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The Algonauts Project: A Platform for Communication between the Sciences of Biological and Artificial IntelligenceMay 14 2019In the last decade, artificial intelligence (AI) models inspired by the brain have made unprecedented progress in performing real-world perceptual tasks like object classification and speech recognition. Recently, researchers of natural intelligence have ... More

Keldysh technique and non-linear sigma-model: basic principles and applicationsJan 23 2009Apr 27 2009The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of underlying microscopic ... More

Coulomb drag at zero temperatureOct 08 2007We show that the Coulomb drag effect exhibits saturation at small temperatures, when calculated to the third order in the interlayer interactions. The zero-temperature transresistance is inversely proportional to the third power of the dimensionless sheet ... More

Keldysh Ginzburg-Landau action of fluctuating superconductorsJun 19 2007Sep 24 2007We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\Delta$-dependent ... More

Coulomb drag in quantum circuitsSep 09 2008Oct 22 2008We study drag effect in a system of two electrically isolated quantum point contacts (QPC), coupled by Coulomb interactions. Drag current exhibits maxima as a function of QPC gate voltages when the latter are tuned to the transitions between quantized ... More

Long-time existence for Yang-Mills flowOct 11 2016We establish that finite-time singularities do not occur in four-dimensional Yang-Mills flow, confirming the conjecture of Schlatter, Struwe, and Tahvildar-Zadeh. The proof relies on a weighted energy identity and sharp decay estimates in the neck region. ... More

Generating Sequences With Recurrent Neural NetworksAug 04 2013Jun 05 2014This paper shows how Long Short-term Memory recurrent neural networks can be used to generate complex sequences with long-range structure, simply by predicting one data point at a time. The approach is demonstrated for text (where the data are discrete) ... More

Characteristic Formulas 50 Years Later (An Algebraic Account)Jul 22 2014The Jankov (characteristic) formulas were introduced by V.Jankov fifty tears ago in 1963. Nowadays the Jankov (or frame) formulas are used in virtually every branch of propositional logic: intermediate, modal, fuzzy, relevant, many-valued, etc. All these ... More

New Algorithms for Solving Tropical Linear SystemsSep 20 2013The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is known, although ... More

Shear viscosity of CFT plasma at finite couplingApr 19 2008May 29 2008We present evidence for the universality of the shear viscosity of conformal gauge theory plasmas beyond infinite coupling. We comment of subtleties of computing the shear viscosity in effective models of gauge/gravity correspondence rather than in string ... More

The Dirichlet Series for the Exterior Square $L$-function on GL(n)Sep 26 2009We present an elementary derivation of the Jacquet-Shalika construction for the exterior square L-function on GL(n), as a classical Dirichlet series in the Fourier coefficients $A(m_1,...,m_{n-1})$.

The X-ray Power Spectral Density Function of the Seyfert Active Galactic Nucleus NGC 7469Oct 15 2010We present the broadband X-ray power spectral density function (PSD) of the X-ray-luminous Seyfert 1.2 NGC 7469, measured from Rossi X-ray Timing Explorer monitoring data and two XMM-Newton observations. We find significant evidence for a turnover in ... More

Black hole spectra in holography: consequences for equilibration of dual gauge theoriesJan 19 2015May 07 2015For a closed system to equilibrate from a given initial condition there must exist an equilibrium state with the energy equal to the initial one. Equilibrium states of a strongly coupled gauge theory with a gravitational holographic dual are represented ... More

Higgs PhysicsDec 14 2014With the discovery of the Higgs, we have access to a plethora of new physical processes that allow us to further test the SM and beyond. We show a convenient way to parametrize these physics using an effective theory for Higgs couplings, discussing the ... More

Boson Sampling is Robust to Small Errors in the Network MatrixDec 08 2014We demonstrate the robustness of BosonSampling to imperfections in the linear optical network that cause a small deviation in the matrix it implements. We show that applying a noisy matrix $\tilde{U}$ that is within $\epsilon$ of the desired matrix $U$ ... More

1D accretion discs around eccentric planets: observable near-infrared variabilityNov 04 2014Dec 29 2014I present the results of 1D models of circumplanetary discs around planets on eccentric orbits. I use a classical viscous heating model to calculate emission fluxes at the wavelengths targeted by the NIRCam instrument on JWST, and compare the variability ... More

