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BEGIN:VEVENT
SUMMARY:Giovanni Bazzoni (Università degli Studi dell'Insubria)
DTSTART;VALUE=DATE-TIME:20201020T150000Z
DTEND;VALUE=DATE-TIME:20201020T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/1
DESCRIPTION:Title: Sy
mmetric and skew-symmetric complex structures\nby Giovanni Bazzoni (Un
iversità degli Studi dell'Insubria) as part of Differential Geometry Semi
nar Torino\n\n\nAbstract\nIn this talk we study the geometry of a complex
manifold $(M\,J)$ endowed with a closed\, non-degenerate 2-form $\\omega$
with respect to which $J$ is either symmetric or skew-symmetric. This lead
s to\, respectively\, complex-symplectic and pseudo-Kähler structures. Co
mplex symplectic structures are related to a number of other geometric str
uctures\, such as (hyper)Kähler\, hypercomplex\, and hypersymplectic. We
are interested in examples of manifolds which carry some of these structur
es\, but no others. Joint work with M. Freibert\, A. Gil García\, A. Lato
rre\, B. Meinke.\n
LOCATION:https://researchseminars.org/talk/DGSTO/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wayne Rossman (Kobe University)
DTSTART;VALUE=DATE-TIME:20201028T090000Z
DTEND;VALUE=DATE-TIME:20201028T100000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/2
DESCRIPTION:Title: Da
rboux flow and semi-discrete mKdV equation\nby Wayne Rossman (Kobe Uni
versity) as part of Differential Geometry Seminar Torino\n\nAbstract: TBA\
n
LOCATION:https://researchseminars.org/talk/DGSTO/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tommaso Pacini (Università degli Studi di Torino)
DTSTART;VALUE=DATE-TIME:20201117T160000Z
DTEND;VALUE=DATE-TIME:20201117T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/3
DESCRIPTION:Title: Fr
om calibrated geometry to holomorphic invariants\nby Tommaso Pacini (U
niversità degli Studi di Torino) as part of Differential Geometry Seminar
Torino\n\n\nAbstract\nThe seminar will address questions such as: (i) How
to use submanifolds to study the ambient space\, (ii) How to use ideas fr
om calibrated geometry to build new holomorphic invariants\, (iii) How to
calculate these invariants\, and why we might care.\nThis will be a non-te
chnical survey of my recent research and of its context within classical c
omplex analysis and the current theory of manifolds with special holonomy.
\n
LOCATION:https://researchseminars.org/talk/DGSTO/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mason Pember (Politecnico di Torino)
DTSTART;VALUE=DATE-TIME:20201120T150000Z
DTEND;VALUE=DATE-TIME:20201120T154000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/4
DESCRIPTION:Title: Sp
herical curves in Lie sphere geometry\nby Mason Pember (Politecnico di
Torino) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nBl
aschke showed that a surface with one family of spherical curvature lines
can be parametrised via a certain flow of an initial curve on a sphere. I
n this talk we characterise when this surface is additionally a Lie applic
able surface\, by restricting the flow and the initial curve. It turns out
that the initial curve must project to a constrained elastic curve in som
e space form\, which leads us to a Lie geometric characterisation of such
curves.\n\nThis talk will be held on the occasion of the PRIN seminar orga
nised by the Politecnico di Torino PRIN unit.\n
LOCATION:https://researchseminars.org/talk/DGSTO/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Vollmer (Politecnico di Torino)
DTSTART;VALUE=DATE-TIME:20201120T155000Z
DTEND;VALUE=DATE-TIME:20201120T163000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/5
DESCRIPTION:Title: Tw
o-dimensional superintegrable metrics with symmetries that preserve geodes
ic curves\nby Andreas Vollmer (Politecnico di Torino) as part of Diffe
rential Geometry Seminar Torino\n\n\nAbstract\nIn 1882\, Sophus Lie formul
ated the task to describe two-dimensional metrics admitting non-trivial sy
mmetries that preserve geodesics up to reparametrisation. Such symmetries
are called projective. Lie's Problem has been resolved in recent years in
terms of a classification up to diffeomorphisms (Bryant-Manno-Matveev 2008
\, Matveev 2012 and Manno-V 2020).\n\nThe talk will focus on a distinct su
bclass of these metrics\, namely those that are superintegrable with quadr
atic integrals of motion. Generally speaking a metric is superintegrable i
f it admits a maximal amount of independent constants of motion.\nMatveev'
s geometries are a particular example\, in which case the projective symme
try is unique. It turns out that all of Matveev's geometries share the sam
e geodesics up to reparametrisation (in other words\, they are projectivel
y equivalent). The associated superintegrable systems are of non-degenerat
e type meaning that they admit a four-parameter potential.\n\nThis talk wi
ll be held on the occasion of the PRIN seminar organised by the Politecnic
