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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:20240910T214235Z
UID:AmSurAmSulGeometry/1
DESCRIPTION:Title: Harmonic flow of geometric structures\nby Henrique S
a Earp (Unicamp) as part of Geometry Webinar AmSur /AmSul\n\nAbstract: TBA
\n
LOCATION:
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:20240910T214235Z
UID:AmSurAmSulGeometry/2
DESCRIPTION:Title: Abelian almost contact structures and connections with s
kew-symmetric torsion\nby Adrian Andrada (Universidad Nacional de Cór
doba) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nAbelian comp
lex structures on Lie groups have proved to be very useful in several area
s of differential and complex geometry. In particular\, an abelian hyperco
mplex structure on a Lie group G (that is\, a pair of anticommuting abelia
n complex structures)\, together with a compatible inner product\, gives r
ise to an invariant hyperKähler with torsion (HKT) structure on G. This m
eans that G admits a (unique) metric connection with skew-symmetric torsio
n (called the Bismut connection) which parallelizes the hypercomplex struc
ture. \nIn this talk we move to the odd-dimensional case and we introduce
the notion of abelian almost contact structures on Lie groups. We study th
eir properties and their relations with compatible metrics. Next we consid
er almost 3-contact Lie groups where each almost contact structure is abel
ian. We study their main properties and we give their classification in di
mension 7. After adding compatible Riemannian metrics\, we study the exist
ence of a certain type of metric connections with skew symmetric torsion\,
introduced recently by Agricola and Dileo and called canonical connection
s. We provide examples of such groups in each dimension 4n+3 and show that
they admit co-compact discrete subgroups\, which give rise to compact alm
ost 3-contact metric manifolds equipped with canonical connections.\n\nTo
participate in the webinar\, please request the link to geodif@unicamp.br
with subject "Webinar AmSur".\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/3
DESCRIPTION:Title: Systolic inequalities for minimal projective planes in R
iemannian projective spaces\nby Lucas Ambrozio (University of Warwick)
as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nThe word "systole
" is commonly used in Geometry to denote the infimum of the length of hom
otopically non-trivial loops in a compact Riemmanian manifold M. In a gene
ralised sense\, we may use it also to refer to the infimum of the k-dimens
ional volume of a class of k-dimensional submanifolds that represent some
non-trivial topology of M. In this talk\, we will discuss some inequalitie
s comparing the systole to other geometric invariants\, e.g. the total vol
ume of M. After reviewing in details the celebrated inequality of Pu regar
ding the systole of Riemannian projective planes\, we will discuss its gen
eralisations to higher dimensions. This is joint work with Rafael Montezum
a.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/4
DESCRIPTION:Title: On integrality for Frobenius manifolds\nby John Alex
ander Cruz Morales (Universidad Nacional de Colombia) as part of Geometry
Webinar AmSur /AmSul\n\n\nAbstract\nWe will revisit the computations of St
okes matrices for tt*-structures done by Cecotti and Vafa in the 90's in t
he context of Frobenius manifolds and the so-called monodromy identity. W
e will argue that those cases provide examples of non-commutative Hodge st
ructures of exponential type in the sense of Katzarkov\, Kontsevich and Pa
ntev.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/5
DESCRIPTION:Title: Uniform measures of dimension 1\nby Mircea Petrache
(Pontificia Universidad Católica de Chile) as part of Geometry Webinar Am
Sur /AmSul\n\n\nAbstract\nIn his fundamental 1987 paper on the geometry of
measures\, Preiss posed the problem of classifying uniform measures in d-
dimensional Euclidean space\, a question at the interface of measure theor
y and differential geometry.\n\n A uniform measure is a positive measure
such that for all $r>0$\, all balls of radius $r$ with center in the suppo
rt of the measure\, are given equal masses.\n It was proved by Kirchheim-P
reiss that a uniform measure in $\\mathbb{R}^d$ is a multiple of the k-dim
ensional Hausdorff measure restricted to a k-dimensional analytic variety.
This establishes the link to differential geometry. An important class of
uniform measures are G-invariant measures\, for G any subgroup of isometr
ies of Euclidean space. These are called homogeneous measures. Intriguing
examples 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 n
ot well understood\, making Preiss' classification question is still widel
y open.\n\n After a historical survey\, I will describe a recent joint pap
er with Paul Laurain\, about uniform measures of dimension 1 in d-dimensio
nal Euclidean space: we prove by a direct approach that these are all give
n by at most countable unions of congruent helices or of congruent toric k
nots. In particular\, 1-dimensional uniform measures with connected suppor
t are homogeneous.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/6
DESCRIPTION:Title: (Purely) coclosed G$_2$-structures on 2-step nilmanifold
s\nby Viviana del Barco (Université Paris-Sud) as part of Geometry We
binar AmSur /AmSul\n\n\nAbstract\nIn Riemannian geometry\, simply connecte
d nilpotent Lie groups endowed with left-invariant metrics\, and their com
pact quotients\, have been the source of valuable examples in the field.
This motivated several authors to study\, in particular\, left-invariant
G$_2$-structures on 7-dimensional nilpotent Lie groups. These structures
could also be induced to the associated compact quotients\, also known as
{\\em nilmanifolds}.\n\nLeft-invariant torsion free G$_2$-structures\, tha
t is\, defined by a simultaneously closed and coclosed positive $3$-form\,
do not exist on nilpotent Lie groups. But relaxations of this condition h
ave been the subject of study on nilmanifolds lately. One of them are cocl
osed G$_2$-structures\, for which the defining $3$-form verifies $d \\star
_{\\varphi}\\varphi=0$\, and more specifically\, purely coclosed structur
es\, which are defined as those which are coclosed and satisfy $\\varphi\\
wedge d \\varphi=0$. \n\nIn this talk\, there will be presented recent cla
ssification results regarding left-invariant coclosed and purely coclosed
G$_2$-structures on 2-step nilpotent Lie groups. Our techniques exploit t
he correspondence between left-invariant tensors on the Lie group and thei
r linear analogues at the Lie algebra level.\nIn particular\, left-invaria
nt G$_2$-structures on a Lie group will be seen as alternating trilinear f
orms defined on the Lie algebra. The coclosed condition now refers to the
Chevalley-Eilenberg differential of the Lie algebra.\nWe also rely on the
particular Lie algebraic structure of metric 2-step nilpotent Lie algebra
s.\n\nOur goals are twofold. On the one hand we give the isomorphism class
es of 2-step nilpotent Lie algebras admitting purely coclosed G$_2$-struct
ures. The analogous result for coclosed structures was obtained by Bagagli
ni\, Fern\\'andez and Fino [Forum Math. 2018]. \n\nOn the other hand\, we
focus on the question of {\\em which metrics} on these Lie algebras can be
induced by a coclosed or purely coclosed structure. We show that any lef
t-invariant 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 ob
tain a method to construct purely coclosed G$_2$-structures. As a conseque
nce\, we obtain new examples of compact nilmanifolds carrying purely cocl
osed G$_2$-structures.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/7
DESCRIPTION:Title: Gap theorems for free-boundary submanifolds\nby Marc
os Petrucio Cavalcante (Universidade Federal de Alagoas) as part of Geomet
ry Webinar AmSur /AmSul\n\n\nAbstract\nLet $M^n$ be a compact $n$-dimensio
nal manifold 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 fro
m the famous Simons pinching theorem that if $|A|^2\\leq \\frac{n}{2-\\fra
c{1}{k}}$\, then either $|A|^2=0$ or $|A|^2=\\frac{n}{2-\\frac{1}{k}}$. Th
e submanifolds on which $|A|^2=\\frac{n}{2-\\frac{1}{k}}$ were characteriz
ed by Lawson (when $k=1$) and by Chern-do Carmo-Kobayashi (for any $k$). \
n\nThese important results say that there exists a gap in the space of min
imal submanifolds in $S^{n+k}$ in terms of the length of their second fund
amental forms and their dimensions. \n\nLatter\, Lawson and Simons proved
a topological gap result without making any assumption on the mean curvatu
re of the submanifold. Namely\, they proved that if $M^n$ is a compact sub
manifold 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 particular\, if $|A|^2< \\min\\{n-1\, 2\\sqrt{n-1}\\}$\, then $M$ is
a homotopy sphere. \n\nIt is well known that free-boundary minimal submani
folds in the unit ball share similar properties as compact minimal submani
folds in the round sphere. For instance\, Ambrozio and Nunes obtained a ge
ometric gap type theorem for free-boundary minimal surfaces $M$ in the Euc
lidean unit $3$-ball $B^3$. They proved that if $|A|^2(x)\\langle x\, N(x)
\\rangle^2\\leq 2$\, 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 first part of this talk\, I will present a generalization of Ambrozio
and Nunes theorem for constant mean curvature surfaces. Precisely\, if the
traceless second fundamental form $\\phi$ of a free-boundary CMC surface
$B^3$ satisfies $|\\phi|^2(x)\\langle x\, N(x)\\rangle^2\\leq (2+H\\langl
e x\, N(x)\\rangle )^2/2$ then $M$ is either a spherical cap or a portion
of a Delaunay surface. This is joint work with Barbosa and Pereira.\n\nIn
the second part\, I will present a topological gap theorem for free-bounda
ry submanifolds in the unit ball. More precisely\, if $|\\phi|^2\\leq \\fr
ac{np}{n-p}$\, then the $p$-th cohomology group of $M$ with real coefficie
nts vanishes. In particular\, if $|\\phi|^2\\leq \\frac{n}{n-1}$\, then $M
$ has only one boundary component. This is joint work with Mendes and Vit
ório.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/9
DESCRIPTION:Title: Pseudo-holomorphic curves and applications to geodesic
