Articles de revista
http://hdl.handle.net/2117/79765
Sun, 25 Aug 2019 01:40:11 GMT2019-08-25T01:40:11ZXiao's conjecture for general fibred surfaces
http://hdl.handle.net/2117/133741
Xiao's conjecture for general fibred surfaces
Barja Yáñez, Miguel Ángel; González Alonso, Víctor; Naranjo Del val, Joan Carles
We prove that the genus g, the relative irregularity qf and the Clifford index cf of a non-isotrivial fibration f satisfy the inequality qf=g-cf. This gives in particular a proof of Xiao’s conjecture for fibrations whose general fibres have maximal Clifford index.
Fri, 31 May 2019 08:04:03 GMThttp://hdl.handle.net/2117/1337412019-05-31T08:04:03ZBarja Yáñez, Miguel ÁngelGonzález Alonso, VíctorNaranjo Del val, Joan CarlesWe prove that the genus g, the relative irregularity qf and the Clifford index cf of a non-isotrivial fibration f satisfy the inequality qf=g-cf. This gives in particular a proof of Xiao’s conjecture for fibrations whose general fibres have maximal Clifford index.Poles of the complex zeta function of a plane curve
http://hdl.handle.net/2117/133127
Poles of the complex zeta function of a plane curve
Blanco Fernández, Guillem
Fri, 17 May 2019 08:11:07 GMThttp://hdl.handle.net/2117/1331272019-05-17T08:11:07ZBlanco Fernández, GuillemA Koszul complex over skew polynomial rings
http://hdl.handle.net/2117/131142
A Koszul complex over skew polynomial rings
Álvarez Montaner, Josep; Boix, Alberto F.; Zarzuela Armengou, Santiago
We construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence
Wed, 03 Apr 2019 06:24:40 GMThttp://hdl.handle.net/2117/1311422019-04-03T06:24:40ZÁlvarez Montaner, JosepBoix, Alberto F.Zarzuela Armengou, SantiagoWe construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequenceCoupling symmetries with Poisson structures
http://hdl.handle.net/2117/131043
Coupling symmetries with Poisson structures
Miranda Galcerán, Eva; Laurent Gengoux, Camille
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein’s splitting theorem for the integrable system is also studied giving some examples in which such a splitting does not exist, i.e. when the integrable system is not, locally, a product of an integrable system on the symplectic leaf and an integrable system on a transversal. The problem of splitting for integrable systems with additional symmetries is also considered.
Mon, 01 Apr 2019 10:42:16 GMThttp://hdl.handle.net/2117/1310432019-04-01T10:42:16ZMiranda Galcerán, EvaLaurent Gengoux, CamilleWe study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein’s splitting theorem for the integrable system is also studied giving some examples in which such a splitting does not exist, i.e. when the integrable system is not, locally, a product of an integrable system on the symplectic leaf and an integrable system on a transversal. The problem of splitting for integrable systems with additional symmetries is also considered.The clay public lecture and conference on the Poincaré Conjecture, Paris, 7-9 June 2010
http://hdl.handle.net/2117/130984
The clay public lecture and conference on the Poincaré Conjecture, Paris, 7-9 June 2010
Miranda Galcerán, Eva
Thu, 28 Mar 2019 12:34:41 GMThttp://hdl.handle.net/2117/1309842019-03-28T12:34:41ZMiranda Galcerán, EvaOn the volume elements of a manifold with transverse zeroes
http://hdl.handle.net/2117/130973
On the volume elements of a manifold with transverse zeroes
Miranda Galcerán, Eva; Cardona Aguilar, Robert
Moser proved in 1965 in his seminal paper [15] that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in the top cohomology group of a manifold coincide. In particular, this yields a classification of compact symplectic surfaces in terms of De Rham cohomology. In this paper we generalize these results for volume forms admitting transversal zeroes. In this case there is also a cohomology capturing the classification: the
relative cohomology with respect to the critical hypersurface. We compare this classification scheme with the classification of Poisson structures on surfaces which are symplectic away from a hypersurface where they fulfill a transversality assumption (b-Poisson structures). We do this using the desingularization technique introduced in [10] and extend it to bm-Nambu structures.
Thu, 28 Mar 2019 10:17:42 GMThttp://hdl.handle.net/2117/1309732019-03-28T10:17:42ZMiranda Galcerán, EvaCardona Aguilar, RobertMoser proved in 1965 in his seminal paper [15] that two volume forms on a compact manifold can be conjugated by a diffeomorphism, that is to say they are equivalent, if and only if their associated cohomology classes in the top cohomology group of a manifold coincide. In particular, this yields a classification of compact symplectic surfaces in terms of De Rham cohomology. In this paper we generalize these results for volume forms admitting transversal zeroes. In this case there is also a cohomology capturing the classification: the
relative cohomology with respect to the critical hypersurface. We compare this classification scheme with the classification of Poisson structures on surfaces which are symplectic away from a hypersurface where they fulfill a transversality assumption (b-Poisson structures). We do this using the desingularization technique introduced in [10] and extend it to bm-Nambu structures.Bouncing cosmologies via modified gravity in the ADM formalism: Application to loop quantum cosmology
http://hdl.handle.net/2117/130899
Bouncing cosmologies via modified gravity in the ADM formalism: Application to loop quantum cosmology
Haro Cases, Jaume; Amorós Torrent, Jaume
We consider the Arnowitt-Deser-Misner formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond general relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the Universe following the spirit of Weyl’s postulate, has been fixed, f theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation; i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued f functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected loop quantum cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.
