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BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (Université de Genève)
DTSTART:20201014T130000Z
DTEND:20201014T140000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/1
DESCRIPTION:Title: Abelianisation of Meromorphic Connections and the Geometric
Exact WKB Method\nby Nikita Nikolaev (Université de Genève) as part
of ICMAT Geometry Seminar\n\n\nAbstract\nI will describe an approach to a
nalysing meromorphic connections on Riemann surfaces called abelianisation
. It can be seen as a generalisation of the abelianisation of Higgs bundle
s (a.k.a.\, the spectral correspondence\, a key step in the analysis of Hi
tchin integrable systems) to flat bundles. This approach emerged in the la
st decade in the work of Gaiotto\, Moore\, Neitzke on spectral networks th
at arise in the context of supersymmetric gauge theories. Our point of vie
w via deformation theory sheds light on the mathematical content of the th
eory of spectral networks and makes clear the relationship with the spectr
al correspondence. Furthermore\, our mathematical formulation allows us to
connect abelianisation with an algebro-geometric formulation of the exact
WKB method\, which is the modern exact reincarnation of the much older WK
B approximation method from quantum mechanics.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miquel Cueca (Universität Göttingen)
DTSTART:20201125T150000Z
DTEND:20201125T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/2
DESCRIPTION:Title: Courant algebroids\, between Lie algebroids and symplectic
manifolds\nby Miquel Cueca (Universität Göttingen) as part of ICMAT
Geometry Seminar\n\n\nAbstract\nIt is well known that Courant algebroids c
an be defined either using a bracket and anchor (similar to Lie algebroids
) or as graded symplectic manifolds (similar to symplectic manifolds). In
this talk I will explore how each of those equivalent definitions can be u
sed to obtain different properties and applications of Courant algebroids
like Cartan calculus and their cohomology\, characteristic classes\, momen
t maps\, Courant sigma model ...\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Franco (Instituto Superior Técnico)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/3
DESCRIPTION:Title: Torsion line bundles and branes on the Hitchin system\n
by Emilio Franco (Instituto Superior Técnico) as part of ICMAT Geometry S
eminar\n\n\nAbstract\nThe locus of the Higgs moduli space fixed under tens
orization by a line bundle of order 2 plays a key role in the work of Haus
el and Thaddeus on topological mirror symmetry. We shall describe the beha
vior under mirror symmetry of this fixed locus.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastien Picard (University of British Columbia)
DTSTART:20201202T150000Z
DTEND:20201202T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/4
DESCRIPTION:Title: PDEs on Non-Kahler Calabi-Yau Manifolds\nby Sebastien P
icard (University of British Columbia) as part of ICMAT Geometry Seminar\n
\n\nAbstract\nWe will discuss the non-Kahler Calabi-Yau geometry introduce
d by string theorists C. Hull and A. Strominger. We propose to study these
spaces via a parabolic PDE which is a nonlinear flow of non-Kahler metric
s. This talk will survey works with T. Collins\, T. Fei\, D.H. Phong\, S.-
T. Yau\, and X.-W. Zhang.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART:20201111T150000Z
DTEND:20201111T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/5
DESCRIPTION:Title: Moment maps in mirror symmetry\nby Tristan Collins (MIT
) as part of ICMAT Geometry Seminar\n\n\nAbstract\nI will discuss an infin
ite dimensional geometric invariant theory approach to the deformed Hermit
ian-Yang-Mills (dHYM)\, and special Lagrangian equations. In the setting
of dHYM\, I will discuss how we can use regularity results for a certain f
ully nonlinear\, degenerate elliptic PDE to study notions of algebraic sta
bility. I will explain how these notions of stability are (and are not) r
elated to Bridgeland stability\, and some applications to related problems
in symplectic geometry. This is joint work with S.-T. Yau.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joana Cirici (Universitat de Barcelona)
DTSTART:20201104T150000Z
DTEND:20201104T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/6
