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Phonon hydrodynamics, thermal conductivity and second sound in 2D crystalsApr 12 2019Starting from our previous work where we have obtained a system of coupled integro-differential equations for acoustic sound waves and phonon density fluctuations in 2D crystals, we derive here the corresponding hydrodynamic equations and study their ... More

Bending mode fluctuations and structural stability of graphene nanoribbonsDec 19 2012We analyze the thermal fluctuations of a narrow graphene nanoribbon. Using a continuum, membrane-like model we study the height-height correlation functions and the destabilization modes corresponding to two different boundaries conditions: ribbons which ... More

Dirichlet boundary conditions in a noncommutative theoryJun 09 2010We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model. After constructing interaction terms that impose the boundary conditions, we discuss their implementation ... More

Improving the Hadronization of QCD currents in TAUOLA and PHOKHARAOct 13 2008We present our study of the hadronization structure of both vector and axial-vector currents leading to decays of the tau into two kaons and a pion. The cornerstones of our framework are the large-N_C limit of QCD, the chiral structure exhibited at low ... More

Two local conditions on the vertex stabiliser of arc-transitive graphs and their effect on the Sylow subgroupsFeb 22 2011In this paper we study $G$-arc-transitive graphs $\Delta$ where the permutation group $G_x^{\Delta(x)}$ induced by the stabiliser $G_x$ of the vertex $x$ on the neighbourhood $\Delta(x)$ satisfies the two conditions given in the introduction. We show ... More

Growth of nanostructures by cluster deposition : a reviewMar 09 1999This paper presents a comprehensive analysis of simple models useful to analyze the growth of nanostructures obtained by cluster deposition. After detailing the potential interest of nanostructures, I extensively study the first stages of growth (the ... More

Orthogonal Schurs for Classical Gauge GroupsSep 04 2013Finite N physics of half-BPS operators for gauge groups SO(N) and Sp(N) has recently been studied[1, 2]. Among other things they showed that, alike U(N), Schur operators (but in the square of their eigenvalues) diagonalize the free field two-point function ... More

A Note in Cosmology and Loop Quantum GravityAug 21 2000One possible description of the very early stages of the evolution of the universe is provided by Chaotic Inflationary Cosmology. For that model the role of the inflaton field is played by quantum gravitational effects. We study if such a picture may ... More

Towards the (Mexican) discovery of second class currents at Belle-IIAug 08 2016Aug 18 2016Within the SM, the yet unmeasured $\tau^-\to\pi^-\eta^{(\prime)}\nu_\tau$ decays are predicted as a suppressed, isospin-violating effect with branching ratios $\lesssim\mathcal{O}(10^{-5})$. However, they can also proceed through other mechanisms (such ... More

Nodal Uniformization of G-bundlesAug 19 2016Aug 26 2016We give a survey of uniformization results for principal bundles on curves. We provide a proof of uniformization for nodal curves; this result is a special case of work of Belkale and Fakhruddin for uniformization on singular curves. We use the uniformization ... More

Mixed Motives and Motivic Birational CoversMay 03 2016Oct 10 2016We introduce a tower of localizing subcategories in Voevodsky's big (closed under infinite coproducts) triangulated category of motives. We show that the tower induces an interesting finite filtration on the motivic cohomology groups of smooth schemes ... More

Helly-type theorems for the diameterSep 25 2015We study versions of Helly's theorem that guarantee that the intersection of a family of convex sets in $R^d$ has a large diameter. This includes colourful, fractional and $(p,q)$ versions of Helly's theorem. In particular, the fractional and $(p,q)$ ... More

Novel charges in CFT'sJun 30 2014In this paper we construct two infinite sets of self-adjoint commuting charges for a quite general CFT. They come out naturally by considering an infinite embedding chain of Lie algebras, an underlying structure that share all theories with gauge groups ... More

