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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

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.

Enhancing active wave absorption in RANS modelsOct 08 2018Nov 06 2018In this work we review the most common methods for absorbing waves in Reynolds-Averaged Navier-Stokes (RANS) models. The limitations of active wave absorption, originating from its initial assumption of linear wave theory in shallow waters are overcome ... More

Addendum to 'The equivariant spectral function of an invariant elliptic operator'Sep 11 2018Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the equivariant ... 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

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

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.

Hilbert's 16th problem. II. Pfaffian equations and variational methodsApr 02 2019Starting from a Pfaffian equation in dimension $N$ and focusing on compact solutions for it, we place in perspective the variational method used in [29] to solve Hilbert's 16th problem. In addition to exploring how this viewpoint can help in detecting ... More

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

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

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

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-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

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.

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

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

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

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

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

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

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

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

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

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

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

Calderón-Hardy spaces with variable exponents and the solution of the equation delta{m}F=f for f in Hp(.)Oct 29 2015We define the Calder\'on-Hardy spaces with variable exponents and then we study the behavior of the operator delta{m} on these spaces.

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

Hadronic currents for $τ^-\toπ^-π^0ν_τ$ and other decays of interest in TAUOLADec 05 2011A new set of hadronic form factors, which has been implemented in TAUOLA, is described.

Young-measure solutions for multidimensional systems of conservation lawsOct 22 2018We explore Young measure solutions of systems of conservation laws through an alternative variational method that introduces a suitable, non-negative error functional to measure departure of feasible fields from being a weak solution. Young measure solutions ... More

Singular equivariant asymptotics and the momentum map. Residue formulae in equivariant cohomologyOct 07 2013Let $M$ be a smooth manifold and $G$ a compact connected Lie group acting on $M$ by isometries. In this paper, we study the equivariant cohomology of ${\bf X}=T^\ast M$, and relate it to the cohomology of the Marsden-Weinstein reduced space via certain ... More

Moreira's Theorem on the arithmetic sum of dynamically defined Cantor setsJul 23 2008We present a complete proof of a theorem of C.G. Moreira. Under mild checkable conditions, the theorem asserts that the Hausdorff dimension of the arithmetic sum of two dynamically defined Cantor subsets of the real line, equals either the sum of the ... More

Pulsar observations at millimetre wavelengthsJun 27 2018Detecting and studying pulsars above a few GHz in the radio band is challenging due to the typical faintness of pulsar radio emission, their steep spectra, and the lack of observatories with sufficient sensitivity operating at high frequency ranges. Despite ... More

A lower bound for the principal eigenvalue of fully nonlinear elliptic operatorsSep 07 2017In this article we present a new technique to obtain a lower bound for the principal Dirichlet eigenvalue of a fully nonlinear elliptic operator. We ilustrate the construction of an appropriate radial function required to obtain the bound in several examples. ... More

Salem sets with no arithmetic progressionsOct 26 2015Oct 30 2015We construct Salem sets in $\mathbb{R}/\mathbb{Z}$ of any dimension (including $1$) which do not contain any arithmetic progressions of length $3$. Moreover, the sets can be taken to be Ahlfors regular if the dimension is less than $1$, and the measure ... More

The politics of physicists social modelsMar 03 2019I give an overview of the topic of this special issue, the applications of (statistical) physics to social sciences at large. I discuss several examples of simple social models put forward by physicists and discuss their interest. I argue that while they ... More

Hadronization in tau -> K K pi nu_tau decaysSep 29 2008Hadronization in tau -> K K pi nu_tau decays is driven by both vector and axial-vector currents that we study, guided by the following principles: The 1/N_C expansion -worked out at leading order, considering only the contribution of the lightest spin ... More

Quantum DecoysAug 08 2003Mar 25 2004Alice communicates with words drawn uniformly amongst $\{\ket{j}\}_{j=1..n}$, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys $\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}$ between her messages. Such pairwise superpositions ... More

On the Orientability of the Slice FiltrationSep 21 2010Apr 14 2011Let $X$ be a Noetherian separated scheme of finite Krull dimension. We show that the layers of the slice filtration in the motivic stable homotopy category $\stablehomotopy$ are strict modules over Voevodsky's algebraic cobordism spectrum. We also show ... More

Multiplicative Properties of the Slice FiltrationJun 10 2008Dec 07 2008We show that the slice filtration introduced by Voevodsky is compatible in a suitable sense with the symmetric monoidal structure in the category of motivic symmetric T-spectra constructed by Jardine. It follows from this compatibility that the zero slice ... More

Transgressions and Holographic Conformal Anomalies for Chern-Simons GravitiesOct 25 2010I present two calculations of the holographic Weyl anomalies induced by Chern-Simons gravity theories alternative to the ones presented in the literature. The calculations presented here rest on the extension from Chern-Simons to Transgression forms as ... More

Compositionality for Presuppositions over TableauxMay 05 1995Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear in them. This ... More