DESCRIPTION:Title: Hidden symmetries on almost Kähler manifolds\nby Joana
Cirici (Universitat de Barcelona) as part of ICMAT Geometry Seminar\n\n\n
Abstract\nI will explain how local identities for almost Kähler manifolds
lead to various unexpected symmetries on certain subspaces of the cohomol
ogy of a compact almost Kähler manifold. This allows to deduce several ge
ometric and topological consequences for these manifolds. In particular\,
we obtain new obstructions to the existence of a symplectic form compatibl
e with a given almost complex structure. This is joint work with Scott Wil
son.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Ward (Harvard)
DTSTART:20201209T150000Z
DTEND:20201209T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/7
DESCRIPTION:Title: Homological mirror symmetry for elliptic Hopf surfaces\
nby Abigail Ward (Harvard) as part of ICMAT Geometry Seminar\n\n\nAbstract
\nWe show evidence that homological mirror symmetry is a phenomenon that e
xists beyond the world of Kähler manifolds by exhibiting HMS-type results
for a family of complex surfaces which includes the classical Hopf surfac
e (S^1 x S^3). Each surface S we consider can be obtained by performing lo
garithmic transformations to the product of P^1 with an elliptic curve. We
use this fact to associate to each S a mirror "non-algebraic Landau-Ginzb
urg model" and an associated Fukaya category\, and then relate this Fukaya
category and the derived category of coherent analytic sheaves on S.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Peón-Nieto (University of Nice / University of Birmingham)
DTSTART:20201118T133000Z
DTEND:20201118T143000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/8
DESCRIPTION:Title: Pure codimensionality of wobbly bundles\nby Ana Peón-N
ieto (University of Nice / University of Birmingham) as part of ICMAT Geom
etry Seminar\n\n\nAbstract\nHiggs bundles on smooth projective curves were
introduced by Hitchin as solutions to gauge equations motivated by physic
s. They can be seen as points of T*N\, where N is the moduli space of vect
or bundles on the curve. The topology of the moduli space of Higgs bundles
is determined by the nilpotent cone\, which is a reducible scheme contain
ing the zero section of T*N--->N. Inside this section\, wobbly bundles are
particularly important\, as this is the locus where any other component i
ntersects N. In fact\, this implies that the geometry of the nilpotent con
e can be described in terms of wobbly bundles. In this talk I will explain
an inductive method to prove pure codimensionality of the wobbly locus\,
as announced in a paper by Laumon from the 80's. We expect our method to y
ield moreover a description of the irreducible components of the nilpotent
cone in arbitrary rank.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Marrero (Universidad de La Laguna)
DTSTART:20201216T150000Z
DTEND:20201216T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/9
DESCRIPTION:Title: Invariant measures for contact Hamiltonian systems: symplec
tic sandwiches with contact bread\nby Juan Carlos Marrero (Universidad
de La Laguna) as part of ICMAT Geometry Seminar\n\n\nAbstract\nIn this ta
lk\, I will present some recent results on the existence of invariant meas
ures for contact Hamiltonian systems. In fact\, we will see that\, under s
ome natural conditions\, Hamiltonian systems on a contact manifold C can b
e split into a Reeb dynamics on an open subset of C and a Liouville dynami
cs on a submanifold of C of codimension 1. For the Reeb dynamics we find a
n invariant measure. Moreover\, we show that\, under certain completeness
conditions\, the existence of an invariant measure for the Liouville dynam
ics can be characterized using the notion of a symplectic sandwich with co
ntact bread.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vicente Muñoz (Universidad de Málaga)
DTSTART:20210317T140000Z
DTEND:20210317T150000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/10
DESCRIPTION:Title: A Smale-Barden manifold admitting K-contact but not Sasaki
an structure\nby Vicente Muñoz (Universidad de Málaga) as part of IC
MAT Geometry Seminar\n\n\nAbstract\nSasakian manifolds are odd-dimensional
counterparts of Kahler manifolds in even dimensions\, with K-contact mani
folds corresponding to symplectic manifolds. In this talk\, we give the fi
