BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Vicente Muñoz (Universidad de Málaga)
DTSTART:20201013T140000Z
DTEND:20201013T150000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/1
DESCRIPTION:Title: K-contact and Sasakian 5-manifolds\nby
Vicente Muñoz (Universidad de Málaga) as part of Geometry in Como\n\n\n
Abstract\nWe construct the first example of a 5-dimensional simply connect
ed compact manifold that admits a K-contact structure but does not admit a
semi-regular Sasakian structure. For this\, we need two ingredients: (a)
to construct a suitable simply connected symplectic 4-manifold with disjoi
nt symplectic surfaces spanning the homology\, all of them but one of genu
s 1 and the other of genus $g>1$\, (b) to prove a bound on the second Bett
i number $b_2$ of an algebraic surface with $b_1=0$ and having disjoint co
mplex curves spanning the homology when all of them but one are of genus 1
and the other of genus $g>1$.\n(joint work with A. Cañas\, J. Rojo\, A.
Viruel).\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Ottaviani (Università di Firenze)
DTSTART:20201117T150000Z
DTEND:20201117T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/2
DESCRIPTION:Title: Eigenvectors and singular t-ples of tensor
s\nby Giorgio Ottaviani (Università di Firenze) as part of Geometry i
n Como\n\n\nAbstract\nThe space of tensors considered in this talk is the
tensor product of some real vector spaces of finite dimension $V_1\,\\ldot
s\,V_d$. This space contains the Segre variety of decomposable (or rank on
e) tensors. There is a natural invariant metric on the space of tensors\,
called Frobenius metric.\n\nIn optimization setting one considers the (com
plex) critical points on the Segre variety of the distance function from a
given tensor\, they are called singular $t$-ples\, among them there is th
e best rank one approximation.\n\nIn the symmetric setting\, when $d=2$\,
these critical points are just the eigenvectors of a symmetric matrix.\n\n
The geometry of the critical points is appealing\, since they lie in a lin
ear space called critical space\, which has dimension smaller than the num
ber of critical points\, in other words the critical points are linearly d
ependent\, unless the matrix case. We expose some properties of singular $
t$-ples.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys (Albert-Ludwigs-Universität Freiburg)
DTSTART:20201215T150000Z
DTEND:20201215T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/3
DESCRIPTION:Title: Gauge theory and $G_2$ geometry\nby An
driy Haydys (Albert-Ludwigs-Universität Freiburg) as part of Geometry in
Como\n\n\nAbstract\n$G_2$ manifolds constitute a class of Einstein seven-m
anifolds and are of substantial interest both in Riemannian geometry and t
heoretical physics. At present a vast number of compact $G_2$ manifolds is
known to exist. In this talk I will discuss a gauge-theoretic approach to
the construction of invariants of compact $G_2$ manifolds. I will focus o
n an interplay between gauge theories in dimensions 7 and 3 and how this c
an be used for the construction of the invariants.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Dileo (Università degli Studi di Bari Aldo Moro)
DTSTART:20210216T150000Z
DTEND:20210216T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/4
DESCRIPTION:Title: 3-(α\,δ)-Sasaki manifolds\nby Giulia
Dileo (Università degli Studi di Bari Aldo Moro) as part of Geometry in
Como\n\n\nAbstract\nI will introduce a special class of almost 3-contact m
etric \nmanifolds\, called 3-$(\\alpha\,\\delta)$-Sasaki\, which is a gene
ralization of \n3-Sasaki manifolds. I will show that they satisfy a genera
l criterion \nfor almost 3-contact metric manifolds to admit a canonical m
etric \nconnection with skew torsion. Various geometric properties of thes
e \nmanifolds can be described\, involving the canonical connection and th
e \nrelation with quaternionic Kähler spaces (joint works with Ilka Agric
ola and Leander Stecker - Marburg).\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Goertsches (Philipps-Universität Marburg)
DTSTART:20210420T140000Z
DTEND:20210420T150000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/5
DESCRIPTION:Title: Hamiltonian non-Kähler actions in low dim
ensions\nby Oliver Goertsches (Philipps-Universität Marburg) as part
of Geometry in Como\n\n\nAbstract\nWe classify 3-valent GKM fiber bundles