flows\nby Umberto Hryniewicz (RWTH Aachen University) as part of Geome
try Webinar AmSur /AmSul\n\n\nAbstract\nThis talk is intended to survey ap
plications of pseudo-holomorphic curves to Reeb ows in dimension three\, w
ith an eye towards geometry. For the geometer the interest stems from the
fact that geodesic \nflows are particular examples of Reeb flows. I will d
iscuss characterizations of lens spaces\, existence/non-existence of close
d geodesics with a given knot type under pinching conditions on the curvat
ure\, sharp systolic inequalities\, existence of elliptic dynamics (in rel
ation to an old conjecture of Poincaré)\, and generalizations of Birkhoff
's annular global surface of section for positively curved 2-spheres.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/10
DESCRIPTION:Title: Diameter and Laplace eigenvalue estimates for homogeneo
us Riemannian manifolds\nby Emilio Lauret (Universidad Nacional del Su
r) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nGiven $G$ a com
pact Lie group and $K$ a closed subgroup of it\, we will study whether the
functional $\\lambda_1(G/K\,g) \\textrm{diam}(G/K\,g)^2$ is bounded by ab
ove among $G$-invariant metrics $g$ on the (compact) homogeneous space $G/
K$. Here\, $\\textrm{diam}(G/K\,g)$ and $\\lambda_1(G/K\,g)$ denote the di
ameter and the smallest positive eigenvalue of the Laplace-Beltrami operat
or associated to $(G/K\,g)$.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/11
DESCRIPTION:Title: A stochastic half-space theorem for minimal surfaces of
$\\mathbb{R}^{3}$.\nby Gregorio Pacelli (Universidade Federal do Cear
á) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nI will talk ab
out a stochastic 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
(recurrent) minimal surface immersed in $\\mathbb{R}^{3}$. Then $\\Sigma \
\cap M \\neq \\emptyset$ unless they are parallel planes. \nThis is a work
in progress with Luquesio Jorge and Leandro Pessoa.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/12
DESCRIPTION:Title: The prescribed Ricci curvature problem for naturally re
ductive metrics on simple Lie groups\nby Romina Arroyo (Universidad Na
cional Cordoba) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nOn
e of the most important challenges of Riemannian geometry is to understand
the Ricci curvature tensor. An interesting open problem related with it i
s to find a Riemannian metric whose Ricci curvature is prescribed\, that i
s\, a Riemannian metric $g$ and a real number $c>0$ satisfying\n\\[\n\\ope
ratorname{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 proble
m within the class of naturally reductive metrics when $M$ is a simple Lie
group\, and present recently obtained results in this setting. \n\nThis t
alk is based on joint works with Mark Gould (The University of Queensland)
Artem Pulemotov (The University of Queensland) and Wolfgang Ziller (Unive
rsity of Pennsylvania).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/13
DESCRIPTION:Title: Convergence of manifolds under volume convergence and u
niform diameter and tensor bounds\nby Raquel Perales (Unam) as part of
Geometry Webinar AmSur /AmSul\n\n\nAbstract\nBased on join work with Alle
n-Sormani and Cabrera Pacheco-Ketterer. Given a Riemannian manifold $M$ an
d a pair of Riemannian tensors $g_0 \\leq g_j$ on $M$ it follows that $vo
l(M)\\leq vol_j(M)$. 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 me
trics $g_j$ defined on $M$ that satisfy \n$g_0\\leq g_j$\, $diam (M_j) \\l
eq D$ and $vol(M_j)\\to vol(M_0)$ then $(M\,g_j)$ converge to $(M\,g_0)$ i
n the volume preserving intrinsic flat sense. I will present examples dem
onstrating that under these conditions we do not necessarily obtain smooth
\, $C^0$ or Gromov-Hausdorff convergence.\n\nFurthermore\, this result can
be applied to show the stability of graphical tori.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/14
DESCRIPTION:Title: Compactness of free boundary CMC surfaces\nby Nicol
au S. Aiex (Auckland) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstra
ct\nWe will talk about the compactness of the space of CMC surfaces on amb
ient manifolds with positive Ricci curvature and convex boundary. We chara
cterize compactness based on geometric information on the surface. This
is analogous to a result of Fraser-Li on free boundary minimal surfaces\,
however\, the lack of a Steklov eigenvalue lower bound makes the proof fa
irly different. The proof is an adaptation of White's proof of the compact
ness of stationary surfaces of parametric elliptic functionals. This is a
joint work with Han Hong.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/15
DESCRIPTION:Title: Sharp systolic inequalities for $3$-manifolds with boun
dary\nby Eduardo R. Longa (USP) as part of Geometry Webinar AmSur /AmS
ul\n\n\nAbstract\nSystolic Geometry dates back to the late 1940s\, with th
e work of Loewner and his student\, Pu. This branch of differential geome
try received more attention after the seminal work of Gromov\, where he p
roved his famous systolic inequality and introduced many important concept
s. In this talk I will recall the notion of systole and present some sharp
systolic inequalities for free boundary surfaces in $3$-manifolds.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/16
DESCRIPTION:Title: Non Canonical Metrics on Diff($S^1$)\nby Daniel Pon
s (UNAB) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nWe review
some of V.I. Arnold’s ideas on diffeomorphism groups on manifolds. When
the underlying manifold is the circle\, we study the geometry of such a g
roup endowed with some metrics.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/17
DESCRIPTION:Title: Deformed G2-instantons\nby Jason Lotay (University
of Oxford) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nDeforme
d G2-instantons are special connections occurring in G2 geometry in 7 dime
nsions. They arise as "mirrors" to certain calibrated cycles\, providing a
n analogue to deformed Hermitian-Yang-Mills connections\, and are critical
points of Chern-Simons-type functional. I will describe an elementary con
struction of the first non-trivial examples of deformed G2-instantons\, an
d their relation to 3-Sasakian geometry\, nearly parallel G2-structures\,
isometric G2-structures\, obstructions in deformation theory\, the topolog
y of the moduli space\, and the Chern-Simons-type functional.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/18
DESCRIPTION:Title: Graft surgeries\nby Elizabeth Gasparim (Universidad
de Norte) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nI will
explain the new concepts of graft surgeries which allow us to modify surf
aces\, Calabi-Yau threefolds and vector bundles over them\, producing a
variety of ways to describe local characteristic classes. In particular\
, we generalize the construction of conifold transition presented by Smit
h-Thomas-Yau.This is joint work with Bruno Suzuki\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/19
DESCRIPTION:Title: Invariant Einstein metrics on real flag manifolds\n
by Lino Grama (Universidade Estadual de Campinas) as part of Geometry Webi
nar AmSur /AmSul\n\n\nAbstract\nIn this talk we will discuss the classific
ation of invariant Einstein metrics on real flag manifolds associated to s
imple and non-compact split real forms of complex classical Lie algebras w
hose isotropy representation decomposes into two or three irreducible sub-
representations. We also discuss some phenomena in real flag manifolds tha
t can not happen in complex flag manifolds. This includes the non-existenc
e of invariant Einstein metric and examples of non-diagonal Einstein metri
cs. This is a joint work with Brian Grajales\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/20
DESCRIPTION:Title: Generalized Ricci flow\nby Mario Garcia-Fernandez (
Universidad Autónoma de Madrid) as part of Geometry Webinar AmSur /AmSul\
n\n\nAbstract\nThe generalized Ricci flow equation is a geometric evolutio
n\nequation which has recently emerged from investigations into\nmathemati
cal physics\, Hitchin’s generalized geometry program\, and\ncomplex geom
etry. The generalized Ricci flow can regarded as a tool for\nconstructing
canonical metrics in generalized geometry and complex\nnon-Kähler geometr
y\, and extends the fundamental Hamilton/Perelman\ntheory of Ricci flow. I
n this talk I will give an introduction to this\ntopic\, with a special em
phasis on examples and geometric aspects of the\ntheory. Based on joint wo
rk with Jeffrey Streets (UC Irvine)\,\narXiv:2008.07004.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/21
DESCRIPTION:Title: Short-time existence for the network flow\nby Marie
l Saez (Pontificia Universidad Católica de Chile) as part of Geometry Web
inar AmSur /AmSul\n\n\nAbstract\nThe network flow is a system of parabolic
differential equations that describes the motion of a family of curves in
which each of them evolves under curve-shortening flow. This problem aris
es naturally in physical phenomena and its solutions present a rich variet
y of behaviors. \n\nThe goal of this talk is to describe some properties o
f this geometric flow and to discuss an alternative proof of short-time ex
istence for non-regular initial conditions. The methods of our proof are b
ased on techniques of geometric microlocal analysis that have been used to
understand parabolic problems on spaces with conic singularities. This is
joint work with Jorge Lira\, Rafe Mazzeo\, and Alessandra Pluda.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/22
DESCRIPTION:Title: Singular Riemannian Foliations and Lie Groupoids\nb
y Ivan Struchiner (Universidade de São Paulo) as part of Geometry Webinar
AmSur /AmSul\n\n\nAbstract\nI will discuss the problem of obtaining a "Ho
lonomy 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 s
tating results which are valid for regular foliations and how they can be
obtained from the Holonomy groupoid of the foliation. Although we do not y
et know how to associate a holonomy groupoid to any SRF\, we can obtain th
e holonomy groupoid of the linearization of the SRF in a tubular neighbour
hood of (the closure of) a leaf. I will explain this construction.\n\nI wi
