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:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/1
DESCRIPTION:Title: K-contact and Sasakian 5-manifolds\nby Vicent
e Muñoz (Universidad de Málaga) as part of Geometry in Como\n\n\nAbstrac
t\nWe construct the first example of a 5-dimensional simply connected comp
act manifold that admits a K-contact structure but does not admit a semi-r
egular Sasakian structure. For this\, we need two ingredients: (a) to cons
truct a suitable simply connected symplectic 4-manifold with disjoint symp
lectic surfaces spanning the homology\, all of them but one of genus 1 and
the other of genus $g>1$\, (b) to prove a bound on the second Betti numbe
r $b_2$ of an algebraic surface with $b_1=0$ and having disjoint complex c
urves spanning the homology when all of them but one are of genus 1 and th
e other of genus $g>1$.\n(joint work with A. Cañas\, J. Rojo\, A. Viruel)
.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giorgio Ottaviani (Università di Firenze)
DTSTART:20201117T150000Z
DTEND:20201117T160000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/2
DESCRIPTION:Title: Eigenvectors and singular t-ples of tensors\n
by Giorgio Ottaviani (Università di Firenze) as part of Geometry in Como\
n\n\nAbstract\nThe space of tensors considered in this talk is the tensor
product of some real vector spaces of finite dimension $V_1\,\\ldots\,V_d$
. This space contains the Segre variety of decomposable (or rank one) tens
ors. There is a natural invariant metric on the space of tensors\, called
Frobenius metric.\n\nIn optimization setting one considers the (complex) c
ritical points on the Segre variety of the distance function from a given
tensor\, they are called singular $t$-ples\, among them there is the best
rank one approximation.\n\nIn the symmetric setting\, when $d=2$\, these c
ritical points are just the eigenvectors of a symmetric matrix.\n\nThe geo
metry of the critical points is appealing\, since they lie in a linear spa
ce called critical space\, which has dimension smaller than the number of
critical points\, in other words the critical points are linearly dependen
t\, unless the matrix case. We expose some properties of singular $t$-ples
.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys (Albert-Ludwigs-Universität Freiburg)
DTSTART:20201215T150000Z
DTEND:20201215T160000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/3
DESCRIPTION:Title: Gauge theory and $G_2$ geometry\nby Andriy Ha
ydys (Albert-Ludwigs-Universität Freiburg) as part of Geometry in Como\n\
n\nAbstract\n$G_2$ manifolds constitute a class of Einstein seven-manifold
s and are of substantial interest both in Riemannian geometry and theoreti
cal 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 co
nstruction of invariants of compact $G_2$ manifolds. I will focus on an in
terplay between gauge theories in dimensions 7 and 3 and how this can be u
sed for the construction of the invariants.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giulia Dileo (Università degli Studi di Bari Aldo Moro)
DTSTART:20210216T150000Z
DTEND:20210216T160000Z
DTSTAMP:20260422T214839Z
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 metric \
nmanifolds\, called 3-$(\\alpha\,\\delta)$-Sasaki\, which is a generalizat
ion of \n3-Sasaki manifolds. I will show that they satisfy a general crite
rion \nfor almost 3-contact metric manifolds to admit a canonical metric \
nconnection with skew torsion. Various geometric properties of these \nman
ifolds can be described\, involving the canonical connection and the \nrel
ation with quaternionic Kähler spaces (joint works with Ilka Agricola and
Leander Stecker - Marburg).\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oliver Goertsches (Philipps-Universität Marburg)
DTSTART:20210420T140000Z
DTEND:20210420T150000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/5
DESCRIPTION:Title: Hamiltonian non-Kähler actions in low dimensions
\nby Oliver Goertsches (Philipps-Universität Marburg) as part of Geom
etry 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 equivari
ant complex rank 2 vector bundles over quasitoric 4-manifolds\, and invest
igate the existence of invariant (stable) almost complex\, symplectic\, an
d Kähler structures on the total space. In this way we obtain infinitely
many new examples of Hamiltonian non-Kähler actions in dimension 6 with p
rescribed shape of the x-ray\, in particular with prescribed number of fix
ed points. We extend our methods to give interesting examples of torus act
ions in dimension 8 that answer a natural cohomological rigidity question.
