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Stochastic averaging for multiscale Markov processes with an application to a Wright-Fisher model with fluctuating selectionApr 07 2015Mar 05 2018Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for every $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes ... More

Supercritical branching diffusions in random environmentSep 08 2011Sep 30 2013Supercritical branching processes in constant environment conditioned on eventual extinction are known to be subcritical branching processes. The case of random environment is more subtle. A supercritical branching diffusion in random environment (BDRE) ... More

Interacting diffusions and trees of excursions: convergence and comparisonApr 06 2011Sep 30 2013We consider systems of interacting diffusions with local population regulation. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and diffusion ... More

The Virgin Island ModelFeb 21 2008Jun 02 2009A continuous mass population model with local competition is constructed where every emigrant colonizes an unpopulated island. The population founded by an emigrant is modeled as excursion from zero of an one-dimensional diffusion. With this excursion ... More

A short proof and a generalization of the BKR-inequalityJul 25 2008Jul 26 2008There is a serious mistake in the proof.

On the Itô-Alekseev-Gröbner formula for stochastic differential equationsDec 24 2018In this article we establish a new formula for the difference of a test function of the solution of a stochastic differential equation and of the test function of an It\^o process. The introduced formula essentially generalizes both the classical Alekseev-Gr\"obner ... More

Multi-level Picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearitiesNov 03 2017Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) have a wide range of applications. In particular, high-dimensional PDEs with gradient-dependent nonlinearities appear often in the state-of-the-art ... More

Differentiability of semigroups of stochastic differential equations with Hölder-continuous diffusion coefficientsMar 28 2018Differentiability of semigroups is useful for many applications. Here we focus on stochastic differential equations whose diffusion coefficient is the square root of a differentiable function but not differentiable itself. For every $m\in\{0,1,2\}$ we ... More

Propagation of chaos and the many-demes limit for weakly interacting diffusions in the sparse regimeApr 03 2018Propagation of chaos is a well-studied phenomenon and shows that weakly interacting diffusions may become independent as the system size converges to infinity. Most of the literature focuses on the case of exchangeable systems where all involved diffusions ... More

Graphical Representation of some Duality Relations in Stochastic Population ModelsJun 26 2007We derive a unified stochastic picture for the duality of a resampling-selection model with a branching-coalescing particle process (cf. http://www.ams.org/mathscinet-getitem?mr=MR2123250) and for the self-duality of Feller's branching diffusion with ... More

Stochastic averaging for multiscale Markov processes with an application to branching random walk in random environmentApr 07 2015Let $Z = (Z_t)_{t\in[0,\infty)}$ be an ergodic Markov process and, for $n\in\mathbb{N}$, let $Z^n = (Z_{n^2 t})_{t\in[0,\infty)}$ drive a process $X^n$. Classical results show under suitable conditions that the sequence of non-Markovian processes $(X^n)_{n\in\mathbb{N}}$ ... More

On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with non-globally monotone coefficientsJan 01 2014We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs). In particular, we estimate the $ L^p $-distance ... More

Branching diffusions in random environmentJul 14 2011Sep 30 2013We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival probability. ... More

Convergence of the stochastic Euler scheme for locally Lipschitz coefficientsDec 14 2009Nov 17 2011Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case ... More

Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficientsMar 26 2012May 09 2013Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for ... More

Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing nonlinearitiesMar 14 2019The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growing ... More

Time Reversal of Some Stationary Jump-Diffusion Processes from Population GeneticsNov 15 2010Jan 13 2011We describe the processes obtained by time reversal of a class of stationary jump-diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, ... More

Loss of regularity for Kolmogorov equationsSep 26 2012Mar 06 2015The celebrated H\"{o}rmander condition is a sufficient (and nearly necessary) condition for a second-order linear Kolmogorov partial differential equation (PDE) with smooth coefficients to be hypoelliptic. As a consequence, the solutions of Kolmogorov ... More

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equationsSep 29 2013Jan 06 2014Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that well-known numerical ... More

Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficientsOct 18 2010Sep 12 2012On the one hand, the explicit Euler scheme fails to converge strongly to the exact solution of a stochastic differential equation (SDE) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient. On the other hand, the ... More

Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficientsMay 04 2009Jul 05 2011The stochastic Euler scheme is known to converge to the exact solution of a stochastic differential equation with globally Lipschitz continuous drift and diffusion coefficient. Recent results extend this convergence to coefficients which grow at most ... More

Strong convergence rates and temporal regularity for Cox-Ingersoll-Ross processes and Bessel processes with accessible boundariesMar 25 2014Cox-Ingersoll-Ross (CIR) processes are widely used in financial modeling such as in the Heston model for the approximative pricing of financial derivatives. Moreover, CIR processes are mathematically interesting due to the irregular square root function ... More

Overcoming the curse of dimensionality in the approximative pricing of financial derivatives with default risksMar 14 2019Parabolic partial differential equations (PDEs) are widely used in the mathematical modeling of natural phenomena and man made complex systems. In particular, parabolic PDEs are a fundamental tool to determine fair prices of financial derivatives in the ... More

Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equationsSep 29 2013Nov 20 2016Exponential integrability properties of numerical approximations are a key tool for establishing positive rates of strong and numerically weak convergence for a large class of nonlinear stochastic differential equations. It turns out that well-known numerical ... More

Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equationsMay 02 2011Sep 10 2013The Euler-Maruyama scheme is known to diverge strongly and numerically weakly when applied to nonlinear stochastic differential equations (SDEs) with superlinearly growing and globally one-sided Lipschitz continuous drift coefficients. Classical Monte ... More

Altruistic defense traits in structured populationsMay 08 2015We propose a model for the frequency of an altruistic defense trait. More precisely, we consider Lotka-Volterra-type models involving a host/prey population consisting of two types and a parasite/predator population where one type of host individuals ... More

Strong convergence of full-discrete nonlinearity-truncated accelerated exponential Euler-type approximations for stochastic Kuramoto-Sivashinsky equationsApr 07 2016May 17 2016This article introduces and analyzes a new explicit, easily implementable, and full discrete accelerated exponential Euler-type approximation scheme for additive space-time white noise driven stochastic partial differential equations (SPDEs) with possibly ... More

Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equationsSep 22 2013Nov 24 2014Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipschitz continuous in the strong L^p-sense with respect to the initial value ... More

On full history recursive multilevel Picard approximations and numerical approximations of high-dimensional nonlinear parabolic partial differential equationsJul 12 2016Parabolic partial differential equations (PDEs) are a fundamental tool in the state-of-the-art pricing and hedging of financial derivatives. The PDEs appearing in such financial engineering applications are often high-dimensional and nonlinear. Since ... More

Ecological and genetic effects of introduced species on their native competitorsAug 06 2012Jan 02 2013Species introductions to new habitats can cause a decline in the population size of competing native species and consequently also in their genetic diversity. We are interested in why these adverse effects are weak in some cases whereas in others the ... More

A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equationsJan 30 2019Deep neural networks and other deep learning methods have very successfully been applied to the numerical approximation of high-dimensional nonlinear parabolic partial differential equations (PDEs), which are widely used in finance, engineering, and natural ... More

Overcoming the curse of dimensionality in the numerical approximation of semilinear parabolic partial differential equationsJul 03 2018For a long time it is well-known that high-dimensional linear parabolic partial differential equations (PDEs) can be approximated by Monte Carlo methods with a computational effort which grows polynomially both in the dimension and in the reciprocal of ... More

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensionsMay 03 2016We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respect ... More

Convergence in Hölder norms with applications to Monte Carlo methods in infinite dimensionsMay 03 2016Mar 16 2017We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respect ... More

Ergodic behavior of locally regulated branching populationsSep 26 2005Mar 30 2007For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. ... More

