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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

Casimir operators, abelian subspaces and u-cohomologyMay 15 2007Jun 05 2007This survey paper is an exposition of old and recent results of Kostant and al. on the relationships between the exterior algebra of a simple Lie algebra and the action of the Casimir operator on it. Our exposition relies on u-cohomology and it is basically ... More

Cyclic generators for irreducible representations of affine Hecke algebrasSep 09 2008Sep 29 2009We give a detailed account of a combinatorial construction, due to Cherednik, of cyclic generators for irreducible modules of the affine Hecke algebra of the general linear group with generic parameter q.

Spherical nilpotent orbits and abelian subalgebras in isotropy representationsJul 12 2016Jul 27 2016Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation ... More

The $\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of ZJul 29 2005Apr 08 2006Let an affine Weyl group $\hat W$ act as a group of affine transformations on a real vector space V. We analyze the $\hat W$-orbit of a regular element in V and deduce applications to Kostant's formula for powers of the Euler product and to the representations ... More

Irreducible representations of YangiansMay 29 2011Sep 04 2011We give explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra and of its twisted analogues, corresponding to symplectic and orthogonal Lie algebras. In particular, we develop the fusion procedure for twisted ... More

Spherical nilpotent orbits and abelian subalgebras in isotropy representationsJul 12 2016Nov 27 2016Let $G$ be a simply connected semisimple algebraic group with Lie algebra $\mathfrak g$, let $G_0 \subset G$ be the symmetric subgroup defined by an algebraic involution $\sigma$ and let $\mathfrak g_1 \subset \mathfrak g$ be the isotropy representation ... More

Enumeration of ad-nilpotent $\frak b$-ideals for simple Lie algebrasNov 03 2000We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.

The adjoint representation inside the exterior algebra of a simple Lie algebraNov 18 2013Apr 27 2015For a simple complex Lie algebra $\mathfrak g$ we study the space of invariants $A=\left( \bigwedge \mathfrak g^*\otimes\mathfrak g^*\right)^{\mathfrak g}$, (which describes the isotypic component of type $\mathfrak g$ in $ \bigwedge \mathfrak g^*$) as ... More

Symmetries of abelian ideals of Borel subalgebrasJan 11 2013Jul 28 2013Elaborating on a paper by Suter, we provide a detailed description of the automorphism group of the poset of abelian ideals in a Borel subalgebra of a finite dimensional complex simple Lie algebra.

ad-nilpotent ideals containing a fixed number of simple root spacesJan 09 2004May 02 2009We give formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a Lie algebra of type B or D containing a fixed number of root spaces attached to simple roots. This result solves positively a conjecture of Panyushev (cf. D. Panyushev, ... More

Abelian subalgebras in Z_2-graded Lie algebras and affine Weyl groupsNov 23 2003Mar 04 2004Let g=g_0+ g_1 be a simple Z_2-graded Lie algebra and let b_0 be a fixed Borel subalgebra of g_0. We describe and enumerate the abelian b_0-stable subalgebras of g_1.

The Bruhat order on abelian ideals of Borel subalgebrasJun 22 2018Sep 17 2018Let G be a quasi simple algebraic group over an algebraically closed field k whose characteristic is not very bad for G, and let B be a Borel subgroup of G with Lie algebra b. Given a B-stable abelian subalgebra a of the nilradical of b, we parametrize ... More

ad-nilpotent $\frak b$-ideals in sl(n) having a fixed class of nilpotence: combinatorics and enumerationApr 17 2000We study the combinatorics of ad-nilpotent ideals of a Borel subalgebra of $sl(n+1,\Bbb C)$. We provide an inductive method for calculating the class of nilpotence of these ideals and formulas for the number of ideals having a given class of nilpotence. ... More

Conformal embeddings and simple current extensionsOct 24 2012Feb 18 2014In this paper we investigate the structure of intermediate vertex algebras associated with a maximal conformal embedding of a reductive Lie algebra in a semisimple Lie algebra of classical type.