rst example of a simply connected compact 5-manifold (Smale-Barden manifol
d) which admits a K-contact structure but does not admit any Sasakian stru
cture\, settling a long standing question of Boyer and Galicki.\n\nFor thi
s\, we translate the question about K-contact 5-manifolds to constructing
symplectic 4-orbifolds with cyclic singularities containing disjoint sympl
ectic surfaces of positive genus. The question on Sasakian 5-manifolds tra
nslates to the existence of algebraic surfaces with cyclic singularities c
ontainig disjoint complex curves of positive genus. A key step consists on
bounding universally the number of singular points of the algebraic surfa
ce.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezequiel Maderna (Universidad de la República)
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/11
DESCRIPTION:Title: Hyperbolic motions of the N-body problem with arbitrary li
mit shape\nby Ezequiel Maderna (Universidad de la República) as part
of ICMAT Geometry Seminar\n\n\nAbstract\nDuring the 20th century\, variati
onal methods were banned from the study of the Newtonian model for gravita
tion. The reason\, already explained by Poincaré\, ceased to be an obstru
ction once Marchal proved that the minimizing curves of the Lagrangian act
ion do not present singularities. The applications did not take long: in t
he first instance\, the existence of periodic orbits with a great diversit
y of symmetry or topological prescriptions was obtained. In this talk I wi
ll explain how variational methods also allow us to address\, in the class
ical N-body problem\, the existence of various forms of expansions. More p
recisely\, we will show how for positive energy levels\, it is possible to
combine with the variational methods some other classical constructions (
such as the Busemann functions\, or the theory of viscosity solutions for
the Hamilton-Jacobi equations) to achieve the existence of hyperbolic moti
ons with arbitrary asymptotic shapes\, starting from also arbitrary positi
ons of the bodies (joint work with A. Venturelli).\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Martínez-Aguinaga (ICMAT-UCM)
DTSTART:20210113T150000Z
DTEND:20210113T160000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/12
DESCRIPTION:Title: The classification problem for (4\,6)-bracket-generating s
tructures\nby Javier Martínez-Aguinaga (ICMAT-UCM) as part of ICMAT G
eometry Seminar\n\n\nAbstract\nThe classification problem for bracket–ge
nerating distributions in differentiable manifolds\nfrom a homotopic viewp
oint has been tackled for certain cases.\n\nGromov classified contact stru
ctures up to homotopy in open manifolds.\nAfterwards\, a subclass of this
type of structures called overtwisted were classified\nin closed manifolds
up to isotopy\, first by Eliashberg in dimension 3 and later on by Borman
\,\nEliashberg and Murphy in all dimensions. McDuff classified even-contac
t structures in\neven-dimensional manifolds\, showing that there exists a
full h-principle.\n\nMore recently\, Casals\, del Pino\, Pérez and Presas
proved an existenceh−principle for Engel structures in smooth 4−manif
olds. On the other hand\, del Pino and Vogel showed that there exists a fu
ll h−principle when restricted to the subclass of overtwisted Engel stru
ctures.\n\nIn this talk we will discuss the classification problem for (4\
,6)−bracket–generating structures through convex integration. This is
work in progress with Alvaro del Pino (Utrecht University).\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Fernández (ICMAT-UCM)
DTSTART:20210203T140000Z
DTEND:20210203T150000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/13
DESCRIPTION:Title: Contactomorphisms of tight contact 3-manifolds\nby Edu
ardo Fernández (ICMAT-UCM) as part of ICMAT Geometry Seminar\n\n\nAbstrac
t\nSince the appearance of Hatcher’s proof of the Smale Conjecture there
has been a huge development in the understanding of the homotopy type of
the diffeomorphism group of a 3-manifold. The\nanalog of the Smale Conject
ure in contact topology is Eliashberg’stheorem about the contractibility
of the space of tight contact structures on the 3-ball. However\, there h
asn’t been much progress in\nthe understanding of the homotopy type of t
he contactomorphism group of a tight contact 3-fold\, the reason being the
lack of a parametric convex surface theory to adapt the cut and paste tec