over n-gons\, show that they are all realized as the projectivization of e
quivariant complex rank 2 vector bundles over quasitoric 4-manifolds\, and
investigate the existence of invariant (stable) almost complex\, symplect
ic\, and Kähler structures on the total space. In this way we obtain infi
nitely many new examples of Hamiltonian non-Kähler actions in dimension 6
with prescribed shape of the x-ray\, in particular with prescribed number
of fixed points. We extend our methods to give interesting examples of to
rus actions in dimension 8 that answer a natural cohomological rigidity qu
estion.\n\nThis is joint work with Panagiotis Konstantis and Leopold Zolle
r.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lidia Stoppino (Università degli Studi di Pavia)
DTSTART:20210119T150000Z
DTEND:20210119T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/6
DESCRIPTION:Title: Slope inequalities for fibred surfaces
\nby Lidia Stoppino (Università degli Studi di Pavia) as part of Geometry
in Como\n\n\nAbstract\nIn this talk I will give an overview of the so-cal
led slope inequalities for fibred surfaces: these are in general lower bou
nds for the slope between the self-intersection of the relative canonical
sheaf and the relative Euler characteristic of the structure sheaf. These
inequalities were studied first in two seminal papers by Cornalba-Harris a
nd Xiao in the '80's\, via two different thechniques. However\, there is a
key assumption that lies underneath both techniques: the linear stability
of the canonical system on the general fibres\, which is equivalet to the
classical Clifford's theorem.\nI will then focus in the influence on the
slope of the following invariants of the fibred surfaces: the relative irr
egularity\, the unitary rank and the gonality and Clifford index. I will d
escribe results due to Xiao\, Barja and myself\, and recently by Lu and Zu
o (who introduced a third new method). Eventually\, I will describe an imp
roved bound obtained very recently in collaboration with my Ph.D. student
Enea Riva. This result is obtained via the Xiao's method. The key assumpti
on is a new Clifford-type bound for non complete subacanonical systems whi
ch -interestingly enough- is not a linear stability result.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Marchesi (Universitat de Barcelona)
DTSTART:20210317T150000Z
DTEND:20210317T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/7
DESCRIPTION:Title: On the stability of logarithmic tangent sh
eaves\nby Simone Marchesi (Universitat de Barcelona) as part of Geomet
ry in Como\n\n\nAbstract\nGiven a hypersurface $D$ in the projective space
$\\mathbb{P}^N$\, we can associate to it its logarithmic tangent sheaf $\
\mathcal{T}_D$\, which is given by the vector fields of $\\mathbb{P}^N$ th
at are tangent to $D$.\n\nFor particular families of hypersurfaces\, such
reflexive sheaf turns out to be a direct sum of line bundles and\, in this
case\, $D$ is called free. This situation has been of special interest i
n the topic of hyperplane arrangements.\n\nGoing on the "opposite directio
n"\, other interesting classes of hypersurfaces give us a stable sheaf $\\
mathcal{T}_D$. We recall\, among many\, the work of Dolgachev-Kapranov\, w
here stability is proven if $D$ is an hyperplane arrangement of at least $
N+2$ hyperplanes\, or the work of Dimca\, where it is proven for $D\\subse
t \\mathbb{P}^3$ with isolated singularities and small Tjurina number.\n\n
In this talk\, we will extend the study of stability to a wider family of
hypersurfaces\, relating it to the degree and dimension of the singular lo
cus of $D$. Furthermore we will show that stability holds for the hypersur
faces defined by determinants. Finally\, for this last set\, we will desc
ribe the moduli map from the quotient which describes the matrices whose d
eterminant defines $D$ and the moduli space of semistable shaves on $\\mat
hbb{P}^N$ that contains $\\mathcal{T}_D$. \n\nThis is a joint work with Da
niele Faenzi.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sönke Rollenske (Philipps-Universität Marburg)
DTSTART:20210518T140000Z
DTEND:20210518T150000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/8
DESCRIPTION:Title: Corona surfaces and extra components in th
e moduli space of stable surfaces\nby Sönke Rollenske (Philipps-Unive
rsität Marburg) as part of Geometry in Como\n\n\nAbstract\nThe moduli spa
ce of stable surfaces is a modular compactification of the\nGiesecker modu
