Results for "Benjamin Erk"

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Photophysics of indole upon x-ray absorptionFeb 08 2018A photofragmentation study of gas-phase indole (C$_8$H$_7$N) upon single-photon ionization at a photon energy of 420 eV is presented. Indole was primarily inner-shell ionized at its nitrogen and carbon $1s$ orbitals. Electrons and ions were measured in ... More
High-repetition-rate and high-photon-flux 70 eV high-harmonic source for coincidence ion imaging of gas-phase moleculesFeb 11 2016Apr 28 2016Unraveling and controlling chemical dynamics requires techniques to image structural changes of molecules with femtosecond temporal and picometer spatial resolution. Ultrashort-pulse x-ray free-electron lasers have significantly advanced the field by ... More
Relations such as Hypernymy: Identifying and Exploiting Hearst Patterns in Distributional Vectors for Lexical EntailmentMay 18 2016Sep 23 2016We consider the task of predicting lexical entailment using distributional vectors. We perform a novel qualitative analysis of one existing model which was previously shown to only measure the prototypicality of word pairs. We find that the model strongly ... More
Coulomb explosion imaging of concurrent CH$_{2}$BrI photodissociation dynamicsOct 06 2017The dynamics following laser-induced molecular photodissociation of gas-phase CH$_{2}$BrI at 271.6 nm were investigated by time-resolved Coulomb explosion imaging using intense near-IR femtosecond laser pulses. The observed delay-dependent photofragment ... More
X-ray diffraction from isolated and strongly aligned gas-phase molecules with a free-electron laserJul 17 2013Jan 28 2014We report experimental results on x-ray diffraction of quantum-state-selected and strongly aligned ensembles of the prototypical asymmetric rotor molecule 2,5-diiodobenzonitrile using the Linac Coherent Light Source. The experiments demonstrate first ... More
Quantum spin pumping with adiabatically modulated magnetic barrier'sMar 29 2003Dec 09 2003A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structure's is investigated. The device for dc- transport does not provide spin-polarized currents, but in the adiabatic regime, when one ... More
On smooth Gorenstein polytopesMar 08 2013A Gorenstein polytope of index r is a lattice polytope whose r-th dilate is a reflexive polytope. These objects are of interest in combinatorial commutative algebra and enumerative combinatorics, and play a crucial role in Batyrev's and Borisov's computation ... More
Games and Meta-Games: Pricing Rules for Combinatorial MechanismsMar 20 2015In settings where full incentive-compatibility is not available, such as core-constraint combinatorial auctions and budget-balanced combinatorial exchanges, we may wish to design mechanisms that are as incentive-compatible as possible. This paper offers ... More
Homogenization of Hamilton-Jacobi equations with rough time dependenceFeb 16 2016We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory spatial dependence and rough time dependence. The time dependence is in the form of the derivative of a continuous path that converges to a possibly nowhere-differentiable path, ... More
A simple proof of Brown's diagonalizability theoremOct 04 2010We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.
Yet another solution to the Burnside problem for matrix semigroupsNov 16 2008We use the kernel category to give a finiteness condition for semigroups. As a consequence we provide yet another proof that finitely generated periodic semigroups of matrices are finite.