AdS boson stars in string theoryOct 28 2015Boson stars are stationary soliton-like gravitational configurations supported by a complex scalar field charged under the global $U(1)$ symmetry. We discuss properties of boson stars in type IIB supergravity approximation to string theory. A notable ... More

Classical Liouville Theory and the Microscopic Interpretation of Black Hole EntropyMar 18 2004In this paper we will give a general introduction to the role of conformal symmetry in the microscopic interpretation of black hole entropy and then compute the entropy of a Schwarzschild black hole by finding a classical central charge of the Virasoro ... More

The Quantum Hall effect, Skyrmions and AnomaliesAug 19 1998We discuss the properties of Skyrmions in the Fractional Quantum Hall effect (FQHE). We begin with a brief description of the Chern-Simons-Landau-Ginzburg description of the FQHE, which provides the framework in which to understand a new derivation of ... More

Effect of dipolar moments in domain sizes of lipid bilayers and monolayersNov 18 2006Dec 14 2006Lipid domains are found in systems such as multi-component bilayer membranes and single component monolayers at the air-water interface. It was shown by Andelman et al. (Comptes Rendus 301, 675 (1985)) and McConnell et al. (Phys. Chem. {\bf 91}, 6417 ... More

On Factoring an Operator Using Elements of its KernelNov 25 2015A well-known theorem factors a scalar coefficient differential operator given a linearly independent set of functions in its kernel. The goal of this paper is to generalize this useful result to other types of operators. In place of the derivation $\partial$ ... More

From rational billiards to dynamics on moduli spacesApr 30 2015Jul 26 2015This short expository note gives an elementary introduction to the study of dynamics on certain moduli spaces, and in particular the recent breakthrough result of Eskin, Mirzakhani, and Mohammadi. We also discuss the context and applications of this result, ... More

Schwarz triangle mappings and Teichmüller curves: the Veech-Ward-Bouw-Möller curvesMar 13 2012Jan 24 2013We study a family of Teichm\"uller curves T(n,m) constructed by Bouw and M\"oller, and previously by Veech and Ward in the cases n=2,3. We simplify the proof that T(n,m) is a Teichm\"uller curve, avoiding the use M\"oller's characterization of Teichm\"uller ... More

Gromov's measure equivalence and rigidity of higher rank latticesNov 01 1999In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the ... More

Plasmon decay and thermal transport from spin-charge coupling in generic Luttinger liquidsDec 20 2014We discuss the violation of spin-charge separation in generic nonlinear Luttinger liquids and investigate its effect on the relaxation and thermal transport of genuine spin-1/2 electron liquids in ballistic quantum wires. We identify basic scattering ... More

Transport theory of superconductors with singular interaction correctionsMay 01 2010We study effects of strong fluctuations on the transport properties of superconductors near the classical critical point. In this regime conductivity is set by the delicate interplay of two competing effects. The first is that strong electron-electron ... More

Interaction corrections to tunneling conductance in ballistic superconductorsApr 19 2009Feb 08 2010It is known that in the two-dimensional disordered superconductors electron-electron interactions in the Cooper channel lead to the negative logarithmic in temperature correction to the tunneling conductance above the critical temperature. Physically ... More

On (Non)Supermodularity of Average Control EnergySep 27 2016Oct 05 2016Given a linear system, we consider the expected energy to move from the origin to a uniformly random point on the unit sphere as a function of the set of actuated variables. We show this function is not necessarily supermodular, correcting some claims ... More

Stochastic selection processesNov 17 2015We propose a mathematical framework for natural selection in finite populations. Traditionally, many of the selection-based processes used to describe cultural and genetic evolution (such as imitation and birth-death models) have been studied on a case-by-case ... More

The Reasonable Effectiveness of Mathematics in the Physical SciencesDec 24 2012Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is discovered; Logicism ... More

Weak measurements of trajectories in quantum systems: classical, Bohmian and sum over pathsNov 14 2014Jun 11 2015Weak values, obtained from weak measurements, attempt to describe the properties of a quantum system as it evolves from an initial to a final state, without practically altering this evolution. Trajectories can be defined from weak measurements of the ... More