o di Torino PRIN unit.\n
LOCATION:https://researchseminars.org/talk/DGSTO/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Lotay (University of Oxford)
DTSTART;VALUE=DATE-TIME:20201201T160000Z
DTEND;VALUE=DATE-TIME:20201201T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/6
DESCRIPTION:Title: Mi
nimal Lagrangians and where to find them\nby Jason Lotay (University o
f Oxford) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nA
classical problem going back to ancient Greece is to find the shortest cu
rve in the plane enclosing a given area: the isoperimetric problem. A simi
lar question is whether given a curve on a surface it can be deformed to a
shortest one. Whilst the solutions to these classical problems are well-k
nown\, natural generalisations in higher dimensions are mostly unsolved. I
will explain how this leads us to the study of minimal Lagrangians and th
e question of how to find them\, which will take us to the interface betwe
en symplectic topology\, Riemannian geometry and analysis of nonlinear PDE
s\, with links to theoretical physics.\n\nThis talk will be held on the oc
casion of the PRIN seminar organised by the Università di Torino PRIN uni
t.\n
LOCATION:https://researchseminars.org/talk/DGSTO/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Ivey (College of Charleston)
DTSTART;VALUE=DATE-TIME:20201214T160000Z
DTEND;VALUE=DATE-TIME:20201214T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/7
DESCRIPTION:Title: Ne
w Integrable Curve Flows in the Pseudoconformal 3-Sphere\nby Thomas Iv
ey (College of Charleston) as part of Differential Geometry Seminar Torino
\n\n\nAbstract\nThe pseudoconformal 3-sphere $S^3$ is the projectivization
of the null cone in $\\mathbb C^3$ with the standard pseudo-Hermitian inn
er product. The Lie group $SU(2\,1)$ fixing this metric naturally acts on
the sphere\, preserving a contact structure\, and can be identified with t
he pseudoconformal frame bundle of $S^3$. By normalizing lifts to the fram
e bundle\, we define scalar geometric invariants for Legendrian curves (L-
curves) in $S^3$\, and for curves transverse to the contact planes (T-curv
es).\nWe seek invariant geometric flows for these parametrized curves that
induce integrable evolution systems for the invariants. While there is an
infinite sequence of geometric flows for L-curves inducing the Boussinesq
hierarchy\, for T-curves there is another infinite sequence of flows that
induces a sequence of 3-component evolution systems for the invariants\,
evidently a novel integrable bi-Hamiltonian hierarchy. This closely resem
bles the NLS hierarchy\, itself realized by a sequence of curve flows in E
uclidean 3-space\, including the vortex filament equation. We discuss som
e common features of these hierarchies\, describe the geometry and dynamic
s of travelling wave solutions (also arising as critical curves for Lagran
gians derived from the conserved densities) and conclude with some open qu
estions.\n
LOCATION:https://researchseminars.org/talk/DGSTO/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Bonsante (Università degli Studi di Pavia)
DTSTART;VALUE=DATE-TIME:20210127T160000Z
DTEND;VALUE=DATE-TIME:20210127T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/8
DESCRIPTION:Title: Mi
nimizing immersions of surfaces in hyperbolic 3-manifolds\nby Francesc
o Bonsante (Università degli Studi di Pavia) as part of Differential Geom
etry Seminar Torino\n\n\nAbstract\nTrapani and Valle proposed to study the
L^1 holomorphic energy of diffeomorphisms between Riemannian surfaces. Th
is is defined as the L^1-norm of the (1\,0)-part of the differential of th
e map. They proved that if the domain and the target are surfaces of negat
ive curvature\, any homotopy class of diffeomorphisms contains a unique mi
nimizer for the functional. In a recent work with Gabriele Mondello and Je
an-Marc Schlenker we tried to generalize the functional in the setting wh
ere the domain is a hyperbolic surface and the target a hyperbolic 3-manif
old. The functional here is the L^1-Shatten energy\, which in fact coincid
es with the L^1-holomorphic energy in the 2-dimensional case. More concret
ely we considered the space of equivariant maps of the universal covering
of a fixed surface of genus g into the hyperbolic space\, and studied map
s which minimize the L^1-Shatten energy on fibers of the monodromy map. We
proved that the space of such minimizing maps is naturally a complex mani
fold of dimension 6g-6\, where g is the genus of the surface\, so that the
monodromy map realize a holomorphic embedding onto some open subset of th
e PSL_2(C)-character variety containing the Fuchsian locus.\n\nIn the talk
I will describe the main results of this joint work.\n
LOCATION:https://researchseminars.org/talk/DGSTO/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Sharp (University of Leeds)
DTSTART;VALUE=DATE-TIME:20210209T160000Z
DTEND;VALUE=DATE-TIME:20210209T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/9