SO(2)-congruent projections of convex bodies with rotation about the originSep 27 2013We prove that if two convex bodies $ K, L \subset \mathbb{R}^3$ satisfy the property that the orthogonal projections of $K$ and $L$ onto every plane containing the origin are roations of each other, then either $K$ and $L$ coincide or $L$ is the image ... More
Bipartite Euler systemsFeb 28 2012If E is an elliptic curve over Q and K is an imaginary quadratic field, there is an Iwasawa main conjecture predicting the behavior of the Selmer group of E over the anticyclotomic Z_p-extension of K. The main conjecture takes different forms depending ... More
Special cohomology classes for modular Galois representationsFeb 28 2012Building on ideas of Vatsal, Cornut proved a conjecture of Mazur asserting the generic nonvanishing of Heegner points on an elliptic curve E as one ascends the anticyclotomic Z_p-extension of a quadratic imaginary extension K/Q. In the present article ... More
Opportunities with top quarks at future circular collidersDec 04 2014We describe various studies relevant for top physics at future circular collider projects currently under discussion. We show how highly-massive top-antitop systems produced in proton-proton collisions at a center-of-mass energy of 100 TeV could be observed ... More
Beyond the Minimal Supersymmetric Standard Model: from theory to phenomenologyFeb 21 2012Thanks to the latest development in the field of Monte Carlo event generators and satellite programs allowing for a straightforward implementation of any beyond the Standard Model theory in those tools, studying the property of any softly-broken supersymmetric ... More
Transverse-momentum, threshold and joint resummations for slepton pair production at hadron collidersOct 10 2007We present precision calculations of the transverse-momentum spectrum and the invariant-mass distribution for slepton pair production at hadron colliders. We implement the transverse-momentum, threshold and joint resummation formalisms at the next-to-leading ... More
Slepton pair production at hadron collidersOct 24 2006In R-parity conserving supersymmetric models, sleptons are produced in pairs at hadron colliders. We show that measurements of the longitudinal single-spin asymmetry at possible polarization upgrades of existing colliders allow for a direct extraction ... More
Twisted derived equivalences for affine schemesNov 11 2013We show how work of Rickard and To\"en completely resolves the question of when two twisted affine schemes are derived equivalent.
On the integral Tate conjecture for finite fields and representation theoryApr 19 2015May 28 2015We describe a new source of counterexamples to the so-called integral Hodge and integral Tate conjectures. As in the other known counterexamples to the integral Tate conjecture over finite fields, ours are approximations of the classifying space of some ... More
On a theorem of Hazrat and HooblerApr 05 2011We use cycle complexes with coefficients in an Azumaya algebra, as developed by Kahn and Levine, to compare the G-theory of an Azumaya algebra to the G-theory of the base scheme. We obtain a sharper version of a theorem of Hazrat and Hoobler in certain ... More
Jet Charge with the ATLAS Detector using $\sqrt{s}=8$ TeV $pp$ Collision DataSep 01 2014The momentum-weighted sum of the charges of tracks associated to a jet provides an experimental handle on the electric charge of fundamental strongly-interacting particles. An overview of a study of this jet charge observable for jets produced in dijet ... More
Summary of progress on the Blaschke conjectureSep 05 2013Aug 03 2015The Blaschke conjecture claims that every compact Riemannian manifold whose injectivity radius equals its diameter is, up to constant rescaling, a compact rank one symmetric space. We summarize the intuition behind this problem, the proof that such manifolds ... More
Analogues elliptiques des nombres multizétasJan 14 2013Jan 12 2015We study functions of an elliptic parameter, which are defined as iterated integrals of elliptic functions. We establish their relation with the "elliptic associators" of our previous work, by means of a functional realization of Lie algebras appearing ... More
Holomorphic Cartan geometries on uniruled surfacesMay 24 2011We classify holomorphic Cartan geometries on every compact complex curve, and on every compact complex surface which contains a rational curve.