ll not assume that the audience has prior knowledge of Singular Riemannian
Foliations or of Lie Groupoids and will try to make the talk accessible t
o a broad audience.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/23
DESCRIPTION:Title: The asymptotic geometry of G$_2$-monopoles\nby Dani
el Fadel (Universidade Federal Fluminense) as part of Geometry Webinar AmS
ur /AmSul\n\n\nAbstract\nG$_2$-geometry is a very rich and vast subject in
Differential Geometry which has been seeing a \nlot of progress in the la
st two decades. There are by now very powerful methods that produce millio
ns of examples of G$_2$ holonomy metrics on the compact setting\n and infi
nitely many on the non-compact setting. Besides these fruitful advances\,
at present\, there is no systematic understanding of these metrics. In fac
t\, a very\n important problem in G$_2$-geometry is to develop methods to
distinguish G$_2$-manifolds. One approach intended at producing invariants
of G$_2$-manifolds is by means\n of higher dimensional gauge theory. G$_2
$-monopoles are solutions to a first order nonlinear PDE for pairs consist
ing of a connection on a principal bundle over \na noncompact G$_2$-manifo
ld and a section of the associated adjoint bundle. They arise as the dimen
sional reduction of the higher dimensional Spin$(7)$-instanton\n equation\
, and are special critical points of an intermediate energy functional rel
ated to the Yang-Mills-Higgs energy.\n\nDonaldson-Segal (2009) suggested t
hat one possible approach to produce an enumerative invariant of (noncompa
ct) G$_2$-manifolds is by considering a ``count" of G$_2$-monopoles\n and
this should be related to conjectural invariants ``counting" rigid coassoc
iate (codimension 3 and calibrated) cycles. Oliveira (2014) started the st
udy of G$_2$-monopoles\n providing the first concrete non-trivial examples
and giving evidence supporting the Donaldson-Segal program by finding fam
ilies of G$_2$-monopoles parametrized by a\n positive real number\, called
the mass\, which in the limit when such parameter goes to infinity concen
trate along a compact coassociative submanifold. In this talk I \nwill exp
lain some recent results\, obtained in collaboration with Ákos Nagy and G
onçalo Oliveira\, which show that the asymptotic behavior satisfied by th
e examples \nare in fact general phenomena which follows from natural assu
mptions such as the finiteness of the intermediate energy. This is a very
much needed development in \norder to produce a satisfactory moduli theory
and making progress towards a rigorous definition of the putative invaria
nt. Time permitting\, I will mention some \ninteresting open problems and
possible future directions in this theory.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/24
DESCRIPTION:Title: Balanced metrics and the Hull-Strominger system\nby
Anna Fino (Università di Torino) as part of Geometry Webinar AmSur /AmSu
l\n\n\nAbstract\nA Hermitian metric on a complex manifold is balanced if i
ts fundamental form is co-closed. An important tool for the study of balan
ced manifolds is the Hull-Strominger system. \nIn the talk I will rev
iew some general results about balanced metrics and present new smoo
th solutions to the Hull-Strominger system\, showing that the Fu-Yau solut
ion on torus bundles over K3 surfaces can be generalized to torus bundles
over K3 orbifolds. The talk is based on a joint work with G. Grantcharo
v and L. Vezzoni.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/25
DESCRIPTION:Title: Existence and non existence of complete area minimizing
surfaces in $\\mathbb{E}(-1\,\\tau)$.\nby Álvaro Krüger Ramos (Univ
ersidade 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 sp
ace of a fibration over $\\mathbb{H}^2$ with bundle curvature $\\tau$. Giv
en a finite collection of simple closed curves in $\\partial_{\\infty}|mat
hbb{E}(-1\,\\tau)$\, we provide sufficient conditions on $\\Gamma$ so that
there exists an area minimizing surface $\\Sigma$ in $\\mathbb{E}(-1\,\\t
au)$ with asymptotic boundary $\\Gamma$. We also present necessary conditi
ons for such a surface $\\Sigma$ to exist. This is joint work with P. Klas
er and A. Menezes.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/26
DESCRIPTION:Title: Isolated singularities of Elliptic Linear Weingarten gr
aphs\nby Asun Jiménez (Universidade Federal Fluminense) as part of Ge
ometry Webinar AmSur /AmSul\n\n\nAbstract\nIn this talk we will study isol
ated singularities of graphs whose mean and Gaussian curvature satisfy the
elliptic linear relation $2\\alpha H+\\beta K=1$\, $\\alpha^2+\\beta>0$.
This family of surfaces includes convex and non-convex singular surfaces a
nd also cusp-type surfaces. We determine in which cases the singularity is
in fact removable\, and classify non-removable isolated singularities in
terms of regular analytic strictly convex curves in $S^2$. This is a joint
work with João P. dos Santos.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/27
DESCRIPTION:Title: Fundamentals of Lie theory for groupoids and algebroids
\nby María Amelia Salazar (Universidade Federal Fluminense) as part o
f Geometry Webinar AmSur /AmSul\n\n\nAbstract\nThe foundation of Lie theor
y is Lie's three theorems that provide a construction of the Lie algebra a
ssociated to any Lie group\; the converses of Lie's theorems provide an in
tegration\, i.e. a mechanism for constructing a Lie group out of a Lie alg
ebra. The Lie theory for groupoids and algebroids has many analogous resul
ts to those for Lie groups and Lie algebras\, however\, it differs in impo
rtant respects: one of these aspects is that there are Lie algebroids whic
h do not admit any integration by a Lie groupoid. In joint work with Cabre
ra and Marcut\, we showed that the non-integrability issue can be overcome
by considering local Lie groupoids instead. In this talk I will explain a
construction of a local Lie groupoid integrating a given Lie algebroid an
d I will point out the similarities with the classical theory for Lie grou
ps and Lie algebras.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/28
DESCRIPTION:Title: Biharmonic hypersurfaces in hemispheres\nby Matheus
Vieira (Universidade Federal do Espírito Santo) as part of Geometry Webi
nar AmSur /AmSul\n\n\nAbstract\nWe consider the Balmuş -Montaldo-Oniciuc'
s conjecture in the case of hemispheres. We prove that a compact non-minim
al biharmonic hypersurface in a hemisphere of $S^{n+1}$ must be the small
hypersphere $S^n(1/\\sqrt{2})$\, provided that $n^2-H^2$ does not change s
ign.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/29
DESCRIPTION:Title: Minimal spheres in ellipsoids\nby Paolo Piccione (U
niversidade de São Paulo) as part of Geometry Webinar AmSur /AmSul\n\n\nA
bstract\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.\, d
etermined by the intersection with a hyperplane. While this is the case if
the ellipsoid is nearly round\, Haslhofer and Ketover have recently shown
the existence of an embedded non-planar minimal 2-sphere in sufficiently
elongated ellipsoids\, with min-max methods. Using bifurcation theory and
the symmetries that arise in the case where at least two semi-axes coincid
e\, we show the existence of arbitrarily many distinct embedded non-planar
minimal 2-spheres in sufficiently elongated ellipsoids of revolution. Thi
s is based on joint work with R. G. Bettiol..\n
LOCATION:https://master.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:20240910T214235Z
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\nAbstr
act\nI shall describe the geometry underlying known examples of explicit m
etrics with holonomy $\\mathrm{SU}(2)$ (dimension 4) and $\\mathrm{G}_2$ (
dimension 7)\, arising from the action of both nilpotent and simple Lie gr
oups.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/31
DESCRIPTION:Title: A diameter gap for isometric quotients of the unit sphe
re\nby Claudio Gorodski (USP) as part of Geometry Webinar AmSur /AmSul
\n\n\nAbstract\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 iso
metric group action has diameter zero or at least\n$\\epsilon$. The novelt
y is the independence of $\\epsilon$ from~$n$.\nThe classification of fini
te simple groups is used in the proof.\n\n(Joint work with C. Lange\, A. L
ytchak and R. A. E. Mendes.)\n
LOCATION:https://master.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:20240910T214235Z
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 $J$-Hermi
tian metric $g$ on a complex manifold $(M\,J)$ is called strong Kähler wi
th torsion (SKT for short) if its $2$-fundamental form $\\omega:=g(J\\cdot
\,\\cdot)$ satisfies $\\partial \\bar \\partial \\omega =0$. \n\nThe aim o
f this talk is to discuss the existence of invariant SKT structures on nil
manifolds. We will prove that any nilmanifold admitting an invariant SKT s
tructure is either a torus or $2$-step nilpotent\, and we will provide exa
mples of invariant SKT structures on $2$-step nilmanifolds in arbitrary di
mensions. \n\nThis talk is based on a joint work with Marina Nicolini.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/34
DESCRIPTION:Title: Geometry and information\nby Sueli I. R. Costa (Uni
versity of Campinas - Brazil) as part of Geometry Webinar AmSur /AmSul\n\n
\nAbstract\nIn this talk it will be presented an introduction and some rec
ent developments in two topics of Geometry we have been working which have
applications in Communications: Lattices and Information Geometry. Lattic
es are discrete additive subgroups of the n-dimensional Euclidean space an
d have been used in coding for reliability and security in transmissions
through different channels. Currently Lattice based cryptography is one of
the main subareas of the so called Post-quantum Cryptography. Information
Geometry is devoted to the study of statistical manifolds of probability
distributions by considering different metrics and divergence measures an
d have been used in several applications related to data analysis. We will
approach here particularly the space of multivariate normal distribution
s 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 Secur
e\nCommunications” Springer\, 2017 \n- S. I. R. Costa\, S. A. Santos\,