The maximum cardinality of minimal inversion complete sets in finite reflection groupsDec 30 2013Sep 17 2014We compute for reflection groups of type $A,B,D,F_4,H_3$ and for dihedral groups a statistic counting the maximal cardinality of a set of elements in the group whose generalized inversions yield the full set of inversions and which are minimal with respect ... More

On special covariants in the exterior algebra of a simple Lie algebraApr 16 2014Sep 08 2014We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the n-th symmetric power of the ... More

Dirac operators and the Very Strange Formula for Lie superalgebrasMay 22 2013Aug 04 2013Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.

On the structure of Borel stable abelian subalgebras in infinitesimal symmetric spacesSep 21 2011Mar 31 2012Let g=g_0+g_1 be a Z_2-graded Lie algebra. We study the posets of abelian subalgebras of g_1 which are stable w.r.t. a Borel subalgebra of g_0. In particular, we find out a natural parametrization of maximal elements and dimension formulas for them. We ... More

Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine settingApr 25 2007Oct 02 2007We extend classical results of Kostant and al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting ... More

Conformal embeddings in affine vertex superalgebrasMar 09 2019This paper is a natural continuation of our previous work on conformal embeddings of vertex algebras [6], [7], [8]. Here we consider conformal embeddings in simple affine vertex superalgebra $V_k(\mathfrak g)$ where $\mathfrak g=\mathfrak g_{\bar 0}\oplus ... More

Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairsFeb 18 2011Jan 10 2012We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs of real Lie ... More

Decomposition rules for conformal pairs associated to symmetric spaces and abelian subalgebras of Z_2-graded Lie algebrasJun 15 2005Jan 23 2006We give uniform formulas for the branching rules of level 1 modules over orthogonal affine Lie algebras for all conformal pairs associated to symmetric spaces. We also provide a combinatorial intepretation of these formulas in terms of certain abelian ... More

On the Kernel of the affine Dirac operatorApr 22 2008Sep 14 2009Let L be a finite-dimensional semisimple Lie algebra with a non-degenerate invariant bilinear form, \sigma an elliptic automorphism of L leaving the form invariant, and A a \sigma-invariant reductive subalgebra of L, such that the restriction of the form ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016Apr 12 2017We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal V_k(\mathfrak g^{\natural})$. A particular ... More

Finite vs infinite decompositions in conformal embeddingsSep 22 2015Apr 06 2016Building on work of the first and last author, we prove that an embedding of simple affine vertex algebras $V_{\mathbf{k}}(\mathfrak g^0)\subset V_{k}(\mathfrak g)$, corresponding to an embedding of a maximal equal rank reductive subalgebra $\mathfrak ... More

Kostant's pair of Lie type and conformal embeddingsFeb 08 2018We deal with some aspects of the theory of conformal embeddings of affine vertex algebras, providing a new proof of the Symmetric Space Theorem and a criterion for conformal embeddings of equal rank subalgebras. We finally study some examples of embeddings ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras II: decompositionsApr 04 2016May 20 2016This paper is a continuation of arXiv:1602.04687. We present methods for computing the explicit decomposition of the minimal simple affine $W$-algebra $W_k(\mathfrak g, \theta)$ at a conformal level $k$ as a module for its maximal affine subalgebra $\mathcal ... More

Conformal embeddings of affine vertex algebras in minimal $W$-algebras I: structural resultsFeb 15 2016Apr 17 2016We find all values of $k\in \mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\mathfrak g,\theta)$ is conformal, where $\mathfrak g$ is a basic simple Lie superalgebra and $-\theta$ its minimal ... More

On classification of non-equal rank affine conformal embeddings and applicationsFeb 20 2017Dec 16 2017We complete the classification of conformal embeddings of a maximally reductive subalgebra $\mathfrak k$ into a simple Lie algebra $\mathfrak g$ at non-integrable non-critical levels $k$ by dealing with the case when $\mathfrak k$ has rank less than that ... More