Characteristic forms of complex Cartan geometriesApr 19 2007Dec 09 2008We calculate relations on characteristic classes which are obstructions preventing closed K\"ahler manifolds from carrying holomorphic Cartan geometries. We apply these relations to give global constraints on the phase spaces of complex analytic determined ... More
Determination of all rational preperiodic points for morphisms of PNOct 23 2012Jul 03 2013For a morphism $f:\P^N \to \P^N$, the points whose forward orbit by $f$ is finite are called preperiodic points for $f$. This article presents an algorithm to effectively determine all the rational preperiodic points for $f$ defined over a given number ... More
Computing Hybridization Networks for Multiple Rooted Binary Phylogenetic Trees by Maximum Acyclic Agreement ForestsAug 13 2014Dec 17 2015It is a known fact that, given two rooted binary phylogenetic trees, the concept of maximum acyclic agreement forests is sufficient to compute hybridization networks with minimum hybridization number. In this work, we demonstrate by first presenting an ... More
Optimal prediction in molecular dynamicsAug 22 2008Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in order to reduce ... More
Cohomological obstruction theory for Brauer classes and the period-index problemSep 12 2009Jul 13 2010Let U be a connected scheme of finite cohomological dimension in which every finite set of points is contained in an affine open subscheme. Suppose that alpha is a class in H^2(U_et,Gm)_{tors}. For each positive integer m, the K-theory of alpha-twisted ... More
Lattice polytopes having h^*-polynomials with given degree and linear coefficientMay 08 2007Nov 29 2007The h^*-polynomial of a lattice polytope is the numerator of the generating function of the Ehrhart polynomial. Let P be a lattice polytope with h^*-polynomial of degree d and with linear coefficient h^*_1. We show that P has to be a lattice pyramid over ... More
Einstein-aether as a quantum effective field theoryMay 14 2009The possibility that Lorentz symmetry is violated in gravitational processes is relatively unconstrained by experiment, in stark contrast with the level of accuracy to which Lorentz symmetry has been confirmed in the matter sector. One model of Lorentz ... More
On the Burnside-Brauer-Steinberg theoremSep 26 2014Oct 04 2014A well-known theorem of Burnside says that if $\rho$ is a faithful representation of a finite group $G$ over a field of characteristic $0$, then every irreducible representation of $G$ appears as a constituent of a tensor power of $\rho$. In 1962, R. ... More
(2+3) dimensional geometrical dual of the complex Klein-Gordon equationJan 30 2008Jan 22 2009In this paper it is shown that an equivalent to the complex Klein-Gordon equation can be obtained from the (2+3) dimensional Einstein equations coupled to a conserved energy momentum tensor. In an explicit toy model we give matching conditions for what ... More
The Brownian Frame Process as a Rough PathFeb 01 2006We introduce the (path-valued) Brownian frame process whose evaluation at time t is the sample path of the underlying Brownian motion run from time t-1 to t. Due to its connections with Gaussian Volterra processes and SDDEs this is an interesting object ... More
The flux-tube model of particle creation in nuclear collisionsJul 08 1999I review some of the history of the flux-tube model, concentrating on work done by the Los Alamos-Tel Aviv collaboration on particle creation and back-reaction in uniform fields and in the central rapidity region. I discuss the incorporation of more realistic ... More
Tangent Lie algebra of derived Artin stacksDec 11 2013Jun 21 2016Since the work of Mikhail Kapranov in [Kap], it is known that the shifted tangent complex $\mathbb{T}_X[-1]$ of a smooth algebraic variety $X$ is endowed with a weak Lie structure. Moreover any complex of quasi-coherent sheaves on $X$ is endowed with ... More
New method for studying steady states in quantum impurity problems: The interacting resonant level modelMar 09 2007Aug 31 2007We develop a new perturbative method for studying any steady states of quantum impurities, in or out of equilibrium. We show that steady-state averages are completely fixed by basic properties of the steady-state (Hershfield's) density matrix along with ... More
