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Two-dimensional metric-affine gravityNov 28 2003There is a number of completely integrable gravity theories in two dimensions. We study the metric-affine approach on a 2-dimensional spacetime and display a new integrable model. Its properties are described and compared with the known results of Poincare ... More

Spin, gravity, and inertiaDec 28 2000The gravitational effects in the relativistic quantum mechanics are investigated. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. As a direct application, we analyze the non-relativistic ... More

On gravitational interaction of fermionsDec 31 2001We discuss some aspects of the gravitational interaction of the relativistic quantum particles with spin 1/2. The exact Foldy-Wouthuysen transformation is constructed for the Dirac particle coupled to the static spacetime metric. The quasi-relativistic ... More

On a model of an unconstrained hyperfluidAug 07 2000A hyperfluid is a classical continuous medium carrying hypermomentum. We modify the earlier developed variational approach to a hyperfluid in such a way that the Frenkel type constraints imposed on the hypermomentum current are eliminated. The resulting ... More

On physical foundations and observational effects of cosmic rotationAug 07 2000An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is paid to the discussion ... More

Conservation laws in gravitational theories with general nonminimal couplingMar 25 2013Apr 18 2013We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength. The obtained ... More

Unraveling gravity beyond Einstein with extended test bodiesJul 15 2013The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the equations of motion ... More

Gated CRF Loss for Weakly Supervised Semantic Image SegmentationJun 11 2019State-of-the-art approaches for semantic segmentation rely on deep convolutional neural networks trained on fully annotated datasets, that have been shown to be notoriously expensive to collect, both in terms of time and money. To remedy this situation, ... More

Generalized deviation equation and determination of the curvature in General RelativityNov 26 2015Feb 29 2016We derive a generalized deviation equation -- analogous to the well-known geodesic deviation equation -- for test bodies in General Relativity. Our result encompasses and generalizes previous extensions of the standard geodesic deviation equation. We ... More

Conservation laws and covariant equations of motion for spinning particlesSep 19 2015We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of motion for test ... More

Invariant conserved currents in gravity theories: diffeomorphisms and local gauge symmetriesDec 20 2007Previously, we have developed a general method to construct invariant conserved currents and charges in gravitational theories with Lagrangians that are invariant under spacetime diffeomorphisms and local Lorentz transformations. This approach is now ... More

Spacetime metric from local and linear electrodynamics: a new axiomatic schemeAug 07 2005We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically charged from neutral ... More

Rotation in string cosmologyFeb 09 2003We describe exact cosmological solutions with rotation and expansion in the low-energy effective string theory. These models are spatially homogeneous (closed Bianchi type IX) and they belong to the family of shear-free metrics which are causal (no closed ... More

Vacuum Einstein Equations in Terms of Curvature FormsMar 24 1996A closed explicit representation of the vacuum Einstein equations in terms of components of curvature 2-forms is given. The discussion is restricted to the case of non-vanishing cubic invariant of conformal curvature spinor. The complete set of algebraic ... More

On the energy-momentum current of the electromagnetic field in a pre-metric axiomatic approach. IMar 07 2001We complete a metric-free axiomatic framework for electrodynamics by introducing the appropriate energy-momentum current Sigma of the electromagnetic field. We start from the Lorentz force density and motivate the form of Sigma. Then we postulate it (fourth ... More

Einstein--Proca model: spherically symmetric solutionsApr 28 2000The Proca wave equation describes a classical massive spin 1 particle. We analyze the gravitational interaction of this vector field. In particular, the spherically symmetric solutions of the Einstein-Proca coupled system are obtained numerically. Although ... More

Collapse Dynamics of a Homopolymer: Theory and SimulationOct 23 2001Feb 08 2002We present a scaling theory describing the collapse of a homopolymer chain in poor solvent. At time t after the beginning of the collapse, the original Gaussian chain of length N is streamlined to form N/g segments of length R(t), each containing g ~ ... More

Gauge Structure of Teleparallel GravityJun 14 2019During the conference "Teleparallel Universes in Salamanca", we became aware of a recent paper [M. Fontanini, E. Huguet, and M. Le Delliou, Phys. Rev. D 99 (2019) 064006] in which some criticisms on the interpretation of teleparallel gravity as a gauge ... More

