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Rings of $SL_2({\mathbb C})$-Characters and the Kauffman Bracket Skein ModuleApr 20 1996Let $M$ be a compact orientable 3-manifold. The set of characters of $SL_2({\mathbb C})$ representations of the fundamental group of $M$ forms a closed affine algebraic set. We show that its coordinate ring is isomorphic to a specialization of the Kauffman ... More

Loops in SL(2,C) and FactorizationJul 03 2017Sep 18 2017In previous work we proved that for a SU(2,C) valued loop having the critical degree of smoothness (one half of a derivative in the L^2 Sobolev sense), the following are equivalent: (1) the Toeplitz and shifted Toeplitz operators associated to the loop ... More

Continuum Variability of Deeply Embedded Protostars as a Probe of Envelope StructureJan 30 2013Stars may be assembled in large growth spurts, however the evidence for this hypothesis is circumstantial. Directly studying the accretion at the earliest phases of stellar growth is challenging because young stars are deeply embedded in optically thick ... More

Homologous Non-isotopic Symplectic Tori in Homotopy Rational Elliptic SurfacesJul 02 2003Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence homeomorphic) to the rational elliptic surface E(1) and is obtained by performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We construct an infinite family of ... More

Homologous non-isotopic symplectic tori in a K3-surfaceMay 14 2003Jul 14 2003For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also explain how ... More

Induced Spin-Currents in Alkali-FilmsMar 01 2004In sandwiches of FeK and FeCs the conduction electrons in the alkali metals have a large mean free path. The experiments suggest that the specular reflection for spin up and down electrons is different at the interface yielding a spin current in the alkali ... More

Skein HomologyJan 17 1997For each skein module we describe a homology theory which, for any three manifold recovers the skein module at its zero level. The theory measures skein-like relations among skein relations, mimicking Hilbert's theory of syzygies. We work explicit examples ... More

Tests of the Las Campanas Distant Cluster Survey from Confirmation Observations for the ESO Distant Cluster SurveyJul 11 2002The ESO Distant Cluster Survey (EDisCS) is a photometric and spectroscopic study of the galaxy cluster population at two epochs, z~0.5 and z~0.8, drawn from the Las Campanas Distant Cluster Survey (LCDCS). We report results from the initial candidate ... More

Maunakea Spectroscopic Explorer Advancing from Conceptual DesignJul 20 2018The Maunakea Spectroscopic Explorer (MSE) project has completed its Conceptual Design Phase. This paper is a status report of the MSE project regarding its technical and programmatic progress. The technical status includes its conceptual design and system ... More

The radial part of the zero-mode Hamiltonian for sigma models with group target spaceMar 28 2004We use geometric arguments to derive a possible form for the radial part of the ``zero-mode Hamiltonian'' for the two dimensional sigma model with target space S^3, or more generally a compact simply connected Lie group.

An invariant measure for the loop space of a simply connected compact symmetric spaceSep 04 2004Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we prove the existence (and conjecture the uniqueness) ... More

Solving for Root Subgroup Coordinates: The SU(2) CaseSep 19 2015Previously we showed that a loop in a simply connected compact Lie group K has a unique triangular factorization if and only if the loop has a unique root subgroup factorization (relative to a choice of a reduced sequence of simple reflections in the ... More

The ice composition in the disk around V883 Ori revealed by its stellar outburstSep 02 2018Feb 07 2019Complex organic molecules (COMs), which are the seeds of prebiotic material and precursors of amino acids and sugars, form in the icy mantles of circumstellar dust grains but cannot be detected remotely unless they are heated and released to the gas phase. ... More

Asymptotic freedom of general relativity and its possible consequencesMay 24 2000The formation of singularities in certain situations, such as the collapse of massive stars, is one of the unresolved issues in classical general relativity. Although no complete theory of quantum gravity exists it is often suggested that quantum gravity ... More

Complex groups and root subgroup factorizationJul 24 2017Dec 26 2017Root subgroup factorization is a refinement of triangular (or LDU) factorization. For a complex reductive Lie group, and a choice of reduced factorization of the longest Weyl group element, the forward map from root subgroup coordinates to triangular ... More

