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BEGIN:VEVENT
SUMMARY:Nikita Nikolaev (Université de Genève)
DTSTART:20201014T130000Z
DTEND:20201014T140000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/1
DESCRIPTION:Title: Abelianisation of Meromorphic Connections and the Ge
ometric Exact WKB Method\nby Nikita Nikolaev (Université de Genève)
as part of ICMAT Geometry Seminar\n\n\nAbstract\nI will describe an approa
ch to analysing meromorphic connections on Riemann surfaces called abelian
isation. It can be seen as a generalisation of the abelianisation of Higgs
bundles (a.k.a.\, the spectral correspondence\, a key step in the analysi
s of Hitchin integrable systems) to flat bundles. This approach emerged in
the last decade in the work of Gaiotto\, Moore\, Neitzke on spectral netw
orks that arise in the context of supersymmetric gauge theories. Our point
of view via deformation theory sheds light on the mathematical content of
the theory of spectral networks and makes clear the relationship with the
spectral correspondence. Furthermore\, our mathematical formulation allow
s us to connect abelianisation with an algebro-geometric formulation of th
e exact WKB method\, which is the modern exact reincarnation of the much o
lder WKB approximation method from quantum mechanics.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miquel Cueca (Universität Göttingen)
DTSTART:20201125T150000Z
DTEND:20201125T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/2
DESCRIPTION:Title: Courant algebroids\, between Lie algebroids and symp
lectic manifolds\nby Miquel Cueca (Universität Göttingen) as part of
ICMAT Geometry Seminar\n\n\nAbstract\nIt is well known that Courant algeb
roids can be defined either using a bracket and anchor (similar to Lie alg
ebroids) or as graded symplectic manifolds (similar to symplectic manifold
s). In this talk I will explore how each of those equivalent definitions c
an be used to obtain different properties and applications of Courant alge
broids like Cartan calculus and their cohomology\, characteristic classes\
, moment maps\, Courant sigma model ...\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/2
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Franco (Instituto Superior Técnico)
DTSTART:20201028T150000Z
DTEND:20201028T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/3
DESCRIPTION:Title: Torsion line bundles and branes on the Hitchin syste
m\nby Emilio Franco (Instituto Superior Técnico) as part of ICMAT Geo
metry Seminar\n\n\nAbstract\nThe locus of the Higgs moduli space fixed und
er tensorization by a line bundle of order 2 plays a key role in the work
of Hausel and Thaddeus on topological mirror symmetry. We shall describe t
he behavior under mirror symmetry of this fixed locus.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/3
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastien Picard (University of British Columbia)
DTSTART:20201202T150000Z
DTEND:20201202T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/4
DESCRIPTION:Title: PDEs on Non-Kahler Calabi-Yau Manifolds\nby Seba
stien Picard (University of British Columbia) as part of ICMAT Geometry Se
minar\n\n\nAbstract\nWe will discuss the non-Kahler Calabi-Yau geometry in
troduced by string theorists C. Hull and A. Strominger. We propose to stud
y these spaces via a parabolic PDE which is a nonlinear flow of non-Kahler
metrics. This talk will survey works with T. Collins\, T. Fei\, D.H. Phon
g\, S.-T. Yau\, and X.-W. Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/4
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tristan Collins (MIT)
DTSTART:20201111T150000Z
DTEND:20201111T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/5
DESCRIPTION:Title: Moment maps in mirror symmetry\nby Tristan Colli
ns (MIT) as part of ICMAT Geometry Seminar\n\n\nAbstract\nI will discuss a
n infinite dimensional geometric invariant theory approach to the deformed
Hermitian-Yang-Mills (dHYM)\, and special Lagrangian equations. In the s
etting of dHYM\, I will discuss how we can use regularity results for a ce
rtain fully nonlinear\, degenerate elliptic PDE to study notions of algebr
aic stability. I will explain how these notions of stability are (and are
not) related to Bridgeland stability\, and some applications to related p
roblems in symplectic geometry. This is joint work with S.-T. Yau.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/5
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joana Cirici (Universitat de Barcelona)
DTSTART:20201104T150000Z
DTEND:20201104T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/6
DESCRIPTION:Title: Hidden symmetries on almost Kähler manifolds\nb
y Joana Cirici (Universitat de Barcelona) as part of ICMAT Geometry Semina
r\n\n\nAbstract\nI will explain how local identities for almost Kähler ma
nifolds lead to various unexpected symmetries on certain subspaces of the
cohomology of a compact almost Kähler manifold. This allows to deduce sev
eral geometric and topological consequences for these manifolds. In partic
ular\, we obtain new obstructions to the existence of a symplectic form co
mpatible with a given almost complex structure. This is joint work with Sc
ott Wilson.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/6
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abigail Ward (Harvard)