Hypotrochoids in conformal restriction systems and Virasoro descendantsSep 21 2012A conformal restriction system is a commutative, associative, unital algebra equipped with a representation of the groupoid of univalent conformal maps on connected open sets of the Riemann sphere, and a family of linear functionals on subalgebras, satisfying ... More
Finite-Temperature Form Factors: a ReviewNov 06 2006Jan 11 2007We review the concept of finite-temperature form factor that was introduced recently by the author in the context of the Majorana theory. Finite-temperature form factors can be used to obtain spectral decompositions of finite-temperature correlation functions ... More
Finite-temperature form factors in the free Majorana theoryJun 14 2005Dec 14 2005We study the large distance expansion of correlation functions in the free massive Majorana theory at finite temperature, alias the Ising field theory at zero magnetic field on a cylinder. We develop a method that mimics the spectral decomposition, or ... More
Fractional Max-PoolingDec 18 2014May 12 2015Convolutional networks almost always incorporate some form of spatial pooling, and very often it is alpha times alpha max-pooling with alpha=2. Max-pooling act on the hidden layers of the network, reducing their size by an integer multiplicative factor ... More
Predicting the variance of a measurement with 1/f noiseMay 17 2013Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For flicker noise, ... More
Microfabrication of Laser-Driven Accelerator StructuresApr 25 2003We discuss the potential for using microfabrication techniques for laser-driven accelerator construction. We introduce microfabrication processes in general, and then describe our investigation of a particular trial process. We conclude by considering ... More
Derivation of effective evolution equations from many body quantum dynamicsOct 20 2009We review some recent results concerning the derivation of effective evolution equations from first principle quantum dynamics. In particular, we discuss the derivation of the Hartree equation for mean field systems and the derivation of the Gross-Pitaevskii ... More
Approximations of pseudo-differential flowsFeb 27 2014Feb 16 2016Given a classical symbol $M$ of order zero, and associated semiclassical operators ${\rm op}_\varepsilon(M),$ we prove that the flow of ${\rm op}_\varepsilon(M)$ is well approximated, in time $O(|\ln \varepsilon|),$ by a pseudo-differential operator, ... More
A fixed point theorem and the existence of a Haar measure for hypergroups satisfying conditions related to amenabilityOct 08 2014In this paper we present a fixed point property for amenable hypergroups which is analogous to Rickert's fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions ... More
Finite speed of propagation for stochastic porous media equationsOct 08 2012We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving ... More
A contraction of the principal series by Berezin-Weyl quantizationJan 21 2014We study a contraction of the principal series representations of a noncompact semisimple Lie group to the unitary irreducible representations of its Cartan motion group by means of the Berezin-Weyl quantization on the coadjoint orbits associated with ... More
A binary deletion channel with a fixed number of deletionsSep 05 2013Suppose a binary string x = x_1...x_n is being broadcast repeatedly over a faulty communication channel. Each time, the channel delivers a fixed number m of the digits (m<n) with the lost digits chosen uniformly at random, and the order of the surviving ... More
The Average Sensitivity of Bounded-Depth FormulasAug 31 2015We show that unbounded fan-in boolean formulas of depth $d+1$ and size $s$ have average sensitivity $O(\frac{1}{d}\log s)^d$. In particular, this gives a tight $2^{\Omega(d(n^{1/d}-1))}$ lower bound on the size of depth $d+1$ formulas computing the \textsc{parity} ... More
Ising and Gross-Neveu model in next-to-leading orderSep 13 2016We study scalar and chiral fermionic models in next-to-leading order with the help of the functional renormalisation group. Their critical behaviour is of special interest in condensed matter systems, in particular graphene. To derive the beta functions, ... More