Interpolation and embeddings of weighted tent spacesSep 18 2015Feb 09 2016Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on $X$ we identify ... More

Fell bundles over groupoidsJul 21 1996The author provides some definitions and structural results about Fell bundles, defined as C^*-algebra bundles over topological groupoids. Such bundles are a mutual generalization of semi-direct products of groups with C^*-algebras and C^*-algebra bundles ... More

Disjoint $n$-amalgamation and pseudofinite countably categorical theoriesOct 13 2015Disjoint $n$-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this paper, we show that if a countably categorical theory $T$ admits an expansion ... More

Lines in supersingular quarticsApr 20 2016We show that the number of lines contained in a supersingular quartic surface is 40 or at most 32, if the characteristic of the field equals 2, and it is 112, 58, or at most 52, if the characteristic equals 3. If the quartic is not supersingular, the ... More

Super-Replication of the Best Pairs Trade in HindsightOct 04 2018Oct 17 2018For a market with $m$ assets and $T$ discrete trading sessions, Ordentlich and Cover (1998) found that the `Cost of Achieving the Best Rebalancing Rule in Hindsight' is $p(T,m)=\sum\limits_{n_1+\cdot\cdot\cdot+n_m=T}\binom{T}{n_1,...,n_m}(n_1/T)^{n_1}\cdot\cdot\cdot(n_m/T)^{n_m}$. ... More

Discriminants and Quasi-symmetryNov 24 2017This paper gives a geometric interpretation of the notion of quasi-symmetric representation and uses this to show that the discriminant locus associated to such a representation is a hyperplane arrangement. Moreover, we identify this hyperplane arrangement, ... More

Mean Curvature Motion of Graphs with Constant Contact Angle and Moving BoundariesMay 29 2008We consider the motion by mean curvature of an $n$-dimensional graph over a time-dependent domain in $\mathbb{R}^n$, intersecting $\mathbb{R}^n$ at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic ... More

Information Rates and post-FEC BER Prediction in Optical Fiber CommunicationsNov 28 2016Information-theoretic metrics to analyze optical fiber communications systems with binary and nonbinary soft-decision FEC are reviewed. The numerical evaluation of these metrics in both simulations and experiments is also discussed. Ready-to-use closed-form ... More

Compact groups and absolute extensorsAug 15 1999We discuss compact Hausdorff groups from the point of view of the general theory of absolute extensors. In particular, we characterize the class of simple, connected and simply connected compact Lie groups as AE(2)-groups the third homotopy group of which ... More

Quantum tasks in holographyFeb 19 2019Mar 05 2019We consider an operational restatement of the holographic principle, which we call the principle of asymptotic quantum tasks. Asymptotic quantum tasks are quantum information processing tasks with inputs given and outputs required on points at the boundary ... More

A volume-based approach to the multiplicative ergodic theorem on Banach spacesFeb 23 2015Dec 07 2015A volume growth-based proof of the Multiplicative Ergodic Theorem for Banach spaces is presented, following the approach of Ruelle for cocycles acting on a Hilbert space. As a consequence, we obtain a volume growth interpretation for the Lyapunov exponents ... More

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part II: The Degenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More

Extremal Numbers for 2 to 1 Directed Hypergraphs with Two Edges Part I: The Nondegenerate CasesJul 18 2016Let a 2 to 1 directed hypergraph be a 3-uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that any directed hypergraph on n ... More

Generators for Coulomb branches of quiver gauge theoriesMar 18 2019We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation ... More

Linear Flows on $κ$-SolenoidsJun 24 1999Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the inverse limit generating the equivalence.