Fluctuations of the partition function in the GREM with external fieldMay 10 2008We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters. We find that ... More

Spin dynamics in gravitational fields of rotating bodies and the equivalence principleJul 24 2009Sep 12 2009We discuss the quantum and classical dynamics of a particle with spin in the gravitational field of a rotating source. A relativistic equation describing the motion of classical spin in curved spacetimes is obtained. We demonstrate that the precession ... More

Real null coframes in general relativity and GPS type coordinatesOct 17 2001Nov 28 2001Based on work of Derrick, Coll, and Morales, we define a `symmetric' null coframe with {\it four real null covectors}. We show that this coframe is closely related to the GPS type coordinates recently introduced by Rovelli.

Spin-torsion coupling and gravitational moments of Dirac fermions: theory and experimental boundsOct 22 2014Jan 29 2015We discuss the quantum dynamics of the Dirac fermion particle in a gauge gravitational field. The minimal as well as the Pauli-type nonminimal coupling of a fermion with external fields is studied, bringing into consideration the notions of the translational ... More

Kantowski-Sachs Brane CosmologyJan 31 2003We consider brane Kantowski-Sachs Universe when bulk space is five-dimensional Anti-deSitter space. The corresponding cosmological equations with perfect fluid are written. For several specific choices of relation between energy and pressure it is found ... More

Constitutive law of nonlocal gravityMar 10 2019We analyze the structure of a recent nonlocal generalization of Einstein's theory of gravitation by Mashhoon et al. By means of a covariant technique, we derive an expanded version of the nonlocality tensor which constitutes the theory. At the lowest ... More

Two-dimensional Decoding Algorithms and Recording Techniques for Bit Patterned Media Feasibility DemonstrationsJun 01 2015Recording experiments and decoding algorithms are presented for evaluating the bit-error-rate of state-of-the-art magnetic bitpatterned media. The recording experiments are performed with a static tester and conventional hard-disk-drive heads. As the ... More

The Aizenman-Sims-Starr scheme for the SK model with multidimensional spinsNov 14 2007Nov 24 2007This paper has been temporarily withdrawn for revision by the authors.

The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spinsFeb 23 2008Feb 24 2009We prove upper and lower bounds on the free energy in the Sherrington-Kirkpatrick model with multidimensional (e.g., Heisenberg) spins in terms of the variational inequalities based on the corresponding Parisi functional. We employ the comparison scheme ... More

Premetric equivalent of general relativity: TeleparallelismNov 17 2016Apr 15 2017In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely topological ... More

General treatment of quantum and classical spinning particles in external fieldsAug 18 2017Nov 08 2017We develop the general theory of spinning particles with electric and magnetic dipole moments moving in arbitrary electromagnetic, inertial and gravitational fields. Both the quantum-mechanical and classical dynamics is investigated. We start from the ... More

Congruence schemesFeb 20 2011Jul 04 2011A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck schemes, on the ... More

A general tensor product theoremFeb 02 2010We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.

A panorama on zeta functionsOct 04 2002Sep 29 2005In this essay I will give a strictly subjective selection of different types of zeta functions. Instead of providing a complete list, I will rather try to give the central concepts and ideas underlying the theory. This article is going to appear in the ... More

Selberg zeta functions for spaces of higher rankSep 27 2002Feb 16 2004The theory of Selberg zeta functions is generalized to higher rank spaces. Applications towards analytic torsion numbers are given.

Class numbers of orders in cubic fieldsMay 24 2000Sep 20 2001We give an asymptotic formula for class numbers of orders in cubic number fields.

Torus actions on compact quotientsApr 30 1996Jun 24 1996We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action of H on the ... More

On the index of Dirac operators on arithmetic quotientsDec 01 1995Dec 15 1995Using the Arthur-Selberg trace formula we express the index of a Dirac operator on an arithmetic quotient over a totally real field with at least two real embeddings as the integral over the index form plus a sum of orbital integrals. For the Euler operator ... More

Regularized and $L^2$-DeterminantsNov 23 1995Mar 18 1996It is shown that in a tower of coverings the regularized determinant of a generalized Laplacian converges to the $L^2$-determinant. This shows generic nontriviality of analytic torsion or regularized determinants since the $L^2$-counterparts are easier ... More

Geometric zeta-functions on p-adic groupsJan 21 1997Apr 21 1997Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The $p$-adic version of the Patterson conjecture is proven.