DTSTART:20201209T150000Z
DTEND:20201209T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/7
DESCRIPTION:Title: Homological mirror symmetry for elliptic Hopf surfac
es\nby Abigail Ward (Harvard) as part of ICMAT Geometry Seminar\n\n\nA
bstract\nWe show evidence that homological mirror symmetry is a phenomenon
that exists beyond the world of Kähler manifolds by exhibiting HMS-type
results for a family of complex surfaces which includes the classical Hopf
surface (S^1 x S^3). Each surface S we consider can be obtained by perfor
ming logarithmic transformations to the product of P^1 with an elliptic cu
rve. We use this fact to associate to each S a mirror "non-algebraic Landa
u-Ginzburg 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://stable.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:20260404T110657Z
UID:ICMAT_Geometry_Seminar/8
DESCRIPTION:Title: Pure codimensionality of wobbly bundles\nby Ana
Peón-Nieto (University of Nice / University of Birmingham) as part of ICM
AT Geometry Seminar\n\n\nAbstract\nHiggs bundles on smooth projective curv
es were introduced by Hitchin as solutions to gauge equations motivated by
physics. They can be seen as points of T*N\, where N is the moduli space
of vector bundles on the curve. The topology of the moduli space of Higgs
bundles is determined by the nilpotent cone\, which is a reducible scheme
containing the zero section of T*N--->N. Inside this section\, wobbly bund
les are particularly important\, as this is the locus where any other comp
onent intersects N. In fact\, this implies that the geometry of the nilpot
ent cone can be described in terms of wobbly bundles. In this talk I will
explain an inductive method to prove pure codimensionality of the wobbly l
ocus\, as announced in a paper by Laumon from the 80's. We expect our meth
od to yield moreover a description of the irreducible components of the ni
lpotent cone in arbitrary rank.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/8
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Juan Carlos Marrero (Universidad de La Laguna)
DTSTART:20201216T150000Z
DTEND:20201216T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/9
DESCRIPTION:Title: Invariant measures for contact Hamiltonian systems:
symplectic sandwiches with contact bread\nby Juan Carlos Marrero (Univ
ersidad de La Laguna) as part of ICMAT Geometry Seminar\n\n\nAbstract\nIn
this talk\, I will present some recent results on the existence of invaria
nt measures for contact Hamiltonian systems. In fact\, we will see that\,
under some natural conditions\, Hamiltonian systems on a contact manifold
C can be split into a Reeb dynamics on an open subset of C and a Liouville
dynamics on a submanifold of C of codimension 1. For the Reeb dynamics we
find an invariant measure. Moreover\, we show that\, under certain comple
teness conditions\, the existence of an invariant measure for the Liouvill
e dynamics can be characterized using the notion of a symplectic sandwich
with contact bread.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/9
/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vicente Muñoz (Universidad de Málaga)
DTSTART:20210317T140000Z
DTEND:20210317T150000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/10
DESCRIPTION:Title: A Smale-Barden manifold admitting K-contact but not
Sasakian structure\nby Vicente Muñoz (Universidad de Málaga) as par
t of ICMAT Geometry Seminar\n\n\nAbstract\nSasakian manifolds are odd-dime
nsional counterparts of Kahler manifolds in even dimensions\, with K-conta
ct manifolds corresponding to symplectic manifolds. In this talk\, we give
the first example of a simply connected compact 5-manifold (Smale-Barden
manifold) which admits a K-contact structure but does not admit any Sasaki
an structure\, settling a long standing question of Boyer and Galicki.\n\n
For this\, we translate the question about K-contact 5-manifolds to constr
ucting symplectic 4-orbifolds with cyclic singularities containing disjoin
t symplectic surfaces of positive genus. The question on Sasakian 5-manifo
lds translates to the existence of algebraic surfaces with cyclic singular
ities containig disjoint complex curves of positive genus. A key step cons
ists on bounding universally the number of singular points of the algebrai
c surface.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ezequiel Maderna (Universidad de la República)
DTSTART:20210127T150000Z
DTEND:20210127T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/11
DESCRIPTION:Title: Hyperbolic motions of the N-body problem with arbit
rary limit shape\nby Ezequiel Maderna (Universidad de la República) a
s part of ICMAT Geometry Seminar\n\n\nAbstract\nDuring the 20th century\,
variational methods were banned from the study of the Newtonian model for
gravitation. The reason\, already explained by Poincaré\, ceased to be an
obstruction once Marchal proved that the minimizing curves of the Lagrang
ian action do not present singularities. The applications did not take lon
g: in the first instance\, the existence of periodic orbits with a great d
iversity of symmetry or topological prescriptions was obtained. In this ta
lk I will explain how variational methods also allow us to address\, in th
e classical N-body problem\, the existence of various forms of expansions.