li space of (canonical models of) projective algebraic\nsurfaces of genera
l type.\nWe show that the compactification has many extra irreducible and\
nconnected components.\nThe construction of examples is phrased in terms o
f a virus surface V\ninfecting suitable non-normal Gorenstein stable surfa
ces and will be\nillustrated by many pictures.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Castrillón (Universidad Complutense de Madrid)
DTSTART:20210615T140000Z
DTEND:20210615T150000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/9
DESCRIPTION:Title: Homogeneous structures in pseudo-Riemannia
n manifolds and beyond\nby Marco Castrillón (Universidad Complutense
de Madrid) as part of Geometry in Como\n\n\nAbstract\nA celebrated result
by Ambrose and Singer characterizes the homogeneity of a pseudo-Riemannian
manifold by a set of partial differential equations satisfied by a tensor
field\, together with some additional conditions of topological nature. W
e will review the geometric information provided by this homogeneous tenso
r in different situations\, being the so-called linear case the most relev
ant instance. From that point\, we will move to recent result on non-neces
sarily metric manifolds where we will explore the characterization of homo
geneity in other contexts as\, for exmaple\, the symplectic of Fedosov cas
e.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Ovando (Universidad Nacional de Rosario/CONICET)
DTSTART:20211123T160000Z
DTEND:20211123T170000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/10
DESCRIPTION:Title: Magnetic trajectories on 2-step nilmanifo
lds\nby Gabriela Ovando (Universidad Nacional de Rosario/CONICET) as p
art of Geometry in Como\n\n\nAbstract\nFrom the perspective of classical m
echanics\, a charged particle moving on a Riemannian manifold $M$ experien
ces a Lorentz force\, and its trajectory is called a magnetic trajectory.
The Lorentz force determines a magnetic field which is introduced as a clo
sed 2-form on $M$. In this work\, we focus on 2-step nilpotent Lie groups
equipped with a left-invariant metric and a left-invariant magnetic field.
The aim is to study magnetic fields\, their corresponding magnetic equat
ions and solutions. We obtain existence results regarding closed 2-forms
and explicit expressions for a family of magnetic trajectories. Some ideas
concerning closedness conditions are analysed.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Massarenti (Università di Ferrara)
DTSTART:20211215T160000Z
DTEND:20211215T170000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/11
DESCRIPTION:Title: Complete symplectic quadrics and Kontsevi
ch moduli spaces of conics in Lagrangian Grassmannians\nby Alex Massar
enti (Università di Ferrara) as part of Geometry in Como\n\n\nAbstract\nG
iven a reductive algebraic group $G$ and a Borel subgroup $B$\, a spherica
l variety is a normal variety admitting an action of $G$ with an open dens
e $B$-orbit.\nA special class of spherical varieties are the so-called won
derful varieties.\nThese are smooth spherical varieties for which we requi
re $G$ to be semisimple and simply connected and the existence of an open
$B$-orbit whose complementary set is a simple normal crossing divisor.\nWe
will construct the wonderful compactification of the space of symmetric\,
symplectic matrices on which the symplectic group acts.\nFurthermore\, we
will compute the Picard group of this compactification and we will study
its birational geometry in low-dimensional cases.\nAs an application\, we
will recover the results on the birational geometry of the Kontsevich spac
es of conics in Grassmannians due to I. Coskun a D. Chen\,\nand we will pr
ove new results on the birational geometry of the Kontsevich spaces of con
ics in Lagrangian Grassmannians.\n\nThis is a joint work with Elsa Cornian
i.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Ovando (Universidad Nacional de Rosario/CONICET)
DTSTART:20211214T160000Z
DTEND:20211214T170000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/12
DESCRIPTION:Title: Magnetic trajectories on 2-step nilmanifo
lds\nby Gabriela Ovando (Universidad Nacional de Rosario/CONICET) as p
art of Geometry in Como\n\n\nAbstract\nFrom the perspective of classical m
echanics\, a charged particle moving on a Riemannian manifold $M$ experien
ces a Lorentz force\, and its trajectory is called a magnetic trajectory.