J. A . Strapasson\, Fisher information distance: A geometrical reading”
Discrete Applied Mathematics\, 197\, 59-69 (2015)\n- J. Pinele \, J. Str
apasson\, S. I. R. Costa\, The Fisher–Rao Distance between Multivariate
between Multivariate Normal Distributions: Special Cases\, Bounds and App
lications\, Entropy 2020\, 22\, 404\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/35
DESCRIPTION:Title: Associative submanifolds in Joyce's generalised Kummer
construction\nby Shubham Dwivedi (Humboldt University\, Berlin) as par
t of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nAssociative submanifolds
are special 3-dimensional manifolds in $\\mathrm{G_2}$ manifolds which ar
e 7-dimensional. They are examples of calibrated submanifolds and there is
a research programme that attempts to count them in order to define numer
ical invariants of $\\mathrm{G_2}$ manifolds\, similar to Gromov-Witten in
variants. However the scarcity of examples of associative submanifolds ma
kes it difficult to work out the details of this programme. In the talk I
will explain how to construct associatives in $\\mathrm{G_2}$ manifolds co
nstructed by Joyce\, whose existence had previously been predicted by phy
sicists. The talk is based on a joint work with Daniel Platt (King's Colle
ge London) and Thomas Walpuski (Humboldt University\, Berlin).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/36
DESCRIPTION:Title: Levi-Civita Ricci-flat metrics on compact Hermitian Wey
l-Einstein manifolds\nby Eder Moraes Correa (UFMG/Unicamp) as part of
Geometry Webinar AmSur /AmSul\n\n\nAbstract\nAs shown in [2]\, the first A
eppli-Chern class of a compact Hermitian manifold can be represented by it
s first Levi-Civita Ricci curvature. From this\, a natural question to ask
(inspired by the Calabi-Yau theorem [3]) is the following: On a compact c
omplex manifold with vanishing first Aeppli-Chern class\, does there exist
a smooth Levi-Civita Ricci-flat Hermitian metric? In general\, it is part
icularly challenging to solve the Levi-Civita Ricci-flat equation\, since
there are non-elliptic terms involved in the underlying PDE problem. In th
is talk\, we will investigate the above question in the setting of compact
Hermitian Weyl-Einstein manifolds. The main purpose is to show that every
compact Hermitian Weyl-Einstein manifold admits a Levi-Civita Ricci-flat
Hermitian metric [1]. This result generalizes previous constructions on Ho
pf manifolds [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] L
iu\, K.\; Yang\, X.\; Ricci curvatures on Hermitian manifolds\, Trans. Ame
r. Math. Soc. 369 (2017)\, no. 7\, 5157-5196.\n\n[3] Yau\, S.-T.\; On the
Ricci curvature of a compact Kähler manifold and the complex Monge-Ampèr
e equation. I\, Comm. Pure Appl. Math. 31 (1978)\, no. 3\, 339-411. MR4803
50.\n
LOCATION:https://master.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:20240910T214235Z
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 interpreted as a critical point of the energy functional\, restricted t
o its isometric class. Hence\, it represents the better $G_2$-structure in
a given family. These kinds of $G_2$-structures are an alternative for th
e study of $G_2$-geometry\, in cases when the torsion free problem is eith
er trivial or obstructed. In general\, there are some known classes of $G_
2$-structures with free-divergence torsion\, namely closed and nearly para
llel $G_2$-structures. In this talk\, we are going to present some unknown
classes of invariant $G_2$-structures with free divergence torsion\, spec
ifically in the context of the 7-sphere and of the solvable Lie groups wit
h a codimension-one Abelian normal subgroup.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/38
DESCRIPTION:Title: Special Lagrangians and Lagrangian mean curvature flow<
/a>\nby Gonçalo Oliveira (UFF) as part of Geometry Webinar AmSur /AmSul\n
\n\nAbstract\n(joint work with Jason Lotay) Richard Thomas and Shing-Tung-
Yau proposed two conjectures on the existence of special Lagrangian subman
ifolds and on the use of Lagrangian mean curvature flow to find them. In t
his talk\, I will report on joint work with Jason Lotay to prove these on
certain symmetric hyperKahler 4-manifolds. If time permits I may also comm
ent on our work in progress to tackle more refined conjectures of Dominic
Joyce regarding the existence of Bridgeland stability conditions on Fukaya
categories and their interplay with Lagrangian mean curvature flow.\n
LOCATION:https://master.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:20240910T214235Z
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\nAbstract\nIn this lecture we establish a natural framework for the stud
y of mean curvature flow solitons in warped product spaces. Our approach a
llows us to identify some natural geometric quantities that satisfy ellipt
ic equations or differential inequalities in a simple and manageable form
for which the machinery of weak maximum principles is valid. The latter is
one of the main tools we apply to derive several new characterizations an
d rigidity results for MCFS that extend to our general setting known prope
rties\, for instance\, in Euclidean space. Besides\, as in Euclidean space
\, MCFS are also stationary immersions for a weighted volume functional. U
nder this point of view\, we are able to find geometric conditions for fin
iteness of the index and some characterizations of stable solitons. \n\nTh
e results of this lecture have been obtained in collaboration with Jorge H
. de Lira\, from Universidade Federal do Ceará\, and Marco Rigoli\, from
Università 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
curvature flow solitons in the presence of conformal vector fields\, The J
ournal 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 sol
itons in warped product spaces. To appear in Revista Matemática Compluten
se (2022).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/40
DESCRIPTION:Title: Lie groupoids and singular Riemannian foliations\nb
y Ivan Struchiner (USP) as part of Geometry Webinar AmSur /AmSul\n\n\nAbst
ract\nI will discuss some aspects of the interplay between Lie groupoids a
nd singular Riemannian foliations. To each singular Riemannian foliation w
e associate a linear holonomy groupoid to a neighbourhood of each leaf. Th
is groupoid is a dense subgroupoid of a proper Lie groupoid. On the other
hand\, Lie groupoids with compatible metrics give rise to singular Riemann
ian foliations. We discuss how far these groupoids are from being a dense
subgroupoid of a proper Lie groupoid.\n\nThe talk will be based on joint w
ork with Marcos Alexandrino\, Marcelo Inagaki and Mateus de Melo.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/41
DESCRIPTION:Title: On the mean exit time of cylindrically bounded submanif
olds of $N\\times \\mathbb{R}$ with bounded mean curvature.\nby Gregor
io Pacelli Bessa (UFC) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstr
act\nWe show that the global mean exit time of cylindrically bounded subma
nifolds of $N\\times \\mathbb{R}$ is finite\, where the sectional curvatur
e $K_N\\leq b\\leq 0$.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/42
DESCRIPTION:Title: Zoll-like metrics in minimal surface theory\nby Luc
as Ambrozio (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
geodesics are periodic and have the same finite fundamental period. In pa
rticular\, (M\,g) is a compact manifold such that each tangent one-dimensi
onal subspace of each one of its points is tangent to some closed geodesic
. Since periodic geodesics are not only periodic orbits of a flow\, but al
so closed curves that are critical points of the length functional\, the n
otion of Zoll metrics admits natural generalisations in the context of min
imal submanifold theory\, that is\, the theory of critical points of the a
rea functional. In this talk\, based on joint work with F. Codá (Princeto
n) and A. Neves (UChicago)\, I will discuss why these new\, generalised no
tions seem relevant to me beyond its obvious geometric appeal\, and discus
s two different methods to obtain infinitely many such examples on spheres
\, with perhaps unexpected properties.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/43
DESCRIPTION:Title: A Nash type theorem and extrinsic surgeries for positiv
e scalar curvature\nby Luis Florit (IMPA) as part of Geometry Webinar
AmSur /AmSul\n\n\nAbstract\nAs shown by Gromov-Lawson and Stolz the only o
bstruction to the existence of positive scalar curvature metrics on closed
simply connected manifolds in dimensions at least five appears on spin ma
nifolds\, and is given by the non-vanishing of the α-genus of Hitchin.\n\
nWhen unobstructed we shall realise a positive scalar curvature metric by
an immersion into Euclidean space whose dimension is uniformly close to th
e classical Whitney upper bound for smooth immersions\, and it is in fact
equal to the Whitney bound in most dimensions. Our main tool is an extrin
sic counterpart of the well-known Gromov-Lawson surgery procedure for cons
tructing positive scalar curvature metrics.\n\nThis is a joint work with B
. Hanke published in Commun. Contemp. Math. 2022.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/44
DESCRIPTION:Title: Non-Kähler Calabi-Yau geometry and pluriclosed flow\nby Mario Garcia-Fernández (Universidad Autónoma de Madrid and ICMAT)
as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn this talk I wil
l overview joint work with J. Jordan and J. Streets\, in arXiv:2106.13716\
, about Hermitian\, pluriclosed metrics with vanishing Bismut-Ricci form.
These metrics give a natural extension of Calabi-Yau metrics to the settin
g of complex\, non-Kählermanifolds\, and arise independently in mathemati
cal physics. We reinterpret this condition in terms of the Hermitian-Einst
ein equation on an associated holomorphic Courant algebroid\, and thus ref
er to solutions as Bismut Hermitian-Einstein. This implies Mumford-Takemot
o slope stability obstructions\, and using these we exhibit infinitely man
y topologically distinct complex manifolds in every dimension with vanishi
ng first Chern class which do not admit Bismut Hermitian-Einstein metrics.
