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The Kazdan-Warner equation on canonically compactifiable graphsJul 26 2017We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resemblance to Laplacians on open pre-compact manifolds.

Courant's Nodal Domain Theorem for Positivity Preserving FormsDec 20 2017We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods. ... More

Deterministic and stochastic damage detection via dynamic response analysisMay 31 2019The paper proposes a method of damage detection in elastic materials, which is based on analyzing the time-dependent (dynamic) response of the material excited by an acoustic signal. Starting from a mathematical model of the acoustic wave, we calibrate ... More

Practical Enclave Malware with Intel SGXFeb 08 2019Modern CPU architectures offer strong isolation guarantees towards user applications in the form of enclaves. For instance, Intel's threat model for SGX assumes fully trusted enclaves, yet there is an ongoing debate on whether this threat model is realistic. ... More

Store-to-Leak Forwarding: Leaking Data on Meltdown-resistant CPUsMay 14 2019Meltdown and Spectre exploit microarchitectural changes the CPU makes during transient out-of-order execution. Using side-channel techniques, these attacks enable leaking arbitrary data from memory. As state-of-the-art software mitigations for Meltdown ... More

A note on Neumann problems on graphsMar 22 2018We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvability for non-empty subgraphs with respect to the vertex boundary and provide ... More

$A_\infty$ Algebras and the Cohomology of Moduli SpacesAug 10 1994Oct 31 1995We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some cycles on the ... More

Page Cache AttacksJan 04 2019We present a new hardware-agnostic side-channel attack that targets one of the most fundamental software caches in modern computer systems: the operating system page cache. The page cache is a pure software cache that contains all disk-backed pages, including ... More

ConTExT: Leakage-Free Transient ExecutionMay 22 2019Out-of-order execution and speculative execution are among the biggest contributors to performance and efficiency of modern processors. However, they are inconsiderate, leaking secret data during the transient execution of instructions. Many solutions ... More

On Some Algebraic Structures Arising in String TheoryDec 11 1992Dec 18 1992Lian and Zuckerman proved that the homology of a topological chiral algebra can be equipped with the structure of a BV-algebra; \ie one can introduce a multiplication, an odd bracket, and an odd operator $\Delta$ having the same properties as the corresponding ... More

Fast Object Learning and Dual-arm Coordination for Cluttered Stowing, Picking, and PackingOct 06 2018Robotic picking from cluttered bins is a demanding task, for which Amazon Robotics holds challenges. The 2017 Amazon Robotics Challenge (ARC) required stowing items into a storage system, picking specific items, and packing them into boxes. In this paper, ... More

On the Measurability of Stochastic Fourier Integral OperatorsMar 15 2019This work deals with the measurability of Fourier integral operators (FIOs) with random phase and amplitude functions. The key ingredient is the proof that FIOs depend continuously on their phase and amplitude functions, taken from suitable classes. The ... More

Fundamentals of cathodoluminescence in a STEM: The impact of sample geometry and electron beam energy on light emission of semiconductorsFeb 19 2019Cathodoluminescence has attracted interest in scanning transmission electron microscopy since the advent of commercial available detection systems with high efficiency, like the Gatan Vulcan or the Attolight M\"onch system. In this work we discuss light ... More

ZombieLoad: Cross-Privilege-Boundary Data SamplingMay 14 2019In early 2018, Meltdown first showed how to read arbitrary kernel memory from user space by exploiting side-effects from transient instructions. While this attack has been mitigated through stronger isolation boundaries between user and kernel space, ... More

On the Kodaira dimension of $\overline{\mathcal{N}}_{g,n}$Nov 03 2018Feb 10 2019We show that the compactification of the moduli space of $n-$nodal curves of genus g, i.e. $\mathcal{N}_{g,n}:= \mathcal{M}_{g,2n} /G$, with $G:=(\mathbb{Z}_2)^n \rtimes S_n$, is of general type for $g \geq 24$, for all $n \in \mathbb{N}$. While this ... More

Equivalences for Morse homologyMay 25 1999An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative gradient flow are ... More

On quotients of $\overline{\mathcal{M}}_{g,n}$ by certain subgroups of $S_n$Apr 29 2019We show that certain quotients of the compactified moduli space of $n-$ pointed genus $g$ curves, $\overline{\mathcal{M}}^G:= \overline{\mathcal{M}}_{g,n} / G$, are of general type, for a fairly broad class of subgroups $G$ of the symmetric group $S_n$ ... More