\n\nThis is joint work with Panagiotis Konstantis and Leopold Zoller.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lidia Stoppino (Università degli Studi di Pavia)
DTSTART:20210119T150000Z
DTEND:20210119T160000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/6
DESCRIPTION:Title: Slope inequalities for fibred surfaces\nby Li
dia Stoppino (Università degli Studi di Pavia) as part of Geometry in Com
o\n\n\nAbstract\nIn this talk I will give an overview of the so-called slo
pe inequalities for fibred surfaces: these are in general lower bounds for
the slope between the self-intersection of the relative canonical sheaf a
nd the relative Euler characteristic of the structure sheaf. These inequal
ities were studied first in two seminal papers by Cornalba-Harris and Xiao
in the '80's\, via two different thechniques. However\, there is a key as
sumption that lies underneath both techniques: the linear stability of the
canonical system on the general fibres\, which is equivalet to the classi
cal Clifford's theorem.\nI will then focus in the influence on the slope o
f the following invariants of the fibred surfaces: the relative irregulari
ty\, the unitary rank and the gonality and Clifford index. I will describe
results due to Xiao\, Barja and myself\, and recently by Lu and Zuo (who
introduced a third new method). Eventually\, I will describe an improved b
ound obtained very recently in collaboration with my Ph.D. student Enea Ri
va. This result is obtained via the Xiao's method. The key assumption is a
new Clifford-type bound for non complete subacanonical systems which -int
erestingly enough- is not a linear stability result.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Marchesi (Universitat de Barcelona)
DTSTART:20210317T150000Z
DTEND:20210317T160000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/7
DESCRIPTION:Title: On the stability of logarithmic tangent sheaves\nby Simone Marchesi (Universitat de Barcelona) as part of Geometry in C
omo\n\n\nAbstract\nGiven a hypersurface $D$ in the projective space $\\mat
hbb{P}^N$\, we can associate to it its logarithmic tangent sheaf $\\mathca
l{T}_D$\, which is given by the vector fields of $\\mathbb{P}^N$ that are
tangent to $D$.\n\nFor particular families of hypersurfaces\, such reflexi
ve 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 in the t
opic of hyperplane arrangements.\n\nGoing on the "opposite direction"\, ot
her interesting classes of hypersurfaces give us a stable sheaf $\\mathcal
{T}_D$. We recall\, among many\, the work of Dolgachev-Kapranov\, where st
ability is proven if $D$ is an hyperplane arrangement of at least $N+2$ hy
perplanes\, or the work of Dimca\, where it is proven for $D\\subset \\mat
hbb{P}^3$ with isolated singularities and small Tjurina number.\n\nIn this
talk\, we will extend the study of stability to a wider family of hypersu
rfaces\, relating it to the degree and dimension of the singular locus of
$D$. Furthermore we will show that stability holds for the hypersurfaces d
efined by determinants. Finally\, for this last set\, we will describe th
e moduli map from the quotient which describes the matrices whose determin
ant defines $D$ and the moduli space of semistable shaves on $\\mathbb{P}^
N$ that contains $\\mathcal{T}_D$. \n\nThis is a joint work with Daniele F
aenzi.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sönke Rollenske (Philipps-Universität Marburg)
DTSTART:20210518T140000Z
DTEND:20210518T150000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/8
DESCRIPTION:Title: Corona surfaces and extra components in the modul
i space of stable surfaces\nby Sönke Rollenske (Philipps-Universität
Marburg) as part of Geometry in Como\n\n\nAbstract\nThe moduli space of s
table surfaces is a modular compactification of the\nGiesecker moduli spac
e of (canonical models of) projective algebraic\nsurfaces of general type.