On a generalization of Matérn hard-core processes with applications to max-stable processesSep 18 2017The Mat\'ern hard-core processes are classical examples for point process models obtained from (marked) Poisson point processes. Points of the original Poisson process are deleted according to a dependent thinning rule, resulting in a process whose points ... More

Quantum integrable Toda like systemsOct 14 1998Using deformation quantization and suitable 2 by 2 quantum $R$-matrices we show that a list of Toda like classical integrable systems given by Y.B.Suris is quantum integrable in the sense that the classical conserved quantities (which are already in involution ... More

Algorithmic Optimisations for Iterative Deconvolution MethodsApr 26 2013We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating these convolution ... More

Optimal Partitioning for Dual-Pivot QuicksortMar 21 2013Oct 13 2015Dual-pivot quicksort refers to variants of classical quicksort where in the partitioning step two pivots are used to split the input into three segments. This can be done in different ways, giving rise to different algorithms. Recently, a dual-pivot algorithm ... More

Open-closed modular operads, Cardy condition and string field theoryNov 26 2016We prove that the modular operad of diffeomorphism classes of Riemann surfaces with both `open' and `closed' boundary components, in the sense of string field theory, is the modular completion of its genus 0 part quotiented by the Cardy condition. We ... More

Neutralino Dark Matter and the CurvatonNov 30 2006Mar 09 2007We build a realistic model of curvaton cosmology, in which the energy content is described by radiation, WIMP dark matter and a curvaton component. We calculate the curvature and isocurvature perturbations, allowing for arbitrary initial density perturbations ... More

A New Riemannian Setting for Surface RegistrationJun 03 2011Sep 19 2014We present a new approach for matching regular surfaces in a Riemannian setting. We use a Sobolev type metric on deformation vector fields which form the tangent bundle to the space of surfaces. In this article we compare our approach with the diffeomorphic ... More

Ground States and Singular Vectors of Convex Variational Regularization MethodsNov 09 2012Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent regularization ... More

A tight bound on the speed-up through storage for quickest multi-commodity flowsJun 18 2014Multi-commodity flows over time exhibit the non-intuitive property that letting flow wait can allow us to send flow faster overall. Fleischer and Skutella (IPCO~2002) show that the speed-up through storage is at most a factor of~$2$, and that there are ... More

On the representation of polyhedra by polynomial inequalitiesMar 26 2002Oct 24 2002A beautiful result of Br\"ocker and Scheiderer on the stability index of basic closed semi-algebraic sets implies, as a very special case, that every $d$-dimensional polyhedron admits a representation as the set of solutions of at most $d(d+1)/2$ polynomial ... More

Pebble Games and Linear EquationsApr 09 2012Mar 24 2015We give a new, simplified and detailed account of the correspondence between levels of the Sherali-Adams relaxation of graph isomorphism and levels of pebble-game equivalence with counting (higher-dimensional Weisfeiler-Lehman colour refinement). The ... More

I^K-convergenceSep 13 2011In this paper we introduce I^K-convergence which is a common generalization of the I^K-convergence of sequences, double sequences and nets. We show that many results that were shown before for these special cases are true for the I^K-convergence, too

Modern Regularization Methods for Inverse ProblemsJan 30 2018Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from linear towards ... More

Pfister's theorem fails in the free caseFeb 09 2011Artin solved Hilbert's $17^{th}$ problem by showing that every positive semidefinite polynomial can be realized as a sum of squares of rational functions. Pfister gave a bound on the number of squares of rational functions: if $p$ is a positive semi-definite ... More

The class of the affine line is a zero divisor in the Grothendieck ring: an improvementApr 22 2016Jul 21 2016Lev A. Borisov has shown that the class of the affine line is a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers. We improve the final formula by removing a factor.