More precisely\, we will show how for positive energy levels\, it is poss
ible to combine with the variational methods some other classical construc
tions (such as the Busemann functions\, or the theory of viscosity solutio
ns for the Hamilton-Jacobi equations) to achieve the existence of hyperbol
ic motions with arbitrary asymptotic shapes\, starting from also arbitrary
positions of the bodies (joint work with A. Venturelli).\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javier Martínez-Aguinaga (ICMAT-UCM)
DTSTART:20210113T150000Z
DTEND:20210113T160000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/12
DESCRIPTION:Title: The classification problem for (4\,6)-bracket-gener
ating structures\nby Javier Martínez-Aguinaga (ICMAT-UCM) as part of
ICMAT Geometry Seminar\n\n\nAbstract\nThe classification problem for brack
et–generating distributions in differentiable manifolds\nfrom a homotopi
c viewpoint has been tackled for certain cases.\n\nGromov classified conta
ct structures up to homotopy in open manifolds.\nAfterwards\, a subclass o
f this type of structures called overtwisted were classified\nin closed ma
nifolds up to isotopy\, first by Eliashberg in dimension 3 and later on by
Borman\,\nEliashberg and Murphy in all dimensions. McDuff classified even
-contact structures in\neven-dimensional manifolds\, showing that there ex
ists a full h-principle.\n\nMore recently\, Casals\, del Pino\, Pérez and
Presas proved an existenceh−principle for Engel structures in smooth 4
−manifolds. On the other hand\, del Pino and Vogel showed that there exi
sts a full h−principle when restricted to the subclass of overtwisted En
gel structures.\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://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eduardo Fernández (ICMAT-UCM)
DTSTART:20210203T140000Z
DTEND:20210203T150000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/13
DESCRIPTION:Title: Contactomorphisms of tight contact 3-manifolds\
nby Eduardo Fernández (ICMAT-UCM) as part of ICMAT Geometry Seminar\n\n\n
Abstract\nSince the appearance of Hatcher’s proof of the Smale Conjectur
e there has been a huge development in the understanding of the homotopy t
ype of the diffeomorphism group of a 3-manifold. The\nanalog of the Smale
Conjecture in contact topology is Eliashberg’stheorem about the contract
ibility of the space of tight contact structures on the 3-ball. However\,
there hasn’t been much progress in\nthe understanding of the homotopy ty
pe of the contactomorphism group of a tight contact 3-fold\, the reason be
ing the lack of a parametric convex surface theory to adapt the cut and pa
ste techniques from smooth topology to the contact setting. In this talk I
will explain how to understand the homotopy type of the space of convex d
isks with 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 applicat
ions of this result. Joint work with Javier Martínez-Aguinagaand Francisc
o Presas\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamas Hausel (Institute of Science and Technology Austria)
DTSTART:20210331T130000Z
DTEND:20210331T140000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/14
DESCRIPTION:Title: Mirror symmetry for Langlands dual Higgs bundles at
the tip of the nilpotent cone\nby Tamas Hausel (Institute of Science
and Technology Austria) as part of ICMAT Geometry Seminar\n\n\nAbstract\nI
will explain 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://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Bode (ICMAT)
DTSTART:20210303T140000Z
DTEND:20210303T150000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/15
DESCRIPTION:Title: Stable knots and links in electromagnetic fields\nby Benjamin Bode (ICMAT) as part of ICMAT Geometry Seminar\n\n\nAbstrac
t\nAn electromagnetic field consists of two time-dependent vector fields o
n $\\mathbb{R}^3$\, namely the electric and the magnetic field\, which tog
ether satisfy Maxwell's equations. Sets of closed flow lines of a vector f
ield form a link. We show that for every link $L$ there is an electromagne
tic field\, whose magnetic field has a set of closed flow lines ambient is
otopic to $L$ for all time. These closed flow lines turn out to be (projec
tions of) real analytic Legendrian links with respect to the standard cont
act structure on the 3-sphere.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wei Gu (Harvard)
DTSTART:20210414T120000Z
DTEND:20210414T130000Z
DTSTAMP:20260404T110657Z
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 prop
ose Picard-Fuchs equations for periods of nonabelian mirrors in this paper
. The number of parameters in our Picard-Fuchs equations is the rank of th
e gauge group of the nonabelian GLSM\, which is eventually reduced to the
actual number of Kähler parameters. These Picard-Fuchs equations are conc
ise and novel. We justify our proposal by reproducing existing mathematica
