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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

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

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

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

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

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

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

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

Existence of nearly holomorphic sections on compact Hermitian symmetric spacesMar 11 2013Let $X=U/K$ be a compact Hermitian symmetric space, and let $\sE$ be a $U$-homogeneous Hermitian vector bundle on $X$. In a previous paper, we showed that the space of nearly holomorphic sections is well-adapted for harmonic analysis in $L^2(X,\sE)$ provided ... 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

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

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

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

Structure of the degenerate principal series on symmetric R-spaces and small representationsDec 14 2012Jan 06 2014Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whose nilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We study the degenerate principal series representations of $G$ on $C^\infty(X)$ in the case where $P$ is ... 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

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

On the Floer homology of cotangent bundlesAug 20 2004Feb 24 2005This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle of a compact orientable manifold M. The first result is a new uniform estimate for the solutions of the Floer equation, which allows ... More

Estimates and computations in Rabinowitz-Floer homologyJul 11 2009Dec 06 2009The Rabinowitz-Floer homology of a Liouville domain W is the Floer homology of the free period Hamiltonian action functional associated to a Hamiltonian whose zero energy level is the boundary of W. It has been introduced by K. Cieliebak and U. Frauenfelder. ... 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

Linear maps preserving orbitsOct 07 2009Nov 03 2010Let H\subset\GL(V) be a connected complex reductive group where V is a finite-dimensional complex vector space. Let v\in V and let G=\{g\in\GL(V)\mid gHv = Hv\}. Following Ra\"is we say that the orbit Hv is \emph{characteristic for H} if the identity ... More

Noncommutative Noether's Problem vs Classical Noether's ProblemMay 04 2018Nov 29 2018We address the Noncommutative Noether's Problem on the invariants of Weyl fields for linear actions of finite groups. We prove that if the variety An(k)/G is rational then the Noncommutative Noether's Problem is positively solved for G and any field k ... More

Gravitational waves from inspiralling compact binaries in conformal gravityFeb 06 2019We investigate the production of gravitational waves during the inspiral of compact binaries close to their merger in the context of conformal gravity models. These models incorporate five massive polarisation degrees of freedom, besides the two massless ... 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 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

Error models in quantum computation: an application of model selectionJul 02 2013Sep 04 2013Threshold theorems for fault-tolerant quantum computing assume that errors are of certain types. But how would one detect whether errors of the "wrong" type occur in one's experiment, especially if one does not even know what type of error to look for? ... More

Representations With a Reduced Null ConeDec 15 2011Let G be a complex reductive group and V a G-module. Let \pi: V \to V//G be the quotient morphism and set N(V) = \pi^{-1}(\pi(0)). We consider the following question. Is the null cone N(V) reduced, i.e., is the ideal of N(V) generated by G-invariant polynomials? ... 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

Single-mode instability in standing-wave lasers: The quantum cascade laser as a self-pumped parametric oscillatorNov 01 2017We report the observation of a clear single-mode instability threshold in continuous-wave Fabry-Perot quantum cascade lasers (QCLs). The instability is characterized by the appearance of sidebands separated by tens of free spectral ranges (FSR) from the ... 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

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

Dynamics of particle uptake at cell membranesMay 03 2019Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While the shape of ... 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

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

Community structure and modularity in networks of correlated brain activityJan 25 2007Jan 30 2007We present an approach to study functional segregation and integration in the living brain based on community structure decomposition determined by maximum modularity. We demonstrate this method with a network derived from functional imaging data with ... More

Is dark energy an effect of averaging?Jan 22 2008The present standard model of cosmology states that the known particles carry only a tiny fraction of total mass and energy of the Universe. Rather, unknown dark matter and dark energy are the dominant contributions to the cosmic energy budget. We review ... More

Contact processes in crowded environmentsApr 05 2013Periodically sheared colloids at low densities demonstrate a dynamical phase transition from an inactive to active phase as the strain amplitude is increased. The inactive phase consists of no collisions/contacts between particles in the steady state ... More

Vicious accelerating walkersAug 11 2011Apr 05 2013A vicious walker system consists of N random walkers on a line with any two walkers annihilating each other upon meeting. We study a system of N vicious accelerating walkers with the velocity undergoing Gaussian fluctuations, as opposed to the position. ... More

Stochastic Dynamics of Nanoparticle and Virus UptakeMay 03 2019The cellular uptake of nanoparticles or viruses requires that the gain of adhesion energy overcomes the cost of plasma membrane bending. It is well known that this leads to a minimal particle size for uptake. Using a simple deterministic theory for this ... More

Index-analysis for a method of lines discretising multirate partial differential algebraic equationsJul 25 2017In radio frequency applications, electric circuits generate signals, which are amplitude modulated and/or frequency modulated. A mathematical modelling yields typically systems of differential algebraic equations (DAEs). A multivariate signal model transforms ... More

Astrophysical Gravitational Waves in Conformal GravityApr 05 2018Apr 23 2018We investigate the gravitational radiation from binary systems in conformal gravity (CG) and massive conformal gravity (MCG). CG might explain observed galaxy rotation curves without dark matter, and both models are of interest in the context of quantum ... 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

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

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

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.

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

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

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

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

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).

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

Stability and secondary resonances in the spatial restricted three-body problem for small mass ratiosAug 14 2017This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L4 in the spatial restricted three-body problem for moderate mass ratios (mu), meaning that mu is smaller than 0.0045. However, we concentrated our investigations ... More

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

Quasiparticle Corrections to the Electronic Properties of Anion Vacancies at GaAs(110) and InP(110)Nov 27 2006We propose a new method for calculating optical defect levels and thermodynamic charge-transition levels of point defects in semiconductors, which includes quasiparticle corrections to the Kohn-Sham eigenvalues of density-functional theory. Its applicability ... More

Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product StatesAug 21 2017Jan 03 2019The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome ... 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

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

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

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

Stability of librational motion in the spatial circular restricted three-body problem for high inclinations and mass ratiosAug 09 2017In the spatial circular restricted three-body problem librational motion around the Lagrangian points $L_4$ and $L_5$ exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability of this librational ... 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

Noncommutative Algebraic Equations and Noncommutative Eigenvalue ProblemApr 12 2000Apr 27 2000We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\lambda$ where $\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem ... More

Sigma-models having supermanifolds as target spacesJun 10 1995We study a topological sigma-model ($A$-model) in the case when the target space is an ($m_0|m_1$)-dimensional supermanifold. We prove under certain conditions that such a model is equivalent to an $A$-model having an ($m_0-m_1$)-dimensional manifold ... More

Does String Theory Have a Duality Symmetry Relating Weak and Strong Coupling?Jul 19 1993The heterotic string theory, compactified to four dimensions, has been conjectured to have a duality symmetry (S duality) that transforms the dilaton nonlinearly. If valid, this symmetry could provide an important means of obtaining information about ... More

A-model and generalized Chern-Simons theoryJan 16 2005Jan 30 2005The relation between open topological strings and Chern-Simons theory was discovered by E. Witten. He proved that A-model on T*M where M is a three-dimensional manifold is equivalent to Chern-Simons theory on M and that A-model on arbitrary Calabi-Yau ... More

Gauge theories on noncommutative spacesNov 29 2000I review my results about noncommutative gauge theories and about the relation of these theories to M(atrix) theory following my lecture on ICMP 2000.