Entwicklung eines Gasmoderators für PositronenAug 23 2016(Translated Title: Development of a positron gas moderator) In this work a positron moderator that is based on inelastic positron scattering in nitrogen gas has been developed and set-up. A positron beam enters a gas cell through a small aperture. In ... More
Global model structures for $*$-modulesJul 01 2016We extend Schwede's work on the unstable global homotopy theory of orthogonal spaces and $\mathcal{L}$-spaces to the category of $*$-modules (i.e., unstable $S$-modules). We prove a theorem which transports model structures and their properties from $\mathcal{L}$-spaces ... More
Random Matrices, Boundaries and BranesMar 03 2016This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In particular, ... More
Computing a Relevant Set of Nonbinary Maximum Acyclic Agreement ForestsDec 17 2015There exist several methods dealing with the reconstruction of rooted phylogenetic networks explaining different evolutionary histories given by rooted binary phylogenetic trees. In practice, however, due to insufficient information of the underlying ... More
Towards a Paraconsistent Quantum Set TheoryNov 05 2015In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani, and topos quantum theory, as developed by Isham, Butterfield and Doring, amongst others. Towards this end, we will study algebraic ... More
A Note on Masspartitions by HyperplanesDec 31 2009A triple of positive integers (d,h,m) is admissible if for any m given masses in R^d there exist h hyperplanes that cut each of these masses into 2^h equal pieces. We present an elementary reduction which combined with results by Ramos (1996) yields all ... More
Semiclassical functional calculus for $h$-dependent functionsJul 22 2015Feb 12 2016We study the functional calculus for operators of the form $f_h(P(h))$ within the theory of semiclassical pseudodifferential operators, where $\{f_h\}_{h\in (0,1]}\subset C^\infty_c(\mathbb{R})$ denotes a family of $h$-dependent functions satisfying some ... More
Volume and lattice points of reflexive simplicesDec 23 2004Jan 15 2007We prove sharp upper bounds on the volume and the number of lattice points on edges of higher-dimensional reflexive simplices. These convex-geometric results are derived from new number-theoretic bounds on the denominators of unit fractions summing up ... More
Global well-posedness for the defocusing, cubic, nonlinear Schrodinger equation when n = 3 via a linear-nonlinear decompositionOct 12 2009Oct 14 2011In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schr{\"o}dinger equation in three dimensions when $n = 3$ when $u_{0} \in H^{s}(\mathbf{R}^{3})$, $s > 3/4$. To this end, we utilize a linear-nonlinear decomposition, ... More
Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr{ö}dinger equation when $d = 2$Jun 07 2010Jul 27 2016In this paper we prove that the defocusing, cubic nonlinear Schr{\"o}dinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R}^{2})$. To do this, we will prove a frequency localized interaction Morawetz estimate ... More
Abstract quotients of profinite groups, after Nikolov and SegalJan 03 2016Nov 22 2016In this expanded account of a talk given at the Oberwolfach Arbeitsgemeinschaft "Totally Disconnected Groups", October 2014, we discuss results of Nikolay Nikolov and Dan Segal on abstract quotients of compact Hausdorff topological groups, paying special ... More
Bilinear Strichartz estimates for the Schr{ö}dinger map problemOct 18 2012Oct 22 2012In this paper we prove bilinear Strichartz estimates for a solution to the Schr{\"o}dinger map problem whose size is small in the critical Strichartz space $| |\nabla|^{\frac{d - 2}{2}} \psi_{x} |_{L_{t,x}^{\frac{2(d + 2)}{d}}}$. These estimates will ... More
Asymptotics of self-similar growth-fragmentation processesJun 02 2016Markovian growth-fragmentation processes introduced by Bertoin extend the pure fragmentation model by allowing the fragments to grow larger or smaller between dislocation events. What becomes of the known asymptotic behaviors of self-similar pure fragmentations ... More