This reformulation also leads to a new description of pluriclosed flow\,
as introduced by Streets and Tian\, implying new global existence results.
In particular\, on all complex non-Kähler surfaces of nonnegative Kodair
a dimension. On complex manifolds which admit Bismut-flat metrics we show
global existence and convergence of pluriclosed flow to a Bismut-flat metr
ic.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/46
DESCRIPTION:Title: Isoparametric foliations and solutions of Yamabe type e
quations on manifolds with boundary.\nby Guillermo Henry (UBA) as part
of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nA foliation such that the
ir regular leaves are parallel CMC hypersurfaces is called isoparametric.
In this talk we are going to discuss some results on the existence of s
olutions of the Yamabe equation on compact Riemannian manifolds with bound
ary induced these type of foliations. Joint work with Juan Zuccotti.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/47
DESCRIPTION:Title: Nilmanifolds: examples and counterexamples in geometry
and topology\nby Raquel Villacampa (CUD- Zaragoza) as part of Geometry
Webinar AmSur /AmSul\n\n\nAbstract\nNilmanifolds are a special type of di
fferentiable compact manifolds defined as the quotient of a nilpotent\, si
mply connected Lie group by a lattice.\n\nSince Thurston used them in 1976
to show an example of a compact complex symplectic manifold being non-Kä
hler\, many other topological and geometrical questions have been answered
using nilmanifolds. In this talk we will show some of these problems suc
h as the holonomy of certain metric connections\, deformations of structur
es or spectral sequences.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/48
DESCRIPTION:Title: On the geometry and the curvature of 3-(α\, δ)-Sasaki
manifolds\nby Ilka Agricola (Marburg) as part of Geometry Webinar AmS
ur /AmSul\n\n\nAbstract\nWe consider $3$-$(\\alpha\, \\delta)$-Sasaki mani
folds\, generalizing the classic 3-Sasaki case. We show\nhow these are clo
sely related to various types of quaternionic Kähler orbifolds via connec
tions\nwith skew-torsion and a canonical submersion. Making use of this re
lation we discuss curvature operators and show that in dimension 7 many su
ch manifolds have strongly positive curvature. Joint work with Giulia Dile
o (Bari) and Leander Stecker (Hamburg).\n
LOCATION:https://master.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:20240910T214235Z
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\nAbs
tract\nA differential $p$-form $\\eta$ on a $n$-dimensional Riemannian man
ifold $(M\,g)$ is called Conformal Killing Yano (CKY for short) if it sati
sfies for any vector field $X$ the following equation\n\\[ \\nabla_X \\et
a=\\dfrac{1}{p+1}\\iota_X\\mathrm{d}\\eta-\\dfrac{1}{n-p+1}X^*\\wedge \\ma
thrm{d}^*\\eta\,\n\\]\nwhere $X^*$ is the dual 1-form of $X$\, $\\mathrm{
d}^*$ is the codifferential\, $\\nabla$ is the Levi-Civita connection asso
ciated to $g$ and $\\iota_X$ is the interior product with $X$. If $\\eta$
is coclosed ($\\mathrm d^*\\eta=0$) then $\\eta$ is said to be a Killing-Y
ano $p$-form (KY for short).\n\nWe study left invariant Conformal Killing
Yano $2$-forms on Lie groups endowed with a left invariant metric. We det
ermine\, up to isometry\, all $5$-dimensional metric Lie algebras under ce
rtain conditions\, admitting a CKY $2$-form. Moreover\, a characterization
of all possible CKY tensors on those metric Lie algebras is exhibited.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/50
DESCRIPTION:Title: Existence of free boundary constant mean curvature disk
s\nby 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 find disk-type surfaces with prescribed constant mean curvature whos
e boundary meets S orthogonally. When S is diffeomorphic to a sphere\, dir
ect minimization could lead to trivial solutions and hence min-max constru
ctions are needed. Among the earliest such constructions is the work of St
ruwe\, who produced the desired free boundary CMC disks for almost every m
ean curvature value up to that of the smallest round sphere enclosing S. I
n a previous joint work with Xin Zhou (Cornell)\, we combined Struwe's met
hod with other techniques to obtain an analogous result for CMC 2-spheres
in Riemannian 3-spheres and were able to remove the "almost every" restric
tion 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 ba
ck to the free boundary problem to refine and improve Struwe's result.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/51
DESCRIPTION:Title: Special classes of transversely Kähler almost contact
metric manifolds\nby Giulia Dileo (Univesity of Bari) as part of Geome
try Webinar AmSur /AmSul\n\n\nAbstract\nI will discuss some special classe
s of almost contact metric manifolds $(M\,\\varphi\,\\xi\,\\eta\,g)$ such
that the structure $(\\varphi\,g)$ is projectable along the 1-dimensional
foliation generated by $\\xi$\, and the transverse geometry is given by a
Kähler structure. I will focus on quasi-Sasakian manifolds and the new c
lass of anti-quasi-Sasakian manifolds. In this case\, the transverse geome
try 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 prin
cipal circle bundles\, investigate Riemannian curvature properties\, and t
he existence of connections with torsion preserving the structure. This is
a joint work with Dario Di Pinto (Bari).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/52
DESCRIPTION:Title: Universes as BigData: Physics\, Geometry and Machine-L
earning\nby Yang-Hui He (London Institute\, Royal Institution & Merton
College\, Oxford University) as part of Geometry Webinar AmSur /AmSul\n\n
\nAbstract\nThe search for the Theory of Everything has led to superstring
theory\, which then led physics\, first to algebraic/differential geometr
y/topology\, and then to computational geometry\, and now to data science.
\nWith a concrete playground of the geometric landscape\, accumulated by t
he collaboration of physicists\, mathematicians and computer scientists ov
er the last 4 decades\, we show how the latest techniques in machine-learn
ing can help explore problems of interest to theoretical physics and to pu
re mathematics.\nAt the core of our programme is the question: how can AI
help us with mathematics?\n
LOCATION:https://master.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:20240910T214235Z
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\nAbstract\nThere is a notion of nilpotent complex structures on nilpo
tent Lie algebras introduced by Cordero-Fernández-Gray-Ugarte (2000). Not
every complex structure on a nilpotent Lie algebra $\\mathfrak{n}$ is nil
potent\, but when $\\mathfrak{n}$ is $2$-step nilpotent any complex struc
ture on $\\mathfrak{n}$ is nilpotent of step either $2$ or $3$ (a fact pro
ved by J. Zhang in 2022). The class of nilpotent complex structures of ste
p $2$ strictly contains the space of abelian and bi-invariant complex stru
ctures on a $2$-step nilpotent Lie algebra. In this work in progress\, we
obtain a characterization of the $2$-step nilpotent Lie algebras whose cor
responding Lie groups admit a left invariant complex structure. We conside
r separately the cases when the complex structure is nilpotent of step $2$
or $3$. Some applications of our results to Hermitian geometry are discus
sed\, for instance\, it turns out that the $2$-step nilpotent Lie algebras
constructed by Tamaru from Hermitian symmetric spaces admit pluriclosed (
or SKT) metrics. We also show that abelian complex structures are frequent
on naturally reductive $2$-step nilmanifolds\, while it is known (Del Bar
co-Moroianu) that these do not admit orthogonal bi-invariant complex struc
tures.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/54
DESCRIPTION:Title: Totally geodesic submanifolds of Hopf-Berger spheres\nby Carlos Olmos (UNC) as part of Geometry Webinar AmSur /AmSul\n\n\nAbs
tract\nA Hopf-Berger sphere of factor $\\tau$ is a sphere which is the to
tal space of a Hopf fibration and such that the Riemannian metric is resca
led by a factor $\\tau\\neq 1$ in the directions of the fibers. A Hopf-Ber
ger sphere is the usual {\\it Berger sphere} for the complex Hopf fibrati
on. A Hopf-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
-constant curvature ($\\bar M$ is compact if and only if $\\tau <1$). A H
opf-Berger sphere has positive curvature if and only if $\\tau <4/3$. A st
andard totally geodesic submanifold of $\\mathsf{S}_t^m(o)$ is obtained as
the intersection of the geodesic sphere with a totally geodesic submanifo
ld of $\\bar M$. We will speak about the classification of totally geodes
ic submanifolds of Hopf-Berger spheres. In particular\, for quaternionic
and octonionic fibrations\, non-standard totally geodesic spheres with th
e same dimension of the fiber appear\, for $\\tau <1/2$. Moreover\, there
are totally geodesic $\\mathbb RP^2$\, and $\\mathbb RP^3$ (with some re
strictions on $\\tau$\, the dimension and the type of the fibration). On
the one hand\, as a consequence of the connectedness principle of Wilking
\, there does not exist a totally geodesic $\\mathbb RP^4$ in a space o
f positive curvature which diffeomorphic to the sphere $S^7$. On the ot
her hand\, we construct an example of a totally geodesic $\\mathbb RP^2$ i
n a Hopf-Berger sphere of dimension $7$ and positive curvature. Natural qu
estion: could there exist a totally geodesic $\\mathbb RP^3$ in a space of
positive curvature which diffeomorphic to $S^7$?.\n\nThis talk is relate
d to a joint work with Alberto Rodríguez-Vázquez.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/55
DESCRIPTION:Title: Infinitesimally Bonnet bendable hypersurfaces\nby R
uy Tojeiro (ICMC-USP (São Carlos)) as part of Geometry Webinar AmSur /AmS
ul\n\n\nAbstract\nThe classical Bonnet problem is to classify all immersi
ons $f\\colon\\\,M^2\\to\\R^3$ into Euclidean three-space that are not det
ermined\,\nup to a rigid motion\, by their induced metric and mean curvatu
re function.\nThe natural extension of Bonnet problem for Euclidean hyper
surfaces of dimension $n\\geq 3$ was studied by Kokubu. In this talk we r
eport on joint work with M. Jimenez\, in which we investigate an infinites
imal version 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
curvature $c$\, for which there exists a (non-trivial) one-parameter fami
ly of immersions $f_t\\colon M^n\\to\\Q_c^{n+1}$\, with $f_0=f$\, whose i
nduced metrics $g_t$ and mean curvature functions $H_t$ coincide ``up to t
he first order"\, that is\, $\\partial/\\partial t|_{t=0}g_t=0=\\partial/\
\partial t|_{t=0}H_t.$\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/56
DESCRIPTION:Title: Kähler-like scalar curvature on homogeneous spaces
\nby Lino Grama (Unicamp) as part of Geometry Webinar AmSur /AmSul\n\n\nAb
stract\nIn this talk\, we will discuss the curvature properties of invaria
nt almost Hermitian geometry on generalized flag manifolds. Specifically\,
we will focus on the "Kähler-like scalar curvature metric" - that is\, a
lmost Hermitian structures $(g\,J)$ satisfying $s=2s_C$\, where $s$ is the
Riemannian scalar curvature and $s_C$ is the Chern scalar curvature. We w
ill provide a classification of such metrics on generalized flag manifolds
whose isotropy representation decomposes into two or three irreducible co
mponents. This is a joint work with A. Oliveira.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/57
DESCRIPTION:Title: On the harmonic flow of geometric structures\nby Da
niel Fadel (IMPA) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\n
In 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 harmonic flow of $H$-structures. This is the negative gradient flow o
f a natural Dirichlet-type energy functional on an isometric class of $H$-
structures on a closed Riemannian $n$-manifold\, where $H$ is the stabiliz
er in $\\mathrm{SO}(n)$ of a finite collection of tensors in $\\mathbb{R}^
n$. Using general Bianchi-type identities of $H$-structures\, we are able
to prove monotonicity formulas for scale-invariant local versions of the e
nergy\, similar to the classic formulas proved by Struwe and Chen (1988-89
) in the theory of harmonic map heat flow. We then deduce a general epsilo
n-regularity result along the harmonic flow and\, more importantly\, we ge
t long-time existence and finite-time singularity results in parallel to t
he classical results proved by Chen-Ding (1990) in harmonic map theory. In
particular\, we show that if the energy of the initial $H$-structure is s
mall enough\, depending on the $C^0$-norm of its torsion\, then the harmon
ic flow exists for all time and converges to a torsion-free $H$-structure.