Notes on nilspaces: algebraic aspectsJan 14 2016May 28 2016These notes constitute the first part of a detailed exposition of the theory of nilspaces developed by Camarena and Szegedy. We treat what can be called the algebraic part of the theory, in which nilspaces are studied without any topological assumption. ... More

Invited review: Graphite and its hidden superconductivityDec 12 2013We review experimental results, from transport to magnetization measurements, on different graphite samples, from bulk oriented graphite, thin graphite films to transmission electron microscope lamellae, that indicate the existence of granular superconductivity ... More

On a variant of Tykhonov regularization in optimal control under PDEsMar 24 2018Apr 01 2019We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state restrictions, in the sense that differential constraints between ... More

Penrose-like inequality with angular momentum for minimal surfacesAug 15 2017Jan 25 2018In axially symmetric spacetimes the Penrose inequality can be strengthened to include angular momentum. We prove a version of this inequality for minimal surfaces, more precisely, a lower bound for the ADM mass in terms of the area of a minimal surface, ... More

Eigenvalue Asymptotics for a Schrödinger Operator with Non-Constant Magnetic Field Along One DirectionJan 20 2015Oct 16 2015We consider the discrete spectrum of the two-dimensional Hamiltonian $H=H_0+V$, where $H_0$ is a Schr\"odinger operator with a non-constant magnetic field $B$ that depends only on one of the spatial variables, and $V$ is an electric potential that decays ... More

Motivic Birational Covers and Finite Filtrations on Chow GroupsOct 01 2014The main goal of this paper is to break up motivic cohomology into smaller pieces as suggested by the conjectural Bloch-Beilinson filtrations for the Chow groups.

On the Hausdorff dimension of pinned distance setsJun 01 2017Jan 26 2018We prove that if $A$ is a Borel set in the plane of equal Hausdorff and packing dimension $s>1$, then the set of pinned distances $\{ |x-y|:y\in A\}$ has full Hausdorff dimension for all $x$ outside of a set of Hausdorff dimension $1$ (in particular, ... More

Singular equivariant asymptotics and the moment map IFeb 09 2009This is the first of a series of papers dealing with the asymptotic behavior of certain integrals occuring in the description of the spectrum of an invariant elliptic operator on a compact Riemannian manifold carrying the action of a compact, connected ... More

Equivariant Lefschetz formulae and heat asymptoticsAug 10 2011We prove an equivariant Lefschetz formula for elliptic complexes over a compact manifold carrying the action of a compact Lie group of isometries via heat equation methods.

Einsteinian cubic gravityJul 21 2016We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives with respect ... More

Four-dimensional black holes in Einsteinian cubic gravityOct 25 2016Jan 22 2017We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordstr\"om-(Anti-)de Sitter (RN-(A)dS) black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are determined by a single ... More

Hadronic and radiative decays of the tau leptonJan 31 2013This PhD thesis studies some hadronic and radiative decays of the tau lepton using a Chiral Lagrangian including resonance fields. After a theoretical introduction, the decays to the $(\pi \pi \pi)^-$, $(KK\pi)^-$ and $\eta^{(\prime)} \pi^- \pi^0$ hadronic ... More

Hadronic matrix elements for TAUOLA: 3 pi and KKpi channelsOct 31 2008We emphasize that the motivation for including our hadronic matrix elements in TAUOLA is not only theoretical. We also show that our expressions describe better the tau to 3pi ALEPH data and are able to fit BABAR data on the isovector component of e^+e^- ... More

A proposal for improving the hadronization of QCD currents in TAUOLAOct 07 2008After overviewing the general features of semileptonic decays of the tau lepton, I will recall the most widely used model for them, namely that of Kuhn-Santamaria (KS), and I will explain the subsequent works that were done along these lines and that ... More

An algebraic study of unitary one dimensional quantum cellular automataDec 05 2005Sep 12 2006We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the ... More

Alternative approach to the regularization of odd dimensional AdS gravityMar 12 2006Aug 23 2007In this paper I present an action principle for odd dimensional AdS gravity which consists of introducing another manifold with the same boundary and a very specific boundary term. This new action allows and alternative approach to the regularization ... More