Cosmology with SKA Radio Continuum SurveysJan 15 2015Radio continuum surveys have, in the past, been of restricted use in cosmology. Most studies have concentrated on cross-correlations with the cosmic microwave background to detect the integrated Sachs-Wolfe effect, due to the large sky areas that can ... More

A Systematic Evaluation of Transient Execution Attacks and DefensesNov 13 2018May 15 2019Research on transient execution attacks including Spectre and Meltdown showed that exception or branch misprediction events might leave secret-dependent traces in the CPU's microarchitectural state. This observation led to a proliferation of new Spectre ... More

CMB foreground measurements through broad-band radio spectro-polarimetry: prospects of the SKA-MPG telescopeJun 11 2019Precise measurement of the foreground synchrotron emission, which contaminates the faint polarized cosmic microwave background radiation (CMB), is a major challenge for the next-generation of CMB experiments. To address this, dedicated foreground measurement ... More

The Valuation of Clean Spread Options: Linking Electricity, Emissions and FuelsMay 10 2012The purpose of the paper is to present a new pricing method for clean spread options, and to illustrate its main features on a set of numerical examples produced by a dedicated computer code. The novelty of the approach is embedded in the use of structural ... More

Homology of Lie algebra of supersymmetriesNov 22 2010We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare algebra. We discuss in detail the calculation in dimensions D=10 and D=6. Our methods can be applied to extended supersymmetry algebra and to other ... More

Transport in a stochastic Goupillaud mediumApr 18 2016This paper is part of a project that aims at modelling wave propagation in random media by means of Fourier integral operators. A partial aspect is addressed here, namely explicit models of stochastic, highly irregular transport speeds in one-dimensional ... More

Fallout: Reading Kernel Writes From User SpaceMay 29 2019Recently, out-of-order execution, an important performance optimization in modern high-end processors, has been revealed to pose a significant security threat, allowing information leaks across security domains. In particular, the Meltdown attack leaks ... More

Integral invariants in flat superspaceMar 08 2014We are solving for the case of flat superspace some homological problems that were formulated by Berkovits and Howe. (Our considerations can be applied also to the case of supertorus.) These problems arise in the attempt to construct integrals invariant ... More

Symplectic branching laws and Hermitian symmetric spacesOct 28 2011Let $G$ be a complex simple Lie group, and let $U \subseteq G$ be a maximal compact subgroup. Assume that $G$ admits a homogenous space $X=G/Q=U/K$ which is a compact Hermitian symmetric space. Let $\mathscr{L} \rightarrow X$ be the ample line bundle ... More

Linear maps preserving fibersSep 14 2007Jan 18 2008Let $G\subset\GL(V)$ be a complex reductive group where $\dim V<\infty$, and let $\pi\colon V\to\quot VG$ be the categorical quotient. Let $\NN:=\pi\inv\pi(0)$ be the null cone of $V$, let $H_0$ be the subgroup of $\GL(V)$ which preserves the ideal $\I$ ... More

Electricity price modeling and asset valuation: a multi-fuel structural approachMay 10 2012We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity spot prices. ... More

Analysis of a Fivefold Symmetric Superposition of Plane WavesMar 17 2012We show that a symmetric superposition of five standing plane waves can be expressed as an infinite series of terms of decreasing wavenumber, where each term is a product of five plane waves. We show that this series converges pointwise in R^2 and uniformly ... More

Laser radio transmitterJan 21 2019Since the days of Hertz, radio transmitters have evolved from rudimentary circuits emitting around 50 MHz to modern ubiquitous Wi-Fi devices operating at gigahertz radio bands. As wireless data traffic continues to increase there is a need for new communication ... More

A PTAS for Scheduling with Tree Assignment RestrictionsSep 23 2010Scheduling with assignment restrictions is an important special case of scheduling unrelated machines which has attracted much attention in the recent past. While a lower bound on approximability of 3/2 is known for its most general setting, subclasses ... More

Morita equivalence of multidimensional noncommutative toriMar 13 1998Aug 20 1998One can describe an $n$-dimensional noncommutative torus by means of an antisymmetric $n\times n$-matrix $\theta$. We construct an action of the group $SO(n,n|\bf Z)$ on the space of antisymmetric matrices and show that, generically, matrices belonging ... More