DESCRIPTION:Title: Ł
ojasiewicz-type inequalities for the H-functional near simple bubble trees
\nby Ben Sharp (University of Leeds) as part of Differential Geometry
Seminar Torino\n\n\nAbstract\nThe H-functional E is a natural variant of t
he Dirichlet energy along maps u from a closed surface S into R^3. Critica
l points of E include conformal parameterisations of constant mean curvatu
re surfaces in R^3. The functional itself is unbounded from above and belo
w on H^1(S\,R^3)\, but all critical points have H-energy E at least 4π/3\
, with equality attained if and only if we are parametrising a round spher
e (so S itself must be a sphere) - this is the classical isoperimetric ine
quality.\n\nHere we will address the simple question: can one approach the
natural lower energy bound by critical points along fixed surfaces of hig
her genus? In fact we prove more subtle quantitative estimates for any (al
most-)critical point whose energy is close to 4π/3. Standard theory tells
us that a sequence of (almost-)critical points on a fixed torus T\, whose
energy approaches 4π/3\, must bubble-converge to a sphere: there is a sh
rinking disc on the torus that gets mapped to a larger and larger region o
f the round sphere\, and away from the disc our maps converge to a constan
t. Thus the limiting object is really a map from a sphere to R^3\, and the
challenge is to compare maps from a torus with the limiting map (i.e. a c
hange of topology in the limit). In particular we can prove a gap theorem
for the lowest energy level on a fixed surface and estimate the rates at w
hich bubbling maps u are becoming spherical in terms of the size of dE[u]
- these are commonly referred to as Łojasiewicz-type estimates. \n\nThis
is a joint work with Andrea Malchiodi (SNS Pisa) and Melanie Rupflin (Oxfo
rd).\n
LOCATION:https://researchseminars.org/talk/DGSTO/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Matveev (Universität Jena)
DTSTART;VALUE=DATE-TIME:20210223T160000Z
DTEND;VALUE=DATE-TIME:20210223T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/10
DESCRIPTION:Title: N
ijenhuis geometry\, multihamiltonian systems of hydrodynamic type and geod
esic equivalence\nby Vladimir Matveev (Universität Jena) as part of D
ifferential Geometry Seminar Torino\n\n\nAbstract\nWe connect two a priori
unrelated topics\, theory of geodesically equivalent metrics in different
ial geometry\, and theory of compatible infinite dimensional Poisson brack
ets of hydrodynamic type in mathematical physics. \n\nNamely\, we prove t
hat a pair of geodesically equivalent metrics such that one is flat produc
es a pair of such brackets. We construct Casimirs for these brackets and t
he corresponding commuting flows. \n\nThere are two ways to produce a larg
e family of compatible Poisson structures from a pair of geodesically equi
valent metrics one of which is flat. One of these families is $(n+1)(n+2)
/2$ dimensional\; we describe it completely and show that it is maximal. A
nother has dimension $\\le n+2$ and is\, in a certain sense\, polynomial.
We show that a nontrivial polynomial family of compatible Poisson structur
es of dimension $n+2$ is unique and comes from a pair of geodesically equi
valent metrics.\n\nThe talk based on a series of joint publications with A
. Bolsinov (Lboro) and A. Konyaev (Moscow)\; the most related one is https
://arxiv.org/abs/2009.07802\n
LOCATION:https://researchseminars.org/talk/DGSTO/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastien Picard (University of British Columbia)
DTSTART;VALUE=DATE-TIME:20210309T160000Z
DTEND;VALUE=DATE-TIME:20210309T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/11
DESCRIPTION:Title: M
etrics Through Non-Kahler Transitions\nby Sebastien Picard (University
of British Columbia) as part of Differential Geometry Seminar Torino\n\n\
nAbstract\nIt was proposed by Clemens\, Friedman and Reid to connect Calab
i-Yau threefolds of different topologies by an operation known as a conifo
ld transition. However\, this process may produce a non-Kahler complex man
ifold with trivial canonical bundle. We will consider conifold transitions
from the point of view of differential geometry and discuss passing speci
al metrics through a non-Kahler transition.\n\nThis is joint work with T.C
. Collins and S.-T. Yau.\n
LOCATION:https://researchseminars.org/talk/DGSTO/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Mazzieri (Università degli Studi di Trento)
DTSTART;VALUE=DATE-TIME:20210324T130000Z
DTEND;VALUE=DATE-TIME:20210324T140000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/12
DESCRIPTION:Title: S
errin-type theorems for domains with disconnected boundary\nby Lorenzo
Mazzieri (Università degli Studi di Trento) as part of Differential Geom
etry Seminar Torino\n\n\nAbstract\nWe prove new optimal symmetry results f
or solutions to the torsion problem on domains with disconnected boundary.