Unitarization of uniformly bounded subgroups in finite von Neumann algebrasFeb 28 2013This note will present a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. The proof involves metric geometric arguments in the non-positively curved space of ... More

Short-axis-mode rotation of a free rigid body by perturbation seriesAug 03 2013A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part of this Hamiltonian ... More

Enhanced TKIP Michael AttacksOct 23 2014This paper presents new attacks against TKIP within IEEE 802.11 based networks. Using the known Beck-Tews attack, we define schemas to con- tinuously generate new keystreams, which allow more and longer arbitrary packets to be injected into the network. ... More

Difference Principle and Black-hole ThermodynamicsJun 26 2009The heuristic principle that constructive dynamics may arise wherever there exists a difference, or gradient, is discussed. Consideration of black-hole entropy appears to provide a clue for setting a lower bound on any extensive measure of such collective ... More

The two-leg t-J ladder: a spin liquid generated by Gutzwiller projection of magnetic bandsApr 01 1998Apr 17 1998The ground state of the two-leg Heisenberg ladder is identified as an RVB type spin liquid, which is generated by Gutzwiller projection of tight-binding bands with flux pi per plaquet. Explicit trial wave functions for the magnon and hole excitations ... More

Landau Level Quantization on the SphereJan 20 2011Mar 06 2011It is well established that the Hilbert space for charged particles in a plane subject to a uniform magnetic field can be described by two mutually commuting ladder algebras. We propose a similar formalism for Landau level quantization involving two mutually ... More

On the linear dispersion--linear potential quantum oscillatorJan 28 2010We solve the bi-linear quantum oscillator H=v|p|+F|x| both quasi-classically and numerically.

Is electromagnetic gauge invariance spontaneously violated in superconductors?Mar 16 2005We aim to give a pedagogical introduction to those elementary aspects of superconductivity which are not treated in the classic textbooks. In particular, we emphasize that global U(1) phase rotation symmetry, and not gauge symmetry, is spontaneously violated, ... More

Denser Egyptian FractionsNov 18 1998An Egyptian fraction is a sum of distinct unit fractions (reciprocals of positive integers). We show that every rational number has Egyptian fraction representations where the number of terms is of the same order of magnitude as the largest denominator, ... More

An annotated bibliography of work related to gender in scienceDec 12 2014Feb 24 2015The purpose of this manuscript is to gather together a large amount of source material pertaining to women in mathematics, from studies of girls in elementary school through data on females winning prizes for mathematical research. Along the way, we have ... More

Morse theory in the 1990'sApr 15 2001This is a survey article on Morse theory based on lectures to graduate students and advanced undergraduates. After a brief review of standard material, mostly without proofs, the Morse theory of complex Grassmannian manifolds is worked out in detail. ... More

Algebraic gamesMay 13 2012Jan 02 2013Two players alternate moves in the following game: Given a finitely generated abelian group A, a move consists of picking some non-zero element a of A. The game then continues with A/<a>. Under the normal play rule, the player with the last possible move ... More

Dynamics of heuristic optimization algorithms on random graphsMar 13 2002Jun 24 2002In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex, ... More

Status of CMB observations in 2015Jun 10 2016Jun 15 2016The 2.725 K cosmic microwave background has played a key role in the development of modern cosmology by providing a solid observational foundation for constraining possible theories of what happened at very large redshifts and theoretical speculation ... More

A statistical inference course based on p-valuesJun 07 2016Introductory statistical inference texts and courses treat the point estimation, hypothesis testing, and interval estimation problems separately, with primary emphasis on large-sample approximations. Here I present an alternative approach to teaching ... More

On similarity of jet quenching and charmonia suppressionJun 02 2016We quantify the magnitude of the parton energy loss in jets in lead-lead collisions at the LHC. We extract the effective color factor characterizing the difference between the in-medium radiation of quark-initiated jets and gluon-initiated jets from the ... More

Why we need to see the dark matter to understand the dark energyOct 30 2007The cosmological concordance model contains two separate constituents which interact only gravitationally with themselves and everything else, the dark matter and the dark energy. In the standard dark energy models, the dark matter makes up some 20% of ... More

BW - Eye Ophthalmologic decision support system based on clinical workflow and data mining techniques-image registration algorithmDec 17 2013Blueworks - Medical Expert Diagnosis is developing an application, BWEye, to be used as an ophthalmology consultation decision support system. The implementation of this application involves several different tasks and one of them is the implementation ... More