On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutionsSep 25 2016We study a class of measures on the real line with a kind of self-similar structure, which we call dynamically driven self-similar measures, and contain proper self-similar measures such as Bernoulli convolutions as special cases. Our main result gives ... More

Finite primitive groups and edge-transitive hypergraphsJul 03 2014We determine all finite primitive groups that are automorphism groups of edge-transitive hypergraphs. This gives an answer to a problem proposed by Babai and Cameron

Constrained optimization through fixed point techniquesSep 18 2014Oct 26 2015We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a certain map. Contrary ... More

Some evidence in favor of Morrey's conjectureJun 27 2014We provide further evidence to favor the fact that rank-one convexity does not imply quasiconvexity for two-component maps in dimension two. We provide an explicit family of maps parametrized by $\tau$, and argue that, for small $\tau$, they cannot be ... More

Prospects for discovery of the τ^- \to π^- \ell^+ \ell^- ν_τ decaysJan 17 2014We study the phenomenology of the \tau^- \to \pi^- \nu_\tau \ell^+ \ell^- decays (\ell = e, \mu), predicting the respective branching ratios and di-lepton invariant-mass spectra. In addition to the model-independent (QED) contributions, we investigate ... More

Infinite type toric varieties and Voronoi TilingsAug 30 2016An infinite type toric variety is a normal toric variety given by a fan with infinitely many cones. We construct examples in this paper coming from representation theory of loop groups. The fans that appear are cones on Voronoi tilings on a vector space ... More

Robust Tverberg and colorful Carathéodory results via random choiceJun 28 2016Nov 09 2016We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem that allow for small sets of points to be removed without breaking the conclusion of the result. This improves the known bounds for Tverberg's ... More

Notes on compact nilspacesMay 28 2016These notes form the second part of a detailed account of the theory of nilspaces developed by Camarena and Szegedy. Here we focus on nilspaces equipped with a compact topology that is compatible with the cube structure, called compact nilspaces. The ... More

Optimal feedback control, linear first-order PDE systems, and obstacle problemsJan 21 2014Mar 09 2015We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings depending both in ... More

A dynamical-system approach to mathematical programmingJan 10 2014Sep 18 2014We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical system are precisely the local solutions of the optimization problem. The general ... More

The automorphism group of the $s$-stable Kneser graphsSep 30 2015Nov 23 2015For $k,s\geq2$, the $s$-stable Kneser graphs are the graphs with vertex set the $k$-subsets $S$ of $\{1,\ldots,n\}$ such that the circular distance between any two elements in $S$ is at least $s$ and two vertices are adjacent if and only if the corresponding ... More

Tensor and Matrix models: a one-night stand or a lifetime romance?Mar 12 2018Mar 28 2018The spectra of energy eigenstates of free tensor and matrix models are organized by Kronecker coefficients and Littlewood-Richardson numbers, respectively. Exploiting recent results in combinatorics for Kronecker coefficients, we derive a formula that ... More

Revisiting the atomic and molecular decomposition of the weighted Hardy spacesOct 02 2017The purpose of this article is to give another molecular decomposition for members of the weighted Hardy spacs.

Robust Tverberg and colorful Carathéodory results via random choiceJun 28 2016May 14 2017We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem with tolerance. In particular, we give bounds for the smallest integer $N=N(t,d,r)$ such that for any $N$ points in $R^d$, there is a partition ... More

Birational Motivic Homotopy Theories and the Slice FiltrationDec 11 2011Nov 15 2012This paper is part of an endeavor to define an analogue of the slice filtration in the unstable motivic homotopy category. Our approach was inspired by the fact that the triangulated structures do not play a relevant role for the construction of birational ... More