From Random Walks to Random Leaps: Generalizing Classic Markov Chains for Big Data ApplicationsAug 10 2017Simple random walks are a basic staple of the foundation of probability theory and form the building block of many useful and complex stochastic processes. In this paper we study a natural generalization of the random walk to a process in which the allowed ... More

MILC Code Performance on High End CPU and GPU Supercomputer ClustersDec 01 2017With recent developments in parallel supercomputing architecture, many core, multi-core, and GPU processors are now commonplace, resulting in more levels of parallelism, memory hierarchy, and programming complexity. It has been necessary to adapt the ... More

The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More

Continued fraction digit averages an Maclaurin's inequalitiesFeb 02 2014Jul 28 2014A classical result of Khinchin says that for almost all real numbers $\alpha$, the geometric mean of the first $n$ digits $a_i(\alpha)$ in the continued fraction expansion of $\alpha$ converges to a number $K = 2.6854520\ldots$ (Khinchin's constant) as ... More

Homeomorphism of S^1 and FactorizationAug 23 2014For each $n > 0$ there is a one complex parameter family of homeomorphisms of the circle consisting of linear fractional transformations `conjugated by $z \to z^n$'. We show that these families are free of relations, which determines the structure of ... More

On invariant measures for the group of diffeomorphisms of the circleDec 29 1996In a previous paper the author constructed biinvariant measures (possibly having values in a line bundle) for a loop group LK (with compact simply connected K) acting on the formal completion of its complexification LG. One motivation for this was to ... More

Spectrum Results with Kogut-Susskind QuarksOct 04 2001Nov 27 2001I summarize recent developments in spectrum calculations using Kogut-Susskind quarks. Theoretical developments include one-loop computations with improved actions. I present some recent simulation results, mostly from a MILC collaboration project using ... More

Scaling functions for O(4) in three dimensionsJul 31 1996Monte Carlo simulation using a cluster algorithm is used to compute the scaling part of the free energy for a three dimensional O(4) spin model. The results are relevant for analysis of lattice studies of high temperature QCD.

Voting patterns in 2016: Exploration using multilevel regression and poststratification (MRP) on pre-election pollsFeb 02 2018Mar 14 2018We analyzed 2012 and 2016 YouGov pre-election polls in order to understand how different population groups voted in the 2012 and 2016 elections. We broke the data down by demographics and state. We display our findings with a series of graphs and maps. ... More

Gaussian Process Landmarking for Three-Dimensional Geometric MorphometricsJul 31 2018Jan 08 2019We demonstrate applications of the Gaussian process-based landmarking algorithm proposed in [T. Gao, S.Z. Kovalsky, and I. Daubechies, SIAM Journal on Mathematics of Data Science (2019)] to geometric morphometrics, a branch of evolutionary biology centered ... More

Invariant measures for unitary forms of Kac-Moody groups, Parts I-IIIOct 09 1995The purpose of this paper is to describe some conjectures and results on the existence and uniqueness of invariant measures on formal completions of Kac-Moody groups and associated homogeneous spaces. Existence is rigorously established in all affine ... More

Glueball SpinDec 15 1999Apr 02 2001The spin of a glueball is usually taken as coming from the spin (and possibly the orbital angular momentum) of its constituent gluons. In light of the difficulties in accounting for the spin of the proton from its constituent quarks, the spin of glueballs ... More

Polymer Collapse on Fluctuating Random SurfacesSep 05 1994Jan 12 1995The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact interactions of relative ... More

On Loop Equations In KdV Exactly Solvable String TheoryNov 30 1991The non-perturbative behaviour of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed ... More

Effective Theories for Circuits and AutomataJun 28 2011Feb 20 2012Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational ... More

Volatility Swap Under the SABR ModelMar 25 2013The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The ... More

(k+1)-sums versus k-sumsNov 19 2010Jun 08 2012A $k$-sum of a set $A\subseteq \mathbb{Z}$ is an integer that may be expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of the number of $(k+1)$-sums to the number of $k$-sums be? Writing $k\wedge A$ for the set of $k$-sums of ... More

On the explanation for quantum statisticsNov 15 2005The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs' paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the ... More