Linear maps preserving invariantsAug 21 2007Nov 13 2007Let $G\subset\GL(V)$ be a complex reductive group. Let $G'$ denote $\{\phi\in\GL(V)\mid p\circ\phi=p\text{for all} p\in\C[V]^G\}$. We show that, in general, $G'=G$. In case $G$ is the adjoint group of a simple Lie algebra $\lieg$, we show that $G'$ is ... More

Market Completion with Derivative SecuritiesMay 31 2015Let $S^F$ be a $\mathbb{P}$-martingale representing the price of a primitive asset in an incomplete market framework. We present easily verifiable conditions on model coefficients which guarantee the completeness of the market in which in addition to ... More

Noncommutative Geometry and Matrix Theory: Compactification on ToriNov 20 1997Feb 13 1998We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond ... More

Adaptive circular deconvolution by model selection under unknown error distributionDec 07 2009Dec 10 2013We consider a circular deconvolution problem, in which the density $f$ of a circular random variable $X$ must be estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y$ of $X$. The additive measurement error is supposed to be ... More

A smooth pseudo-gradient for the Lagrangian action functionalDec 23 2008Nov 04 2009We study the action functional associated to a smooth Lagrangian function on the cotangent bundle of a manifold, having quadratic growth in the velocities. We show that, although the action functional is in general not twice differentiable on the Hilbert ... More

Partially adaptive nonparametric instrumental regressionMar 16 2010Apr 10 2012We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed estimator is based ... More

Vector Fields and Luna StrataOct 16 2011May 23 2012Let V be a G-module where G is a complex reductive group. Let Z:=V//G denote the categorical quotient. One can ask if the Luna stratification of Z is intrinsic. That is, if phi : Z\to Z is any automorphism, does phi send strata to strata? In a paper of ... More

A Morse theoretic description of string topologySep 04 2008Oct 18 2008Let M be a closed, oriented, n-dimensional manifold. In this paper we give a Morse theoretic description of the string topology operations introduced by Chas and Sullivan, and extended by the first author, Jones, Godin, and others. We do this by studying ... More

Boundary representation of Dirichlet forms on discrete spacesNov 22 2017We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form methods.

NetSpectre: Read Arbitrary Memory over NetworkJul 27 2018In this paper, we present NetSpectre, a generic remote Spectre variant 1 attack. For this purpose, we demonstrate the first access-driven remote Evict+Reload cache attack over network, leaking 15 bits per hour. Beyond retrofitting existing attacks to ... More

Malware Guard Extension: Using SGX to Conceal Cache AttacksFeb 28 2017Mar 01 2017In modern computer systems, user processes are isolated from each other by the operating system and the hardware. Additionally, in a cloud scenario it is crucial that the hypervisor isolates tenants from other tenants that are co-located on the same physical ... More

Decoupling Supergravity from the SuperstringApr 05 2007We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10 -- d)-torus. For dimensions d = 2 and d = 3 it is possible to define a limit ... More

DRAMA: Exploiting DRAM Addressing for Cross-CPU AttacksNov 27 2015Jun 28 2016In cloud computing environments, multiple tenants are often co-located on the same multi-processor system. Thus, preventing information leakage between tenants is crucial. While the hypervisor enforces software isolation, shared hardware, such as the ... More

Malware Guard Extension: Using SGX to Conceal Cache AttacksFeb 28 2017May 22 2019In modern computer systems, user processes are isolated from each other by the operating system and the hardware. Additionally, in a cloud scenario it is crucial that the hypervisor isolates tenants from other tenants that are co-located on the same physical ... More

A Systematic Search for Molecular Outflows Toward Candidate Low-Luminosity Protostars and Very Low Luminosity ObjectsSep 11 2012We present a systematic single-dish search for molecular outflows toward a sample of 9 candidate low-luminosity protostars and 30 candidate Very Low Luminosity Objects (VeLLOs; L_int < 0.1 L_sun). The sources are identified using data from the Spitzer ... More

Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite MeasureApr 23 2018In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators ... More

Probing F-theory With Multiple BranesDec 05 1996We study multiple 3-branes on an F theory orientifold. The world-volume theory of the 3-branes is d=4, N=2 Sp(2k) gauge theory with an antisymmetric tensor and four flavors of matter in the fundamental. The solution of this gauge theory is found for vanishing ... More