Tensor product varieties and crystals. GL caseMar 05 2001Mar 07 2001The role of Spaltenstein varieties in the tensor product for GL is explained. In particular a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient ... More

Unparticle actions and gauge invarianceOct 21 2008Jan 23 2009We show that the requirement of gauge invariance is not enough to fix the form of interactions between unparticles and gauge fields, thus revealing a wide new class of gauged unparticle actions. Our approach also allows us to construct operators which ... More

Time inhomogeneous Fokker-Plank equation for wave distributions in the Abelian sandpile modelFeb 02 2000Jan 18 2001The time and size distribution of the waves of topplings in the Abelian sandpile model are expressed as the first arrival at the origin distribution for a scale invariant, time inhomogeneous Fokker-Planck equation. Assuming a linear conjecture for the ... More

Thermal Gauge Field TheoriesMay 18 2001May 31 2001The real- and imaginary-time-formalisms of thermal field theory and their extension to gauge theories is reviewed. Questions of gauge (in-)dependence are discussed in detail, in particular the possible gauge dependences of the singularities of dressed ... More

Resumming the pressureAug 31 1998Sep 21 1998The convergence properties of the resummed thermal perturbation series for the thermodynamic pressure are investigated by comparison with the exact results obtained in large-N phi^4 theory and possibilities for improvements are discussed. By going beyond ... More

Ihara zeta functions and class numbersMar 30 2014The prime geodesic theorem for cycles in Bruhat-Tits buildings is applied to unit groups of division algebras to derive new asymptotic assertion on class numbers of orders in imaginary quadratic fields.

Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group CohomologyMar 06 2014Apr 14 2014We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the ... More

On systems of equations in free abelian groupsJan 28 2014In this paper we study the asymptotic probability that a random system of equations in free abelian group $\mathbb{Z}^m$ of rank $m$ is solvable. Denote $SAT(\mathbb{Z}^m, k, n)$ and $SAT_{\mathbb{Q}^m}(\mathbb{Z}^m, k, n)$ the sets of all systems of ... More

Mode switching in ring lasers with delayed optical feedbackDec 25 2013We have demonstrated that a rather weak external optical feedback with delay can lead to the mode switching of the counterpropogating modes. The delay time should be longer then any system characteristic time. The equations describing the ring resonator ... More

Ground-state degeneracy for abelian anyons in the presence of gapped boundariesJun 18 2013Gapped phases with long-range entanglement may admit gapped boundaries. If the boundary is gapped, the ground-state degeneracy is well-defined and can be computed using methods of Topological Quantum Field Theory. We derive a general formula for the ground-state ... More

Lambda Calculus SynopsisApr 02 2013Oct 24 2013This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional lambda calculus. ... More

New Bounds for the Acyclic Chromatic IndexDec 19 2014Jan 26 2016An edge coloring of a graph $G$ is called an acyclic edge coloring if it is proper and every cycle in $G$ contains edges of at least three different colors. The least number of colors needed for an acyclic edge coloring of $G$ is called the acyclic chromatic ... More

On Haar systems for groupoidsMay 27 2016Jun 17 2016It is shown that a locally compact groupoid with open range map does not always admit a Haar system. It then is shown how to construct a Haar system if the stability groupoid and the quotient by the stability groupoid both admit one.

Nature of the Quantum PotentialMar 01 2016Apr 16 2016In this paper we suggest a natural interpretation of the de Broglie-Bohm quantum potential, as the energy due to the oscillating electromagnetic field (virtual photon) coupled with moving charged particle. Generalization of the Schr\"{o}dinger equation ... More

A token-passing net implementation of optimal reduction with embedded read-backDec 09 2015Dec 14 2015In this paper, we introduce a new interaction net implementation of optimal reduction for pure untyped lambda calculus. Unlike others, our implementation allows to reach normal form regardless of interaction net reduction strategy using the approach of ... More

Token-passing Optimal Reduction with Embedded Read-backSep 13 2016We introduce a new interaction net implementation of optimal reduction for the pure untyped lambda calculus. Unlike others, our implementation allows to reach normal form regardless of the interaction net reduction strategy using the approach of so-called ... More