Geometric and analytic properties of families of hypersurfaces in Eguchi-Hanson spaceApr 26 2001Oct 12 2001We study the geometry of families of hypersurfaces in Eguchi-Hanson space that arise as complex line bundles over curves in $S^2$ and are three-dimensional, non-compact Riemannian manifolds, which are foliated in Hopf tori for closed curves. They are ... More

Self-affine sets and the continuity of subadditive pressureSep 18 2013The affinity dimension is a number associated to an iterated function system of affine maps, which is fundamental in the study of the fractal dimensions of self-affine sets. De-Jun Feng and the author recently solved a folklore open problem, by proving ... More

Self-organizing dynamical networks able to learn autonomouslySep 28 2018We present a model for the time evolution of network architectures based on dynamical systems. We show that the evolution of the existence of a connection in a network can be described as a stochastic non-markovian telegraphic signal (NMTS). Such signal ... More

Causality: a decision theoretic approachDec 18 2018Feb 20 2019We propose a decision-theoretic model akin to Savage (1972) that is useful for defining causal effects. Within this framework, we define what it means for a decision maker (DM) to act as if the relation between the two variables is causal. Next, we provide ... More

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizationsMay 14 2019This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their in-plane and out-of-plane ... More

The dimension of weakly mean porous measures: a probabilistic approachOct 07 2010Using probabilistic ideas, we prove that the packing dimension of a mean porous measure is strictly smaller than the dimension of the ambient space. Moreover, we give an explicit bound for the packing dimension, which is asymptotically sharp in the case ... More

On distance sets, box-counting and Ahlfors-regular setsMay 01 2016May 21 2017We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent $s>1$. As a corollary, we improve upon a recent result of Orponen, by showing that if $A$ is Ahlfors-regular of dimension ... More

The equivariant spectral function of an invariant elliptic operator. $L^p$-bounds, caustics, and concentration of eigenfunctionsDec 07 2015Sep 17 2017Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a compact Lie group $G$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. Using Fourier integral operator techniques, we ... More

Universal black hole stability in four dimensionsApr 10 2017Apr 24 2017We show that four-dimensional black holes become stable below certain mass when the Einstein-Hilbert action is supplemented with higher-curvature terms. We prove this to be the case for an infinite family of ghost-free theories involving terms of arbitrarily ... More

Robust Tverberg and colorful Carathéodory results via random choiceJun 28 2016Sep 14 2016We use the probabilistic method to obtain versions of the colorful Carath\'eodory theorem and Tverberg's theorem that allow for arbitrary small sets of points to be removed without breaking the conclusion of the result. This improves the known bounds ... More

Be/X-ray binariesJan 26 2011The purpose of this work is to review the observational properties of Be/X-ray binaries. The open questions in Be/X-ray binaries include those related to the Be star companion, that is, the so-called "Be phenomenon", such as, timescales associated to ... More

On the nature of the X-ray source 1E 1024.0--5732/Wack 2134Mar 12 1999Two different models have been put forward to explain the origin of the X-ray emission of the unusual X-ray source 1E 1024.0-5732/Wack 2134: a high-mass X-ray binary system (HMXB) and a colliding wind binary (CWB). We present new optical and X-ray data ... More

The Unstable Slice FiltrationJan 17 2012Feb 28 2013The main goal of this paper is to construct an analogue of Voevodsky's slice filtration in the motivic unstable homotopy category. The construction is done via birational invariants, this is motivated by the existence of an equivalence of categories between ... More

On the Functoriality of the Slice FiltrationFeb 01 2010Sep 10 2012Let $k$ be a field with resolution of singularities, and $X$ a separated $k$-scheme of finite type with structure map $g$. We show that the slice filtration in the motivic stable homotopy category commutes with pullback along $g$. Restricting the field ... More

A network-based prediction of retail stores commercial categories and optimal locationsAug 30 2006I study the spatial organization of retail commercial activities. These are organized in a network comprising "anti-links", i.e. links of negative weight. From pure location data, network analysis leads to a community structure that closely follows the ... More