The Lattice Fermi SurfaceOct 08 2001The Nambu - Jona-Lasinio model in 2+1 dimensions is simulated for non-zero baryon chemical potential with a diquark source term. No evidence for a BCS condensate or gap is seen at high density; rather, critical behaviour with novel exponents is observed, ... More

Improving the Lattice QED ActionNov 24 1994Strongly coupled QED is a model whose physics is dominated by short-ranged effects. In order to assess which features of numerical simulations of the chiral phase transition are universal and which are not, we have formulated a quenched version of the ... More

Monte Carlo Study of the 3D Thirring ModelFeb 05 1997I review three different non-perturbative approaches to the three dimensional Thirring model: the 1/N_f expansion, Schwinger-Dyson equations, and Monte Carlo simulation. Simulation results are presented to support the existence of a non-perturbative fixed ... More

Up to and beyond ninth order in opacity: Radiative energy loss with GLVApr 29 2008A new examination of the GLV all-orders opacity result for radiative energy loss is presented. The opacity expansion is shown to be a Dyson expansion of a Schrodinger-like (or diffusion) equation, a form also found in BDMPS-Z-ASW, AMY and Higher Twist ... More

Nuts have no hairAug 18 1995We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat ${\rm C}^{2}$-metrics $g_{\mu\nu}$ on a 4-dimensional complete manifold ${\cal M}$ of topology ${\rm R}^{2} \times {\rm S}^{2}$ which have (at least) ... More

On the unimodality of power transformations of positive stable densitiesFeb 19 2010Nov 15 2013Let $Z_\alpha$ be a positive $\alpha-$stable random variable and $r\in{\bf R}.$ We show the existence of an unbounded open domain $D$ in $[1/2,1]\times{\bf R}$ with a cusp at $(1/2,-1/2)$, characterized by the complete monotonicity of the function $F_{\alpha, ... More

NPPT Bound Entanglement ExistsAug 31 2006Every dXd bipartite system is shown to have a large family of undistillable states with nonpositive partial transpose (NPPT). This family subsumes the family of conjectured NPPT bound entangled Werner states. In particular, all one-copy undistillable ... More

A Relativistic Conical Function and its Whittaker LimitsNov 01 2011In previous work we introduced and studied a function $R(a_{+},a_{-},{\bf c};v,\hat{v})$ that is a generalization of the hypergeometric function ${}_2F_1$ and the Askey-Wilson polynomials. When the coupling vector ${\bf c}\in{\mathbb C}^4$ is specialized ... More

Controlling inclusive cross sections in parton shower + matrix element mergingNov 23 2012Dec 03 2012We propose an extension of matrix element plus parton shower merging at tree level to preserve inclusive cross sections obtained from the merged and showered sample. Implementing this constraint generates approximate next-to-leading order (NLO) contributions ... More

Bend conductance of crossed wires in the presence of Andreev scatteringApr 12 1994We study the 4-probe bend conductance $G_{14,32}$ of a mesoscopic crossed wire structure in the ballistic regime in the absence of a magnetic field, which for normal devices is usually negative. We predict that for sufficiently large devices and for small ... More

Natural Entanglement in Bose-Einstein CondensatesOct 18 2001Every Bose-Einstein condensate is in a highly entangled state, as a consequence of the fact that the particles in a condensate are distributed over space in a coherent way. It is proved that any two regions within a condensate of finite particle number ... More

Towards Critical Physics in 2+1d with U(2N)-Invariant FermionsOct 14 2016Interacting theories of N relativistic fermion flavors in reducible spinor representations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall ... More

Resolving the observer reference class problem in cosmologyJul 14 2017The assumption that we are typical observers plays a core role in attempts to make multiverse theories empirically testable. A widely shared worry about this assumption is that it suffers from systematic ambiguity concerning the reference class of observers ... More

Non-Gaussianities in a two-field generalization of Natural InflationNov 23 2017We describe a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally ... More

The Maser-Starburst connection in NGC253Nov 07 2017NGC253 is one of the closest starburst galaxies to the Milky Way and as such it has been studied in detail across the electromagnetic spectrum. Recent observations have detected the first extragalactic class I methanol masers at 36 and 44 GHz and the ... More