The Lorentz force determines a magnetic field which is introduced as a clo
sed 2-form on $M$. In this work\, we focus on 2-step nilpotent Lie groups
equipped with a left-invariant metric and a left-invariant magnetic field.
The aim is to study magnetic fields\, their corresponding magnetic equat
ions and solutions. We obtain existence results regarding closed 2-forms
and explicit expressions for a family of magnetic trajectories. Some ideas
concerning closedness conditions are analysed.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (Universitat Politècnica de Catalunya)
DTSTART:20220323T160000Z
DTEND:20220323T170000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/13
DESCRIPTION:Title: To b or not to b\, that is the question\nby Eva Miranda (Universitat Politècnica de Catalunya) as part of Geom
etry in Como\n\n\nAbstract\nb-Structures are hidden in many places\, on ma
nifolds with boundary and associated index formulae (Melrose\, Nest-Tsygan
)\, in the geometry of pseudo-Riemannian geodesics (Khesin-Tabachnikov) an
d in the regularization transformations in celestial mechanics (Mc Gehee).
We will give a panorama talk on b-structures in the symplectic and contac
t realm describing some of the main techniques and some open problems.\n\n
Data for Zoom:\n\nMeeting ID: 917 9437 1036\n\nAccess code: 330550\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucía Martín Merchán (Università degli Studi di Torino)
DTSTART:20220126T160000Z
DTEND:20220126T170000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/14
DESCRIPTION:Title: A compact non-formal closed $G_2$ manifol
d with $b_1=1$\nby Lucía Martín Merchán (Università degli Studi di
Torino) as part of Geometry in Como\n\n\nAbstract\nA $G_2$ structure on a
7-dimensional Riemannian manifold determined by a certain type of 3-form
$\\varphi$. These are classified into 16 types according to PDEs involving
$\\varphi$\; for instance\, the $G_2$ structure is torsion-free if $\\var
phi$ is parallel\, closed if $\\varphi$ is closed and cocalibrated if $\\v
arphi$ is co-closed. This talk contributes to understanding topological pr
operties of compact manifolds with a closed $G_2$ structure that cannot be
endowed with any torsion-free $G_2$ structure. Namely\, we construct such
a manifold that is non-formal and has first Betti number $b_1=1$. The sta
rting point is a nilmanifold $(M\,\\varphi)$ with a closed $G_2$ structure
that admits an involution preserving $\\varphi$ such that the quotient $M
/\\mathbb{Z}_2$ is a non-formal orbifold with $b_1=1$. Then we perform a r
esolution of these singularities obtaining a manifold endowed with a close
d $G_2$ structure\; we finally prove that the resolution verifies the same
topological properties and do not admit any torsion-free $G_2$ structure.