Chern-Simons Supersymmetric BranesAug 23 2000In this paper we continue the study of the model proposed in the previous paper hep-th/0002077. The model consist of a system of extended objects of diverse dimensionalities, with or without boundaries, with actions of the Chern-Simons form for a supergroup. ... More

Transgression forms as unifying principle in field theoryDec 20 2005In this work I consider extensions of Chern-Simons gravities and supergravities associated to the use of Transgression forms as actions, instead of Chern-Simons forms. It is noted that Transgression Forms yields a essencially unique prescription of boundary ... More

Action Principles for Transgression and Chern-Simons AdS GravitiesJul 22 2014Aug 06 2014Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the ... More

Brownian motion on stationary random manifoldsAug 15 2014We introduce the notion of a stationary random manifold and develop the basic entropy theory for it. Examples include manifolds admitting a compact quotient under isometries and generic leaves of a compact foliation. We prove that the entropy of an ergodic ... More

A different look at controllabilityJan 14 2014We explore further controllability problems through a standard least square approach. By setting up a suitable error functional $E$, and putting $m(\ge0)$ for the infimum, we interpret approximate controllability by asking $m=0$, while exact controllability ... More

On annular maps of the torus and sublinear diffusionOct 31 2013Nov 05 2013There is a classification by Misiurewicz and Ziemian of elements in Homeo$_0(\mathbf{T}^2)$ by their rotation set $\rho$, according to wether $\rho$ is a point, a segment or a set with nonempty interior. A recent classification of nonwandering elements ... More

Spectral Functions in QFTMay 16 2015We present a pedagogical exposition of some applications of functional methods in quantum field theory: we use heat-kernel and zeta-function techniques to study the Casimir effect, the pair production in strong electric fields, quantum fields at finite ... More

On distance sets, box-counting and Ahlfors-regular setsMay 01 2016Aug 12 2016We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent $s>1$. As a corollary, we improve upon a recent result of Orponen, by showing that if $A$ is Ahlfors-regular of dimension ... More

On a variant of Tykhonov regularization in optimal control under PDEsMar 24 2018We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state constraints. In addition to exploring basic issues like existence ... More

Boundedness of generalized Riesz potentials on the variable Hardy spacesJul 30 2016We study the boundedness from Hp(.) into Lq(.) of certain generalized Riesz potentials and the Hp(.)-Hq(.) boundedness of the Riesz potential. Both results are achieved via the finite atomic decomposition developed in [4].

A Note on Hardy Spaces and Bounded OperatorsFeb 26 2015Mar 02 2015In this note we show that if f belongs to Hp(Rn)\capLs(Rn), where 0 < p <= 1 < s < 1, then there exists a (p;infinite)-atomic decomposition which converges to f in Ls(Rn). From this fact, we prove that a bounded operator T on Ls(Rn) can be extended to ... More

Reeb stability and the Gromov-Hausdorff limits of leaves in compact foliationsApr 23 2013We show that the Gromov-Hausdorff limit of a sequence of leaves in a compact foliation is a covering space of the limiting leaf which is no larger than this leaf's holonomy cover. We also show that convergence to such a limit is smooth instead of merely ... More

Overlapping self-affine setsAug 16 2004We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F.Przytycki and M.Urbanski. We extend their ... More

Reduced Weyl asymptotics for pseudodifferential operators on bounded domains I. The finite group caseOct 12 2005Jul 21 2007Let $G\subset \O(n)$ be a group of isometries acting on $n$-dimensional Euclidean space $\R^n$, and ${\bf{X}}$ a bounded domain in $\R^n$ which is transformed into itself under the action of G. Consider a symmetric, classical pseudodifferential operator ... More

Equal coefficients and tolerance in coloured Tverberg partitionsApr 05 2012Apr 23 2012The coloured Tverberg theorem was conjectured by B\'ar\'any, Lov\'{a}sz and F\"uredi and asks whether for any d+1 sets (considered as colour classes) of k points each in R^d there is a partition of them into k colourful sets whose convex hulls intersect. ... More