Moreover\, we prove that the harmonic flow of $H$-structures develops a f
inite time singularity if the initial energy is sufficiently small but the
re is no torsion-free $H$-structure in the homotopy class of the initial $
H$-structure. Finally\, based on the analogous work of He-Li (2021) for al
most complex structures\, we give a general construction of examples where
the later finite-time singularity result applies on the flat $n$-torus\,
provided the $n$-th homotopy group of the quotient $\\mathrm{SO}(n)/H$ is
non-trivial\; e.g. when $n=7$ and $H=\\mathrm{G}_2$\, or when $n=8$ and $H
=\\mathrm{Spin}(7)$.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/58
DESCRIPTION:Title: Maximal vorticity of sections of the orthonormal frame
bundle via calibrations\nby Marcos Salvai (FAMAF\, Universidad Naciona
l de Córdoba\, Argentina) as part of Geometry Webinar AmSur /AmSul\n\n\nA
bstract\nLet M be an oriented three dimensional Riemannian manifold. We
define a notion of vorticity of local sections of the bundle SO(M) -> M o
f all its positively oriented orthonormal tangent frames. When M is a sp
ace form\, we relate the concept to a suitable invariant split pseudo-Riem
annian metric on Iso_o (M) equiv SO(M): A local section has positive vorti
city if and only if it determines a space-like submanifold. In the Euclide
an case we find explicit homologically volume maximizing sections using a
split special Lagrangian calibration. We introduce the concept of optimal
vorticity and give an optimal screwed global section for the three-sphere.
We prove that it is also homologically volume maximizing (now using a com
mon one-point split calibration). Besides\, we show that no optimal sectio
n can exist in the Euclidean and hyperbolic cases.\n\nM. Salvai\, A split
special Lagrangian calibration associated with frame vorticity\, accepted
for publication in Adv. Calc. Var.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/59
DESCRIPTION:Title: Magnetic trajectories on the Heisenberg group of dimens
ion three\nby Mauro Subils (UN Rosario) as part of Geometry Webinar Am
Sur /AmSul\n\n\nAbstract\nA magnetic trajectory is a curve $\\gamma$ on a
Riemannian manifold $(M\, g)$ satisfying the equation:\n$$\\nabla_{\\gamm
a'}{\\gamma'}= q F\\gamma'$$\nwhere $\\nabla$ is the corresponding Levi
-Civita connection and $F$ is a skew-symmetric $(1\,1)$-tensor such that
the corresponding 2-form $g(F\\cdot \,\\cdot)$ is closed.\n\nIn this talk
we are going to describe all magnetic trajectories on the Heisenberg Lie g
roup of dimension three $H_3$ for any invariant Lorentz force. We will wri
te explicitly the magnetic equations and show that the solutions are descr
ibed by Jacobi's elliptic functions. As a consequence\, we will prove the
existence and characterize the periodic magnetic trajectories.\nThen we wi
ll induce the Lorentz force to a compact quotient $H_3/\\Gamma$ and study
the periodic magnetic trajectories there\, proving its existence for any e
nergy level when $F$ is non-exact. \n\nThis is a joint work with Gabriel
a Ovando (UNR).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/63
DESCRIPTION:Title: The width of curves in Riemannian manifolds\nby Raf
ael Montezuma (UFC) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract
\nIn this talk we develop a Morse-Lusternik-Schnirelmann theory for the di
stance between two points of a smoothly embedded circle in a complete Riem
annian manifold. This theory suggests very naturally a definition of width
that generalises the classical definition of the width of plane curves. P
airs of points of the circle realising the width bound one or more minimis
ing geodesics that intersect the curve in special configurations. When the
circle bounds a totally convex disc\, we classify the possible configurat
ions under a further geometric condition. We also present properties and c
haracterisations of curves that can be regarded as the Riemannian analogue
s of plane curves of constant width. This talk is based on a joint work wi
th Lucas Ambrozio (IMPA) and Roney Santos (UFC).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/64
DESCRIPTION:Title: Heteroclinic solutions and a Morse-theoretic approach t
o an Allen-Cahn approximation of mean curvature flows\nby Pedro Gaspar
(Pontificia Universidad Católica de Chile) as part of Geometry Webinar A
mSur /AmSul\n\n\nAbstract\nThe Allen–Cahn equation is a semilinear parab
olic partial differential equation that models phase-transition and phase-
separation phenomena and which provides a regularization for the mean curv
ature flow (MCF)\, one of the most studied extrinsic geometric flows. \nIn
this talk\, we employ Morse-theoretical considerations to construct etern
al solutions of the Allen–Cahn equation that connect unstable equilibria
in compact manifolds. We describe the space of such solutions in a round
3-sphere under a low-energy assumption\, and indicate how these solutions
could be used to produce geometrically interesting MCFs. This is joint wor
k with Jingwen Chen (University of Pennsylvania).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/65
DESCRIPTION:Title: $G_2$-instantons on nilpotent Lie groups\nby Vivian
a del Barco (Unicamp) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstra
ct\nIn this talk we will discuss recent advancements on G$_2$-instantons o
n 7-dimensional 2-step nilpotent Lie groups endowed with a left-invariant
coclosed G$_2$-structures. I will present necessary and sufficient conditi
ons for the characteristic connection of the G$_2$-structure to be an inst
anton\, in terms of the torsion of the G$_2$-structure\,\nthe torsion of t
he connection and the Lie group structure. These conditions allow to show
that the metrics corresponding to the G$_2$-instantons define a naturally
reductive structure on the simply connected 2-step nilpotent Lie group wit
h left-invariant Riemannian metric. This is a joint work with Andrew Clark
e and Andrés Moreno.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/66
DESCRIPTION:Title: Constant Q-curvature metrics\nby Rayssa Caju (Unive
rsidad de Chile) as part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nO
ver the past few decades\, there has been significant exploration of the i
nterplay between geometry and partial differential equations. In particula
r\, some problems arising in conformal geometry\, such as\nthe classical Y
amabe problem\, can be reduced to the study of PDEs with critical exponent
on\nmanifolds. More recently\, the so-called Q-curvature equation\, a fou
rth-order elliptic PDE with\ncritical exponent\, is another class of confo
rmal equations that has drawn considerable attention\nby its relation with
a natural concept of curvature. In this talk\, I would like to motivate t
hese\nproblems from a geometric and analytic perspective\, and discuss som
e recent developments in the\narea\, in particular regarding the singular
Q-curvature problem.\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/67
DESCRIPTION:Title: Real semi-simple Lie algebras are determined by their I
wasawa subalgebras.\nby Michael Jablonski (University of Oklahoma) as
part of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nReal semi-simple Lie
algebras arise naturally both algebraically\, in the study of Lie theory\,
and geometrically\, in the study of symmetric spaces. After recalling why
these algebras are of interest\, we will investigate their uniqueness pro
perties through the lens of special subalgebras\, the so-called Iwasawa su
balgebras. While the results are algebraic\, the tools to obtain them come
from the Riemannian geometry of solvmanifolds. We will finish the talk wi
th a quick discussion of the complex setting and how it differs from the r
eal setting. This is joint work with Jon Epstein (McDaniel College).\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/68
DESCRIPTION:Title: The Einstein-Hilbert functional in Kähler and Sasaki g
eometry\nby Eveline Legendre (U. Lyon) as part of Geometry Webinar AmS
ur /AmSul\n\n\nAbstract\nIn this talk I will present a recent joint work w
ith Abdellah Lahdilli and Carlo Scarpa where\, given a polarised Kähler m
anifold $(M\,L)$\, we consider the circle bundle associated to the polariz
ation with the induced transversal holomorphic structure. The space of con
tact structures compatible with this transversal structure is naturally id
entified with a bundle\, of infinite rank\, over the space of Kähler metr
ics in the first Chern class of L. We show that the Einstein--Hilbert func
tional of the associated Tanaka--Webster connections is a functional on th
is bundle\, whose critical points are constant scalar curvature Sasaki str
uctures. In particular\, when the group of automorphisms of $(M\,L)$ is di
screte\, these critical points correspond to constant scalar curvature Kä
hler metrics in the first Chern class of $L$. If time permits\, I will exp