Pentagrams, inscribed polygons, and Prym varietiesJul 13 2016Sep 30 2016The pentagram map is a discrete integrable system on the moduli space of planar polygons. The corresponding first integrals are so-called monodromy invariants $E_1, O_1, E_2, O_2,\dots$ By analyzing the combinatorics of these invariants, R.Schwartz and ... More

Nonlinear Predictor Feedback for Input-Affine Systems with Distributed Input DelaysJan 01 2016Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero. Stabilization of ... More

The Local Action LemmaOct 06 2014Mar 17 2015The Lov\'{a}sz Local Lemma is a very powerful tool in probabilistic combinatorics, that is often used to prove existence of combinatorial objects satisfying certain constraints. Moser and Tardos have shown that the LLL gives more than just pure existence ... More

Generalized argument shift method and complete commutative subalgebras in polynomial Poisson algebrasJun 14 2014Jul 07 2014The Mischenko-Fomenko argument shift method allows to construct commutative subalgebras in the symmetric algebra $S(\mathfrak g)$ of a finite-dimensional Lie algebra $\mathfrak g$. For a wide class of Lie algebras, these commutative subalgebras appear ... More

Stability in bi-Hamiltonian systems and multidimensional rigid bodyNov 17 2013Jun 14 2014The presence of two compatible Hamiltonian structures is known to be one of the main, and the most natural, mechanisms of integrability. For every pair of Hamiltonian structures, there are associated conservation laws (first integrals). Another approach ... More

Cohomology of congruence schemesJul 23 2013Modules for sesquiads and congruence schemes are introduced. It is shown that the corresponding categories are belian and that base change functors establish an ascent datum which allows for a cohomology theory to be established.

Equilibrium traffic flow of a mixture of cars with different propertiesAug 12 2009Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of different ... More

Non-amenability of product replacement graphsMay 10 2013We prove non-amenability of the product replacement graphs \Gamma_n(G) for uniformly non-amenable groups. We also prove it for Z-large groups, when n is sufficiently large. It follows that \Gamma_n(G) is non-amenable when n is sufficiently large for hyperbolic ... More

N=2 supersymmetric extensions of relativistic Toda latticeApr 08 2019N=2 supersymmetric extensions of both the periodic and non-periodic relativistic Toda lattices are built within the framework of the Hamiltonian formalism. A geodesic description in terms of a non-metric connection is discussed.

Intersection of conjugate solvable subgroups in symmetric groupsJan 16 2017It is shown that for a solvable subgroup $G$ of an almost simple group $S$ which socle is isomorphic to $A_n$ $ (n\ge5)$ there are $x,y,z,t \in S$ such that $G \cap G^x \cap G^y \cap G^z \cap G^t =1.$

On the Lagrangian Structure of the Discrete Isospectral and Isomonodromic TransformationsNov 05 2007Feb 13 2013We establish the Lagrangian nature of the discrete isospectral and isomonodromic dynamical systems corresponding to the re-factorization transformations of the rational matrix functions on the Riemann sphere. Specifically, in the isospectral case we generalize ... More

Representing scenarios for process evolution managementJul 05 2018In the following writing we discuss a conceptual framework for representing events and scenarios from the perspective of a novel form of causal analysis. This causal analysis is applied to the events and scenarios so as to determine measures that could ... More

Higman's PORC conjecture for a family of groupsOct 01 2007We prove that the number of groups of order $p^n$ whose Frattini subgroup is central is for fixed $n$ a PORC (`polynomial on residue classes') function of $p$. This extends a result of G. Higman.

