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Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019Mar 25 2019In this paper we study the $\eta'$ in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip in ... More

Chiral observables and topology in hot QCD with two families of quarksMay 15 2018Nov 08 2018We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected ... More

Bulk transitions of twelve flavor QCD and $U_A(1)$ symmetryNov 10 2011We present an update on our ongoing study on the nature of the bulk transition observed at strong coupling in the SU(3) gauge theory with N_f = 12 flavors in the fundamental representation. We show evidence that there is a first order chiral symmetry ... More

Approaching ConformalityNov 06 2014We investigate the preconformal region of the phase diagram of SU(3) theories with fundamental flavors. We have simulated SU(3) theories with six and eight fundamental flavors at volumes 32^3 x 64. We use the generated configurations to measure the string ... More

The bulk transition of QCD with twelve flavors and the role of improvementSep 25 2012We study the SU(3) gauge theory with Nf=12 flavors in the fundamental representation by use of lattice simulations with staggered fermions. With a non-improved action we observe a chiral zero-temperature (bulk) transition separating a region at weak coupling, ... More

Topology (and axion's properties) from lattice QCD with a dynamical charmMay 04 2017We present results on QCD with four dynamical flavors in the temperature range $0.9 \lesssim T/T_c \lesssim 2$. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic ... More

Pseudo-Critical Temperature and Thermal Equation of State from $N_f=2$ Twisted Mass Lattice QCDDec 05 2012We report about the current status of our ongoing study of the chiral limit of two-flavor QCD at finite temperature with twisted mass quarks. We estimate the pseudo-critical temperature $T_c$ for three values of the pion mass in the range of $m_\mathrm{PS} ... More

Computing Matveev's complexity via crystallization theory: the boundary caseOct 16 2012The notion of Gem-Matveev complexity has been introduced within crystallization theory, as a combinatorial method to estimate Matveev's complexity of closed 3-manifolds; it yielded upper bounds for interesting classes of such manifolds. In this paper ... More

Lattice Monte-Carlo study of pre-conformal dynamics in strongly flavoured QCD in the light of the chiral phase transition at finite temperatureDec 05 2012Mar 18 2013We study the thermal phase transition in colour SU(3) Quantum Chromodynamics (QCD) with a variable number of fermions in the fundamental representation by using lattice Monte-Carlo simulations. We collect the (pseudo) critical couplings for N_f=(0, 4, ... More

G-degree for singular manifoldsJun 22 2017Dec 15 2017The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). ... More

Complexity computation for compact 3-manifolds via crystallizations and Heegaard diagramsMar 01 2012The idea of computing Matveev complexity by using Heegaard decompositions has been recently developed by two different approaches: the first one for closed 3-manifolds via crystallization theory, yielding the notion of Gem-Matveev complexity; the other ... More

The physics of eight flavoursOct 09 2008When the flavour content of QCD is increased sufficiently, the theory develops a non-trivial infra red fixed point. Thus, for a number of flavours above a certain critical value, but not yet so high that asymptotic freedom is lost, QCD becomes a conformal ... More

Thermodynamic Study for Conformal Phase in Large Nf Gauge TheoryNov 04 2011We investigate the chiral phase transition at finite temperature (T) in colour SU(3) Quantum Chromodynamics (QCD) with six species of fermions (Nf = 6) in the fundamental representation. The simulations have been performed by using lattice QCD with improved ... More

Chiral phase transition at finite temperature and conformal dynamics in large Nf QCDOct 14 2011Mar 09 2012We investigate the chiral phase transition at finite temperature (T) in colour SU(Nc=3) Quantum Chromodynamics (QCD) with six species of fermions (Nf=6) in the fundamental representation by using lattice QCD with improved staggered fermions. By considering ... More

Traces of a fixed point: Unravelling the phase diagram at large NfNov 11 2009With a sufficiently high number of fundamental fermionic flavours present, Yang-Mills theory develops an infrared fixed point and becomes (quasi-)conformal in nature. The range of flavour numbers for which this occurs defines the conformal window, the ... More