lain how we associate a two real parameters family of these contact struct
ures 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 show that the existence of cscK metrics on a polarized manifold impl
ies K-semistability\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/69
DESCRIPTION:Title: Weyl structures with special holonomy on compact confor
mal manifolds\nby Andrei Moroianu (Paris-Saclay/CNRS) as part of Geome
try Webinar AmSur /AmSul\n\n\nAbstract\nWe consider compact conformal mani
folds $(M\,[g])$ endowed with a closed Weyl structure $\\nabla$\, i.e. a t
orsion-free connection preserving the conformal structure\, which is local
ly but not globally the Levi-Civita connection of a metric in $[g]$. Our a
im is to classify all such structures when both $\\nabla$ and $\\nabla^g$\
, the Levi-Civita connection of $g$\, have special holonomy. In such a set
ting\, $(M\,[g]\,\\nabla)$ is either flat\, or irreducible\, or carries a
locally conformally product (LCP) structure.\nSince the flat case is alrea
dy completely classified\, we focus on the last two cases.\nWhen $\\nabla$
has irreducible holonomy we prove that $(M\,g)$ is either Vaisman\, or a
mapping torus of an isometry of a compact nearly Kähler or nearly paralle
l $\\mathrm{G}_2$ manifold\, while in the LCP case we prove that $g$ is ne
ither Kähler nor Einstein\, thus reducible by the Berger-Simons Theorem\,
and we obtain the local classification of such structures in terms of ada
pted metrics. This is joint work with Florin Belgun and Brice Flamencourt.
\n
LOCATION:https://master.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:20240910T214235Z
UID:AmSurAmSulGeometry/70
DESCRIPTION:Title: Compactness of singular solutions to the GJMS equation<
/a>\nby João Henrique Santos de Andrade (USP) as part of Geometry Webinar
AmSur /AmSul\n\n\nAbstract\nWe study some compactness properties of the s
et of conformally flat singular metrics with constant positive $Q$-curvatu
re (integer or fractional) on a finitely punctured sphere.\nBased on some
recent classification results\, we focus on some cases of integer $Q$-curv
ature. We introduce a notion of necksize for these metrics in our moduli s
pace\, which we use to characterize compactness. More precisely\, we prove
that if the punctures remain separated and the necksize at each puncture
is bounded away from zero along a sequence of metrics\, then a subsequence
converges with respect to the Gromov-Hausdorff metric. Our proof relies o
n an upper bound estimate which is proved using moving planes and a blow-u
p argument. This is combined with a lower bound estimate which is a conseq
uence of a removable singularity theorem. We also introduce a homological
invariant which may be of independent interest for upcoming research.\n
LOCATION:
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:20240910T214235Z
UID:AmSurAmSulGeometry/71
DESCRIPTION:Title: Rigidity of compact quasi-Einstein manifolds with bound
ary\nby Ernani Ribeiro Jr. (Universidade Federal do Ceará - UFC) as p
art of Geometry Webinar AmSur /AmSul\n\n\nAbstract\nIn this talk\, we disc
uss the geometry of compact quasi-Einstein manifolds with boundary. This t
opic is directly related to warped product Einstein metrics\, static space
s and smooth metric measure spaces. We show that a 3-dimensional simply co
nnected compact quasi-Einstein manifold with boundary and constant scalar
curvature 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 manifo
ld with boundary and constant scalar curvature is isometric to either the
standard hemisphere $S^4_{+}\,$ or the cylinder $I\\times S^3$ with produc
t metric\, or the product space $S^2_{+}\\times S^2$ with the doubly warpe
d product metric. Other related results for arbitrary dimensions are also
discussed. This is a joint work with J. Costa and D. Zhou.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jakob Stein (Unicamp)
DTSTART;VALUE=DATE-TIME:20240503T170000Z
DTEND;VALUE=DATE-TIME:20240503T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
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\
nAbstract\nAsymptotically locally conical (ALC) metrics can be viewed as h
igher-dimensional analogues of ALF gravitational instantons\, such as the
Taub-NUT metric. In the setting of special holonomy\, families of Yang-Mil
ls instantons on ALC G2-metrics are expected to display some of the same f
eatures as the families of instantons on ALF spaces\, studied recently by
Cherkis-Larrain-Hubach-Stern. We will demonstrate this relationship explic
itly in the cohomogeneity one setting\, and study the behaviour of Yang-Mi
lls instantons as the underlying geometry varies in a one-parameter family
. This talk features two ongoing joint works\, one with Matt Turner\, and
one with Lorenzo Foscolo and Calum Ross.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Gorginyan (IMPA)
DTSTART;VALUE=DATE-TIME:20240517T170000Z
DTEND;VALUE=DATE-TIME:20240517T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/73
DESCRIPTION:Title: Quaternionic-solvable hypercomplex nilmanifolds\nby
Yulia Gorginyan (IMPA) as part of Geometry Webinar AmSur /AmSul\n\n\nAbst
ract\nA hypercomplex structure on a Lie algebra is a triple of complex str
uctures I\, J\, and K satisfying the quaternionic relations. A quaternioni
c-solvable Lie algebra is a Lie algebra\, admitting a finite filtration by
quaternionic-invariant subalgebras\, such that each successive quotient i
s abelian. We will discuss the quaternionic-solvable hypercomplex structur
es on a nilpotent Lie algebra and hypercomplex nilmanifolds\, correspondin
g to them.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francisco Vittone (UNRosario)
DTSTART;VALUE=DATE-TIME:20240531T170000Z
DTEND;VALUE=DATE-TIME:20240531T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/74
DESCRIPTION:Title: Nullity and Symmetry in homogeneous Spaces\nby Fran
cisco Vittone (UNRosario) as part of Geometry Webinar AmSur /AmSul\n\n\nAb
stract\nIn any Riemannian manifold one can define two natural subspaces of
each tangent space. The first is given by the nullity of the curvature te
nsor\, and the second is given by the parallel Killing vector fields at a
point (transvections). In a homogeneous spaces\, both subspaces allow to d
efine invariant distributions\, called the nullity distribution and the di
stribution of symmetry\, which are related to each other. We present some
recent works which study the restrictions that the existence of nullity im
poses in the Lie algebra of the whole isometry group of a Riemannian homog
eneous space and its relation to the distribution of symmetry. We finally
introduce some work in progress on the extension of these concepts to Lore
ntzian homogeneous spaces.\n
LOCATION:
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:20240910T214235Z
UID:AmSurAmSulGeometry/75
DESCRIPTION:Title: Tangent ray foliations and outer billiards\nby Yami
le Godoy (Universidad Nacional de Córdoba) as part of Geometry Webinar Am
Sur /AmSul\n\n\nAbstract\nGiven a smooth closed strictly convex curve $\\g
amma$ in the plane and a point $x$ outside of $\\gamma$\, there are two ta
ngent lines to $\\gamma$ through $x$\; choose one of them consistently\,
say\, the right one from the viewpoint of $x$\, and the outer billiard ma
p $B$ is defined by reflecting $x$ about the point of tangency. We observ
e that the good definition and the injectivity of the plane outer billiard
map is a consequence of the fact that the tangent rays associated to both
tangent vectors to $\\gamma$ determine foliations of the exterior of the
curve. \n\nIn this talk\, we will present the results obtained from a g
eneralization of the problem of defining outer billiards in higher dimensi
ons. Let $v$ be a smooth unit vector field on a complete\, umbilic (but n
ot 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 necessary and sufficient conditions on $v$ for t
he rays with initial velocities $v$ (and $-v$) to foliate the exterior $U$
of $N$. We find and explore relationships among these vector fields and g
eodesic vector fields on $N$. When the rays corresponding to each of $\\pm
v$ foliate $U$\, $v$ induces an outer billiard map whose billiard table i
s $U$. We describe the unit vector fields on $N$ whose associated outer bi
lliard map is volume preserving.\n\nThis is a joint work with Michael Harr
ison (Institute for Advanced Study\, Princeton) and Marcos Salvai (UNC\, A
rgentina).\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Tolcachier (UNCordoba)
DTSTART;VALUE=DATE-TIME:20240419T170000Z
DTEND;VALUE=DATE-TIME:20240419T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/76
DESCRIPTION:Title: Complex solvmanifolds with holomorphically trivial cano
nical bundle\nby Alejandro Tolcachier (UNCordoba) as part of Geometry
Webinar AmSur /AmSul\n\n\nAbstract\nThe canonical bundle of a complex mani
fold $(M\,J)$\, with $\\operatorname{dim}_{\\mathbb{C}} M=n$\, is defined