A Markov growth process for Macdonald's distribution on reduced wordsSep 26 2014We give an algorithmic-bijective proof of Macdonald's reduced word identity in the theory of Schubert polynomials, in the special case where the permutation is dominant. Our bijection uses a novel application of David Little's generalized bumping algorithm. ... More
A solution to one of Knuth's permutation problemsApr 23 2010We answer a problem posed recently by Knuth: an n-dimensional box, with edges lying on the positive coordinate axes and generic edge lengths W_1 < W_2 < ... < W_n, is dissected into n! pieces along the planes x_i = x_j. We describe which pieces have the ... More
On the Birational Geometry of Schubert VarietiesAug 27 2012Mar 05 2015We classify all Q-factorializations of (co)minuscule Schubert varieties by using their Mori dream space structure. As a corollary we obtain a description of all IH-small resolutions of (co)minuscule Schubert varieties generalizing results of Perrin. We ... More
A Noncommutative Borsuk-Ulam Theorem for Natsume-Olsen SpheresMar 06 2015Sep 27 2015Natsume-Olsen noncommutative spheres are C*-algebras which generalize C(S^k) when k is odd. These algebras admit natural actions by finite cyclic groups, and if one of these actions is fixed, any equivariant homomorphism between two Natsume-Olsen spheres ... More
The Hartogs extension phenomenon for holomorphic parabolic and reductive geometriesFeb 23 2013Jul 25 2016Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric ... More
A bound for the splitting of smooth Fano polytopes with many verticesSep 25 2014Aug 10 2015The classification of toric Fano manifolds with large Picard number corresponds to the classification of smooth Fano polytopes with large number of vertices. A smooth Fano polytope is a polytope that contains the origin in its interior such that the vertex ... More
Turaev-Viro invariants as an extended TQFT IIIDec 02 2010Aug 30 2011In the third paper in this series, we examine the Reshetikhin-Turaev and Turaev-Viro TQFTs at the level of surfaces. In particular, we show that for a closed surface $\Sigma$, $Z_{TV, \mathcal{C}}(\Sigma) \cong Z_{RT, Z(\C)}(\Sigma)$, thus extending the ... More
Gorenstein toric Fano varietiesMay 24 2004We investigate Gorenstein toric Fano varieties by combinatorial methods using the notion of a reflexive polytope which appeared in connection to mirror symmetry. The paper contains generalisations of tools and previously known results for nonsingular ... More
Geometrizing the Quantum - A Toy ModelApr 19 2010It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally "curved" space-time. This shows that it is possible to formulate quantum mechanics as ... More
Quantizing Geometry or Geometrizing the Quantum?Apr 16 2010Apr 19 2010The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an approach the quantum ... More
Nonequilibrium density matrix for thermal transport in quantum field theoryDec 05 2012In these notes I explain how to describe one-dimensional quantum systems that are simultaneously near to, but not exactly at, a critical point, and in a far-from-equilibrium steady state. This description uses a density matrix on scattering states (of ... More
Conformal loop ensembles and the stress-energy tensorSep 07 2012We give a construction of the stress-energy tensor of conformal field theory (CFT) as a local "object" in conformal loop ensembles CLE_\kappa, for all values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the central charges 0 < c ... More
Factorisation of conformal maps on finitely connected domainsJul 04 2011Let $U$ be a multiply connected domain of the Riemann sphere $\hat{C}$ whose complement $\hat{C}\setminus U$ has $N<\infty$ components. We show that every conformal map on $U$ can be written as a composition of $N$ maps conformal on simply connected domains. ... More
The Cartan-Hadamard Theorem for Metric Spaces with Local BicombingsSep 23 2015The classical Cartan-Hadamard Theorem was generalized by W. Ballmann for metric spaces with non-positive curvature and by S. Alexander and R. Bishop for locally convex metric spaces. In this paper, we prove the Cartan-Hadamard Theorem in a more general ... More
On the endomorphism monoid of a profinite semigroupMar 19 2010Necessary and sufficient conditions are given for the endomorphism monoid of a profinite semigroup to be profinite. A similar result is established for the automorphism group.