Homotopy principles for equivariant isomorphismsMar 03 2015May 02 2017Let $G$ be a reductive complex Lie group acting holomorphically on Stein manifolds $X$ and $Y$. Let $p_X\colon X\to Q_X$ and $p_Y\colon Y\to Q_Y$ be the quotient mappings. When is there an equivariant biholomorphism of $X$ and $Y$? A necessary condition ... More

Community Paper on Radio Astronomy InfrastructuresFeb 23 2018Radio astronomy has experienced phenomenal progress in recent years due to advances in digital technologies and processing speed, the development of new technologies, and the prospect for new powerful facilities A new generation of radio interferometers ... More

Linking multipole vectors and pseudoentropies for CMB analysisMay 03 2019Multipole vectors and pseudoentropies provide powerful tools for a numerically fast and vivid investigation of possible statistically anisotropic, respectively non-Gaussian signs in CMB temperature fluctuations. After reviewing and linking these two conceptions ... More

On the Mean-Field Limit of Bosons with Coulomb Two-Body InteractionMay 28 2008Aug 31 2009In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large ... More

An equivariant parametric Oka principle for bundles of homogeneous spacesDec 21 2016We prove a parametric Oka principle for equivariant sections of a holomorphic fibre bundle $E$ with a structure group bundle $\mathscr G$ on a reduced Stein space $X$, such that the fibre of $E$ is a homogeneous space of the fibre of $\mathscr G$, with ... More

Orientation effects in Bipolar nebulaeSep 17 2006We show that the inclination to the line of sight of bipolar nebulae strongly affects some of their observed properties. We model these objects as having a spherically symmetric Planetary Nebula and a dusty equatorial density enhancement that produces ... More

Homology of Lie algebra of supersymmetries and of super Poincare Lie algebraJun 01 2011Aug 09 2011We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For dimensions $D=10,11$ ... More

On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley's Cutting Plane AlgorithmMay 20 2019Recently, Kronqvist et al.~\cite{KronqvistLundellWesterlund2016} rediscovered the supporting hyperplane algorithm of Veinott~\cite{Veinott1967} and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper ... More

Radiative corrections to the pressure and the one-loop polarization tensor of massless modes in SU(2) Yang-Mills thermodynamicsMar 09 2006Nov 27 2006We compute the one-loop polarization tensor $\Pi$ for the on-shell, massless mode in a thermalized SU(2) Yang-Mills theory being in its deconfining phase. Postulating that SU(2)$_{\tiny{CMB}}\stackrel{\tiny{today}}=U(1)_Y$, we discuss $\Pi$'s effect on ... More

Linear-Time Data Dissemination in Dynamic NetworksJan 24 2017Mar 29 2017Broadcasting and convergecasting are pivotal services in distributed systems, in particular, in wireless ad-hoc and sensor networks, which are characterized by time- varying communication graphs. We study the question of whether it is possible to disseminate ... More

KeyDrown: Eliminating Keystroke Timing Side-Channel AttacksJun 20 2017Besides cryptographic secrets, side-channel attacks also leak sensitive user input. The most accurate attacks exploit cache timings or interrupt information to monitor keystroke timings and subsequently infer typed words and sentences. Previously proposed ... More

Charge Transport and Conductance Switching of Redox-active Azulene DerivativesSep 01 2017Azulene (Az) is a non-alternating, aromatic hydrocarbon composed of a five-membered, electron-rich and a seven-membered, electron-poor ring; an electron distribution that provides intrinsic redox activity. By varying the attachment points of the two electrode-bridging ... More

Nethammer: Inducing Rowhammer Faults through Network RequestsMay 13 2018A fundamental assumption in software security is that memory contents do not change unless there is a legitimate deliberate modification. Classical fault attacks show that this assumption does not hold if the attacker has physical access. Rowhammer attacks ... More

Investigation of neutron-induced reaction at the Goethe University FrankfurtMay 11 2019We present first results and plans for future neutron activation measurements at the Goethe University Frankfurt. The measurements were performed at the Van-de-Graaff accelerator employing the 7Li(p,n) reaction.