Natural Cohomology on $\mathbb{P}^1 \times \mathbb{P}^1$Aug 22 2018A vector bundle on a projective variety has a natural cohomology if for every twist its cohomology is concentrated in a single degree. Eisenbud and Schreyer conjectured there should be vector bundles on $\mathbb{P}^1 \times \mathbb{P}^1$ with natural ... More

Shapes Characterization on Address Event Representation Using Histograms of Oriented Events and an Extended LBP ApproachFeb 09 2018Address Event Representation is a thriving technology that could change digital image processing paradigm. This paper proposes a methodology to characterize the shape of objects using the streaming of asynchronous events. A new descriptor that enhances ... More

Tverberg partitions as weak epsilon-netsNov 30 2017Jun 10 2018We prove a Tverberg-type theorem using the probabilistic method. Given $\varepsilon >0$, we find the smallest number of partitions of a set $X$ in $R^d$ into $r$ parts needed in order to induce at least one Tverberg partition on every subset of $X$ with ... More

Discrete-time quantum walks and gauge theoriesOct 30 2017A quantum computer, i.e. utilizing the resources of quantum physics, superposition of states and entanglement, could furnish an exponential gain in computing time. A simulation using such resources is called a quantum simulation. The advantage of quantum ... More

Effect of curvature and normal forces on motor regulation of ciliaMay 10 2019Cilia are ubiquitous organelles involves in eukaryotic motility. They are long, slender, and motile protrusions from the cell body. They undergo active regular oscillatory beating patterns that can propel cells, such as the algae Chlamydomonas, through ... More

Penrose-like inequality with angular momentum for general horizonsOct 24 2018In axially symmetric space-times it is expected that the Penrose inequality can be strengthened to include angular momentum. In a recent work [2] we have proved a weaker version of this inequality for minimal surfaces, using the monotonicity of the Geroch ... More

Singular equivariant asymptotics and Weyl's lawJan 10 2010Aug 11 2011We study the spectrum of an invariant, elliptic, classical pseudodifferential operator on a closed G-manifold M, where G is a compact, connected Lie group acting effectively and isometrically on M. Using resolution of singularities, we determine the asymptotic ... More

Addendum to "Singular equivariant asymptotics and Weyl's law"Jul 20 2015Sep 01 2015Let $M$ be a closed Riemannian manifold carrying an effective and isometric action of a compact connected Lie group $G$. We derive a refined remainder estimate in the stationary phase approximation of certain oscillatory integrals on $T^\ast M \times ... More

A Modified Multifractal Formalism for a Class of Self-Similar MeasuresAug 03 2004The multifractal spectrum of a Borel measure $\mu$ in $\mathbb{R}^n$ is defined as \[ f_\mu(\alpha) = \dim_H {x:\lim_{r\to 0} \frac{\log \mu(B(x,r))}{\log r}=\alpha}. \] For self-similar measures under the open set condition the behavior of this and related ... More

Spectral Functions of Singular OperatorsMar 28 2007Oct 28 2014The asymptotic expansion of the heat-kernel for small values of its argument has been studied in many different cases and has been applied to 1-loop calculations in Quantum Field Theory. In this thesis we consider this asymptotic behavior for certain ... More

Singular equivariant asymptotics and the moment map IIJun 12 2009This is the second of a series of papers dealing with the asymptotic behavior of certain integrals occuring in the description of the spectrum of an invariant elliptic operator on a compact Riemannian manifold carrying the action of a compact, connected ... More

Projections of self-similar and related fractals: a survey of recent developmentsJan 05 2015In recent years there has been much interest -and progress- in understanding projections of many concrete fractals sets and measures. The general goal is to be able to go beyond general results such as Marstrand's Theorem, and quantify the size of every ... More