Hom complexes and homotopy theory in the category of graphsMay 10 2006Jul 07 2008We investigate a notion of $\times$-homotopy of graph maps that is based on the internal hom associated to the categorical product in the category of graphs. It is shown that graph $\times$-homotopy is characterized by the topological properties of the ... More

On minimal Lefschetz decompositions for GrassmanniansAug 10 2011Feb 23 2012We construct two Lefschetz decompositions of the derived category of coherent sheaves on the Grassmannian of $k$-dimensional subspaces in a vector space of dimension $n$. Both of them admit a Lefschetz basis consisting of equivariant vector bundles. We ... More

Algebraic properties of CFT coset construction and Schramm-Loewner evolutionDec 19 2011Schramm-Loewner evolution appears as the scaling limit of interfaces in lattice models at critical point. Critical behavior of these models can be described by minimal models of conformal field theory. Certain CFT correlation functions are martingales ... More

Locally standard torus actions and sheaves over Buchsbaum posetsJan 20 2015Feb 24 2015We consider a sheaf of exterior algebras on a simplicial poset $S$ and introduce a notion of homological characteristic function. Two natural objects are associated with these data: a graded sheaf $\mathcal{I}$ and a graded cosheaf $\widehat{\Pi}$. When ... More

Locally standard torus actions and h'-vectors of simplicial posetsJan 28 2015We consider the orbit type filtration on a manifold $X$ with locally standard action of a compact torus and the corresponding homological spectral sequence $(E_X)^r_{*,*}$. If all proper faces of the orbit space $Q=X/T$ are acyclic, and the free part ... More

Characteristic classes of flags of foliations and Lie algebra cohomologyMar 08 2013Aug 25 2014We prove the conjecture by Feigin, Fuchs and Gelfand describing the Lie algebra cohomology of formal vector fields on an $n$-dimensional space with coefficients in symmetric powers of the coadjoint representation. We also compute the cohomology of the ... More

Torus action on quaternionic projective plane and related spacesMar 08 2019For an action of a compact torus $T$ on a smooth compact manifold~$X$ with isolated fixed points the number $\frac{1}{2}\dim X-\dim T$ is called the complexity of the action. In this paper we study certain examples of torus actions of complexity one and ... More

Certain Examples of Deformed Preprojective Algebras and Geometry of Their *-RepresentationsFeb 02 2005We consider algebras $e_i \Pi^\lambda(Q) e_i$ obtained from deformed preprojective algebra of affine type $\Pi^\lambda(Q)$ and an idempotent $e_i$ for certain concrete value of the vector $\lambda$ which corresponds to the traces of $-1\in SU(2, C)$ in ... More

Curvature of Poisson pencils in dimension threeDec 13 2012Aug 22 2016A Poisson pencil is called flat if all brackets of the pencil can be simultaneously locally brought to a constant form. Given a Poisson pencil on a 3-manifold, we study under which conditions it is flat. Since the works of Gelfand and Zakharevich, it ... More

Definitive Computation of Bernstein-Sato PolynomialsMar 24 2000Let n and d be positive integers, let k be a field and let P(n,d;k) be the space of the polynomials in n variables of degree at most d with coefficients in k. Let B(n,d) be the set of the Bernstein-Sato polynomials of all polynomials in P(n,d;k) as k ... More

Higher Green's functions for modular formsApr 20 2008Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation $\Delta f=0$ ... More

On Limits and Colimits Of Comodules over a Coalgebra in a Tensor CategorySep 11 2013Dec 05 2013We show that the category of comodules over a coassociative coalgebra in a complete, cocomplete and well-powered category has limits and colimits under additional assumptions.

Homology cycles in manifolds with locally standard torus actionsFeb 04 2015Feb 06 2015Let $X$ be a $2n$-manifold with a locally standard action of a compact torus $T^n$. If the free part of action is trivial and proper faces of the orbit space $Q$ are acyclic, then there are three types of homology classes in $X$: (1) classes of face submanifolds; ... More

Buchstaber numbers and classical invariants of simplicial complexesFeb 15 2014Buchstaber invariant is a numerical characteristic of a simplicial complex, arising from torus actions on moment-angle complexes. In the paper we study the relation between Buchstaber invariants and classical invariants of simplicial complexes such as ... More

On intrinsic isometries to Euclidean spaceMar 29 2010I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of inverse limits of Euclidean d-polyhedra.