Factorization of a Matrix Differential Operator Using Functions in its KernelSep 17 2015Just as knowing some roots of a polynomial allows one to factor it, a well-known result provides a factorization of any scalar differential operator given a set of linearly independent functions in its kernel. This note provides a straight-forward generalization ... More

Regulator constants of integral representations of finite groupsMar 30 2017Dec 22 2018Let G be a finite group and p be a prime. We investigate isomorphism invariants of $\mathbb{Z}_{p}[G]$-lattices whose extension of scalars to $\mathbb{Q}_p$ is self-dual, called regulator constants. These were originally introduced by Dokchitser--Dokchitser ... More

Factor equivalence of Galois modules and regulator constantsSep 17 2012Jun 21 2013We compare two approaches to the study of Galois module structures: on the one hand factor equivalence, a technique that has been used by Fr\"ohlich and others to investigate the Galois module structure of rings of integers of number fields and of their ... More

Asymptotic cohomological functions on projective varietiesJan 27 2005In this paper we define certain analogues of the volume of a divisor - called asymptotic cohomological functions - and investigate their behaviour on the Neron--Severi space. We establish that asymptotic cohomological functions are invariant with respect ... More

Hurwitz equivalence of braid monodromies and extremal elliptic surfacesNov 02 2009We discuss the equivalence between the categories of certain ribbon graphs and subgroups of the modular group $\Gamma$ and use it to construct exponentially large families of not Hurwitz equivalent simple braid monodromy factorizations of the same element. ... More

Elliptic curves with p-Selmer growth for all pApr 05 2012Jun 21 2013It is known, that for every elliptic curve over Q there exists a quadratic extension in which the rank does not go up. For a large class of elliptic curves, the same is known with the rank replaced by the 2-Selmer group. We show, however, that there exists ... More

Periodic resolutions and self-injective algebras of finite typeAug 09 2008Sep 16 2008We say that an algebra A is periodic if it has a periodic projective resolution as an (A,A)-bimodule. We show that any self-injective algebra of finite representation type is periodic. To prove this, we first apply the theory of smash products to show ... More

On the unit distance problemSep 23 2017The Erd\H os unit distance conjecture in the plane says that the number of pairs of points from a point set of size $n$ separated by a fixed (Euclidean) distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best known bound is $Cn^{\frac{4}{3}}$. ... More

Tent spaces over metric measure spaces under doubling and related assumptionsMay 10 2013Sep 25 2013In this article, we define the Coifman-Meyer-Stein tent spaces $T^{p,q,\alpha}(X)$ associated with an arbitrary metric measure space $(X,d,\mu)$ under minimal geometric assumptions. While gradually strengthening our geometric assumptions, we prove duality, ... More

Poisson--Dirichlet distribution for random Belyi surfacesJan 19 2005Nov 21 2006Brooks and Makover introduced an approach to studying the global geometric quantities (in particular, the first eigenvalue of the Laplacian, injectivity radius and diameter) of a ``typical'' compact Riemann surface of large genus based on compactifying ... More

Admissibility in Positive LogicsOct 27 2016The paper studies admissibility of multiple-conclusion rules in the positive logics. Using modification of a method used by M.~Wajsberg in the proof of the separation theorem, it is shown that the problem of admissibility in positive logics is equivalent ... More

The Alexander module of a trigonal curve. IIFeb 17 2012Sep 19 2012We complete the enumeration of the possible roots of the Alexander polynomial (both conventional and over finite fields) of a trigonal curve. The curves are not assumed proper or irreducible.

Plane sextics with a type $\mathbf{E}_6$ singular pointJul 27 2009Jan 25 2010We give a classification up to equisingular deformation and compute the fundamental groups of maximizing plane sextics with a type $\mathbf{E}_6$ singular point.

Fundamental groups of symmetric sextics. IIMay 15 2008We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities $2\bold{A}_8$ or $\bold{A}_{17}$. We also compute the fundamental groups of a number of other sextics, both of and not of ... More

Zariski $k$-plets via dessins d'enfantsOct 01 2007Apr 17 2008We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian.

On the Picard group of a Delsarte surfaceJul 01 2013We suggest an algorithm computing, in some cases, an explicit generating set for the N\'eron--Severi lattice of a Delsarte surface.