An application of collapsing levels to the representation theory of affine vertex algebrasJan 30 2018Oct 27 2018We discover a large class of simple affine vertex algebras $V_{k} (\mathfrak g)$, associated to basic Lie superalgebras $\mathfrak g$ at non-admissible collapsing levels $k$, having exactly one irreducible $\mathfrak g$-locally finite module in the category ... More

Regularity Properties of Constrained Set-Valued MappingsSep 09 2002In these notes, we present a general result concerning the Lipschitz regularity of a certain type of set-valued maps often found in constrained optimization and control problems. The class of multifunctions examined in this paper is characterized by means ... More

Mining the Blazar SkyDec 15 2000We present the results of our methods to "mine" the blazar sky, i.e., select blazar candidates with very high efficiency. These are based on the cross-correlation between public radio and X-ray catalogs and have resulted in two surveys, the Deep X-ray ... More

Ground-State Entanglement in Interacting Bosonic GraphsNov 10 2003We consider a collection of bosonic modes corresponding to the vertices of a graph $\Gamma.$ Quantum tunneling can occur only along the edges of $\Gamma$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the ... More

Mode Entanglement and Entangling power in Bosonic GraphsApr 23 2003We analyze the quantum entanglement properties of bosonic particles hopping over graph structures.Mode-entanglement of a graph vertex with respect the rest of the graph is generated, starting from a product state, by turning on for a finite time a tunneling ... More

A Sample-oriented Catalogue of BL Lacertae ObjectsNov 15 1995We present a catalogue of 233 BL Lacertae objects compiled through an extensive bibliographic search updated to mid-1995. A large fraction of the sources listed in the catalogue belongs to well-defined samples and can be used for statistical purposes. ... More

The ROSAT X-ray Spectra of BL Lacertae ObjectsJan 17 1996We study the X-ray spectra of 85 BL Lacertae objects using the hardness ratios as given in the WGA catalogue of {\it ROSAT} sources. This sample includes all WGA BL Lacs with high-quality data and comprises about 50 per cent of presently known BL Lacs. ... More

Quantum chaos and operator fidelity metricMar 06 2009We show that the recently introduced operator fidelity metric provides a natural tool to investigate the cross-over to quantum chaotic behaviour. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. ... More

The Connection between X-ray- and Radio-Selected BL Lacertae ObjectsDec 20 1994We explain the properties of X-ray selected BL Lacertae objects, under the assumption that they constitute the small minority of the BL Lac population with energy cutoff located in the UV/X-ray band, as suggested by their multifrequency spectra. In particular, ... More

A simplified view of blazars: contribution to the X-ray and gamma-ray cosmic backgroundsApr 08 2015The "blazar simplified view" is a new paradigm that explains well the diverse statistical properties of blazars observed over the entire electromagnetic spectrum on the basis of minimal assumptions on blazars' physical and geometrical properties. In this ... More

Existence and Uniqueness of Solutions for Coupled Hybrid Systems of Differential EquationsJul 09 2018In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in which the ... More

Lipschitzian Estimates in Discrete-Time Constrained Stochastic Optimal ControlJun 05 2002This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We derive accurate ... More

ad-nilpotent ideals of a Borel subalgebra IIIMar 05 2003Sep 30 2003This paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a Borel subalgebra. Our main result is a nice uniform formula for the dimension of maximal ideals in these posets. We also obtain ... More

Truth Validation with EvidenceFeb 15 2018In the modern era, abundant information is easily accessible from various sources, however only a few of these sources are reliable as they mostly contain unverified contents. We develop a system to validate the truthfulness of a given statement together ... More