\nTime permitting\, we discuss their relations with the uniqueness theore
m for the Schwarzschild-de Sitter static black hole in general relativity.
\nThe results are obtained in collaboration with V. Agostiniani and S. Bo
rghini.\n
LOCATION:https://researchseminars.org/talk/DGSTO/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Ustinovskiy (New York University)
DTSTART;VALUE=DATE-TIME:20210412T150000Z
DTEND;VALUE=DATE-TIME:20210412T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/13
DESCRIPTION:Title: G
ibbons-Hawking ansatz and Generalized Kahler solitons\nby Yury Ustinov
skiy (New York University) as part of Differential Geometry Seminar Torino
\n\n\nAbstract\nIn the last decades geometric flows have been proved to be
a powerful tool in the classification and uniformization problems in geom
etry and topology. Despite the wide range of applicability of the existing
analytical methods\, we are still lacking efficient tools adapted to the
study of general (non-Kahler) complex manifolds. In my talk I will discuss
the pluriclosed flow - a modification of the Ricci flow - which was intro
duced by Streets and Tian\, and shares many nice features of the Ricci flo
w. The important open questions driving the ongoing research in complex ge
ometry are the classification of compact non-Kahler surfaces\, and the Glo
bal Spherical Shell conjecture. Our hope is that understanding the long-ti
me behaviour and singularities of the pluriclosed flow well enough\, we ca
n use it to approach these open questions.\n\nTo apply an analytic flow to
any geometric problem\, we need to make the first necessary step - classi
fy the stationary points of the flow\, and\, more generally\, its solitons
(stationary points modulo diffeomorphisms). For the pluriclosed flow\, th
is question reduces to a non-linear elliptic PDE for an Hermitian metric o
n a given complex manifold. We will discuss this problem on compact/comple
te complex surfaces\, and provide exhaustive classification under natural
extra geometric assumptions. In the course of our classification we will d
iscover a natural extension of the famous Gibbons-Hawking ansatz for hyper
Kahler manifolds.\n
LOCATION:https://researchseminars.org/talk/DGSTO/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christos-Raent Onti (University of Cyprus)
DTSTART;VALUE=DATE-TIME:20210429T150000Z
DTEND;VALUE=DATE-TIME:20210429T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/14
DESCRIPTION:Title: A
class of Einstein submanifolds of Euclidean space\nby Christos-Raent
Onti (University of Cyprus) as part of Differential Geometry Seminar Torin
o\n\n\nAbstract\nThe knowledge on the subject of Euclidean Einstein subman
ifolds\, except those with constant sectional curvature\, is quite limited
. In fact\, as far as we know\, until now the only classification result a
vailable under purely intrinsic assumptions is in the case of hypersurface
s\, due to an observation by Cartan communicated by Thomas in 1937 and the
work of Fialkow from 1938. In the talk\, I will discuss the characterizat
ion of a class of Einstein manifolds isometrically immersed into Euclidean
space as rotational submanifolds. The highlight is for submanifolds in co
dimension two since in this case our assumptions are purely intrinsic. Thi
s is a joint work with Marcos Dajczer (IMPA) and Theodoros Vlachos (Univer
sity of Ioannina).\n
LOCATION:https://researchseminars.org/talk/DGSTO/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Moroianu (Université Paris-Saclay)
DTSTART;VALUE=DATE-TIME:20210511T150000Z
DTEND;VALUE=DATE-TIME:20210511T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/15
DESCRIPTION:Title: M
etric connections with parallel torsion\nby Andrei Moroianu (Universit
é Paris-Saclay) as part of Differential Geometry Seminar Torino\n\n\nAbst
ract\nThe torsion of every metric connection on a Riemannian manifold has
three components: one totally skew-symmetric\, one of vectorial type\, and
one of twistorial type. In the first part of the talk I will explain the
classification of complete simply connected Riemannian manifolds carrying
a metric connection whose torsion is parallel\, has non-zero vectorial com
ponent and vanishing twistorial component. In the second part I will desc
ribe the case where the only non-vanishing component of the torsion is tot
ally skew-symmetric. Although apparently simpler than the previous case\,
the situation here is much more involved and a complete classification is
currently not available. The talk is based on joint works with Mihaela Pil
ca and Uwe Semmelmann.\n
LOCATION:https://researchseminars.org/talk/DGSTO/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Tinaglia (King's College London)
DTSTART;VALUE=DATE-TIME:20210519T090000Z
DTEND;VALUE=DATE-TIME:20210519T100000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/16