l results\, namely Picard-Fuchs equations of Grassmannians and Calabi-Yau
manifolds as complete intersections in Grassmannians. Furthermore\, our ap
proach can be applied to other nonabelian GLSMs\, so we compute Picard-Fuc
hs equations of some other Fano-spaces\, which were not calculated in the
literature before. Finally\, the cohomology-valued generating functions of
mirrors can be read off from our Picard-Fuchs equations. Using these gene
rating functions\, we compute Gromov-Witten\ninvariants of various Calabi-
Yau manifolds\, including complete intersection Calabi-Yau manifolds in Gr
assmannians and non-complete intersection Calabi-Yau examples such as Pfaf
fian Calabi-Yau threefold and Gulliksen-Negård Calabi-Yau threefold\, and
find agreement with existing results in the literature. The generating fu
nctions we propose for non-complete intersection Calabi-Yau manifolds are
genuinely new.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ángel González-Prieto (Universidad Autónoma de Madrid)
DTSTART:20210217T140000Z
DTEND:20210217T150000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/17
DESCRIPTION:Title: Interference phenomena in parabolic character varie
ties\nby Ángel González-Prieto (Universidad Autónoma de Madrid) as
part of ICMAT Geometry Seminar\n\n\nAbstract\nThe algebraic structure of t
he moduli spaces of representations of surface groups (aka character varie
ties) has been widely studied in the past decades\, partially due to their
close relation with the moduli spaces of Higgs bundles and flat connectio
ns. Nevertheless\, very little is known about the geometry of character va
rieties when we allow poles in the Higgs field\, the so-called parabolic s
etting. In this framework\, new singularities arise in the moduli space th
at prevent the classical methods to work.\n\nIn this talk\, we will introd
uce a new hope: Topological Quantum Field Theories (TQFTs). We will constr
uct a TQFT that encodes the Grothendieck motives of parabolic character va
rieties and we will\napply it to obtain explicit expressions of these moti
ves\, even with highly non-generic parabolic data. This framework also pro
vides a new interpretation of the singularities: at the side of the TQFT t
hey arise as an interference phenomenon that leads to drastic changes in t
he geometry.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andoni de Arriba de La Hera (ICMAT-UCM)
DTSTART:20210428T120000Z
DTEND:20210428T130000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/18
DESCRIPTION:Title: Superconformal vertex algebras from Killing spinors
\nby Andoni de Arriba de La Hera (ICMAT-UCM) as part of ICMAT Geometry
Seminar\n\n\nAbstract\nVertex algebras\, introduced by Borcherds to prove
the Monstruous Moonshine Conjecture\, play an important role in many area
s of mathematics\, such as the representation theory of Kac-Moody algebras
and the geometric Langlands correspondence. They have a physical interpre
tation in 2-dimensional conformal field theory\, and have had a strong imp
act in geometry\, first by the construction of the chiral de Rham complex
by Malikov-Schechtmann-Vaintrob\, and more recently by the construction of
new superconformal structures on this complex by Heluani-Zabzine among ot
hers.\n\n\nThe aim of this talk is to present a new method to construct em
beddings of the N=2 superconformal vertex algebra\, responsible for mirror
symmetry\, into the affinization of a quadratic Lie algebra. The new inpu
t for the construction is a solution of the "Killing spinor equations" on
the quadratic Lie algebra. These equations can be regarded as purely algeb
raic conditions on the quadratic Lie algebra\, but in fact come from geome
try and physics\, specifically from the approach to special holonomy based
on generalized geometry on Courant algebroids. To illustrate this\, I wil
l present a geometric example given by a homogeneous Hopf surface. This ta
lk is based on joint work with Luis Álvarez-Cónsul and Mario Garcia-Fern
andez in arxiv:2012.01851.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martí Lahoz (Universitat de Barcelona)
DTSTART:20210512T120000Z
DTEND:20210512T130000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/19
DESCRIPTION:Title: Stability conditions in families\nby Martí Lah
oz (Universitat de Barcelona) as part of ICMAT Geometry Seminar\n\n\nAbstr
act\nIn this talk\, I will present a new construction of families of polar
ized hyperkähler manifolds associated to families of cubic fourfolds. The
construction is based on technical progress in the theory of Bridgeland s
tability conditions on derived categories of algebraic varieties. More spe
cifically\, we develop a theory of Bridgeland stability conditions and mod
uli spaces of semistable objects for a family of varieties\, as well as a
version of that for families of Kuznetsov subcategories\, that can be thou
ght as non-commutative varieties. \n\nSince the derived category of a cubi