Normalizing inclusive rare B decaysMay 02 2008Sep 26 2008The inclusive semileptonic branching ratio is often employed to normalize other inclusive B decays. Using recent determinations of the non-perturbative parameters of the Operator Product Expansion we compute the normalization factor for the branching ... More

A simplified view of blazars: comparison with multi-frequency observationsAug 29 2013We have recently proposed a new scenario where blazars are classified as flat-spectrum radio quasars or BL Lacs according to the prescriptions of unified schemes, and to a varying combination of Doppler boosted radiation from the jet, emission from the ... More

Open book decompositions versus prime factorizations of closed, oriented 3-manifoldsJul 08 2014Let $M$ be a closed, oriented, connected 3--manifold and $(B,\pi)$ an open book decomposition on $M$ with page $\Sigma$ and monodromy $\varphi$. It is easy to see that the first Betti number of $\Sigma$ is bounded below by the number of $S^2\times S^1$--factors ... More

Knot Floer homology detects genus-one fibred knotsMar 18 2006Dec 05 2006Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on Gabai's theory of sutured manifold decomposition and contact topology. We implement this strategy for genus-one knots, ... More

One cannot hear the density of a drum (and further aspects of isospectrality)Jul 01 2013Oct 11 2013It is well known that certain pairs of planar domains have the same spectra of the Laplacian operator. We prove that these domains are still isospectral for a wider class of physical problems, including the cases of heterogeneous drums and of quantum ... More

Can one hear the density of a drum? Weyl's law for inhomogeneous mediaDec 08 2009We generalize Weyl's law to inhomogeneous bodies in $d$ dimensions. Using a perturbation scheme recently obtained by us in Ref. \cite{Amore09}, we have derived an explicit formula, which describes the asymptotic behavior of the eigenvalues of the negative ... More

A method for classical and quantum mechanicsNov 13 2004In many physical problems it is not possible to find an exact solution. However, when some parameter in the problem is small, one can obtain an approximate solution by expanding in this parameter. This is the basis of perturbative methods, which have ... More

A new approach to resummation: Parametric Perturbation TheoryMay 08 2007We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are constrained ... More

Non perturbative regularization of one loop integrals at finite temperatureMar 18 2005Mar 21 2005A method devised by the author is used to calculate analytical expressions for one loop integrals at finite temperature. A non-perturbative regularization of the integrals is performed, yielding expressions of non-polynomial nature. A comparison with ... More

Measurements of inclusive jet and dijet cross sections at the Large Hadron ColliderOct 07 2015This review discusses the measurements of the inclusive jet and dijet cross section performed by the experimental collaborations at the LHC during what is now being called LHC Run 1 (2009 - 2013). It summarises some of the experimental challenges and ... More

Nonlinear surface waves on the plasma-vacuum interfaceDec 29 2015In this paper we study the propagation of weakly nonlinear surface waves on a plasma-vacuum interface. In the plasma region we consider the equations of incompressible magnetohydrodynamics, while in vacuum the magnetic and electric fields are governed ... More

Generalized plane waves in AdSNov 16 2015Dec 20 2015We classify solutions to Einstein's equations in AdS with constant boundary stress tensor, which in general is not diagonalizable, i.e. it does not admit a reference frame. New solutions are found, and in the context of the AdS/CFT duality they should ... More

Heterogeneous systems in $d$ dimensions: lower spectrumAug 19 2014We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically approximated by ... More

Unified Schemes and the two Classes of BL LacsJan 11 1999I briefly summarize the main tenets of unified schemes of BL Lacs and low-luminosity radio galaxies, discussing in particular the evolution of this field after the Como 1988 meeting. I also examine some of the open problems and complications of the simplest ... More

Belief revision by examplesSep 18 2014A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but the problem of obtaining ... More

Discord and non-classicality in probabilistic theoriesDec 21 2011Quantum discord quantifies non-classical correlations in quantum states. We introduce discord for states in causal probabilistic theories, inspired by the original definition proposed in Ref. [17]. We show that the only probabilistic theory in which all ... More