QCD thermodynamics from an imaginary mu_B: results on the four flavor lattice modelJun 09 2004Jun 21 2004We study four flavor QCD at nonzero temperature and density by analytic continuation from an imaginary chemical potential. The explored region is T = 0.95 T_c < T < 3.5 T_c, and the baryochemical potentials range from 0 to approx. 500 MeV. Observables ... More

The bulk transition of many-flavour QCD and the search for a UVFP at strong couplingDec 29 2010We explore the nature of the bulk transition observed at strong coupling in the SU(3) gauge theory with Nf=12 fermions in the fundamental representation. The transition separates a weak coupling chirally symmetric phase from a strong coupling chirally ... More

Study of finite temperature QCD with 2+1 flavors via Taylor expansion and imaginary chemical potentialDec 21 2010We study QCD with 2+1 flavors at nonzero temperature and nonzero chemical potential. We present preliminary results obtained from lattice calculations performed with an improved staggered fermions action (p4-action) on lattice with temporal extent N_t ... More

The physics of eight flavoursApr 17 2008May 30 2008We study Quantum Chromodynamics with eight flavours by use of lattice simulations and present evidence that the theory still breaks chiral symmetry in the zero temperature, continuum limit. This confirms that the lower end of the conformal window of QCD ... More

On the spectrum of QCD-like theories and the conformal windowJan 09 2012We report on the spectrum of the SU(3) gauge theory with twelve flavours in the fundamental representation of the gauge group. We isolate distinctive features of the hadronic phase - the one proper of QCD at zero temperature - and the so called conformal ... More

Topology in colored tensor models via crystallization theoryApr 10 2017Mar 07 2018The aim of this paper is twofold. On the one hand, it provides a review of the links between random tensor models, seen as quantum gravity theories, and the PL-manifolds representation by means of edge-colored graphs (crystallization theory). On the other ... More

Glueballs and the superfluid phase of Two-Color QCDApr 30 2008Aug 22 2008We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two color QCD. The simulations are carried out on a $6^3 \times 12$ lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions ... More

Eigenvalues of the QCD Dirac operator at finite temperature and densitySep 15 2000We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement ... More

Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019In this paper we study the $\eta'$ mass in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip ... More

The strongly interacting Quark Gluon Plasma, and the critical behaviour of QCD at imaginary chemical potentialMay 25 2007Jun 07 2007We explore the highly non-perturbative hot region of the QCD phase diagram close to Tc by use of an imaginary chemical potential mu which avoids the sign problem. The number density and the quark number susceptibility are consistent with a critical behaviour ... More

Lowest eigenvalues of the Dirac operator for two color QCD at finite densityOct 11 2001We investigate the eigenvalue spectrum of the staggered Dirac matrix in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the temperature phase transition, the low-lying Dirac spectrum is well described by random ... More

Lowest eigenvalues of the Dirac operator for two color QCD at nonzero chemical potentialOct 11 2001We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) and U(1) gauge theory as well as in full QCD with two colors and finite chemical potential. Along the strong-coupling axis up to the phase transition, the low-lying Dirac spectrum ... More

QCD at High Temperature : Results from Lattice Simulations with an Imaginary muNov 15 2005We summarize our results on the phase diagram of QCD with emphasis on the high temperature regime. For $T \ge 1.5 T_c$ the results are compatible with a free field behavior, while for $T \simeq 1.1 T_c$ this is not the case, clearly exposing the strongly ... More

Dirac and Gor'kov spectra in two color QCD with chemical potentialOct 11 2000We analyze the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the deconfinement transition are examined. ... More

Galois representations attached to abelian varieties of CM typeJun 15 2015Aug 12 2015Let $K$ be a number field, $A/K$ be an absolutely simple abelian variety of CM type, and $\ell$ be a prime number. We give explicit bounds on the degree over $K$ of the division fields $K(A[\ell^n])$, and when $A$ is an elliptic curve we also describe ... More