Kitaev MaterialsJan 24 2017In transition-metal compounds with partially filled $4d$ and $5d$ shells spin-orbit entanglement, electronic correlations, and crystal-field effects conspire to give rise to a variety of novel forms of topological quantum matter. This includes Kitaev ... More

Numerical study of the $2+1d$ Thirring model with U($2N$)-invariant fermionsAug 25 2017In 2+1 dimensions the global U($2N$) symmetry associated with massless Dirac fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U($2N$)-invariant limit in interacting ... More

The Spectral Gap of Sparse Random DigraphsAug 01 2017The second largest eigenvalue of a transition matrix $P$ has connections with many properties of the underlying Markov chain, and especially its convergence rate towards the stationary distribution. In this paper, we give an asymptotic upper bound for ... More

A remark on the group-completion theoremSep 07 2017Suppose that $M$ is a topological monoid satisfying $\pi_0M=\mathbb{N}$ to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\infty}\rightarrow \Omega BM$ defined on an infinite mapping telescope ... More

Query-driven Data Completeness Management (PhD Thesis)Nov 11 2014Apr 01 2015Knowledge about data completeness is essentially in data-supported decision making. In this thesis we present a framework for metadata-based assessment of database completeness. We discuss how to express information about data completeness and how to ... More

Global existence and convergence for a higher order flow in conformal geometryApr 22 2004We study a higher-order parabolic equation which generalizes the Ricci flow on two-dimensional surfaces. The metric is deformed conformally with a speed given by the Q-curvature of the metric. Under a condition on the Q-curvature of the initial metric ... More

Retrieving the three-dimensional matter power spectrum and galaxy biasing parameters from lensing tomographyFeb 09 2012Apr 16 2012With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can be harnessed to constrain the three-dimensional (3D) matter power spectrum over a range of redshift and physical scale. By combining galaxy-galaxy lensing ... More

On the Computation of the Shannon Capacity of a Discrete Channel with NoiseJan 30 2017Jan 31 2017Muroga [M52] showed how to express the Shannon channel capacity of a discrete channel with noise [S49] as an explicit function of the transition probabilities. His method accommodates channels with any finite number of input symbols, any finite number ... More

Finding generically stable measuresSep 18 2010We discuss two constructions for obtaining generically stable Keisler measures in an NIP theory. First, we show how to symmetrize an arbitrary invariant measure to obtain a generically stable one from it. Next, we show that suitable sigma-additive probability ... More

On dp-minimal ordered structuresSep 23 2009We show some basic facts about dp-minimal ordered structures. The main results are : dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal. ... More

Metric Diophantine approximation with respect to planar distance functionsJan 27 2004We outline a proof of an analogue of Khintchine's Theorem in R^2, where the ordinary height is replaced by a distance function satisfying an irrationality condition as well as certain decay and symmetry conditions.

A theorem of Poincaré-Hopf typeMay 28 2009We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincar\'e-Hopf formula is then a consequence of the smooth Poincar\'e-Hopf theorem and of additivity of the Euler-Poincar\'e characteristic ... More

On the distribution of powers of real numbers modulo 1Nov 18 2014Given a strictly increasing sequence of positive real numbers tending to infinity $(q_{n})_{n=1}^{\infty}$, and an arbitrary sequence of real numbers $(r_{n})_{n=1}^{\infty}.$ We study the set of $\alpha\in(1,\infty)$ for which $\lim_{n\to\infty}\|\alpha^{q_{n}}-r_{n}\|= ... More

Proceedings Sixth Workshop on Trends in Functional Programming in EducationMay 11 2018The Sixth International Workshops on Trends in Functional Programming in Education, TFPIE 2017, was held on 22 June 2017 at the University of Kent, in Canterbury, UK, and was co-located with TFP, the Symposium on Trends in Functional Programming. The ... More

Tropical linear spaces and tropical convexityMay 08 2015In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult ... More

Diophantine approximation and the solubility of the Schroedinger equationOct 22 2002Apr 29 2003We characterise the set of periods for which number theoretical obstructions prevent us from finding periodic solutions of the Schroedinger equation on a two dimensional torus as well as the asymptotic occurrence of possible resonances.