DESCRIPTION:Title: T
he geometry of constant mean curvature surfaces in Euclidean space\nby
Giuseppe Tinaglia (King's College London) as part of Differential Geometr
y Seminar Torino\n\n\nAbstract\nI will begin by reviewing classical geomet
ric properties of constant mean curvature surfaces\, H>0\, in R^3. I will
then talk about several more recent results for surfaces embedded in R^3 w
ith constant mean curvature\, such as curvature and radius estimates. I wi
ll show applications of such estimates including a characterisation of the
round sphere as the only simply-connected surface embedded in R^3 with co
nstant mean curvature and area estimates for compact surfaces embedded in
a flat torus with constant mean curvature and finite genus. I will also ta
lk about the geometry of compact hyper surfaces embedded in a manifold wit
h constant mean curvature and finite index.\n
LOCATION:https://researchseminars.org/talk/DGSTO/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nicolina Istrati (Philipps Universität Marburg)
DTSTART;VALUE=DATE-TIME:20210608T150000Z
DTEND;VALUE=DATE-TIME:20210608T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/17
DESCRIPTION:Title: O
n some variational problems in conformal geometry\nby Nicolina Istrati
(Philipps Universität Marburg) as part of Differential Geometry Seminar
Torino\n\n\nAbstract\nI will present several natural functionals defined o
n a conformal class of almost Hermitian metrics on a compact manifold\, an
d I will establish their Euler-Lagrange equations. I will show that the Ga
uduchon metrics appear naturally as the unique extremal metrics of one suc
h functional. Next\, a new class of metrics will be introduced\, also appe
aring as extremal in complex dimension two. I will show that these new met
rics\, while not Gauduchon in general\, give again unique representatives\
, up to constant multiples\, of conformal classes of almost Hermitian metr
ics. This is joint work with D. Angella\, A. Otiman and N. Tardini.\n
LOCATION:https://researchseminars.org/talk/DGSTO/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viviana del Barco (Universidade Estadual de Campinas)
DTSTART;VALUE=DATE-TIME:20210623T150000Z
DTEND;VALUE=DATE-TIME:20210623T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/18
DESCRIPTION:Title: (
Purely) coclosed G$_2$-structures on 2-step nilmanifolds\nby Viviana d
el Barco (Universidade Estadual de Campinas) as part of Differential Geome
try Seminar Torino\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. T
his motivated several authors to study\, in particular\, left-invariant G$
_2$-structures on 7-dimensional nilpotent Lie groups. These structures cou
ld also be induced to the associated compact quotients\, also known as nil
manifolds.\n\nLeft-invariant torsion free G$_2$-structures\, that is\, def
ined by a simultaneously closed and coclosed positive $3$-form\, do not ex
ist on nilpotent Lie groups. But relaxations of this condition have been t
he subject of study on nilmanifolds lately. One of them are coclosed G$_2$
-structures\, for which the defining $3$-form verifies $\\mathrm{d} \\star
_{g_\\varphi}\\varphi=0$\, and more specifically\, purely coclosed structu
res\, which are defined as those which are coclosed and satisfy $\\varphi\
\wedge \\mathrm{d} \\varphi=0$. \n\nIn this talk\, there will be presented
recent classification results regarding left-invariant coclosed and purel
y coclosed G$_2$-structures on 2-step nilpotent Lie groups. \n\nOur result
s are twofold. On the one hand we give the isomorphism classes of 2-step n
ilpotent Lie algebras admitting purely coclosed G$_2$-structures. The anal
ogous result for coclosed structures was obtained by Bagaglini\, Fernánde
z and Fino [Forum Math. 2018]. \n\nOn the other hand\, we focus on the que
stion of which metrics on these Lie algebras can be induced by a coclosed
or purely coclosed structure. We show that any left-invariant metric is in
duced by a coclosed structure\, whereas every Lie algebra admitting purely
coclosed structures admits metrics which are not induced by any such a st
ructure. In the way of proving these results we obtain a method to constru
ct purely coclosed G$_2$-structures. As a consequence\, we obtain new exam
ples of compact nilmanifolds carrying purely coclosed G$_2$-structures. \n
\nThis is joint work with Andrei Moroianu and Alberto Raffero.\n
LOCATION:https://researchseminars.org/talk/DGSTO/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Cho (TU Wien)
DTSTART;VALUE=DATE-TIME:20211012T150000Z
DTEND;VALUE=DATE-TIME:20211012T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/19
DESCRIPTION:Title: M
onodromy of discrete Darboux transformations\nby Joseph Cho (TU Wien)
as part of Differential Geometry Seminar Torino\n\n\nAbstract\nThe monodro