Explicit surjectivity of Galois representations attached to abelian surfaces and $\operatorname{GL}_2$-varietiesNov 06 2014Dec 31 2015Let $A$ be an absolutely simple abelian variety without (potential) complex multiplication, defined over the number field $K$. Suppose that either $\dim A=2$ or $A$ is of $\operatorname{GL}_2$-type: we give an explicit bound $\ell_0(A,K)$ such that, for ... More

On the uniform Rasmussen-Tamagawa conjecture in the CM caseNov 29 2015We prove a uniform version of a finiteness conjecture due to Rasmussen and Tamagawa in the case of CM abelian varieties. This extends recent results concerning CM elliptic curves to CM abelian varieties of arbitrary dimension.

Abelian varieties of Weil type and Kuga-Satake varietiesNov 14 2002We analyze the relationship between abelian fourfolds of Weil type and Hodge structures of type K3, and we extend some of these correspondences to the case of arbitrary dimension.

Computing the geometric endomorphism ring of a genus 2 JacobianOct 30 2016We describe an algorithm, based on the properties of the characteristic polynomials of Frobenius, to compute $\operatorname{End}_{\overline{K}}(A)$ when $A$ is the Jacobian of a nice genus-2 curve over a number field $K$. We use this algorithm to confirm ... More

On the $L$-polynomials of curves over finite fieldsJul 19 2018Fix a finite field $\mathbb{F}_q$ of odd characteristic and an integer $g \geq 1$. We prove that the $\mathbb{Q}$-vector space spanned by the $L$-polynomials of curves of genus $g$ over $\mathbb{F}_q$ has dimension $g+1$.

An explicit open image theorem for products of elliptic curvesJan 19 2015Nov 29 2015Let $K$ be a number field and $E_1, \ldots, E_n$ be elliptic curves over $K$, pairwise non-isogenous over $\overline{K}$ and without complex multiplication over $\overline{K}$. We study the image of the adelic representation of the absolute Galois group ... More

Explicit open image theorems for abelian varieties with trivial endomorphism ringAug 06 2015Jan 04 2016Let $K$ be a number field and $A/K$ be an abelian variety of dimension $g$ with $\operatorname{End}_{\overline{K}}(A)=\mathbb{Z}$. We provide a semi-effective bound $\ell_0(A/K)$ such that the natural Galois representation attached to $T_\ell A$ is onto ... More

Roots of unity and torsion points of abelian varietiesJul 03 2015Dec 31 2015We answer a question raised by Hindry and Ratazzi concerning the intersection between cyclotomic extensions of a number field $K$ and extensions of $K$ generated by torsion points of an abelian variety over $K$. We prove that a weak version of the property ... More

Science with an ngVLA: Deuteration in starless and prestellar coresOct 16 2018In dense starless and protostellar cores, the relative abundance of deuterated species to their non-deuterated counterparts can become orders of magnitude greater than in the local interstellar medium. This enhancement proceeds through multiple pathways ... More

Magnetostatic problems in fractal domainsMay 21 2018Dec 03 2018We consider a magnetostatic problem in a 3D "cylindrical" domain of Koch type. We prove existence and uniqueness results for both the fractal and pre-fractal problems and we investigate the convergence of the pre-fractal solutions to the limit fractal ... More

P wave bottomonium spectral functions in the QGP from lattice NRQCDNov 05 2013We present an overview of bottomonium spectral functions in the quark-gluon plasma, obtained by the FASTSUM collaboration, using lattice QCD simulations with two light quark flavours on anisotropic lattices. The bottom quark is treated nonrelativistically. ... More

Symmetries and spectrum of SU(2) Lattice Gauge Theory at finite chemical potentialFeb 25 1999We study SU(2) Lattice Gauge Theory with dynamical fermions at non-zero chemical potential $\mu$. The symmetries special to SU(2) for staggered fermions on the lattice are discussed explicitly and their relevance to spectroscopy and condensates at non-zero ... More