Constructive Gelfand duality for non-unital commutative C*-algebrasDec 05 2014Feb 03 2015We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonunital C*-algebras and locally compact completely regular locales, that ideals ... More

Alternatives for optimization in systems and control: convex and non-convex approachesMay 01 2012In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it is clear that ... More

A heteroclinic orbit connecting traveling waves pertaining to different nonlinearitiesJun 13 2017In this paper we consider a semilinear parabolic equation in an infinite cylinder. The spatially varying nonlinearity is such that it connects two (spatially independent) bistable nonlinearities in a compact set in space. We prove that, given such a setting, ... More

An almost-integral universal Vassiliev invariant of knotsMay 23 2001Sep 05 2002A `total Chern class' invariant of knots is defined. This is a universal Vassiliev invariant which is integral `on the level of Lie algebras' but it is not expressible as an integer sum of diagrams. The construction is motivated by similarities between ... More

Introduction to Modular FormsJul 04 2014We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes are based on ... More

Some integral curvature estimates for the Ricci flow in four dimensionsApr 10 2015We consider solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, four dimensional manifolds without boundary. We prove integral curvature estimates which are valid for any such solution. In the case that the scalar curvature is bounded and T is finite, ... More

A note on singularities in finite time for the constrained Willmore flowJul 05 2018This work investigates the formation of singularities under the steepest descent $L^2$-gradient flow of the functional $\mathcal W_{\lambda_1, \lambda_2}$, the sum of the Willmore energy, $\lambda_1$ times the area, and $\lambda_2$ times the signed volume ... More

Adiabatic limits of co-associative Kovalev-Lefschetz fibrationsMar 28 2016Apr 26 2016We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.

Brane Effective Actions, Kappa-Symmetry and ApplicationsOct 11 2011Nov 22 2011This is a review on brane effective actions, their symmetries and some of its applications. Its first part uncovers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects : the identification of their ... More

Extremal black holes, Holography & Coarse grainingJun 01 2011Jul 30 2011I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the half-BPS sector ... More

The geometry of null rotation identificationsMar 21 2002Apr 16 2002The geometry of flat spacetime modded out by a null rotation (boost+rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, ... More

Automorphisms as brane non-local transformationsOct 26 2000The relation among spacetime supersymmetry algebras and superbrane actions is further explored. It is proved that $SL(2,\bR)$ belongs to the automorphism group of the ${\cal N}=2$ D=10 type IIB SuperPoincar\'e algebra. Its SO(2) subgroup is identified ... More

Some New Bounds on the Entropy Numbers of Diagonal OperatorsMar 01 2019Entropy numbers are an important tool for quantifying the compactness of operators. Besides establishing new upper bounds on the entropy numbers of diagonal operators $D_\sigma$ from $\ell_p$ to $\ell_q$, where $p\not=q$, we investigate the optimality ... More

The growth rate and dimension theory of beta-expansionsAug 30 2012Oct 15 2012In a recent paper of Feng and Sidorov they show that for $\beta\in(1,\frac{1+\sqrt{5}}{2})$ the set of $\beta$-expansions grows exponentially for every $x\in(0,\frac{1}{\beta-1})$. In this paper we study this growth rate further. We also consider the ... More

Summability of Superstring TheoryMar 11 1998Mar 20 1998Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined estimates of large-order bosonic string amplitudes, the super-Schottky group ... More

Scalar Field Theory in Curved Space and the Definition of MomentumFeb 09 1997Dec 22 1997Some general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of constant curvature ... More

Meromorphic Szego functions and asymptotic series for Verblunsky coefficientsFeb 23 2005We prove that the Szeg\H{o} function, $D(z)$, of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponentials. We relate the positions of the poles of $D(z)^{-1}$ to the exponential ... More

Maximizing Riesz means of anisotropic harmonic oscillatorsDec 29 2017Oct 08 2018We consider problems related to the asymptotic minimization of eigenvalues of anisotropic harmonic oscillators in the plane. In particular we study Riesz means of the eigenvalues and the trace of the corresponding heat kernels. The eigenvalue minimization ... More

Local asymptotic normality for shape and periodicity of a signal in the drift of a degenerate diffusion with internal variablesMar 08 2019Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is driven by possibly ... More

Quasi-modularity of generalized sum-of-divisors functionsJun 16 2015Jul 24 2015In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jacobi forms, and prove that they are quasi-modular forms.