\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Russo (Università degli Studi di Catania)
DTSTART:20220216T160000Z
DTEND:20220216T170000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/15
DESCRIPTION:Title: Explicit unirationality of some moduli sp
aces of K3 surfaces via trisecant flops\nby Francesco Russo (Universit
à degli Studi di Catania) as part of Geometry in Como\n\n\nAbstract\nThe
19-dimensional moduli space $F_g$ of polarized K3 surfaces of genus $g$ (a
nd degree $2g-2$) is known to be unirational for some low values of $g$\,
due to results by Mukai\, Nuer\, Farkas and Verra. However\, only for very
few values of $g$ the construction of unirationality provides a computer-
implementable algorithm to determine the equations of the general member o
f $F_g$. We shall present the relations between some K3 surfaces and some
special cubic fourfolds and describe a procedure to determine explicitly t
he equations of the general K3 surface of genus $g$ as a function of a num
ber of specific independent variables. This procedure can be easily implem
ented in Macaulay2 and\, in particular\, it yields the explicit unirationa
lity of $F_g$ for $g=11\,14\,20\,22$. This is based on joint works with Gi
ovanni Staglianò.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Bricalli\, Filippo Favale (Università di Pavia)
DTSTART:20220429T150000Z
DTEND:20220429T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/16
DESCRIPTION:Title: Lefschetz properties for jacobian rings o
f cubic fourfolds and other Artinian algebras\nby Davide Bricalli\, Fi
lippo Favale (Università di Pavia) as part of Geometry in Como\n\nAbstrac
t: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (Università degli Studi di Torino)
DTSTART:20220519T150000Z
DTEND:20220519T160000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/17
DESCRIPTION:Title: An overview on closed $G_2$-structures\nby Anna Fino (Università degli Studi di Torino) as part of Geometry i
n Como\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Rojo Carulli (Universidad Politécnica de Madrid)
DTSTART:20221201T151500Z
DTEND:20221201T161500Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/18
DESCRIPTION:Title: Sasakian vs K-contact geometry\nby Ju
an Rojo Carulli (Universidad Politécnica de Madrid) as part of Geometry i
n Como\n\n\nAbstract\nIn differential geometry\, a recurrent theme is to s
tudy how close the existence of a certain geometric structure on a manifol
d places it from the algebraic-geometry world\, in a broad sense.\n\nFor e
ven dimension\, the most famous instance of this problem has been the symp
lectic vs Kählerian question\, concerning the existence of symplectic non
-Kählerian manifolds. This problem has been intensively studied in the pa
st decades\, and has been an important source of development for the area
known as symplectic topology.\n\nFor odd dimension\, an analogous problem
is the K-contact vs Sasakian question\, which tries to understand which ma
nifolds (if any) admits K-contact but not Sasakian structures.\nIn this ta
lk we will explain a bit the analogies and differences between the two que
stions\, and explore some of the results obtained in the past recent years
for the latter\, particularly in the five dimensional and simply connecte
d case.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Noja (Ruprecht-Karls-Universität Heidelberg)
DTSTART:20230223T151500Z
DTEND:20230223T161500Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/19
DESCRIPTION:Title: Nilpotence Varieties\, Pure Spinors Super
fields and Supersymmetry\nby Simone Noja (Ruprecht-Karls-Universität
Heidelberg) as part of Geometry in Como\n\n\nAbstract\nIn this talk I will
introduce a mathematical perspective on the pure spinor superfield formal
ism\, showing how to recover (all) supersymmetry multiplets from geometric
data related to the nilpotence variety of a certain Poincaré superalgebr
a. After discussing some lower dimensional examples\, I will focus on the
relevant case of supersymmetry in six dimensions\, where the nilpotence va
riety is given by a four dimensional Segre variety. If time permits\, I wi
ll explain how nilpotence varieties of classical Lie superalgebras are rel
ated to the superconformal field theories (and hence AdS/CFT conjecture).\