\nWe show that the compactification has many extra irreducible and\nconnec
ted components.\nThe construction of examples is phrased in terms of a vir
us surface V\ninfecting suitable non-normal Gorenstein stable surfaces and
will be\nillustrated by many pictures.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Castrillón (Universidad Complutense de Madrid)
DTSTART:20210615T140000Z
DTEND:20210615T150000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/9
DESCRIPTION:Title: Homogeneous structures in pseudo-Riemannian manif
olds and beyond\nby Marco Castrillón (Universidad Complutense de Madr
id) as part of Geometry in Como\n\n\nAbstract\nA celebrated result by Ambr
ose and Singer characterizes the homogeneity of a pseudo-Riemannian manifo
ld by a set of partial differential equations satisfied by a tensor field\
, together with some additional conditions of topological nature. We will
review the geometric information provided by this homogeneous tensor in di
fferent situations\, being the so-called linear case the most relevant ins
tance. From that point\, we will move to recent result on non-necessarily
metric manifolds where we will explore the characterization of homogeneity
in other contexts as\, for exmaple\, the symplectic of Fedosov case.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Ovando (Universidad Nacional de Rosario/CONICET)
DTSTART:20211123T160000Z
DTEND:20211123T170000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/10
DESCRIPTION:Title: Magnetic trajectories on 2-step nilmanifolds
\nby Gabriela Ovando (Universidad Nacional de Rosario/CONICET) as part of
Geometry in Como\n\n\nAbstract\nFrom the perspective of classical mechanic
s\, a charged particle moving on a Riemannian manifold $M$ experiences a L
orentz force\, and its trajectory is called a magnetic trajectory. The Lor
entz force determines a magnetic field which is introduced as a closed 2-f
orm on $M$. In this work\, we focus on 2-step nilpotent Lie groups equippe
d with a left-invariant metric and a left-invariant magnetic field. The ai
m is to study magnetic fields\, their corresponding magnetic equations an
d solutions. We obtain existence results regarding closed 2-forms and exp
licit expressions for a family of magnetic trajectories. Some ideas concer
ning closedness conditions are analysed.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Massarenti (Università di Ferrara)
DTSTART:20211215T160000Z
DTEND:20211215T170000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/11
DESCRIPTION:Title: Complete symplectic quadrics and Kontsevich modu
li spaces of conics in Lagrangian Grassmannians\nby Alex Massarenti (U
niversità di Ferrara) as part of Geometry in Como\n\n\nAbstract\nGiven a
reductive algebraic group $G$ and a Borel subgroup $B$\, a spherical varie
ty is a normal variety admitting an action of $G$ with an open dense $B$-o
rbit.\nA special class of spherical varieties are the so-called wonderful
varieties.\nThese are smooth spherical varieties for which we require $G$
to be semisimple and simply connected and the existence of an open $B$-orb
it whose complementary set is a simple normal crossing divisor.\nWe will c
onstruct the wonderful compactification of the space of symmetric\, symple
ctic matrices on which the symplectic group acts.\nFurthermore\, we will c
ompute the Picard group of this compactification and we will study its bir
ational geometry in low-dimensional cases.\nAs an application\, we will re
cover the results on the birational geometry of the Kontsevich spaces of c
onics in Grassmannians due to I. Coskun a D. Chen\,\nand we will prove new
results on the birational geometry of the Kontsevich spaces of conics in
Lagrangian Grassmannians.\n\nThis is a joint work with Elsa Corniani.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gabriela Ovando (Universidad Nacional de Rosario/CONICET)
DTSTART:20211214T160000Z
DTEND:20211214T170000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/12
DESCRIPTION:Title: Magnetic trajectories on 2-step nilmanifolds
\nby Gabriela Ovando (Universidad Nacional de Rosario/CONICET) as part of
Geometry in Como\n\n\nAbstract\nFrom the perspective of classical mechanic
s\, a charged particle moving on a Riemannian manifold $M$ experiences a L
orentz force\, and its trajectory is called a magnetic trajectory. The Lor
entz force determines a magnetic field which is introduced as a closed 2-f
orm on $M$. In this work\, we focus on 2-step nilpotent Lie groups equippe
d with a left-invariant metric and a left-invariant magnetic field. The ai
m is to study magnetic fields\, their corresponding magnetic equations an
d solutions. We obtain existence results regarding closed 2-forms and exp
licit expressions for a family of magnetic trajectories. Some ideas concer
ning closedness conditions are analysed.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Miranda (Universitat Politècnica de Catalunya)
DTSTART:20220323T160000Z
DTEND:20220323T170000Z
DTSTAMP:20260422T214839Z
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 Geometry in