Pseudocompact paratopological groups that are topologicalJun 08 2014We obtain necessary and sufficient conditions when a pseudocompact paratopological group is topological. (2-)pseudocompact and countably compact paratopological groups that are not topological are constructed. It is proved that each 2-pseudocompact paratopological ... More

Ocean gravitational-modes in transient neutron starsNov 30 2015The neutron star ocean is a plasma of ions and electrons that extends from the base of the neutron star's envelope to a depth where the plasma crystallizes into a solid crust. During an accretion outburst in an X-ray transient, material accumulates in ... More

The spectral norm error of the naive Nystrom extensionOct 24 2011The naive Nystrom extension forms a low-rank approximation to a positive-semidefinite matrix by uniformly randomly sampling from its columns. This paper provides the first relative-error bound on the spectral norm error incurred in this process. This ... More

Special relativity as classical kinematics of a particle with the upper bound on its speed. Part II. The general Lorentz transforrmation and the generalized velocity composition theoremMay 09 2014The kinematics of a particle with the upper bound on the particle's speed (a modification of classical kinematics where such a restriction is absent) has been developed in [arXiv:1204.5740]. It was based solely on classical mechanics without employing ... More

A Short Note on Mapping CylindersJun 06 2012Jul 13 2012Given a homotopy equivalence f between two topological spaces we assemble well known pieces and unfold them into an explicit formula for a strong deformation retraction of the mapping cylinder of f onto its top.

Extending and Characterizing Quantum Magic GamesSep 18 2012The Mermin-Peres magic square game is a cooperative two-player nonlocal game in which shared quantum entanglement allows the players to win with certainty, while players limited to classical operations cannot do so, a phenomenon dubbed "quantum pseudo-telepathy". ... More

Resolving disagreement for eta/s in a CFT plasma at finite couplingMay 17 2008The ratio of shear viscosity to entropy density in a strongly coupled CFT plasma can be computed using the AdS/CFT correspondence either from equilibrium correlation functions or from the Janik-Peschanski dual of the boost invariant plasma expansion. ... More

N=2* hydrodynamicsJun 23 2004Using gauge theory /string theory correspondence certain universal aspects of the strongly coupled four dimensional gauge theory hydrodynamics were established in hep-th/0311175. The analysis were performed in the framework of ``membrane paradigm'' approach ... More

Localization and holography in N=2 gauge theoriesApr 20 2013Sep 18 2013We compare exact results from Pestun's localization of SU(N) N=2^* gauge theory on S^4 with available holographic models. While localization can explain the Coulomb branch vacuum of the holographic Pilch-Warner flow, it disagrees with the holographic ... More

Quantum phase transitions in cascading gauge theoryAug 30 2011We study a ground state of N=1 supersymmetric SU(K+P) x SU(K) cascading gauge theory of Klebanov et.al [1,2] on R x S^3 at zero temperature. A radius of S^3 sets a compactification scale mu. An interplay between mu and the strong coupling scale Lambda ... More

On SUGRA description of boost-invariant conformal plasma at strong couplingMar 24 2008Mar 26 2008We study string theory duals of the expanding boost invariant conformal gauge theory plasmas at strong coupling. The dual supergravity background is constructed as an asymptotic late-time expansion, corresponding to equilibration of the gauge theory plasma. ... More

Bulk viscosity of gauge theory plasma at strong couplingAug 27 2007Sep 01 2007We propose a lower bound on bulk viscosity of strongly coupled gauge theory plasmas. Using explicit example of the N=2^* gauge theory plasma we show that the bulk viscosity remains finite at a critical point with a divergent specific heat. We present ... More

Transport properties of cascading gauge theoriesSep 12 2005Cascading gauge theories of Klebanov et.al. provide a model within a framework of gauge theory/string theory duality for a four dimensional non-conformal gauge theory with a spontaneously generated mass scale. Using the dual supergravity description we ... More

On effective action of string theory flux compactificationsDec 07 2003Feb 12 2004We discuss four dimensional effective actions of string theory flux compactifications. These effective actions describe four dimensional gravity coupled to overall Kahler modulus of the compactification manifold. We demonstrate the agreement between ten ... More

On the thermodynamic instability of LSTJul 12 2001Jul 20 2001The high energy thermodynamics of Little String Theory (LST) is known to be unstable. An unresolved question is whether the corresponding instability in LST holographic dual is of stringy or supergravity origin. We study UV thermodynamics of a large metric ... More

New type scalar fields for cosmic accelerationJun 07 2006We present a model where a non-conventional scalar field may act like dark energy leading to cosmic acceleration. The latter is driven by an appropriate field configuration, which result in an effective cosmological constant. The potential role of such ... More