n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Gómez Nicolás (Universidad de Cantabria)
DTSTART:20230523T141500Z
DTEND:20230523T151500Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/20
DESCRIPTION:Title: Structures on generalized geometry\nb
y Pablo Gómez Nicolás (Universidad de Cantabria) as part of Geometry in
Como\n\n\nAbstract\nGeneralized Geometry was introduced at the beginning o
f XXI century by N. Hitchin\, M. Gualtieri and G. Cavalcanti. This theory
is based on the study of the generalized tangent bundle or big tangent bun
dle\, defined as the Whitney sum of the tangent and the cotangent bundle o
f a manifold.\n\nAs in the case of geometric structures defined on a manif
old\, different "generalized geometric structures" can be defined on the g
eneralized tangent bundle\, such as metrics\, complex structures\, paracom
plex structures\, etc. The first important examples of generalized complex
structures were given by M. Gualtieri\, showing that both complex structu
res and symplectic structures defined on a manifold can be understood as g
eneralized complex structures. In this seminar\, we shall show that many o
ther structures appear in Generalized Geometry if we take a less restricti
ve definition than the original one given by M. Gualtieri. In this way\, w
e shall compare which are the similarities and differences between working
on the tangent bundle or the generalized tangent bundle of a manifold.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Gil García (Universität Hamburg)
DTSTART:20231130T140000Z
DTEND:20231130T150000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/21
DESCRIPTION:Title: Pseudo-Kähler and hypersymplectic struct
ures on semidirect products\nby Alejandro Gil García (Universität Ha
mburg) as part of Geometry in Como\n\nLecture held in Room V2.10\, Via Val
leggio 11\, Como.\n\nAbstract\nWe study left-invariant pseudo-Kähler and
hypersymplectic structures on semidirect products $G\\rtimes H$\; we work
at the level of the Lie algebra $\\mathfrak{g}\\rtimes\\mathfrak{h}$. In p
articular we consider the structures induced on $\\mathfrak{g}\\rtimes\\ma
thfrak{h}$ by existing pseudo-Kähler structures on $\\mathfrak{g}$ and $\
\mathfrak{h}$\; we classify all semidirect products of this type with $\\m
athfrak{g}$ of dimension $4$ and $\\mathfrak{h}=\\mathbb{R}^2$. In the hyp
ersymplectic setting\, we consider a more general construction on semidire
ct products. We construct new $2$-step nilpotent hypersymplectic Lie algeb
ras\; to our knowledge\, these are the first such examples whose underlyin
g complex structure is not abelian. This is a joint work with Diego Conti
(https://arxiv.org/abs/2310.20660)\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Angella (Università degli Studi di Firenze)
DTSTART:20240206T143000Z
DTEND:20240206T153000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/22
DESCRIPTION:Title: Constructing and Machine Learning Calabi-
Yau Five-Folds\nby Daniele Angella (Università degli Studi di Firenze
) as part of Geometry in Como\n\n\nAbstract\nThe significance of Calabi-Ya
u manifolds transcends both Complex Geometry and String Theory.\nOne possi
ble approach to constructing Calabi-Yau manifolds involves intersecting hy
persurfaces within the product of projective spaces\, defined by polynomia
ls of a specific degree.\nWe show a method to construct all possible compl
ete intersections Calabi-Yau five-folds within a product of four or less
complex projective spaces\, with up to four constraints. This results in a
comprehensive set of 27\,068 distinct spaces.\nFor approximately half of
these constructions\, excluding the product spaces\, we can compute the co
homological data\, yielding 2\,375 distinct Hodge diamonds.\nWe present di
stributions of the invariants and engage in a comparative analysis with th
eir lower-dimensional counterparts.\nSupervised machine learning technique
s are applied to the cohomological data. The Hodge number $h^{1\,1}$ can b
e learnt with high efficiency\; however\, accuracy diminishes for other Ho
dge numbers due to the extensive ranges of potential values.\n\nThe talk i
s a joint collaboration with Rashid Alawadhi\, Andrea Leonardo\, and Tancr