Wed, 27 Mar 2019 07:37:11 GMThttp://hdl.handle.net/2117/1308992019-03-27T07:37:11ZHaro Cases, JaumeAmorós Torrent, JaumeWe consider the Arnowitt-Deser-Misner formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond general relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the Universe following the spirit of Weyl’s postulate, has been fixed, f theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation; i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued f functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected loop quantum cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.Decomposition spaces and restriction species
http://hdl.handle.net/2117/130730
Decomposition spaces and restriction species
Gálvez Carrillo, Maria Immaculada; Kock, Joachim; Tonks, Andrew
We show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general construction of incidence coalgebras of decomposition spaces. We introduce directed restriction species that subsume Schmitt’s restriction species and also induce decomposition spaces. Whereas ordinary restriction species are presheaves on the category of finite sets and injections, directed restriction species are presheaves on the category of finite posets and convex maps. We also introduce the notion of monoidal (directed) restriction species, which induce monoidal decomposition spaces and hence bialgebras, most often Hopf algebras. Examples of this notion include rooted forests, directed graphs, posets, double posets, and many related structures. A prominent instance of a resulting incidence bialgebra is the Butcher–Connes–Kreimer Hopf algebra of rooted trees. Both ordinary and directed restriction species are shown to be examples of a construction of decomposition spaces from certain cocartesian fibrations over the category of finite ordinals that are also cartesian over convex maps. The proofs rely on some beautiful simplicial combinatorics, where the notion of convexity plays a key role. The methods developed are of independent interest as techniques for constructing decomposition spaces
Thu, 21 Mar 2019 16:00:30 GMThttp://hdl.handle.net/2117/1307302019-03-21T16:00:30ZGálvez Carrillo, Maria ImmaculadaKock, JoachimTonks, AndrewWe show that Schmitt’s restriction species (such as graphs, matroids, posets, etc.) naturally induce decomposition spaces (a.k.a. unital 2-Segal spaces), and that their associated coalgebras are an instance of the general construction of incidence coalgebras of decomposition spaces. We introduce directed restriction species that subsume Schmitt’s restriction species and also induce decomposition spaces. Whereas ordinary restriction species are presheaves on the category of finite sets and injections, directed restriction species are presheaves on the category of finite posets and convex maps. We also introduce the notion of monoidal (directed) restriction species, which induce monoidal decomposition spaces and hence bialgebras, most often Hopf algebras. Examples of this notion include rooted forests, directed graphs, posets, double posets, and many related structures. A prominent instance of a resulting incidence bialgebra is the Butcher–Connes–Kreimer Hopf algebra of rooted trees. Both ordinary and directed restriction species are shown to be examples of a construction of decomposition spaces from certain cocartesian fibrations over the category of finite ordinals that are also cartesian over convex maps. The proofs rely on some beautiful simplicial combinatorics, where the notion of convexity plays a key role. The methods developed are of independent interest as techniques for constructing decomposition spacesQualitative study in loop quantum cosmology
http://hdl.handle.net/2117/130636
Qualitative study in loop quantum cosmology
Aresté Saló, Llibert; Amorós Torrent, Jaume; Haro Cases, Jaume
This work contains a detailed qualitative analysis, in general relativity and in loop quantum cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear equation of state (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e. to show whether the other orbits converge or diverge to these analytic solutions at early and late times.
Wed, 20 Mar 2019 07:09:32 GMThttp://hdl.handle.net/2117/1306362019-03-20T07:09:32ZAresté Saló, LlibertAmorós Torrent, JaumeHaro Cases, JaumeThis work contains a detailed qualitative analysis, in general relativity and in loop quantum cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear equation of state (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e. to show whether the other orbits converge or diverge to these analytic solutions at early and late times.Convexity for Hamiltonian torus actions on b-symplectic manifolds
http://hdl.handle.net/2117/130271
Convexity for Hamiltonian torus actions on b-symplectic manifolds
Guillemin, Victor; Miranda Galcerán, Eva; Pires, Ana Rita; Scott, Geoffrey
n [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic manifolds. The modular weights of the action on the connected components of the exceptional hypersurface play a fundamental role: either they are all zero and the moment map behaves as in classic symplectic one, or they are all nonzero and the moment map behaves as in the toric b-symplectic case studied in [GMPS].
Tue, 12 Mar 2019 15:41:42 GMThttp://hdl.handle.net/2117/1302712019-03-12T15:41:42ZGuillemin, VictorMiranda Galcerán, EvaPires, Ana RitaScott, Geoffreyn [GMPS] we proved that the moment map image of a b-symplectic toric manifold is a convex b-polytope. In this paper we obtain convexity results for the more general case of non-toric hamiltonian torus actions on b-symplectic manifolds. The modular weights of the action on the connected components of the exceptional hypersurface play a fundamental role: either they are all zero and the moment map behaves as in classic symplectic one, or they are all nonzero and the moment map behaves as in the toric b-symplectic case studied in [GMPS].