Endogenous games with goals: side-payments among goal-directed artificial agentsNov 13 2013Nov 14 2013Artificial agents are typically oriented to the realization of an externally assigned task and try to optimize over secondary aspects of plan execution such time lapse or power consumption, technically displaying a quasi-dichotomous preference relation. ... More

Multipartite entanglement in qubit systemsNov 05 2008We introduce a potential of multipartite entanglement for a system of n qubits, as the average over all balanced bipartitions of a bipartite entanglement measure, the purity. We study in detail its expression and look for its minimizers, the maximally ... More

Comparative study of Rare Gas-H$_2$ triatomic complexesMay 15 2008This paper presents a comparative analysis of complexes made of one Rare Gas (Rg) atom and molecular hydrogen, for all five stable Rg atoms. In particular, the vibrational band origins have been calculated, as well as the structural properties of the ... More

Can Social Networks help the progress of Astrophysics and Cosmology? An experiment in the field of Galaxy KinematicsApr 07 2010This paper is crucial part of an experiment aimed to investigate whether Social Networks can be of help for Astrophysics. In the present case, in helping to eliminate the deep-routed wrong misconception of Flat Rotation Curves of Spiral Galaxies, more ... More

Derived categories and Kummer varietiesFeb 18 2006Dec 18 2006We prove that if two abelian varieties have equivalent derived categories then the derived categories of the smooth stacks associated to the corresponding Kummer varieties are equivalent as well. The second main result establishes necessary and sufficient ... More

Multiparton Interactions and Double Parton Scatterings in CMSSep 03 2013Multiparton interactions are introduced in order to explain a wide range of phenomena in p-p collisions. We present the most recent CMS measurements sensitive to multiparton interactions and hard double parton scattering at 7 TeV. In particular, the W+dijet ... More

Heavy flavor physics with CMSSep 05 2011Sep 13 2011Different recent results from CMS Collaboration on Quarkonia Physics and Heavy Quarks production are presented. All these results have been obtained analyizing the data of $pp$ collisions at sqrt{s}=7 TeV provided by the LHC and collected by the CMS detector ... More

The Quantum Hall Effect in GrapheneJan 29 2011Apr 24 2012We investigate the quantum Hall effect in graphene. We argue that in graphene in presence of an external magnetic field there is dynamical generation of mass by a rearrangement of the Dirac sea. We show that the mechanism breaks the lattice valley degeneracy ... More

The Ellipsoidal Universe in the Planck Satellite EraJan 22 2014May 14 2014Recent Planck data confirm that the cosmic microwave background displays the quadru-pole power suppression together with large scale anomalies. Progressing from previous results, that focused on the quadrupole anomaly, we strengthen the proposal that ... More

Comment on the evidence of the Higgs boson at LHCSep 14 2012We comment on the Standard Model Higgs boson evidence from LHC. We propose that the new resonance at 125 GeV could be interpreted as a pseudoscalar meson with quantum number $J^{PC} = 0^{- +}$. We show that this pseudoscalar could mimic the decays of ... More

On the Large Scale CMB PolarizationJan 15 2010Mar 17 2010We discuss the large scale polarization of the cosmic microwave background induced by the anisotropy of the spatial geometry of our universe. Assuming an eccentricity at decoupling of about $0.64 10^{-2}$, we find an average large scale polarization $\Delta ... More

Recoil momentum spectrum in directional dark matter detectorsSep 10 2002Sep 24 2002Directional dark matter detectors will be able to record the recoil momentum spectrum of nuclei hit by dark matter WIMPs. We show that the recoil momentum spectrum is the Radon transform of the WIMP velocity distribution. This allows us to obtain analytic ... More

Optical depth evaluation in pixel microlensingNov 02 1998We propose an estimator of the microlensing optical depth from pixel lensing data that involves only measurable quantities. In comparison to the only previously proposed estimator, it has the advantage of not being limited to events with large magnification ... More