hniques from smooth topology to the contact setting. In this talk I will e
xplain how to understand the homotopy type of the space of convex disks wi
th fixed Legendrian boundary. As a consequence\, the homotopy type of any
tight contact 3-fold can be computed in terms of the homotopy type of\nthe
diffeomorphism group. If time permits I will present some applications of
this result. Joint work with Javier Martínez-Aguinagaand Francisco Presa
s\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Hausel (Institute of Science and Technology Austria)
DTSTART:20210331T130000Z
DTEND:20210331T140000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/14
DESCRIPTION:Title: Mirror symmetry for Langlands dual Higgs bundles at the ti
p of the nilpotent cone\nby Tamas Hausel (Institute of Science and Tec
hnology Austria) as part of ICMAT Geometry Seminar\n\n\nAbstract\nI will e
xplain what we can prove and what we conjecture about the mirror of Hecke
transformed Hitchin section motivated by symmetry ideas of Kapustin-Witten
. The talk is based on arXiv:2101.08583 joint with Hitchin.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Bode (ICMAT)
DTSTART:20210303T140000Z
DTEND:20210303T150000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/15
DESCRIPTION:Title: Stable knots and links in electromagnetic fields\nby B
enjamin Bode (ICMAT) as part of ICMAT Geometry Seminar\n\n\nAbstract\nAn e
lectromagnetic field consists of two time-dependent vector fields on $\\ma
thbb{R}^3$\, namely the electric and the magnetic field\, which together s
atisfy Maxwell's equations. Sets of closed flow lines of a vector field fo
rm a link. We show that for every link $L$ there is an electromagnetic fie
ld\, whose magnetic field has a set of closed flow lines ambient isotopic
to $L$ for all time. These closed flow lines turn out to be (projections o
f) real analytic Legendrian links with respect to the standard contact str
ucture on the 3-sphere.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Gu (Harvard)
DTSTART:20210414T120000Z
DTEND:20210414T130000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/16
DESCRIPTION:Title: Nonabelian mirrors and Gromov-Witten theory\nby Wei Gu
(Harvard) as part of ICMAT Geometry Seminar\n\n\nAbstract\nWe propose Pic
ard-Fuchs equations for periods of nonabelian mirrors in this paper. The n
umber of parameters in our Picard-Fuchs equations is the rank of the gauge
group of the nonabelian GLSM\, which is eventually reduced to the actual
number of Kähler parameters. These Picard-Fuchs equations are concise and
novel. We justify our proposal by reproducing existing mathematical resul
ts\, namely Picard-Fuchs equations of Grassmannians and Calabi-Yau manifol
ds as complete intersections in Grassmannians. Furthermore\, our approach
can be applied to other nonabelian GLSMs\, so we compute Picard-Fuchs equa
tions of some other Fano-spaces\, which were not calculated in the literat
ure before. Finally\, the cohomology-valued generating functions of mirror
s can be read off from our Picard-Fuchs equations. Using these generating
functions\, we compute Gromov-Witten\ninvariants of various Calabi-Yau man
ifolds\, including complete intersection Calabi-Yau manifolds in Grassmann
ians and non-complete intersection Calabi-Yau examples such as Pfaffian Ca
labi-Yau threefold and Gulliksen-Negård Calabi-Yau threefold\, and find a
greement with existing results in the literature. The generating functions
we propose for non-complete intersection Calabi-Yau manifolds are genuine
ly new.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ángel González-Prieto (Universidad Autónoma de Madrid)
DTSTART:20210217T140000Z
DTEND:20210217T150000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/17
DESCRIPTION:Title: Interference phenomena in parabolic character varieties\nby Ángel González-Prieto (Universidad Autónoma de Madrid) as part of
ICMAT Geometry Seminar\n\n\nAbstract\nThe algebraic structure of the modu
li spaces of representations of surface groups (aka character varieties) h
as been widely studied in the past decades\, partially due to their close
relation with the moduli spaces of Higgs bundles and flat connections. Nev
ertheless\, very little is known about the geometry of character varieties
when we allow poles in the Higgs field\, the so-called parabolic setting.