my of Darboux transformations of smooth isothermic surfaces can be simplif
ied via the gauge theoretic approach. In pursuit of the discrete analogue\
, we consider the discrete curve case. In particular\, using a quaternioni
c approach\, we not only solve the monodromy of discrete Darboux transform
ations\, but also obtain explicit parametrisations for closed discrete Dar
boux transformations of a discrete circle.\n
LOCATION:https://researchseminars.org/talk/DGSTO/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Romina Arroyo (Universidad Nacional de Córdoba)
DTSTART;VALUE=DATE-TIME:20211102T160000Z
DTEND;VALUE=DATE-TIME:20211102T170000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/20
DESCRIPTION:Title: O
n the signature of the Ricci curvature on nilmanifolds\nby Romina Arro
yo (Universidad Nacional de Córdoba) as part of Differential Geometry Sem
inar Torino\n\n\nAbstract\nIn this talk I will present a joint work with R
amiro Lafuente (The University of Queensland) in which we completely descr
ibe all possible signatures for the Ricci curvature of left-invariant metr
ics on nilmanifolds. To do that\, we use ideas from GIT to construct a met
ric whose Ricci curvature has a signature with as many zeros as possible\,
and then we apply an Implicit Function Theorem argument.\n
LOCATION:https://researchseminars.org/talk/DGSTO/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katrin Leschke (University of Leicester)
DTSTART;VALUE=DATE-TIME:20211109T150000Z
DTEND;VALUE=DATE-TIME:20211109T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/21
DESCRIPTION:Title: L
inks between the integrable systems of a CMC surface\nby Katrin Leschk
e (University of Leicester) as part of Differential Geometry Seminar Torin
o\n\n\nAbstract\nA CMC surface in 3-space is constrained Willmore and isot
hermic. It is well known that these 3 surface classes are each determined
by a family of flat connections. In this talk we discuss links between the
corresponding families of flat connections: we show that parallel section
s of the associated family of flat connections of the harmonic Gauss map g
ive algebraically the parallel sections of the other families. In particul
ar\, we obtain links between transformations of CMC surfaces\, isothermic
surfaces and constrained Willmore surfaces which are given by parallel sec
tions\, such as the associated family\, the simple factor dressing and the
Darboux transformation.\n
LOCATION:https://researchseminars.org/talk/DGSTO/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Sroka (Jagiellonian University)
DTSTART;VALUE=DATE-TIME:20211130T150000Z
DTEND;VALUE=DATE-TIME:20211130T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/22
DESCRIPTION:Title: T
he conjecture of Alesker and Verbitsky under hyperKähler assumption.\
nby Marcin Sroka (Jagiellonian University) as part of Differential Geometr
y Seminar Torino\n\n\nAbstract\nI will discuss the advances towards provin
g the so called\nquaternionic Calabi conjecture. I will focus on the recen
t result in this\ndirection due to Dinew and myself. I will include the di
scussion on the\nMonge-Ampère type equations in quaternionic geometry fro
m the unifying\nperspective (in the spirit of Harvey-Lawson).\n
LOCATION:https://researchseminars.org/talk/DGSTO/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Mramor (John Hopkins University)
DTSTART;VALUE=DATE-TIME:20211207T150000Z
DTEND;VALUE=DATE-TIME:20211207T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/23
DESCRIPTION:Title: S
ome new applications of the mean curvature flow to self shrinkers\nby
Alex Mramor (John Hopkins University) as part of Differential Geometry Sem
inar Torino\n\n\nAbstract\nThe mean curvature flow\, where one deforms a s
ubmanifold by its mean curvature vector\, is known to in many cases develo
p singularities. These are points where the curvature along the flow blows
up\, or in some sense where the submanifold pinches. This makes the study
of singularities vital to fully utilize the flow. Arguably the most basic
local models for singularities are self shrinkers\, called such because t
hey evolve by dilations. In this talk I’ll discuss some applications of
the mean curvature flow to the study of self shrinkers in $\\mathbb{R}^{3}
$ and $\\mathbb{R}^{4}$.\n
LOCATION:https://researchseminars.org/talk/DGSTO/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Mira (Universidad Politécnica de Cartagena)
DTSTART;VALUE=DATE-TIME:20220111T150000Z
DTEND;VALUE=DATE-TIME:20220111T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/24
DESCRIPTION:Title: T
he Bernstein problem for Weingarten surfaces\nby Pablo Mira (Universid
ad Politécnica de Cartagena) as part of Differential Geometry Seminar Tor
ino\n\n\nAbstract\nA surface in Euclidean $3$-space is an elliptic Weingar