Evidence for "sterile neutrino" dark matter?Aug 17 1998I show that it may be possible to explain the present evidence for a gamma-ray emission from the galactic halo as due to halo WIMP annihilations. Not only the intensity and spatial pattern of the halo emission can be matched but also the relic density ... More

Holographic Bound in Quantum Field Energy Density and Cosmological ConstantJul 15 2012Jul 21 2012The cosmological constant problem is reanalyzed by imposing the limitation of the number of degrees of freedom (d.o.f.) due to entropy bounds directly in the calculation of the energy density of a field theory. It is shown that if a quantum field theory ... More

Work fluctuations for a Brownian particle between two thermostatsMay 02 2006We explicitly determine the large deviation function of the energy flow of a Brownian particle coupled to two heat baths at different temperatures. This toy model, initially introduced by Derrida and Brunet [B. Derrida and E. Brunet, in "Einstein aujourd'hui", ... More

Threshold resummation of Drell-Yan rapidity distributionsSep 07 2006Dec 04 2006We present a derivation of the threshold resummation formula for the Drell-Yan rapidity distribution. Our argument is valid for all values of rapidity and to all orders in perturbative QCD and can be applied to all Drell-Yan processes in a universal way, ... More

Supersonic Turbulence and the Fragmentation of a Cold MediumJun 01 1995The role played by velocity fields in the fragmentation of a cold medium and in the formation of protostars is studied. The velocity field is modeled with a compressible turbulent flow. A supersonic turbulent velocity field can fragment the medium into ... More

Computation on a Noiseless Quantum Code and SymmetrizationJan 16 1999Jun 09 1999Let ${\cal H}$ be the state-space of a quantum computer coupled with the environment by a set of error operators spanning a Lie algebra ${\cal L}.$ Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal C}\subset{\cal H}$ annihilated ... More

The Atiyah Patodi Singer index formula for measured foliationsJul 04 2009Let $X_0$ be a compact Riemannian manifold with boundary endowed with a oriented, measured even dimensional foliation with purely transverse boundary. Let $X$ be the manifold with cylinder attached and extended foliation. We prove that the $L^2$--measured ... More

The Atiyah Patodi Singer signature formula for measured foliationsJan 02 2009Jan 06 2009Let $(X_0,\mathcal{F}_0) $ be a compact manifold with boundary endowed with a foliation $\mathcal{F}_0$ which is assumed to be measured and transverse to the boundary. We denote by $\Lambda$ a holonomy invariant transverse measure on $(X_0,\mathcal{F}_0) ... More

The Calderon projection over C* algebrasJul 08 2013Jul 10 2013We construct the Calderon projection on the space of Cauchy datas for a twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus for operators acting on bundles of finitely generated $C^*$--Hilbert modules on a compact manifold with ... More

Statistical Model Checking for Biological ApplicationsMay 12 2014Jun 13 2014In this paper we survey recent work on the use of statistical model checking techniques for biological applications. We begin with an overview of the basic modelling techniques for biochemical reactions and their corresponding stochastic simulation algorithm ... More

On the moduli space of the Schwarzenberger bundlesSep 14 2000Jul 13 2001By proving a particular case of a conjecture of Drezet, we show that a component of the Maruyama scheme of the semi-stable sheaves on the projective space $\PP^n$ of rank n and Chern polynomial $(1+t)^{n+2}$ is isomorphic to the Kronecher moduli $N(n+1,2,n+2)$, ... More

Unions of admissible relationsApr 08 2017Feb 04 2018We show that a variety $\mathcal V$ is congruence distributive if and only if there is some $h$ such that the inclusion (1) $\Theta \cap ( \sigma \circ \sigma ) \subseteq ( \Theta \cap \sigma ) \circ ( \Theta \cap \sigma ) \circ \dots $ ($h$ factors) ... More

On tolerances representable as $R \circ R^-$Oct 02 2006We give examples and counterexamples concerning varieties in which every tolerance is representable as $R \circ R^-$, for some reflexive and admissible relation $R$.