Remote Mobile Manipulation with the Centauro Robot: Full-body Telepresence and Autonomous Operator AssistanceAug 05 2019Solving mobile manipulation tasks in inaccessible and dangerous environments is an important application of robots to support humans. Example domains are construction and maintenance of manned and unmanned stations on the moon and other planets. Suitable ... More

A VR System for Immersive Teleoperation and Live Exploration with a Mobile RobotAug 08 2019Applications like disaster management and industrial inspection often require experts to enter contaminated places. To circumvent the need for physical presence, it is desirable to generate a fully immersive individual live teleoperation experience. However, ... More

Controlled generation of a pn-junction in a waveguide integrated graphene photodetectorOct 18 2016With its electrically tunable light absorption and ultrafast photoresponse, graphene is a promising candidate for high-speed chip-integrated photonics. The generation mechanisms of photosignals in graphene photodetectors have been studied extensively ... More

Kassiopeia: A Modern, Extensible C++ Particle Tracking PackageDec 01 2016The Kassiopeia particle tracking framework is an object-oriented software package using modern C++ techniques, written originally to meet the needs of the KATRIN collaboration. Kassiopeia features a new algorithmic paradigm for particle tracking simulations ... More

NimbRo Rescue: Solving Disaster-Response Tasks through Mobile Manipulation Robot MomaroOct 02 2018Oct 15 2018Robots that solve complex tasks in environments too dangerous for humans to enter are desperately needed, e.g. for search and rescue applications. We describe our mobile manipulation robot Momaro, with which we participated successfully in the DARPA Robotics ... More

Automated Detection, Exploitation, and Elimination of Double-Fetch Bugs using Modern CPU FeaturesNov 03 2017Double-fetch bugs are a special type of race condition, where an unprivileged execution thread is able to change a memory location between the time-of-check and time-of-use of a privileged execution thread. If an unprivileged attacker changes the value ... More

Learning to Improve Capture Steps for Disturbance Rejection in Humanoid SoccerSep 28 2018Over the past few years, soccer-playing humanoid robots have advanced significantly. Elementary skills, such as bipedal walking, visual perception, and collision avoidance have matured enough to allow for dynamic and exciting games. When two robots are ... More

Humanoid TeenSize Open Platform NimbRo-OPSep 28 2018In recent years, the introduction of affordable platforms in the KidSize class of the Humanoid League has had a positive impact on the performance of soccer robots. The lack of readily available larger robots, however, severely affects the number of participants ... More

An exponential time upper bound for Quantum Merlin-Arthur games with unentangled proversOct 28 2015We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless EXP=NEXP. The ... More

Morita equivalence and dualityMay 07 1998It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus. We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a generalization of non-classical ... More

Grassmannian and string theoryOct 16 1996Dec 02 1996Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new facts supporting ... More

On the solutions to the string equationSep 10 1991The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact ... More

Gauge theories on noncommutative euclidean spacesNov 20 2001Nov 30 2001We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.

Theta-functions on noncommutative toriJul 25 2001Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of projective modules over noncommutative tori (theta-vectors). The theory of ... More

Noncommutative instantons: a new approachFeb 26 2001We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field ... More

An exponential time upper bound for Quantum Merlin-Arthur games with unentangled proversOct 28 2015Nov 28 2016We prove a deterministic exponential time upper bound for Quantum Merlin-Arthur games with k unentangled provers. This is the first non-trivial upper bound of QMA(k) better than NEXP and can be considered an exponential improvement, unless EXP=NEXP. The ... More

Brill-Noether theory for cyclic coversMar 16 2016Nov 15 2018The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series of dimension ... More

Noncommutative supergeometry and dualityDec 22 1999Apr 27 2000We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras and prove a ... More

Semiclassical approximation in Batalin-Vilkovisky formalismOct 21 1992Oct 23 1992The geometry of supermanifolds provided with $Q$-structure (i.e. with odd vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic structure ) and $S$-structure (volume element) or with various combinations of these structures is studied. ... More

Colliding Axion-Dilaton Plane Waves from Black HolesJul 28 1997Aug 01 1997The colliding plane wave metric discovered by Ferrari and Iba\~{n}ez to be locally isometric to the interior of a Schwarzschild black hole is extended to the case of general axion-dilaton black holes. Because the transformation maps either black hole ... More

Proof of the Goldbach conjecture in a more stringent formMar 27 2007May 03 2007With an artificial (p', n')-system it has been proved that even numbers > (p(x))^2 are the sum of two p > p(x).