ten surface if its principal curvatures are related by a smooth\, symmetri
c\, elliptic equation $W(k_1\,k_2)=0$. A well known open problem\, propose
d for instance by Rosenberg and Sa Earp in 1994\, is to solve the Bernstei
n problem for this class of surfaces\, that is: are planes the only entire
elliptic Weingarten graphs? Up to now\, it is only known that the answer
is positive if the Weingarten equation is uniformly elliptic\, i.e.\, if t
he derivatives of $W$ with respect to $k_1$ and $k_2$ lie between two posi
tive constants (for example\, minimal or CMC surfaces are uniformly ellipt
ic with this terminology). This result follows from a deep theorem by L. S
imon on entire graphs with quasiconformal Gauss map. In this talk we pres
ent two theorems. In the first one\, we extend the solution to the Bernste
in problem in the uniformly elliptic case to multigraphs\, proving that pl
anes are the only complete uniformly elliptic Weingarten surfaces whose Ga
uss map image lies in an open hemisphere. In the second one\, we will solv
e in the affirmative the Bernstein problem for Weingarten graphs for a lar
ge class of non-uniformly elliptic Weingarten equations. This is a joint w
ork with Isabel Fernández and José A. Gálvez.\n
LOCATION:https://researchseminars.org/talk/DGSTO/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mario Schulz (Westfälische Wilhelms-Universität Münster)
DTSTART;VALUE=DATE-TIME:20220125T140000Z
DTEND;VALUE=DATE-TIME:20220125T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/25
DESCRIPTION:Title: N
oncompact self-shrinkers for mean curvature flow\nby Mario Schulz (Wes
tfälische Wilhelms-Universität Münster) as part of Differential Geometr
y Seminar Torino\n\n\nAbstract\nIn his lecture notes on mean curvature flo
w\, Ilmanen conjectured the existence of noncompact self-shrinkers with ar
bitrary genus. We employ min-max techniques to give a rigorous existence p
roof for these surfaces. Conjecturally\, the self-shrinkers that we obtain
have precisely one (asymptotically conical) end. We confirm this for larg
e genus via a precise analysis of the limiting object of sequences of such
self-shrinkers for which the genus tends to infinity.\n\nJoint work with
Reto Buzano and Huy The Nguyen.\n
LOCATION:https://researchseminars.org/talk/DGSTO/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Domínguez-Vázquez (University of Santiago de Compostela)
DTSTART;VALUE=DATE-TIME:20220208T150000Z
DTEND;VALUE=DATE-TIME:20220208T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/26
DESCRIPTION:Title: I
nhomogeneous isoparametric hypersurfaces in symmetric spaces of noncompact
type\nby Miguel Domínguez-Vázquez (University of Santiago de Compos
tela) as part of Differential Geometry Seminar Torino\n\n\nAbstract\nA hyp
ersurface of a Riemannian manifold is called isoparametric if its nearby p
arallel hypersurfaces have constant mean curvature. Homogeneous hypersurfa
ces\, that is\, codimension one orbits of isometric actions\, constitute
a fundamental class of examples. The problem of determining which spaces w
ith a large isometry group admit inhomogeneous isoparametric hypersurfaces
has a long history that traces back to Élie Cartan.\n\nIn this talk\, I
will report on a joint work with Víctor Sanmartín-López where we constr
uct the first examples of inhomogeneous isoparametric hypersurfaces in eve
ry symmetric space of noncompact type and rank at least three.\n
LOCATION:https://researchseminars.org/talk/DGSTO/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xi Sisi Shen (Columbia University)
DTSTART;VALUE=DATE-TIME:20220222T150000Z
DTEND;VALUE=DATE-TIME:20220222T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/27
DESCRIPTION:Title: M
etrics of constant Chern scalar curvature and a Chern-Calabi flow\nby
Xi Sisi Shen (Columbia University) as part of Differential Geometry Semina
r Torino\n\n\nAbstract\nWe discuss the existence problem of constant Chern
scalar curvature metrics on a compact complex manifold. We prove a priori
estimates for these metrics conditional on an upper bound on the entropy\
, extending a recent result by Chen-Cheng in the Kähler setting. In addit
ion\, we show how these estimates can be used to prove a convergence resul
t for a Hermitian analogue of the Calabi flow on compact complex manifolds
with vanishing first Bott-Chern class.\n
LOCATION:https://researchseminars.org/talk/DGSTO/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mattia Fogagnolo (Centro De Giorgi - SNS)
DTSTART;VALUE=DATE-TIME:20220322T150000Z
DTEND;VALUE=DATE-TIME:20220322T160000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/28
DESCRIPTION:Title: N
ew integral estimates in substatic manifolds and the Alexandrov Theorem\nby Mattia Fogagnolo (Centro De Giorgi - SNS) as part of Differential Ge
ometry Seminar Torino\n\n\nAbstract\nThe classical Alexandrov Theorem in t