Density profiles of small Dirac operator eigenvalues for two color QCD at nonzero chemical potential compared to matrix modelsSep 12 2004We investigate the eigenvalue spectrum of the staggered Dirac matrix in two color QCD at finite chemical potential. The profiles of complex eigenvalues close to the origin are compared to a complex generalization of the chiral Gaussian Symplectic Ensemble, ... More

Towards thermodynamics with $N_f=2+1+1$ twisted mass quarksNov 07 2013We present preliminary results achieved within a recently started project dealing with QCD thermodynamics in the presence of a fully dynamical second quark family. We are employing the Wilson twisted mass discretization. To reduce the amount of zero temperature ... More

Chiral Symmetry Restoration and Realisation of the Goldstone Mechanism in the U(1) Gross-Neveu Model at Non-Zero Chemical PotentialFeb 25 1999We simulate the Gross-Neveu model in 2+1 dimensions at nonzero baryon density (chemical potential mu =/= 0). It is possible to formulate this model with a real action and therefore to perform standard hybrid Monte Carlo simulations with mu =/= 0 in the ... More

Thermodynamics of $n$-$p$ condensate in asymmetric nuclear matterJul 19 1999We study the neutron-proton pairing in nuclear matter as a function of isospin asymmetry at finite temperatures and the saturation density using realistic nuclear forces and Brueckner-renormalized single particle spectra. Our computation of the thermodynamic ... More

Reductions of points on algebraic groupsDec 08 2016Aug 01 2017Let $A$ be the product of an abelian variety and a torus defined over a number field $K$. Fix some prime number $\ell$. If $\alpha \in A(K)$ is a point of infinite order, we consider the set of primes $\mathfrak p$ of $K$ such that the reduction $(\alpha ... More

The bottomonium spectrum at finite temperature from $N_f=2+1$ lattice QCDFeb 25 2014We present results on the bottomonium spectrum at temperatures above and below the deconfinement crossover temperature, $T_c$, from dynamical lattice QCD simulations. The heavy quark is treated with a non-relativistic effective field theory on the lattice ... More

Bottomonium spectrum at finite temperatureNov 13 2013Nov 15 2013We investigate the modification of S and P wave states in the bottomonium spectrum above and below the deconfinement crossover temperature through their spectral functions obtained from the maximum entropy method. Anisotropic ensembles with $N_f=2+1$ ... More

Thermal transition temperature from twisted mass QCDSep 20 2010We present the current status of lattice simulations with N_f=2 maximally twisted mass Wilson fermions at finite temperature. In particular, the determination of the thermal transition temperature is discussed.

Correspondences between K3 surfacesNov 07 2002May 05 2003In this paper we show that there is a correspondence between some $K3$ surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show the existence ... More

Abelian varieties as automorphism groups of smooth projective varietiesJan 06 2018We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

I, Quantum Robot: Quantum Mind control on a Quantum ComputerDec 25 2008May 28 2009The logic which describes quantum robots is not orthodox quantum logic, but a deductive calculus which reproduces the quantum tasks (computational processes, and actions) taking into account quantum superposition and quantum entanglement. A way toward ... More

Minimax solutions for a problem with sign changing nonlinearity and lack of strict convexityOct 25 2013A result of existence of a nonnegative and a nontrivial solution is proved via critical point theorems for non smooth functionals. The equation considered presents a convex part and a nonlinearity which changes sign.