Porosity, dimension, and local entropies: a surveyOct 25 2011Porosity and dimension are two useful, but different, concepts that quantify the size of fractal sets and measures. An active area of research concerns understanding the relationship between these two concepts. In this article we will survey the various ... More

Improved bounds for the dimensions of planar distance setsNov 08 2018We obtain new lower bounds on the Hausdorff dimension of distance sets and pinned distance sets of planar Borel sets of dimension slightly larger than $1$, improving recent estimates of Keleti and Shmerkin, and of Liu in this regime. In particular, we ... More

Four-dimensional black holes in Einsteinian cubic gravityOct 25 2016We construct static and spherically symmetric generalizations of the Schwarzschild- and Reissner-Nordstr\"om-(Anti) de Sitter (RN-(A)dS) black-hole solutions in four-dimensional Einsteinian cubic gravity (ECG). The solutions are determined by a single ... More

Hadronic decays of the tau lepton into K K pion modes within Resonance Chiral TheorySep 24 2007Tau decays into hadrons have a twofold interest: On the one hand, they are a clean environment for studying the hadronization of the left-handed current of QCD, while, on the other side, provide relevant dynamical information of the resonances that mediate ... More

Quantum Computation explained to my MotherMay 08 2003There are many falsely intuitive introductions to quantum theory and quantum computation in a handwave. There are also numerous documents which teach those subjects in a mathematically sound manner. To my knowledge this paper is the shortest of the latter ... More

The maximum order of the elements of a finite symplectic group of even characteristicFeb 02 2013We give an exact formula, as a function of m and q, for the maximum order of the elements of the finite symplectic group Sp(2m,q), with q even, and of its automorphism group.

Semiregular elements in cubic vertex-transitive graphs and the restricted Burnside problemNov 30 2012In this paper, we prove that the maximal order of a semiregular element in the automorphism group of a cubic vertex-transitive graph X does not tend to infinity as the number of vertices of X tends to infinity. This gives a solution (in the negative) ... More

The equivariant spectral function of an invariant elliptic operator. $L^p$-bounds, caustics and concentration of eigenfunctionsDec 07 2015Jun 21 2016Let $M$ be a compact boundaryless manifold, carrying an effective and isometric action of a compact connected Lie group $G$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. Using Fourier integral operator techniques, we prove ... More

An application of the Local C(G,T) Theorem to a conjecture of WeissSep 16 2015Let $\Gamma$ be a connected $G$-vertex-transitive graph, let $v$ be a vertex of $\Gamma$ and let $G_v^{\Gamma(v)}$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\Gamma(v)$. The graph $\Gamma$ is said ... More

Resonance Chiral Lagrangians and alternative approaches to hadronic tau decaysOct 30 2014Nov 14 2014Exclusive semi-leptonic decays of the tau lepton offer a clean probe to study the hadronization of QCD currents in its non-perturbative regime and learn about resonance dynamics, which drives strong interactions in these processes. In this theory outlook, ... More

Gauge Symmetries and Holographic Anomalies of Chern-Simons and Transgression AdS GravityAug 06 2014We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, ... More

Failure of Breit-Wigner and success of dispersive descriptions of the τ^-\to K^-ην_τdecaysJan 20 2014The \tau^-\to K^-\eta\nu_\tau decays have been studied using Chiral Perturbation Theory extended by including resonances as active fields. We have found that the treatment of final state interactions is crucial to provide a good description of the data. ... More

Weak limits in non-linear conductivityFeb 03 2014The problem of characterizing weak limits of sequences of solutions for a non-linear diffusion equation of $p$-laplacian type is addressed. It is formulated in terms of certain moments of underlying Young measures associated with main fields corresponding ... More

Agujeros negros cuánticos en la teoría de cuerdas tipo-IIAOct 21 2013In the context of Type-IIA String Theory compactified to four dimensions on a Calabi-Yau manifold (CY), we study the effect of considering perturbative and non-perturbative corrections (in alpha prime) to the prepotential of the resulting effective Supergravity ... More