as the $n$-th exterior power of its holomorphic tangent bundle and it is a
holomorphic line bundle over $M$. Complex manifolds with holomorphically
trivial canonical bundle are important in differential\, complex\, and alg
ebraic geometry and also have relations with theoretical physics. It is we
ll known that every nilmanifold $\\Gamma\\backslash G$ equipped with an in
variant complex structure has (holomorphically) trivial canonical bundle\,
due to the existence of an invariant \n (holomorphic) trivializing sectio
n. 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-invaria
nt trivializing holomorphic section of its canonical bundle. This new phen
omenon lead us to study the existence of holomorphic trivializing sections
in two stages. In the invariant case\, we will characterize this existenc
e in terms of the 1-form $\\psi$ naturally defined in terms of the Lie alg
ebra of $G$ and $J$ by $\\psi(x)=\\operatorname{Tr} (J\\operatorname{ad} x
)-\\operatorname{Tr} \\operatorname{ad} (Jx)$. For the non-invariant case\
, we will provide an algebraic obstruction for a solvmanifold to have a tr
ivial canonical bundle (or\, more generally\, holomorphically torsion) and
we will explicitly construct\, in certain examples\, a trivializing secti
on of the canonical bundle that is non-invariant. We will apply this const
ruction to hypercomplex geometry to provide a negative answer to a questio
n posed by M. Verbitsky. Based on joint work with Adrián Andrada.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luigi Vezzoni (University of Torino)
DTSTART;VALUE=DATE-TIME:20240628T170000Z
DTEND;VALUE=DATE-TIME:20240628T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/77
DESCRIPTION:Title: Geometric flows of Hermitian metrics on Lie groups\
nby Luigi Vezzoni (University of Torino) as part of Geometry Webinar AmSur
/AmSul\n\n\nAbstract\nThe talk focuses on geometric flows of Hermitian me
trics on non-Kähler manifolds\, paying\nparticular attention to the famil
y of Hermitian curvature flows introduced by Streets and Tian.\nIt will be
shown that\, under suitable assumptions\, a Hermitian Curvature flow star
ting from a\nleft-invariant Hermitian metric on a Lie group has a long tim
e solution converging to a soliton\, up to renormalization. The study of s
olitons and static solutions of geometric flows on Lie groups will be also
addressed. The last part of the talk is about a work in progress on the S
econd Chern-Ricci flow on complex parallelizable manifolds. \n \nThe resu
lts are in collaboration with Lucio Bedulli\, Nicola Enrietti\, Anna Fino\
, Ramiro Lafuente and Mattia Pujia.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keti Tenenblat (UnB)
DTSTART;VALUE=DATE-TIME:20240830T170000Z
DTEND;VALUE=DATE-TIME:20240830T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/79
DESCRIPTION:Title: Classes of nonlinear PDEs related to metrics of constan
t curvature\nby Keti Tenenblat (UnB) as part of Geometry Webinar AmSu
r /AmSul\n\n\nAbstract\nIn this talk\, I will survey some aspects relating
classes of PDEs with metrics on a 2-\ndimensional manifold with non zero
constant Gaussian curvature. The notion of a differential equation (or sys
tem of equations) describing pseudo-spherical surfaces (curvature -1) or s
pherical surfaces (curvature 1) will be introduced. Such equations have re
markable properties. Each equation is the integrability condition of a lin
ear problem explicitly given. The linear problem may provide solutions for
the equation by using Bäcklund type transformations or by applying the i
nverse scattering method. Moreover\, the geometric properties of the surfa
ces may provide infinitely many conservation laws. Very well known equatio
ns such as the sine-Gordon\, Korteveg de Vries\, Non Linear Schrödinger\,
Camassa-Holm\, short-pulse equation\, elliptic sine-Gordon\, etc. are exa
mples of large classes of equations related to metrics with non zero const
ant curvature. Classical and more recent results characterizing and classi
fying certain types of equations will be mentioned. Examples and illustrat
ions will be included. Some higher dimensions generalizations will be ment
ioned.\n
LOCATION:
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Soldatenkov (UFF)
DTSTART;VALUE=DATE-TIME:20240913T170000Z
DTEND;VALUE=DATE-TIME:20240913T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/80
DESCRIPTION:Title: Lagrangian fibrations and degenerate twistor deformatio
ns\nby Andrey Soldatenkov (UFF) as part of Geometry Webinar AmSur /AmS
ul\n\nInteractive livestream: https://meet.google.com/nzd-idoy-zej\nView-o
nly livestream: https://meet.google.com/nzd-idoy-zej\n\nAbstract\nThe noti
on of a Lagrangian fibration is central for the classical symplectic geome
try and mathematical physics. Holomorphic Lagrangian fibrations also natur
ally appear In the context of complex geometry: the most well known exampl
es are the Hitchin systems and the Mukai systems. In this talk we will foc
us on the case when the total space of the fibration is a compact hyperkä
hler manifold X. We will construct a special family of deformations of the
complex structure on X parametrized by the affine line and preserving the
Lagrangian fibration. I will explain why the deformed complex structures
admit Kähler metrics and if time permits talk about some applications of
this fact. The talk will be based on a joint work with Misha Verbitsky.\n
LOCATION:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonardo Cavenaghi (Unicamp)
DTSTART;VALUE=DATE-TIME:20240927T170000Z
DTEND;VALUE=DATE-TIME:20240927T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/81
DESCRIPTION:Title: Atoms for stacks\nby Leonardo Cavenaghi (Unicamp) a
s part of Geometry Webinar AmSur /AmSul\n\nInteractive livestream: https:/
/meet.google.com/nzd-idoy-zej\nView-only livestream: https://meet.google.c
om/nzd-idoy-zej\n\nAbstract\nIn this talk\, we quickly recall the concept
of atoms from Katzarkov-Kontsevich-Pantev-Yu. This Gromov-Witten-based con
struction recently led to new birational invariants. We explain how this i
dea can be generalized to produce birational invariants for stacks and G-b
irational invariants for smooth projective varieties with regular G-action
s. This talk is based on ongoing joint work with L. Grama\, L. Katzarkov\,
and M. Kontsevich.\n
LOCATION:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
BEGIN:VEVENT
SUMMARY:Barbara Nelli (l'Aquila)
DTSTART;VALUE=DATE-TIME:20241011T170000Z
DTEND;VALUE=DATE-TIME:20241011T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/82
DESCRIPTION:by Barbara Nelli (l'Aquila) as part of Geometry Webinar AmSur
/AmSul\n\nInteractive livestream: https://meet.google.com/nzd-idoy-zej\nVi
ew-only livestream: https://meet.google.com/nzd-idoy-zej\nAbstract: TBA\n
LOCATION:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euripedes da Silva (ITC)
DTSTART;VALUE=DATE-TIME:20241025T170000Z
DTEND;VALUE=DATE-TIME:20241025T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/83
DESCRIPTION:by Euripedes da Silva (ITC) as part of Geometry Webinar AmSur
/AmSul\n\nInteractive livestream: https://meet.google.com/nzd-idoy-zej\nVi
ew-only livestream: https://meet.google.com/nzd-idoy-zej\nAbstract: TBA\n
LOCATION:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roney Santos (USP)
DTSTART;VALUE=DATE-TIME:20241108T170000Z
DTEND;VALUE=DATE-TIME:20241108T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/84
DESCRIPTION:Title: The Ricci condition for warped metrics\nby Roney Sa
ntos (USP) as part of Geometry Webinar AmSur /AmSul\n\nInteractive livestr
eam: https://meet.google.com/nzd-idoy-zej\nView-only livestream: https://m
eet.google.com/nzd-idoy-zej\n\nAbstract\nWe would like to introduce and di
scuss the recent concept of a Ricci surface. There are abstract surfaces t
hat\, under a natural curvature restriction\, admits local minimal embeddi
ng in the three-dimensional Euclidean space as a minimal surface\, which m
eans that Ricci surfaces offer an "intrinsic" way to see minimal surfaces
of $\\mathbb{R}^3$. Our goal is to present the classification of Ricci sur
faces endowed with a warped metric\, and apply it to the study of rotation
al and ruled Ricci surfaces immersed in $\\mathbb{R}^3$. This talk is base
d on works joint with Alcides de Carvalho\, Iury Domingos and Feliciano Vi
tório.\n
LOCATION:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lotay (Oxford)
DTSTART;VALUE=DATE-TIME:20241206T170000Z
DTEND;VALUE=DATE-TIME:20241206T180000Z
DTSTAMP;VALUE=DATE-TIME:20240910T214235Z
UID:AmSurAmSulGeometry/85
DESCRIPTION:by Jason Lotay (Oxford) as part of Geometry Webinar AmSur /AmS
ul\n\nInteractive livestream: https://meet.google.com/nzd-idoy-zej\nView-o
nly livestream: https://meet.google.com/nzd-idoy-zej\nAbstract: TBA\n
LOCATION:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
URL:https://meet.google.com/nzd-idoy-zej
END:VEVENT
END:VCALENDAR