Como\n\n\nAbstract\nb-Structures are hidden in many places\, on manifolds
with boundary and associated index formulae (Melrose\, Nest-Tsygan)\, in
the geometry of pseudo-Riemannian geodesics (Khesin-Tabachnikov) and in th
e regularization transformations in celestial mechanics (Mc Gehee). We wil
l give a panorama talk on b-structures in the symplectic and contact realm
describing some of the main techniques and some open problems.\n\nData fo
r Zoom:\n\nMeeting ID: 917 9437 1036\n\nAccess code: 330550\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucía Martín Merchán (Università degli Studi di Torino)
DTSTART:20220126T160000Z
DTEND:20220126T170000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/14
DESCRIPTION:Title: A compact non-formal closed $G_2$ manifold 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-dime
nsional Riemannian manifold determined by a certain type of 3-form $\\varp
hi$. These are classified into 16 types according to PDEs involving $\\var
phi$\; for instance\, the $G_2$ structure is torsion-free if $\\varphi$ is
parallel\, closed if $\\varphi$ is closed and cocalibrated if $\\varphi$
is co-closed. This talk contributes to understanding topological propertie
s of compact manifolds with a closed $G_2$ structure that cannot be endowe
d with any torsion-free $G_2$ structure. Namely\, we construct such a mani
fold that is non-formal and has first Betti number $b_1=1$. The starting p
oint is a nilmanifold $(M\,\\varphi)$ with a closed $G_2$ structure that a
dmits an involution preserving $\\varphi$ such that the quotient $M/\\math
bb{Z}_2$ is a non-formal orbifold with $b_1=1$. Then we perform a resoluti
on of these singularities obtaining a manifold endowed with a closed $G_2$
structure\; we finally prove that the resolution verifies the same topolo
gical properties and do not admit any torsion-free $G_2$ structure.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Russo (Università degli Studi di Catania)
DTSTART:20220216T160000Z
DTEND:20220216T170000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/15
DESCRIPTION:Title: Explicit unirationality of some moduli spaces of
K3 surfaces via trisecant flops\nby Francesco Russo (Università degl
i Studi di Catania) as part of Geometry in Como\n\n\nAbstract\nThe 19-dime
nsional moduli space $F_g$ of polarized K3 surfaces of genus $g$ (and degr
ee $2g-2$) 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 va
lues of $g$ the construction of unirationality provides a computer-impleme
ntable algorithm to determine the equations of the general member of $F_g$
. We shall present the relations between some K3 surfaces and some special
cubic fourfolds and describe a procedure to determine explicitly the equa
tions of the general K3 surface of genus $g$ as a function of a number of
specific independent variables. This procedure can be easily implemented i
n Macaulay2 and\, in particular\, it yields the explicit unirationality of
$F_g$ for $g=11\,14\,20\,22$. This is based on joint works with Giovanni
Staglianò.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Bricalli\, Filippo Favale (Università di Pavia)
DTSTART:20220429T150000Z
DTEND:20220429T160000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/16
DESCRIPTION:Title: Lefschetz properties for jacobian rings of cubic
fourfolds and other Artinian algebras\nby Davide Bricalli\, Filippo F
avale (Università di Pavia) as part of Geometry in Como\n\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (Università degli Studi di Torino)
DTSTART:20220519T150000Z
DTEND:20220519T160000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/17
DESCRIPTION:Title: An overview on closed $G_2$-structures\nby
Anna Fino (Università degli Studi di Torino) as part of Geometry in Como\
n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Rojo Carulli (Universidad Politécnica de Madrid)
DTSTART:20221201T151500Z
DTEND:20221201T161500Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/18
DESCRIPTION:Title: Sasakian vs K-contact geometry\nby Juan Rojo
Carulli (Universidad Politécnica de Madrid) as part of Geometry in Como\
n\n\nAbstract\nIn differential geometry\, a recurrent theme is to study ho
w close the existence of a certain geometric structure on a manifold place
s it from the algebraic-geometry world\, in a broad sense.\n\nFor even dim
ension\, the most famous instance of this problem has been the symplectic
vs Kählerian question\, concerning the existence of symplectic non-Kähle
rian manifolds. This problem has been intensively studied in the past deca
des\, and has been an important source of development for the area known a
s symplectic topology.\n\nFor odd dimension\, an analogous problem is the
K-contact vs Sasakian question\, which tries to understand which manifolds
(if any) admits K-contact but not Sasakian structures.\nIn this talk we w
ill explain a bit the analogies and differences between the two questions\
, and explore some of the results obtained in the past recent years for th
e latter\, particularly in the five dimensional and simply connected case.