In this framework\, new singularities arise in the moduli space that prev
ent the classical methods to work.\n\nIn this talk\, we will introduce a n
ew hope: Topological Quantum Field Theories (TQFTs). We will construct a T
QFT that encodes the Grothendieck motives of parabolic character varieties
and we will\napply it to obtain explicit expressions of these motives\, e
ven with highly non-generic parabolic data. This framework also provides a
new interpretation of the singularities: at the side of the TQFT they ari
se as an interference phenomenon that leads to drastic changes in the geom
etry.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andoni de Arriba de La Hera (ICMAT-UCM)
DTSTART:20210428T120000Z
DTEND:20210428T130000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/18
DESCRIPTION:Title: Superconformal vertex algebras from Killing spinors\nb
y Andoni de Arriba de La Hera (ICMAT-UCM) as part of ICMAT Geometry Semina
r\n\n\nAbstract\nVertex algebras\, introduced by Borcherds to prove the Mo
nstruous Moonshine Conjecture\, play an important role in many areas of ma
thematics\, such as the representation theory of Kac-Moody algebras and th
e geometric Langlands correspondence. They have a physical interpretation
in 2-dimensional conformal field theory\, and have had a strong impact in
geometry\, first by the construction of the chiral de Rham complex by Mali
kov-Schechtmann-Vaintrob\, and more recently by the construction of new su
perconformal structures on this complex by Heluani-Zabzine among others.\n
\n\nThe aim of this talk is to present a new method to construct embedding
s of the N=2 superconformal vertex algebra\, responsible for mirror symmet
ry\, into the affinization of a quadratic Lie algebra. The new input for t
he construction is a solution of the "Killing spinor equations" on the qua
dratic Lie algebra. These equations can be regarded as purely algebraic co
nditions on the quadratic Lie algebra\, but in fact come from geometry and
physics\, specifically from the approach to special holonomy based on gen
eralized geometry on Courant algebroids. To illustrate this\, I will prese
nt a geometric example given by a homogeneous Hopf surface. This talk is b
ased on joint work with Luis Álvarez-Cónsul and Mario Garcia-Fernandez i
n arxiv:2012.01851.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martí Lahoz (Universitat de Barcelona)
DTSTART:20210512T120000Z
DTEND:20210512T130000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/19
DESCRIPTION:Title: Stability conditions in families\nby Martí Lahoz (Uni
versitat de Barcelona) as part of ICMAT Geometry Seminar\n\n\nAbstract\nIn
this talk\, I will present a new construction of families of polarized hy
perkähler manifolds associated to families of cubic fourfolds. The constr
uction is based on technical progress in the theory of Bridgeland stabilit
y conditions on derived categories of algebraic varieties. More specifical
ly\, we develop a theory of Bridgeland stability conditions and moduli spa
ces of semistable objects for a family of varieties\, as well as a version
of that for families of Kuznetsov subcategories\, that can be thought as
non-commutative varieties. \n\nSince the derived category of a cubic fourf
old has an associated non-commutative K3 surface\, this allows us to gener
alize the powerful Mukai’s theory for moduli spaces of stable sheaves on
K3 surfaces to the setting of cubic fourfolds.\n\nThis is joint work with
A. Bayer\, E. Macrì\, H. Nuer\, A. Perry\, and P. Stellari.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerard Freixas (Institut de Mathématiques de Jussieu)
DTSTART:20210526T133000Z
DTEND:20210526T143000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/20
DESCRIPTION:Title: Non-abelian Hodge theory and complex Chern-Simons line bun
dle\nby Gerard Freixas (Institut de Mathématiques de Jussieu) as part
of ICMAT Geometry Seminar\n\n\nAbstract\nIn this talk I will present a ne
w construction of the complex Chern-Simons line bundle on the moduli space
of flat vector bundles on a family of Riemann surfaces. Our point of view