Real Kodaira surfacesApr 21 2004In this paper we give the topological classification of real primary Kodaira surfaces and we describe in detail the structure of the corresponding moduli space. One of the main tools is the orbifold fundamental group of a real variety. Our first result ... More

The space density of z>4 blazarsJan 09 2019High redshift blazars are an important class of Active Galactic Nuclei (AGN) that can provide an independent estimate of the supermassive black-hole mass function in high redshift radio-loud AGN without the bias due to absorption along the line-of-sight. ... More

On a plane section of an integral curve in positive characteristicSep 21 2010If $C \subset P^3_k$ is an integral curve and $k$ an algebraically closed field of characteristic 0, it is known that the points of the general plane section $C \cap H$ of $C$ are in uniform position. From this it follows easily that the general minimal ... More

Quark-gluon plasma phenomenology from the latticeOct 18 2013The FASTSUM Collaboration has calculated several quantities relevant for QCD studies at non-zero temperature using the lattice technique. We report here our results for the (i) interquark potential in charmonium; (ii) bottomonium spectral functions; and ... More

S wave bottomonium states moving in a quark-gluon plasma from lattice NRQCDOct 10 2012Feb 28 2013We extend our study of bottomonium spectral functions in the quark-gluon plasma to nonzero momentum. We use lattice QCD simulations with two flavours of light quark on highly anisotropic lattices and treat the bottom quark with nonrelativistic QCD (NRQCD). ... More

What happens to the Upsilon and eta_b in the quark-gluon plasma? Bottomonium spectral functions from lattice QCDSep 21 2011Nov 21 2011We study bottomonium spectral functions in the quark-gluon plasma in the Upsilon and eta_b channels, using lattice QCD simulations with two flavours of light quark on highly anisotropic lattices. The bottom quark is treated with nonrelativistic QCD (NRQCD). ... More

Two topics from lattice NRQCD at non-zero temperature: heavy quark mass dependence and S-wave bottomonium states moving in a thermal bathOct 29 2012Using Non-Relativistic QCD (NRQCD), we study heavy quark mass dependence of S-wave and P-wave bottomonium correlators for 0.42Tc <= T <= 2.09Tc and study spectral functions of S-wave bottomonium states moving in a thermal bath at these temperatures using ... More

Bottomonium at Non-zero Temperature from Lattice Non-relativistic QCDSep 07 2011Sep 12 2011The temperature dependence of bottomonium states at temperatures above and below $T_c$ is presented, using non-relativistic dynamics for the bottom quark and full relativistic lattice QCD simulations for two light flavors on a highly anisotropic lattice. ... More

Nonorientable 3-manifolds admitting coloured triangulations with at most 30 tetrahedraMay 10 2007We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid ... More

Higher dimensional Automorphic Lie AlgebrasApr 26 2015The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key feature of ... More

Decoherence and Loss of Entanglement in Acoustic Black HolesJun 06 2012We studied the process of decoherence in acoustic black holes. We focused on the ion trap model proposed by Horstmann et al. (Phys. Rev. Lett. 104, 250403 (2010)) but the formalism is general to any experimental implementation. For that particular setup, ... More

Closed time path approach to the Casimir energy in real mediaApr 28 2014The closed time path formalism is applied, in the framework of open quantum systems, to study the time evolution of the expectation value of the energy-momentum tensor of a scalar field in the presence of real materials. We analyze quantum fluctuations ... More

A census of genus two 3-manifolds up to 42 coloured tetrahedraFeb 03 2009We improve and extend to the non-orientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra.

Telecom photon interface of solid-state quantum nodesApr 02 2019Solid-state spins such as nitrogen-vacancy (NV) center are promising platforms for large-scale quantum networks. Despite the optical interface of NV center system, however, the significant attenuation of its zero-phonon-line photon in optical fiber prevents ... More

A new empirical method to estimate the molecular gas mass in galaxiesMay 06 2019We find a tight correlation between the dust extinction, traced by the Balmer Decrement (BD$=$H$\alpha$/H$\beta$), the CO(1-0) line luminosity (L$_{CO}$) and total molecular gas mass (M$_{H2}$) in a sample of $222$ local star-forming galaxies drawn from ... More

Decay of Positive Waves for $n \times n$ Hyperbolic Systems of Balance LawsSep 25 2009We prove Ole\u \i nik-type decay estimates for entropy solutions of $n\times n$ strictly hyperbolic systems of balance laws built out of a wave-front tracking procedure inside which the source term is treated as a nonconservative product localized on ... More