\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Noja (Ruprecht-Karls-Universität Heidelberg)
DTSTART:20230223T151500Z
DTEND:20230223T161500Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/19
DESCRIPTION:Title: Nilpotence Varieties\, Pure Spinors Superfields
and Supersymmetry\nby Simone Noja (Ruprecht-Karls-Universität Heidelb
erg) as part of Geometry in Como\n\n\nAbstract\nIn this talk I will introd
uce a mathematical perspective on the pure spinor superfield formalism\, s
howing how to recover (all) supersymmetry multiplets from geometric data r
elated to the nilpotence variety of a certain Poincaré superalgebra. Afte
r discussing some lower dimensional examples\, I will focus on the relevan
t case of supersymmetry in six dimensions\, where the nilpotence variety i
s given by a four dimensional Segre variety. If time permits\, I will expl
ain how nilpotence varieties of classical Lie superalgebras are related to
the superconformal field theories (and hence AdS/CFT conjecture).\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Gómez Nicolás (Universidad de Cantabria)
DTSTART:20230523T141500Z
DTEND:20230523T151500Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/20
DESCRIPTION:Title: Structures on generalized geometry\nby Pablo
Gómez Nicolás (Universidad de Cantabria) as part of Geometry in Como\n\
n\nAbstract\nGeneralized Geometry was introduced at the beginning of XXI c
entury by N. Hitchin\, M. Gualtieri and G. Cavalcanti. This theory is base
d on the study of the generalized tangent bundle or big tangent bundle\, d
efined as the Whitney sum of the tangent and the cotangent bundle of a man
ifold.\n\nAs in the case of geometric structures defined on a manifold\, d
ifferent "generalized geometric structures" can be defined on the generali
zed tangent bundle\, such as metrics\, complex structures\, paracomplex st
ructures\, etc. The first important examples of generalized complex struct
ures were given by M. Gualtieri\, showing that both complex structures and
symplectic structures defined on a manifold can be understood as generali
zed complex structures. In this seminar\, we shall show that many other st
ructures appear in Generalized Geometry if we take a less restrictive defi
nition than the original one given by M. Gualtieri. In this way\, we 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://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandro Gil García (Universität Hamburg)
DTSTART:20231130T140000Z
DTEND:20231130T150000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/21
DESCRIPTION:Title: Pseudo-Kähler and hypersymplectic structures on
semidirect products\nby Alejandro Gil García (Universität Hamburg)
as part of Geometry in Como\n\nLecture held in Room V2.10\, Via Valleggio
11\, Como.\n\nAbstract\nWe study left-invariant pseudo-Kähler and hypersy
mplectic structures on semidirect products $G\\rtimes H$\; we work at the
level of the Lie algebra $\\mathfrak{g}\\rtimes\\mathfrak{h}$. In particul
ar we consider the structures induced on $\\mathfrak{g}\\rtimes\\mathfrak{
h}$ by existing pseudo-Kähler structures on $\\mathfrak{g}$ and $\\mathfr
ak{h}$\; we classify all semidirect products of this type with $\\mathfrak
{g}$ of dimension $4$ and $\\mathfrak{h}=\\mathbb{R}^2$. In the hypersympl
ectic setting\, we consider a more general construction on semidirect prod
ucts. We construct new $2$-step nilpotent hypersymplectic Lie algebras\; t
o our knowledge\, these are the first such examples whose underlying compl
ex structure is not abelian. This is a joint work with Diego Conti (https:
//arxiv.org/abs/2310.20660)\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele Angella (Università degli Studi di Firenze)
DTSTART:20240206T143000Z
DTEND:20240206T153000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/22
DESCRIPTION:Title: Constructing and Machine Learning Calabi-Yau Fiv
e-Folds\nby Daniele Angella (Università degli Studi di Firenze) as pa
rt of Geometry in Como\n\n\nAbstract\nThe significance of Calabi-Yau manif
olds transcends both Complex Geometry and String Theory.\nOne possible app
roach to constructing Calabi-Yau manifolds involves intersecting hypersurf
aces within the product of projective spaces\, defined by polynomials of a
specific degree.\nWe show a method to construct all possible complete int
ersections Calabi-Yau five-folds within a product of four or less complex
projective spaces\, with up to four constraints. This results in a compre
hensive set of 27\,068 distinct spaces.\nFor approximately half of these c
onstructions\, excluding the product spaces\, we can compute the cohomolog
ical data\, yielding 2\,375 distinct Hodge diamonds.\nWe present distribut