is based on Deligne's formalism of functorial integrals of characteristic
classes\, developed in his interpretation of Arakelov geometry and Quille
n's work on determinant bundles. For this\, we replace hermitian metrics o
n vector bundles by flat relative connections\, and integrals of secondary
Bott-Chern classes by a relative Chern-Simons theory. Our construction ma
kes use of an intermediate result on extensions of flat relative connectio
n to global ones\, related to the deformation theory of harmonic maps. We
will conclude with some applications to projective structures on families
of Riemann surfaces and moduli spaces of curves.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Hernández Herrero (Cornell University)
DTSTART:20210609T090000Z
DTEND:20210609T100000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/21
DESCRIPTION:Title: Moduli of sheaves via affine Grassmannians\nby Andrés
Hernández Herrero (Cornell University) as part of ICMAT Geometry Seminar
\n\n\nAbstract\nA useful tool in the study of the moduli space of stable v
ector\nbundles on a smooth curve C is the existence of the Mumford compact
ification\, which is constructed by adding a boundary parametrizing semist
able vector bundles. If we replace the smooth curve C by a higher dimensio
nal variety X\, then a compactification can be obtained by allowing vector
bundles to degenerate to an object known as a "torsion-free sheaf". Giese
ker and Maruyama constructed moduli spaces of semistable torsion-free shea
ves on such a variety X. More generally\, Simpson constructed moduli space
s of semistable pure sheaves supported on smaller subvarieties of X. All o
f these constructions use the methods of geometric invariant theory (GIT).
\n\nThe moduli problem of sheaves on X is more naturally parametrized by a
geometric object M called an "algebraic stack". In this talk I will expla
in an alternative GIT-free construction of the moduli space of semistable
pure sheaves that is intrinsic to the moduli stack M. This approach also y
ields a Harder-Narasimhan stratification of the unstable locus of the stac
k. Our main technical tools are the theory of $\\Theta$-stability introduc
ed by Halpern-Leistner and some recent methods developed by Alper\, Halper
n-Leistner and Heinloth. In order to apply these recent results\, one need
s to show some monotonicity conditions for a polynomial numerical invarian
t on the stack. We prove monotonicity by defining a higher dimensional ana
logue of the affine Grassmannian for pure sheaves. If time allows\, I will
also explain how these ideas can be applied to some other moduli problems
. This talk is based on joint work with Daniel Halpern-Leistner and Trevor
Jones.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel S. Graça (Universidade do Algarve)
DTSTART:20210519T100000Z
DTEND:20210519T110000Z
DTSTAMP:20260422T225755Z
UID:ICMAT_Geometry_Seminar/22
DESCRIPTION:Title: Computability\, noncomputability\, and dynamical systems\nby Daniel S. Graça (Universidade do Algarve) as part of ICMAT Geometr
y Seminar\n\n\nAbstract\nIn this talk we will analyse several interconnect
ions between computability and dynamical systems theory. In computability
theory one is interested in knowing whether a problem is algorithmically s
olvable\, where the notion of algorithm is made precise via an appropriate
model of computation such as Turing machines. A remarkable insight from c
omputability theory is that there are noncomputable problems which are alg
orithmically unsolvable\, such as Hilbert's 10th problem. In this talk we
will survey two types of results. First we will study the computational po
wer of some classes of smooth dynamical systems. Second\, building on the
previous results and on the framework of computable analysis when appropri
ate\, we study the computability of some problems related to smooth dynami
cal systems (finding invariant sets\, basins of attraction\, etc.)\, showi
ng that some of those problems are noncomputable.\n
LOCATION:https://researchseminars.org/talk/ICMAT_Geometry_Seminar/22/
END:VEVENT
END:VCALENDAR