Cubic nonlinear Schrodinger equation on three dimensional balls with radial dataAug 28 2006We prove wellposedness of the Cauchy problem for the cubic nonlinear Schrodinger equation with Dirichlet boundary conditions and radial data on 3D balls. The main argument is based on a bilinear eigenfunction estimate and the use of $X^{s,b}$ spaces. ... More

Quasi-phase-matched high harmonic generation in corrugated micrometer-scale waveguidesSep 02 2016The high harmonic generation in periodically corrugated submicrometer waveguides is studied numerically. Plasmonic field enhancement in the vicinity of the corrugations allows to use low pump intensities. Simultaneously, periodic placement of the corrugations ... More

Nonarchimedean coalgebras and coadmissible modulesOct 14 2014We show that basic notions of locally analytic representation theory can be reformulated in the language of topological coalgebras (Hopf algebras) and comodules. We introduce the notion of admissible comodule and show that it corresponds to the notion ... More

On induced locally analytic representations of locally analytic groupsSep 03 2009Sep 03 2013Let G be a locally analytic group and H < G - a locally analytic subgroup. The main result is the condition (similar to Frommer-Orlik-Strauch theorem) for induction of locally analytic H-representation to G to be irreducible. Also this paper contains ... More

Noncollapsing solution below r_c for a randomly forced particleApr 24 2000Apr 16 2002We show that a noncollapsing solution below r_c can be constructed for the dynamics of randomly forced particle interacting with a dissipative boundary. The scaling analysis predicts a divergent collision rate at the boundary for the noncollapsing solution. ... More

Random Walk Approach to Simple Evolution ModelNov 20 1995Jan 21 1996The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same as in the previous ... More

Near horizon geometry of extremal black holes and Banados-Silk-West effectJan 07 2013Jul 27 2013Recently, Banados, Silk and West analyzed a collision of two particles near the horizon of the extremal Kerr black hole and demonstrated that the energy in the center-of-mass frame can be arbitrarily large provided the angular momentum of one of the colliding ... More

Comment on ``High Temperature Fermion Propagator -- Resummation and Gauge Dependence of the Damping Rate''Apr 06 1992Baier et al. have reported the damping rate of long-wavelength fermionic excitations in high-temperature QED and QCD to be gauge-fixing-dependent even within the resummation scheme due to Braaten and Pisarski. It is shown that this problem is caused by ... More

Arnold's problem on paper foldingApr 05 2010It is a story about the problem whether folding a square on the plane can increase its perimeter. The paper is written primary for school students.

Invariants, cohomology, and automorphic forms of higher orderNov 07 2008Jan 08 2012A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that ... More

Invariant triple productsMar 18 2005Feb 24 2006It is shown that the space of invariant trilinear forms on smooth representations of a semisimple Lie group is finite dimensional if the group is a product of Lorentz groups.

A simple trace formula for arithmetic groupsDec 17 1999We deduce from Arthur's trace formula a formula with only orbital integrals on the geometric side.

Geometric Zeta Functions, $L^2$-Theory, and Compact Shimura ManifoldsMar 07 1995We define geometric zeta functions for locally symmetric spaces as generalizations of the zeta functions of Ruelle and Selberg. As a special value at zero we obtain the Reidemeister torsion of the manifold. For hermitian spaces these zeta functions have ... More

Harmonic Analysis over adelic spacesAug 02 2007Aug 21 2007Extending ideas of A.N. Parshin and D.V. Osipov, Harmonic Analysis is developed for filtered infinite dimensional modules over a ring. We establish Pontryagin duality, the Fourier inversion formula, Plancherel formula and Poisson summation formula for ... More

The prime geodesic theorem for higher rank spacesAug 27 2002Sep 29 2005The prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula that is based on work of Andreas Juhl.

Harmonic Analysis on the quotient $\Q^\times\ltimes\Q\bs\A^1\ltimes \A$Sep 03 1999Let $G$ be the semidirect product $\A^1\ltimes \A$ of the adeles and the norm 1 ideles. Let $\Ga$ be the discrete subgroup $\Q^\times\ltimes\Q$. In this paper the trace formula for this setting is established and used to give the complete decomposition ... More

Equivariant torsion of locally symmetric spacesMar 05 1996The equivariant holomorphic torsion of a compact locally symmetric manifold and an automorphism is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.

Comment on ``Capacity of the Hopfield model''Jul 28 1997In a recent paper ``The capacity of the Hopfield model, J. Feng and B. Tirozzi claim to prove rigorous results on the storage capacity that are in conflict with the predictions of the replica approach. We show that their results are in error and that ... More