ions of the invariants and engage in a comparative analysis with their low
er-dimensional counterparts.\nSupervised machine learning techniques are a
pplied to the cohomological data. The Hodge number $h^{1\,1}$ can be learn
t with high efficiency\; however\, accuracy diminishes for other Hodge num
bers due to the extensive ranges of potential values.\n\nThe talk is a joi
nt collaboration with Rashid Alawadhi\, Andrea Leonardo\, and Tancredi Sch
ettini Gherardini.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicoletta Tardini (Università degli Studi di Parma)
DTSTART:20240208T143000Z
DTEND:20240208T153000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/23
DESCRIPTION:Title: Cohomological Properties of Hypercomplex Manifol
ds\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 structure $(I
\,J\,K)$ and a real and positive\n(in the quaternionic sense) $\\partial$-
closed $(2\,0)$ form (here the bidegree and $\\partial$ are taken with res
pect to the complex structure $I$). Examples of these manifolds are hyperk
ähler manifolds. We will discuss the cohomological behavior of HKT manifo
lds and we will present some numerical characterizations for the existence
of such metrics. \n\nThese are joint works with Giovanni Gentili and Mehd
i Lejmi.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Sferruzza (Università dell'Insubria)
DTSTART:20240419T130000Z
DTEND:20240419T140000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/24
DESCRIPTION:Title: A brief introduction to formality of differentia
ble manifolds\nby Tommaso Sferruzza (Università dell'Insubria) as par
t of Geometry in Como\n\n\nAbstract\nIn the context of differentiable mani
folds\, a relevant role is played by the notion of formality\, introduced
by Quillen ('69) and Sullivan ('77). A differentiable manifold is said to
be formal if its homotopy type (up to torsion) can be recoved by its cohom
ology ring. A natural cohomological obstruction to formality is given by t
he existence of non vanishing Massey products\, whereas\, in the early 00'
s\, Kotschick defined a stronger notion of formality\, involving the exist
ence of special Riemannian metrics. In this talk\, I will give the main de
finitions and their interplay\, provide the classical examples of (non) fo
rmal differentiable manifolds and exhibit the topological obstructions rel
ated to formality.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baptiste Chantraine (Université de Nantes)
DTSTART:20240514T130000Z
DTEND:20240514T140000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/25
DESCRIPTION:Title: Product structure in locally conformally symplec
tic geometry\nby Baptiste Chantraine (Université de Nantes) as part o
f Geometry in Como\n\n\nAbstract\nLocally conformally symplectic structure
s (lcs) generalise symplectic manifolds by studying closed non-degenerate
2-forms with value in a flat line bundle. In this talk\, after introducing
the subject and its relations with contact and symplectic geometry\, I wi
ll talk about a construction of twisted product of lcs manifolds. This con
struction allows to relates fixed point of Hamiltonian diffeomorphisms to
Lagrangian intersections (and this to relate the number of such fixed poin
t to Novikov homology of the Lee class of the flat bundle). This is a join
t work with Kevin Sackel.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Magliaro (Università dell'Insubria)
DTSTART:20240704T130000Z
DTEND:20240704T140000Z
DTSTAMP:20260422T214839Z
UID:DifferentialAndAlgebraicGeometry/26
DESCRIPTION:Title: Sharp pinching theorems for complete CMC submani
folds in the sphere\nby Marco Magliaro (Università dell'Insubria) as
part of Geometry in Como\n\n\nAbstract\nIn 1968 Simons proved that if a co
mpact\, minimal submanifold of the unit sphere $f:M^n\\to\\mathbb S^{n+p}$
has second fundamental form satisfying $|A|^2\\le np/(2p-1)$\, then eithe
r $|A|\\equiv0$ and $M$ is a great sphere\, or $|A|^2\\equiv np/(2p-1)$. L
awson and Chern\, do Carmo & Kobayashi characterized the latter case and p
roved that if $|A|^2\\equiv np/(2p-1)$\, then $M$ is a Clifford torus or a
Veronese surface. This pinching theorem was later generalized by Alencar
& do Carmo for compact CMC hypersurfaces of the sphere and by Santos for c
ompact PMC submanifolds of the sphere. In this talk we extend the results
by Simons\, Lawson\, Chern\, do Carmo & Kobayashi and Alencar & do Carmo t
o complete submanifolds of the sphere. We also partially generalize the re
sult of Santos in dimension $n\\le6$. This is joint work with L. Mari\, F.
Roing and A. Savas-Halilaj.\n
LOCATION:https://researchseminars.org/talk/DifferentialAndAlgebraicGeometr
y/26/
END:VEVENT
END:VCALENDAR