Mass Equidistribution for Automorphic Forms of Cohomological Type on GL_2Jun 16 2010Aug 13 2010We extend Holowinsky and Soundararajan's proof of quantum unique ergodicity for holomorphic Hecke modular forms on SL(2,Z), by establishing it for automorphic forms of cohomological type on GL_2 over an arbitrary number field which satisfy the Ramanujan ... More

Upper bounds for Maass forms on semisimple groupsMay 27 2014Dec 19 2017We prove a power saving over the local bound for the sup norm of Hecke-Maass forms on any quasi-split semisimple real group that is not isogenous to a product of odd special unitary groups.

Restrictions of SL_3 Maass forms to maximal flat subspacesAug 04 2013Aug 26 2014Let \psi be a Hecke-Maass form on a cubic division algebra over \Q. We apply arithmetic amplification to improve the local bound for the L^2 norm of \psi restricted to maximal flat subspaces.

How to determine a K3 surface from a finite automorphismApr 29 2016Dec 13 2017In this article we pursue the question when an automorphism determines a (complex) K3 surface up to isomorphism. We prove that if the automorphism is finite non-symplectic and the transcendental lattice small, then the isomorphism class of the K3 surface ... More

Locality estimates for Fresnel-wave-propagation and stability of X-ray phase contrast imaging with finite detectorsMay 16 2018Nov 05 2018Coherent wave-propagation in the near-field Fresnel-regime is the underlying contrast-mechanism to (propagation-based) X-ray phase contrast imaging (XPCI), an emerging lensless technique that enables 2D- and 3D-imaging of biological soft tissues and other ... More

Local smoothing results for the Ricci flow in dimensions two and threeSep 19 2012Jun 20 2013We present local estimates for solutions to the Ricci flow, without the assumption that the solution has bounded curvature. These estimates lead to a generalisation of one of the pseudolocality results of G.Perelman in dimension two.

Curves between Lipschitz and $C^1$ and their relation to geometric knot theoryFeb 29 2016In this article we investigate regular curves whose derivatives have vanishing mean oscillations. We show that smoothing these curves using a standard mollifier one gets regular curves again. We apply this result to solve a couple of open problems. We ... More

Exceptional digit frequencies and expansions in non-integer basesNov 28 2017In this paper we study the set of digit frequencies that are realised by elements of the set of $\beta$-expansions. The main result of this paper demonstrates that as $\beta$ approaches $1,$ the set of digit frequencies that occur amongst the set of $\beta$-expansions ... More

Front blocking versus propagation in the presence of a drift term in the direction of propagationMar 08 2018Oct 12 2018In this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged. We give explicit conditions on the drift term for ... More

Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systemsMar 19 2019We study a class of Lindblad equation on finite-dimensional fermionic systems. The model is obtained as the continuous-time limit of a repeated interaction process between fermionic systems with quadratic Hamiltonians, a setup already used by Platini ... More

Kähler-Einstein metrics and algebraic structures on limit spacesMar 28 2016This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.

Green functions for the Dirac operator under local boundary conditions and applicationsMar 07 2007In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary condition. Then we give ... More

Wrong side of the tracks: Big Data and Protected CategoriesDec 15 2014Jun 24 2016When we use machine learning for public policy, we find that many useful variables are associated with others on which it would be ethically problematic to base decisions. This problem becomes particularly acute in the Big Data era, when predictions are ... More

Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groupsDec 11 2010Dec 14 2010Let $G$ be an almost simple group. We prove that if $x \in G$ has prime order $p \ge 5$, then there exists an involution $y$ such that $<x,y>$ is not solvable. Also, if $x$ is an involution then there exist three conjugates of $x$ that generate a nonsolvable ... More

Towards a Theory of GlueDec 17 2012We propose and study the notions of behaviour type and composition operator making a first step towards the definition of a formal framework for studying behaviour composition in a setting sufficiently general to provide insight into how the component-based ... More