he Euclidean space asserts that any bounded set with a smooth boundary of
constant mean curvature is a ball.\nThis result can be more quantitatively
expressed by showing that an integral deficit from being of constant mea
n curvature dominates suitable analytic quantities that vanish exactly whe
n the domain is a ball. In this talk\, we provide generalizations of this
in the context of substatic manifolds with boundary\, that constitute a va
st generalization of the family of manifolds with nonnegative Ricci curvat
ure\, and that are of particular importance in General Relativity. Our app
roach is based on the discovery of a vector field with nonnegative diverge
nce involving the solution to a torsion-like boundary value problem introd
uced by Li-Xia in a related earlier work.\nThe talk is based on a joint wo
rk with A. Pinamonti (Trento).\n
LOCATION:https://researchseminars.org/talk/DGSTO/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodora Bourni (University of Tennessee Knoxville)
DTSTART;VALUE=DATE-TIME:20220405T140000Z
DTEND;VALUE=DATE-TIME:20220405T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/30
DESCRIPTION:Title: C
onvex ancient solutions to free boundary curve shortening flow\nby The
odora Bourni (University of Tennessee Knoxville) as part of Differential G
eometry Seminar Torino\n\n\nAbstract\nIn this talk we construct and classi
fy convex ancient curve shortening flows in the disc with free boundary on
the circle. This work is joint with Mat Langford.\n
LOCATION:https://researchseminars.org/talk/DGSTO/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Stanfield (University of Queensland)
DTSTART;VALUE=DATE-TIME:20220419T080000Z
DTEND;VALUE=DATE-TIME:20220419T090000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/32
DESCRIPTION:Title: C
ompact Gauduchon-Flat Hermitian manifolds\nby James Stanfield (Univers
ity of Queensland) as part of Differential Geometry Seminar Torino\n\n\nAb
stract\nOn a non-Kähler Hermitian manifold\, the complex structure is not
parallel with respect to the Levi-Civita connection. Instead\, it is natu
ral to consider non-symmetric connections compatible with both metric and
complex structures. In the 90's\, Gauduchon identified a canonical one-par
ameter family of such Hermitian connections which includes the Chern and B
ismut connections. In this talk we will discuss some recent progress in un
derstanding the geometry of these so-called Gauduchon connections\, detail
ing a proof of a conjecture of Yang and Zheng. Namely that other than the
Chern or Bismut cases\, compact Hermitian manifolds with flat Gauduchon co
nnections are Kähler.\n
LOCATION:https://researchseminars.org/talk/DGSTO/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Bolsinov (Loughborough University)
DTSTART;VALUE=DATE-TIME:20220531T140000Z
DTEND;VALUE=DATE-TIME:20220531T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/33
DESCRIPTION:Title: O
n integrability of geodesic flows on 3-dimensional manifolds\nby Alexe
y Bolsinov (Loughborough University) as part of Differential Geometry Semi
nar Torino\n\n\nAbstract\nThe goal of the talk is to discuss the behaviour
of geodesics on 3-manifolds $M$ with $SL(2\,\\mathbb R)$ geometry\, one
of the eight natural geometries according to Thurston\, appearing on three
-dimensional manifolds. It has been known that the corresponding geodesi
c flows cannot be integrable\, however\, this particular case has not been
studied in detail. The situation turned out quite interesting: we have
observed (joint work with Alexander Veselov and Yiru Ye) that the phase
space $T^*M$ contains to two open domains\, complementary to each other an
d having common boundary\, with integrable and chaotic behaviour of geode
sics. In the integrable domain\, we have integrability in the class of re
al-analytic integrals\, whereas in the chaotic domain the geodesic flow h
as positive topological entropy. As a specific example\, we study in more
detail the geodesic flow on the modular 3-manifold $M=SL(2\,\\R)/ SL(2\,
\\mathbb Z)$ homeomorphic to the complement of a trefoil knot $\\mathcal K
$ in 3-sphere.\n\nI will try to talk about these results in the context of
a more general problem on topological obstructions to integrability of ge
odesic flows on smooth manifolds following papers by V. V. Kozlov\, I. A.
Taimanov and L. Butler.\n
LOCATION:https://researchseminars.org/talk/DGSTO/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Pozzetta (Università di Napoli)
DTSTART;VALUE=DATE-TIME:20220503T140000Z
DTEND;VALUE=DATE-TIME:20220503T150000Z
DTSTAMP;VALUE=DATE-TIME:20220528T201037Z
UID:DGSTO/34
DESCRIPTION:by Marco Pozzetta (Università di Napoli) as part of Different
ial Geometry Seminar Torino\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/DGSTO/34/
END:VEVENT
END:VCALENDAR