Causality: a decision theoretic approachDec 18 2018We 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

A complete degeneration of the moduli of $G$-bundles on a curveNov 26 2013Dec 24 2013For a semi simple group G it is known the moduli stack of principal G-bundles over a fixed nodal curve is not complete. Finding a completion requires compactifying the group G. However it was shown in [34] that this is not sufficient to complete the moduli ... More

Balanced Convex Partitions of Measures in $\mathbb{R}^d$Oct 29 2010May 12 2011We will prove the following generalization of the ham sandwich Theorem, conjectured by Imre B\'ar\'any. Given a positive integer $k$ and $d$ nice measures $\mu_1, \mu_2,..., \mu_d$ in $\mathbb{R}^d$ such that $\mu_i (\mathds{R}^d) = k$ for all $i$, there ... More

Semileptonic $τ$ decays: powerful probes of non-standard charged current weak interactionsMar 07 2019When looking for heavy ($\mathcal{O}$(few TeV)) New Physics, the most efficient way to benefit from both high and low-energy measurements simultaneously is the use of the Standard Model Effective Field Theory (SMEFT). In this talk I highlight the importance ... More

A remark on certain integral operators of fractional typeMar 09 2017We study the Hp-Lq boundedness of certain integral operators of fractional type.

Hunting Vector Bundles on $\mathbb{P}^1 \times \mathbb{P}^1$Oct 12 2017May 07 2018Boij-S\"oderberg theory concerns resolutions of graded modules over a polynomial ring over a field. Specifically Boij-S\"oderberg theory gives a description of the cone of Betti diagrams for Cohen-Macaulay modules. Eisenbud and Schreyer discovered a duality ... More

A new way to construct 1-singular Gelfand-Tsetlin modulesMar 21 2017We present a simplified way to construct the Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb C)$ related to a $1$-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic Gelfand-Tsetlin ... More

Localization of elementary systems in the theory of WignerSep 20 1999Starting from Wigner's theory of elementary systems and following a recent approach of Schroer we define certain subspaces of localized wave functions in the underlying Hilbert space with the help of the theory of modular von-Neumann algebras of Tomita ... More

Analysis on real affine G-varietiesSep 05 2003We consider the action of a real linear algebraic group $G$ on a smooth, real affine algebraic variety $M\subset \R^n$, and study the corresponding left regular $G$-representation on the Banach space $C_0(M)$ of continuous, complex valued functions on ... More

Adapting the time-step to recover the asymptotic behavior in a blow-up problemJul 19 2004The equation $u_t = \Delta u + u^p$ with homegeneous Dirichlet boundary conditions has solutions with blow-up if $p > 1$. An adaptive time-step procedure is given to reproduce the asymptotic behvior of the solutions in the numerical approximations. We ... More

Overdetermined elliptic problems in topological disksOct 27 2016We introduce a method, based on the Poincare-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs ... More

On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutionsSep 25 2016Nov 21 2018We 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

On the exceptional set for absolute continuity of Bernoulli convolutionsMar 16 2013Aug 05 2013We prove that the set of exceptional $\lambda\in (1/2,1)$ such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convolutions, with the exceptional set independent of the bias. This improves ... More

Pseudodifferential operators on prehomogeneous vector spacesFeb 09 2004Let $G_\C$ be a connected, linear algebraic group defined over $\R$, acting regularly on a finite dimensional vector space $V_\C$ over $\C$ with $\R$-structure $V_\R$. Assume that $V_\C$ posseses a Zariski-dense orbit, so that $(G_\C,\rho,V_\C)$ becomes ... More

Rotation Vectors for Homeomorphisms of Non-Positively Curved ManifoldsDec 30 2009Sep 12 2011Rotation vectors, as defined for homeomorphisms of the torus that are isotopic to the identity, are generalized to such homeomorphisms of any complete Riemannian manifold with non-positive sectional curvature. These generalized rotation vectors are shown ... More

Explicit construction of effective flux functions for Riemann solutionsJan 16 2017For a family of Riemann problems for systems of conservation laws, we construct a flux function that is scalar and is capable of describing the Riemann solution of the original system.

Pricing of Basket Options Using Polynomial ApproximationsApr 11 2014In this paper we use Bernstein and Chebyshev polynomials to approximate the price of some basket options under a bivariate Black-Scholes model. The method consists in expanding the price of a univariate related contract after conditioning on the remaining ... More

$\mathcal A$-compact mappingsMay 29 2015Jan 25 2016For a fixed Banach operator ideal $\mathcal A$, we use the notion of $\mathcal A$-compact sets of Carl and Stephani to study $\mathcal A$-compact polynomials and $\mathcal A$-compact holomorphic mappings. Namely, those mappings $g\colon X\rightarrow Y$ ... More

Four-dimensional black holes in Einsteinian cubic gravityOct 25 2016Nov 09 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