complex solvmanifolds such a section may or may not exist. In this talk\,
we will see an example of a complex solvmanifold with a non-invariant triv
ializing holomorphic section of its canonical bundle. This new phenomenon
lead us to study the existence of holomorphic trivializing sections in two
stages. In the invariant case\, we will characterize this existence in te
rms of the 1-form $\\psi$ naturally defined in terms of the Lie algebra of
$G$ and $J$ by $\\psi(x)=\\operatorname{Tr} (J\\operatorname{ad} x)-\\ope
ratorname{Tr} \\operatorname{ad} (Jx)$. For the non-invariant case\, we wi
ll provide an algebraic obstruction for a solvmanifold to have a trivial c
anonical bundle (or\, more generally\, holomorphically torsion) and we wil
l explicitly construct\, in certain examples\, a trivializing section of t
he canonical bundle that is non-invariant. We will apply this construction
to hypercomplex geometry to provide a negative answer to a question posed
by M. Verbitsky. Based on joint work with Adrián Andrada.\n
LOCATION:https://researchseminars.org/talk/AmSurAmSulGeometry/76/
END:VEVENT
END:VCALENDAR