AGB stars in the Local Group, and beyondJul 14 2004I summarize the current status of surveys for late-type M, and Carbon stars in the Local Group based on three different approaches that make use of the characteristics of these stars: spectral characteristics using narrow-band filters, infrared characteristics, ... More

Unbounded Lookahead in WMSO+U GamesSep 24 2015Jan 26 2016Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. We consider delay games with winning conditions expressed in weak monadic second order logic with the unbounding ... More

A minimal surface with unbounded curvatureJun 17 2010We construct a complete, embedded minimal surface in euclidean 3-space which has unbounded Gaussian curvature. It has infinite genus, infinitely many catenoidal type ends and one limit end.

Proximity in the curve complex: boundary reduction and bicompressible surfacesOct 11 2004Jan 12 2005Suppose N is a compressible boundary component of a compact orientable irreducible 3-manifold M and Q is an orientable properly embedded essential surface in M in which each component is incident to N and no component is a disk. Let VN and QN denote respectively ... More

Automorphisms of the 3-sphere that preserve a genus two Heegaard splittingJul 16 2003An updated proof of a 1933 theorem of Goeritz, exhibiting a finite set of generators for the group of automorphisms of the 3-sphere that preserve a genus two Heegaard splitting. The group is analyzed via its action on a certain connected 2-complex. (The ... More

Heegaard splittings of compact 3-manifoldsJul 24 2000An expository survey article on Heegaard splittings

Large photon number extraction from individual atoms trapped in an optical latticeNov 24 2010Mar 22 2011The atom-by-atom characterization of quantum gases requires the development of novel measurement techniques. One particularly promising new technique demonstrated in recent experiments uses strong fluorescent laser scattering from neutral atoms confined ... More

Fast (Multi-)Evaluation of Linearly Recurrent Sequences: Improvements and ApplicationsNov 08 2005For a linearly recurrent vector sequence P[n+1] = A(n) * P[n], consider the problem of calculating either the n-th term P[n] or L<=n arbitrary terms P[n_1],...,P[n_L], both for the case of constant coefficients A(n)=A and for a matrix A(n) with entries ... More

Real Hypercomputation and ContinuityAug 15 2005Feb 22 2006By the sometimes so-called 'Main Theorem' of Recursive Analysis, every computable real function is necessarily continuous. We wonder whether and which kinds of HYPERcomputation allow for the effective evaluation of also discontinuous f:R->R. More precisely ... More

Time's Arrow from the Multiverse Point of ViewAug 31 2006Jul 22 2014In this paper I suggest a possible explanation for the asymmetry of time. In the case that I study, the dynamical laws and the boundary conditions are symmetric, but the behavior of time is not. The underlying mechanism is statistical and closely related ... More

A Semi-Classical Approach to Gravitation, Mass and SpinAug 16 2000Jul 22 2014In this paper, we use methods from differential geometry and statistical mechanics to investigate a model for the concept of mass. The theory is not quantum mechanical in the usual sense, although certain features like multiple histories and uncertainty ... More

On the E-polynomials of a family of Character VarietiesJun 07 2010We compute the E-polynomials of a family of twisted character varieties by proving they have polynomial count, and applying a result of N. Katz on the counting functions. To compute the number of GF(q)-points of these varieties as a function of q, we ... More

Localization in Lattice Gauge Theory and a New Multigrid MethodMay 05 1994We show numerically that the lowest eigenmodes of the 2-dimensional Laplace-operator with SU(2) gauge couplings are strongly localized. A connection is drawn to the Anderson-Localization problem. A new Multigrid algorithm, capable to deal with these modes, ... More

The principle of indirect eliminationAug 14 1995The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large, the modes thus ... More

Newton's Constant isn't constantDec 08 2000This article contains a brief pedagogical introduction to various renormalization group related aspects of quantum gravity with an emphasis on the scale dependence of Newton's constant and on black hole physics.

Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic ShellsJun 16 2010The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled ... More

Comments on the Sign and Other Aspects of Semiclassical Casimir EnergiesSep 16 2005Oct 27 2005The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The so defined semiclassical Casimir energy coincides ... More

Causal Space-Times on a Null LatticeSep 10 2015Mar 10 2016I investigate a discrete model of quantum gravity on a causal null-lattice with \SLC structure group. The description is geometric and foliates in a causal and physically transparent manner. The general observables of this model are constructed from local ... More

Irreducible Scalar Many-Body Casimir Energies: Theorems and Numerical StudiesDec 14 2011We define irreducible N-body spectral functions and Casimir energies and consider a massless scalar quantum field interacting locally by positive potentials with classical objects. Irreducible N-body spectral functions in this case are shown to be conditional ... More

Numerical Analysis of some Generalized Casimir PistonsOct 06 2008The Casimir force due to a scalar field on a piston in a cylinder of radius $r$ with a spherical cap of radius $R>r$ is computed numerically in the world-line approach. A geometrical subtraction scheme gives the finite interaction energy that determines ... More

Equivariant Gauge Fixing of SU(2) Lattice Gauge TheoryMay 21 1998Oct 21 1998I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group and an equivariant BRST symmetry that is physically equivalent to the standard SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete symmetries of the lattice ... More

Matrix-valued Bessel processesDec 20 2012Jun 23 2015This paper introduces a matrix analog of the Bessel processes, taking values in the closed set $E$ of real square matrices with nonnegative determinant. They are related to the well-known Wishart processes in a simple way: the latter are obtained from ... More

Non-representability of finite projective planes by convex setsAug 27 2009We prove that there is no d such that all finite projective planes can be represented by convex sets in R^d, answering a question of Alon, Kalai, Matousek, and Meshulam. Here, if P is a projective plane with lines l_1,...,l_n, a representation of P by ... More

The periodic $μ$-$b$-equation and Euler equations on the circleOct 09 2010May 04 2011In this paper, we study the $\mu$-variant of the periodic $b$-equation and show that this equation can be realized as a metric Euler equation on the Lie group $\Diff^{\infty}(\S)$ if and only if $b=2$ (for which it becomes the $\mu$-Camassa-Holm equation). ... More

The curvature of semidirect product groups associated with two-component Hunter-Saxton systemsOct 12 2010May 04 2011In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its $\mu$-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group $\Diff(\S)$ with a space of scalar ... More

Theory of electric dipole moments and lepton flavour violationAug 12 2016Electric dipole moments and charged-lepton flavour-violating processes are extremely sensitive probes for new physics, complementary to direct searches as well as flavour-changing processes in the quark sector. Beyond the "smoking-gun" feature of a potential ... More

Tensor categorical foundations of algebraic geometryOct 07 2014Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete tensor categories ... More

On the volume of tubular neighborhoods of real algebraic varietiesOct 13 2012Sep 28 2013The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition numbers in numerical ... More

Pure spinor superfields -- an overviewJul 06 2013Maximally supersymmetric theories do not allow off-shell superspace formulations with traditional superfields containing a finite set of auxiliary fields. It has become clear that off-shell supersymmetric action formulations of such models can be achieved ... More

Towards a manifestly supersymmetric action for 11-dimensional supergravityDec 09 2009Dec 11 2009We investigate the possibility of writing a manifestly supersymmetric action for 11-dimensional supergravity. The construction involves an explicit relation between the fields in the super-vielbein and the super-3-form, and uses non-minimal pure spinors. ... More

Why Don't We Have a Covariant Superstring Field Theory?Oct 04 1994This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods are reviewed. ... More

Double supergeometryMar 15 2016Mar 17 2016A geometry of superspace corresponding to double field theory is developed, with type II supergravity in D=10 as the main example. The formalism is based on an orthosymplectic extension OSp(d,d|2s) of the continuous T-duality group. Covariance under generalised ... More