On Even Linear Indexed Languages with a Reduction to the Learning of Context-Free LanguagesDec 01 2013Aug 23 2014This paper presents a restricted form of linear indexed grammars, called even linear indexed grammars, which yield the even linear indexed languages. These languages properly contain the context-free languages and are contained in the set of linear indexed ... More
Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loopsJul 17 2015Sep 14 2016We consider the general spin-1 SU(2) invariant Heisenberg model with a two-body interaction. A random loop model is introduced and relations to quantum spin systems is proved. Using this relation it is shown that for dimensions 3 and above N\'eel order ... More
Central derivatives of L-functions in Hida familiesFeb 28 2012We prove a result of the following type: given a Hida family of modular forms, if there exists a weight two form in the family whose L-function vanishes to exact order one at s=1, then all but finitely many weight two forms in the family enjoy this same ... More
Complex multiplication cycles and Kudla-Rapoport divisorsMar 03 2013We study the intersections of special cycles on a unitary Shimura variety of signature (n-1,1), and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures ... More
Intersection theory on Shimura surfaces IIFeb 28 2012This is the third of a series of papers relating intersections of special cycles on the integral model of a Shimura surface to Fourier coefficients of Hilbert modular forms. More precisely, we embed the Shimura curve over Q associated to a rational quaternion ... More
Twisted Gross-Zagier theoremsFeb 28 2012The theorems of Gross-Zagier and Zhang relate the N\'eron-Tate heights of complex multiplication points on the modular curve X_0(N) (and on Shimura curve analogues) with the central derivatives of automorphic L-functions. We extend these results to include ... More
Chaotic Brane InflationNov 16 2012Mar 18 2014We illustrate a framework for constructing models of chaotic inflation where the inflaton is the position of a D3 brane along the universal cover of a string compactification. In our scenario, a brane rolls many times around a non-trivial one-cycle, thereby ... More
Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperatureJul 05 2009Jun 02 2014The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the B\"uttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter ... More
Summary of progress on the Blaschke conjectureSep 05 2013Nov 15 2016The Blaschke conjecture claims that every compact Riemannian manifold whose injectivity radius equals its diameter is, up to constant rescaling, a compact rank one symmetric space. We summarize the intuition behind this problem, the proof that such manifolds ... More
Lifting locally homogeneous geometric structuresAug 16 2011We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.
Assessing Wikipedia-Based Cross-Language Retrieval ModelsJan 10 2014This work compares concept models for cross-language retrieval: First, we adapt probabilistic Latent Semantic Analysis (pLSA) for multilingual documents. Experiments with different weighting schemes show that a weighting method favoring documents of similar ... More
A logical treatment of special relativity, with and without faster-than-light observersJun 25 2013There are three goals of this thesis. First: to present a concise yet accessible description of basic mathematical logic and model theory. Second: to develop an axiomatization of special relativity using only two undefined predicates. Ideally, these axioms ... More
Finding Rational Periodic Points on Wehler K3 SurfacesJan 23 2008Mar 12 2010This article examines dynamical systems on a class of K3 surfaces in $\mathbb{P}^{2} \times \mathbb{P}^{2}$ with an infinite automorphism group. In particular, this article develops an algorithm to find $\mathbb{Q}$-rational periodic points using information ... More
Representation growth and representation zeta functions of groupsSep 13 2012We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as ... More
On background-independent renormalization of spin foam modelsJul 29 2014Sep 09 2014In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical ... More
On knottings in the physical Hilbert space of LQG as given by the EPRL modelJun 03 2010We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the ... More
Periods and algebraic deRham cohomologyJun 07 2005It is known that the algebraic \deRham cohomology group $\hDR{i}(X_0/\Q)$ of a nonsingular variety $X_0/\Q$ has the same rank as the rational singular cohomology group $\h^i\sing(\Xh;\Q)$ of the complex manifold $\Xh$ associated to the base change $X_0\times_{\Q}\C$. ... More
Sparse arrays of signatures for online character recognitionAug 01 2013Dec 01 2013In mathematics the signature of a path is a collection of iterated integrals, commonly used for solving differential equations. We show that the path signature, used as a set of features for consumption by a convolutional neural network (CNN), improves ... More
A general approach of least squares estimation and optimal filteringMay 27 2013The least squares method allows fitting parameters of a mathematical model from experimental data. This article proposes a general approach of this method. After introducing the method and giving a formal definition, the transitivity of the method as ... More
Cooperads as Symmetric SequencesOct 07 2013We give a brief overview of the basics of cooperad theory using a new definition which lends itself to easy example creation and verification. We also apply our definition to build the parenthesization and cosimplicial structures exhibited by cooperads ... More