A density result for Sobolev spaces in dimension two, and applications to stability of nonlinear Neumann problemsOct 27 2005We prove that if $\Om \subseteq \R^2$ is bounded and $\R^2 \setminus \Om$ satisfies suitable structural assumptions (for example it has a countable number of connected components), then $W^{1,2}(\Om)$ is dense in $W^{1,p}(\Om)$ for every $1\le p<2$. The ... More

Einstein-Born-Infeld gravastar models, dark matter and accretion mechanismsMar 26 2019Gravastar models have recently been proposed as an alternative to black holes, mainly to avoid the pro\-ble\-ma\-tic issues associated with event horizons and singularities. In this work, a regular variety of gravastar models within the context of Einstein-Born-Infeld ... More

Integrability and linear stability of nonlinear wavesJul 29 2017Jun 15 2018It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized ... More

Automorphic Lie Algebras and Cohomology of Root SystemsDec 22 2015This paper defines a cohomology theory of root systems which emerges naturally in the context of Automorphic Lie Algebras (ALiAs) but applies more generally to deformations of Lie algebras obtained by assigning a monomial in a finite number of variables ... More

Decoherence during Inflation: the generation of classical inhomogeneitiesJun 08 2005Aug 23 2005We show how the quantum to classical transition of the cosmological fluctuations produced during inflation can be described by means of the influence functional and the master equation. We split the inflaton field into the system-field (long-wavelength ... More

Invariant submanifolds of metric contact pairsSep 03 2015We show that $\phi$-invariant submanifolds of metric contact pairs with orthogonal characteristic foliations make constant angles with the Reeb vector fields. Our main result is that for the normal case such submanifolds of dimension at least $2$ are ... More

A second order gradient flow of p-elastic planar networksMay 16 2019We consider a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths. We construct a weak solution of the flow by means of an implicit variational scheme. We show long-time existence of the evolution ... More

Observability of rectangular membranes and plates on small setsAug 21 2013Since the works of Haraux and Jaffard we know that rectangular plates may be observed by subregions not satisfying the geometrical control condition. We improve these results by observing only on an arbitrarily short segment inside the domain. The estimates ... More

Curve shortening flow coupled to lateral diffusionOct 21 2015We present and analyze a semi-discrete finite element scheme for a system consisting of a geometric evolution equation for a curve and a parabolic equation on the evolving curve. More precisely, curve shortening flow with a forcing term that depends on ... More

Generalized companion matrix for approximate GCDFeb 09 2011We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which ... More

On the Koszul cohomology of canonical and Prym-canonical binary curvesJul 13 2012Mar 04 2013In this paper we study Koszul cohomology and the Green and Prym-Green conjectures for canonical and Prym-canonical binary curves. We prove that if property $N_p$ holds for a canonical or a Prym-canonical binary curve of genus $g$ then it holds for a generic ... More

Automorphic Lie Algebras with dihedral symmetryOct 10 2014The concept of Automorphic Lie Algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. Automorphic Lie Algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever-Novikov ... More

Some results on the second Gaussian map for curvesMay 22 2008We study the second Gaussian map for a curve X of genus g, in relation with the second fundamental form of the period map. We exhibit a class of infinitely many curves with surjective second Gaussian map. We compute its rank on the hyperelliptic and trigonal ... More

On the first Gaussian map for Prym-canonical line bundlesOct 29 2012Jun 25 2013We prove by degeneration to Prym-canonical binary curves that the first Gaussian map of the Prym canonical line bundle $\omega_C \otimes A$ is surjective for the general point [C,A] of R_g if g >11, while it is injective if g < 12.