c fourfold has an associated non-commutative K3 surface\, this allows us t
o generalize the powerful Mukai’s theory for moduli spaces of stable she
aves on K3 surfaces to the setting of cubic fourfolds.\n\nThis is joint wo
rk with A. Bayer\, E. Macrì\, H. Nuer\, A. Perry\, and P. Stellari.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/1
9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerard Freixas (Institut de Mathématiques de Jussieu)
DTSTART:20210526T133000Z
DTEND:20210526T143000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/20
DESCRIPTION:Title: Non-abelian Hodge theory and complex Chern-Simons l
ine bundle\nby Gerard Freixas (Institut de Mathématiques de Jussieu)
as part of ICMAT Geometry Seminar\n\n\nAbstract\nIn this talk I will prese
nt a new construction of the complex Chern-Simons line bundle on the modul
i 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 charact
eristic classes\, developed in his interpretation of Arakelov geometry and
Quillen's work on determinant bundles. For this\, we replace hermitian me
trics on vector bundles by flat relative connections\, and integrals of se
condary Bott-Chern classes by a relative Chern-Simons theory. Our construc
tion makes use of an intermediate result on extensions of flat relative co
nnection to global ones\, related to the deformation theory of harmonic m
aps. We will conclude with some applications to projective structures on f
amilies of Riemann surfaces and moduli spaces of curves.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/2
0/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Hernández Herrero (Cornell University)
DTSTART:20210609T090000Z
DTEND:20210609T100000Z
DTSTAMP:20260404T110657Z
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 s
table vector\nbundles on a smooth curve C is the existence of the Mumford
compactification\, which is constructed by adding a boundary parametrizing
semistable vector bundles. If we replace the smooth curve C by a higher d
imensional variety X\, then a compactification can be obtained by allowing
vector bundles to degenerate to an object known as a "torsion-free sheaf"
. Gieseker and Maruyama constructed moduli spaces of semistable torsion-fr
ee sheaves on such a variety X. More generally\, Simpson constructed modul
i spaces of semistable pure sheaves supported on smaller subvarieties of X
. All of these constructions use the methods of geometric invariant theory
(GIT).\n\nThe moduli problem of sheaves on X is more naturally parametriz
ed by a geometric object M called an "algebraic stack". In this talk I wil
l explain an alternative GIT-free construction of the moduli space of semi
stable pure sheaves that is intrinsic to the moduli stack M. This approach
also yields a Harder-Narasimhan stratification of the unstable locus of t
he stack. Our main technical tools are the theory of $\\Theta$-stability i
ntroduced by Halpern-Leistner and some recent methods developed by Alper\,
Halpern-Leistner and Heinloth. In order to apply these recent results\, o
ne needs to show some monotonicity conditions for a polynomial numerical i
nvariant on the stack. We prove monotonicity by defining a higher dimensio
nal analogue of the affine Grassmannian for pure sheaves. If time allows\,
I will also explain how these ideas can be applied to some other moduli p
roblems. This talk is based on joint work with Daniel Halpern-Leistner and
Trevor Jones.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/2
1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel S. Graça (Universidade do Algarve)
DTSTART:20210519T100000Z
DTEND:20210519T110000Z
DTSTAMP:20260404T110657Z
UID:ICMAT_Geometry_Seminar/22
DESCRIPTION:Title: Computability\, noncomputability\, and dynamical sy
stems\nby Daniel S. Graça (Universidade do Algarve) as part of ICMAT
Geometry Seminar\n\n\nAbstract\nIn this talk we will analyse several inter
connections between computability and dynamical systems theory. In computa
bility theory one is interested in knowing whether a problem is algorithmi
cally solvable\, where the notion of algorithm is made precise via an appr
opriate model of computation such as Turing machines. A remarkable insight
from computability theory is that there are noncomputable problems which
are algorithmically unsolvable\, such as Hilbert's 10th problem. In this t
alk we will survey two types of results. First we will study the computati
onal power of some classes of smooth dynamical systems. Second\, building
on the previous results and on the framework of computable analysis when a
ppropriate\, we study the computability of some problems related to smooth
dynamical systems (finding invariant sets\, basins of attraction\, etc.)\
, showing that some of those problems are noncomputable.\n
LOCATION:https://stable.researchseminars.org/talk/ICMAT_Geometry_Seminar/2
2/
END:VEVENT
END:VCALENDAR