Inequalities for generalized minorsMar 11 2013It is a classical result that the absolute value of any $k$-minor of an $r\times s$ real or complex matrix is bounded by the product of its first $k$ singular values. We generalize this statement to the context of real or complex simple Jordan pairs with ... More

Quantum curvesJan 08 2014Aug 16 2014One says that a pair (P,Q) of ordinary differential operators specify a quantum curve if [P,Q]=const. If a pair of difference operators (K,L) obey the relation KL=const LK we say that they specify a discrete quantum curve. This terminology is prompted ... More

Axiomatic conformal theory in dimensions >2 and AdS/CT correspondenceSep 27 2015May 07 2016We formulate axioms of conformal theory (CT) in dimensions $>2$ modifying Segal's axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT one includes also a condition of existence of energy-momentum tensor.) We use these axioms to ... More

Space and time from translation symmetryJan 06 2006May 16 2009We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.

Noncommutative supergeometry, duality and deformationsOct 28 2002Oct 28 2002We introduce a notion of $Q$-algebra that can be considered as a generalization of the notion of $Q$-manifold (a supermanifold equipped with an odd vector field obeying $\{Q,Q\} =0$). We develop the theory of connections on modules over $Q$-algebras and ... More

Quantum observables, Lie algebra homology and TQFTApr 25 1999Let us consider a Lie (super)algebra $G$ spanned by $T_{\alpha}$ where $T_{\alpha}$ are quantum observables in BV-formalism. It is proved that for every tensor $c^{\alpha_1...\alpha_k}$ that determines a homology class of the Lie algebra $G$ the expression ... More

Brill-Noether theory for cyclic coversMar 16 2016The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series of dimension ... More

Hilbert series of nearly holomorphic sections on generalized flag manifoldsMar 12 2014Apr 09 2014Let X=G/P be a complex flag manifold and E->X be a G-homogeneous holomorphic vector bundle. Fix a U-invariant Kaehler metric on X with U in G maximal compact. We study the sheaf of nearly holomorphic sections and show that the space of global nearly holomorphic ... More

Nearly holomorphic sections on compact Hermitian symmetric spacesSep 11 2012Let X be a K\"ahler manifold, and E be a Hermitian vector bundle on X. We investigate the space N(X,E) of nearly holomorphic sections in E, which generalizes the notion of nearly holomorphic functions introduced by Shimura. If X=U/K is a compact Hermitian ... More

Higher Laplacians on pseudo-Hermitian symmetric spacesOct 14 2014Let $X=G/H$ be a symmetric space for a real simple Lie group $G$, equipped with a $G$-invariant complex structure. Then, $X$ is a pseudo-Hermitian manifold, and in this geometric setting, higher Laplacians $L_m$ are defined for each positive integer $m$, ... More

Electronic structure of the pyrochlore metals Cd2Os2O7 and Cd2Re2O7Aug 14 2001First principles density functional calculations within the local spin density approximation (LSDA) and the generalized gradient approximation (GGA) are reported for pyrochlore Cd$_2$Os$_2$O$_7$ and Cd$_{2}$Re$_{2}$O$_7$. The transition metal $t_{2g}$ ... More

Active elastic dimers: Cells moving on rigid tracksJun 18 2014Experiments suggest that the migration of some cells in the three-dimensional extra cellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional model cell ... More

Reionization and dark matter decayMay 12 2016Sep 06 2016Cosmic reionization and dark matter decay can impact observations of the cosmic microwave sky in a similar way. A simultaneous study of both effects is required to constrain unstable dark matter from cosmic microwave background observations. We compare ... More

Topological quantum field theoriesNov 29 2000Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of topological quantum field ... More

Superanalogs of symplectic and contact geometry and their applications to quantum field theoryJun 17 1994The paper contains a short review of the theory of symplectic and contact manifolds and of the generalization of this theory to the case of supermanifolds. It is shown that this generalization can be used to obtain some important results in quantum field ... More

Geometry of Batalin-Vilkovisky quantizationMay 26 1992The present paper is devoted to the study of geometry of Batalin-Vilkovisky quantization procedure. The main mathematical objects under consideration are P-manifolds and SP-manifolds (supermanifolds provided with an odd symplectic structure and, in the ... More