edi Schettini Gherardini.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicoletta Tardini (Università degli Studi di Parma)
DTSTART:20240208T143000Z
DTEND:20240208T153000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/23
DESCRIPTION:Title: Cohomological Properties of Hypercomplex
Manifolds\nby Nicoletta Tardini (Università degli Studi di Parma) as
part of Geometry in Como\n\n\nAbstract\nHyperkähler with torsion (HKT for
short) manifolds are smooth manifolds\nendowed with a hypercomplex struct
ure $(I\,J\,K)$ and a real and positive\n(in the quaternionic sense) $\\pa
rtial$-closed $(2\,0)$ form (here the bidegree and $\\partial$ are taken w
ith respect to the complex structure $I$). Examples of these manifolds are
hyperkähler manifolds. We will discuss the cohomological behavior of HKT
manifolds and we will present some numerical characterizations for the ex
istence of such metrics. \n\nThese are joint works with Giovanni Gentili a
nd Mehdi Lejmi.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Sferruzza (Università dell'Insubria)
DTSTART:20240419T130000Z
DTEND:20240419T140000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/24
DESCRIPTION:Title: A brief introduction to formality of diff
erentiable manifolds\nby Tommaso Sferruzza (Università dell'Insubria)
as part of Geometry in Como\n\n\nAbstract\nIn the context of differentiab
le manifolds\, a relevant role is played by the notion of formality\, intr
oduced by Quillen ('69) and Sullivan ('77). A differentiable manifold is s
aid to be formal if its homotopy type (up to torsion) can be recoved by it
s cohomology ring. A natural cohomological obstruction to formality is giv
en by the existence of non vanishing Massey products\, whereas\, in the ea
rly 00's\, Kotschick defined a stronger notion of formality\, involving th
e existence of special Riemannian metrics. In this talk\, I will give the
main definitions and their interplay\, provide the classical examples of (
non) formal differentiable manifolds and exhibit the topological obstructi
ons related to formality.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Chantraine (Université de Nantes)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/25
DESCRIPTION:Title: Product structure in locally conformally
symplectic geometry\nby Baptiste Chantraine (Université de Nantes) as
part of Geometry in Como\n\n\nAbstract\nLocally conformally symplectic st
ructures (lcs) generalise symplectic manifolds by studying closed non-dege
nerate 2-forms with value in a flat line bundle. In this talk\, after intr
oducing the subject and its relations with contact and symplectic geometry
\, I will talk about a construction of twisted product of lcs manifolds. T
his construction allows to relates fixed point of Hamiltonian diffeomorphi
sms to Lagrangian intersections (and this to relate the number of such fix
ed point to Novikov homology of the Lee class of the flat bundle). This is
a joint work with Kevin Sackel.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Magliaro (Università dell'Insubria)
DTSTART:20240704T130000Z
DTEND:20240704T140000Z
DTSTAMP:20260404T110655Z
UID:DifferentialAndAlgebraicGeometry/26
DESCRIPTION:Title: Sharp pinching theorems for complete CMC
submanifolds in the sphere\nby Marco Magliaro (Università dell'Insubr
ia) as part of Geometry in Como\n\n\nAbstract\nIn 1968 Simons proved that
if a compact\, minimal submanifold of the unit sphere $f:M^n\\to\\mathbb S
^{n+p}$ has second fundamental form satisfying $|A|^2\\le np/(2p-1)$\, the
n either $|A|\\equiv0$ and $M$ is a great sphere\, or $|A|^2\\equiv np/(2p
-1)$. Lawson and Chern\, do Carmo & Kobayashi characterized the latter cas
e and proved that if $|A|^2\\equiv np/(2p-1)$\, then $M$ is a Clifford tor
us or a Veronese surface. This pinching theorem was later generalized by A
lencar & do Carmo for compact CMC hypersurfaces of the sphere and by Santo
s for compact PMC submanifolds of the sphere. In this talk we extend the r
esults by Simons\, Lawson\, Chern\, do Carmo & Kobayashi and Alencar & do
Carmo to complete submanifolds of the sphere. We also partially generalize
the result of Santos in dimension $n\\le6$. This is joint work with L. Ma
ri\, F. Roing and A. Savas-Halilaj.\n
LOCATION:https://stable.researchseminars.org/talk/DifferentialAndAlgebraic
Geometry/26/
END:VEVENT
END:VCALENDAR