Siegel metric and curvature of the moduli space of curvesMay 22 2008We study the curvature of the moduli space M_g of curves of genus g with the Siegel metric induced by the period map. We give an explicit formula for the holomorphic sectional curvature of M_g along a Schiffer variation at a point P on the curve X, in ... More

Etale homotopy types of moduli stacks of algebraic curves with symmetriesApr 21 2004Using the machinery of etale homotopy theory a' la Artin-Mazur we determine the etale homotopy types of moduli stacks over $\bar{\Q}$ parametrizing families of algebraic curves of genus g greater than 1 endowed with an action of a finite group G of automorphisms, ... More

Compact 3-manifolds via 4-colored graphsApr 18 2013Sep 22 2015We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the ... More

Van Geemen--Sarti involutions and elliptic fibrations on K3 surfaces double cover of $\mathbb{P}^2$Oct 28 2011Jan 29 2015In this paper we classify the elliptic fibrations on K3 surfaces which are the double cover of a blow up of $\mathbb{P}^2$ branched along rational curves and we give equations for many of these elliptic fibrations. Thus we obtain a classification of the ... More

On the second gaussian map for curves on a K3 surfaceMay 14 2009Mar 04 2010By a theorem of Wahl, for canonically embedded curves which are hyperplane sections of K3 surfaces, the first gaussian map is not surjective. In this paper we prove that if C is a general hyperplane section of high genus (greater than 280) of a general ... More

Hilbert functions and set of points in $\mathbb P^1\times \mathbb P^1$Sep 21 2010Sep 06 2011In this paper we determine a class of admissible matrices which are the Hilbert functions of some 0-dimensional schemes in $\mathbb P^1\times\mathbb P^1$.

Dynamics of an Acoustic Black Hole as an Open Quantum SystemAug 01 2012We studied the process of decoherence induced by the presence of an environment in acoustic black holes, using the open quantum system approach, thus extending previous work. We focused on the ion trap model but the formalism is general to any experimental ... More

Isotypical Components of Rational FunctionsNov 19 2015A finite group of Moebius transformations acts on the field of rational functions, which in turn decomposes into isotypical components. In spite of the modest group sizes, it is a substantial computational problem to obtain an explicit description of ... More

Hopf bifurcation analysis of the generalized Lorenz system with time delayed feedback controlJun 18 2014Jan 02 2015In this work we propose a feedback approach to regulate the chaotic behavior of the whole family of the generalized Lorenz system, by designing a nonlinear delayed feedback control. We first study the effect of the delay on the dynamics of the system ... More

Cross-diffusion driven instability in a predator-prey system with cross-diffusionNov 07 2013Feb 19 2014In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism ... More

A note about complexity of lens spacesSep 23 2013Oct 16 2013Within crystallization theory, (Matveev's) complexity of a 3-manifold can be estimated by means of the combinatorial notion of GM-complexity. In this paper, we prove that the GM-complexity of any lens space L(p,q), with p greater than 2, is bounded by ... More

ad-Nilpotent ideals of a Borel subalgebra IIJun 08 2001Dec 17 2001We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of \check{Q}/(h+1)\check{Q} under the Weyl group (\check{Q} being the coroot lattice and h the Coxeter number of g). From this ... More

Comparison Principles for subelliptic equations of Monge-Ampere typeFeb 11 2008We present two comparison principles for viscosity sub- and supersolutions of Monge-Ampere-type equations associated to a family of vector fields. In particular, we obtain the uniqueness of a viscosity solution to the Dirichlet problem for the equation ... More

Minimal Free Resolutions of 0-Dimensional Schemes in P1 \times P1Aug 19 2011Let X be a zero-dimensional scheme in P1 \times P1. Then X has a minimal free resolution of length 2 if and only if X is ACM. In this paper we determine a class of reduced schemes whose resolutions, similarly to the ACM case, can be obtained by their ... More

Elastic flow interacting with a lateral diffusion process: The one-dimensional graph caseJul 26 2017A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which is enabled ... More

Abstract Canonical InferenceJun 17 2004Sep 13 2006An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction ... More