A congruence identity satisfied by m-permutable varietiesAug 27 2005We present a new and useful congruence identity satisfied by m-permutable varieties.

Tight contact structures on Seifert manifolds over T^2 with one singular fibreJul 25 2003Aug 18 2005In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.

Weak and local versions of measurabilityApr 06 2014Local versions of measurability have been around for a long time. Roughly, one splits the notion of $\mu $-completeness into pieces, and asks for a uniform ultrafilter over $\mu $ satisfying just some piece of $\mu $-completeness. Analogue local versions ... More

Generalized Frolík classesMar 08 2015The class $\mathfrak C $ relative to countably compact topological spaces and the class $\mathfrak P$ relative to pseudocompact spaces introduced by Z. Frol\'ik are naturally generalized relative to every topological property. We provide a characterization ... More

Topological spaces compact with respect to a set of filtersOct 08 2012Mar 15 2013If $\mathcal P$ is a family of filters over some set $I$, a topological space $X$ is \emph{sequencewise $\mathcal P$-\brfrt compact} if, for every $I$-indexed sequence of elements of $X$, there is $F \in \mathcal P$ such that the sequence has an $F$-limit ... More

For Hausdorff spaces, $H$-closed = $D$-pseudocompact for all ultrafilters $D$Jul 07 2011Oct 22 2011We prove that, for an arbitrary topological space $X$, the following two conditions are equivalent: (a) Every open cover of $X$ has a finite subset with dense union (b) $X$ is $D$-pseudocompact, for every ultrafilter $D$. Locally, our result asserts that ... More

On overtwisted, right-veering open booksJul 26 2011Jan 01 2012We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda-Kazez-Matic. The page of all our open books is a four-holed sphere and the underlying 3-manifolds ... More

Rational homology cobordisms of plumbed 3-manifoldsFeb 13 2015Mar 30 2015We investigate rational homology cobordisms of 3-manifolds with non-zero first Betti number. This is motivated by the natural generalization of the slice-ribbon conjecture to multicomponent links. In particular we consider the problem of which rational ... More

Tensored Segre classesMay 30 2016We study a class obtained from the Segre class $s(Z,Y)$ of an embedding of schemes by incorporating the datum of a line bundle on $Z$. This class satisfies basic properties analogous to the ordinary Segre class, but leads to remarkably simple formulas ... More

Projective duality and a Chern-Mather involutionJan 20 2016Feb 11 2016We observe that linear relations among Chern-Mather classes of projective varieties are preserved by projective duality. We deduce the existence of an explicit involution on a part of the Chow group of projective space, encoding the effect of duality ... More

How many hypersurfaces does it take to cut out a Segre class?Apr 29 2016Oct 17 2016We prove an identity of Segre classes for zero-schemes of compatible sections of two vector bundles. Applications include bounds on the number of equations needed to cut out a scheme with the same Segre class as a given subscheme of (for example) a projective ... More

Segre classes as integrals over polytopesJul 02 2013We prove a formula for the Segre classes of monomial schemes as integrals over suitable Newton regions.

Weighted Chern-Mather classes and Milnor classes of hypersurfacesDec 17 1998We introduce a class extending the notion of Chern-Mather class to possibly nonreduced schemes, and use it to express the difference between Schwartz-MacPherson's Chern class and the class of the virtual tangent bundle of a singular hypersurface of a ... More

Verdier specialization via weak factorizationSep 13 2010Apr 07 2012Let X in V be a closed embedding, with V - X nonsingular. We define a constructible function on X, agreeing with Verdier's specialization of the constant function 1 when X is the zero-locus of a function on V. Our definition is given in terms of an embedded ... More