A Direct Sampler for G-Wishart VariatesApr 04 2013The G-Wishart distribution is the conjugate prior for precision matrices that encode the conditional independencies of a Gaussian graphical model. While the distribution has received considerable attention, posterior inference has proven computationally ... More

Nested Bethe Ansatz and Finite Dimensional Canonical Commutation RelationsApr 24 2000Recent interest in discrete, classical integrable systems has focused on their connection to quantum integrable systems via the Bethe equations. In this note, solutions to the rational nested Bethe ansatz (RNBA) equations are constructed using the ``completed ... More

Spectral Difference Equations Satisfied by KP Soliton WavefunctionsNov 11 1998The Baker-Akhiezer (wave) functions corresponding to soliton solutions of the KP hierarchy are shown to satisfy eigenvalue equations for a commutative ring of translational operators in the spectral parameter. In the rational limit, these translational ... More

Bispectrality of $N$-Component KP Wave Functions: A Study in Non-CommutativityMay 11 2015Nov 01 2015A wave function of the $N$-component KP Hierarchy with continuous flows determined by an invertible matrix $H$ is constructed from the choice of an $MN$-dimensional space of finitely-supported vector distributions. This wave function is shown to be an ... More

Grassmannians, Nonlinear Wave Equations and Generalized Schur FunctionsNov 11 1998Feb 26 1999A set of functions is introduced which generalizes the famous Schur polynomials and their connection to Grasmannian manifolds. These functions are shown to provide a new method of constructing solutions to the KP hierarchy of nonlinear partial differential ... More

Bispectral KP Solutions and Linearization of Calogero-Moser Particle SystemsDec 14 1994Dec 15 1994A new construction using finite dimensional dual grassmannians is developed to study rational and soliton solutions of the KP hierarchy. In the rational case, properties of the tau function which are equivalent to bispectrality of the associated wave ... More

Schwarz triangle mappings and Teichmüller curves: abelian square-tiled surfacesMar 13 2012Oct 17 2012We consider normal covers of CP^1 with abelian deck group, branched over at most four points. Families of such covers yield arithmetic Teichm\"uller curves, whose period mapping may be described geometrically in terms of Schwarz triangle mappings. These ... More

Ground state of a large number of particles on a frozen topographyJan 25 2006Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical ... More

Crossover in the local density of states of mesoscopic SNS junctionsMay 05 2008Andreev levels deplete energy states above the superconductive gap, which leads to the peculiar nonmonotonous crossover in the local density of states of mesoscopic superconductor/normal-metal/superconductor junctions. This effect is especially pronounced ... More

The Cosmological ConstantNov 23 2012Contrary to popular mythology, Einstein did not invent the cosmological constant just in order construct his model universe. He discussed it earlier in "The Foundations of General Relativity" in connection with the proper structure of the source-free ... More

A Note on Optimality of Quantum Circuits over Metaplectic BasisJun 07 2016Jun 09 2016Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate $R=|0\rangle \langle 0| + |1\rangle \langle 1| - |2\rangle \langle 2|$. It is arguably, a ternary basis with the simplest ... More

Applications of Thin OrbitsJun 20 2016This text is based on a series of three expository lectures on a variety of topics related to "thin orbits," as delivered at Durham University's Easter School on "Dynamics and Analytic Number Theory" in April 2014. The first lecture reviews closed geodesics ... More

Tensor networks for dynamic spacetimesNov 18 2016Existing tensor network models of holography are limited to representing the geometry of constant time slices of static spacetimes. We study the possibility of describing the geometry of a dynamic spacetime using tensor networks. We find it is necessary ... More

Physics and Chemistry of Purcell's AlignmentJan 17 1995Paramagnetic alignment of suprathermally rotating grains is discussed in view of recent progress in understanding subtle processes taking place over grain surface. It is shown that in typical ISM conditions, grains with surfaces of amorphous H$_{2}$O ... More

On the biregular geometry of Fulton-MacPherson configuration spacesMar 22 2016Let $X[n]$ be the Fulton-MacPherson configuration space of $n$ ordered points on a smooth projective variety $X$. We prove that if either $n\neq 2$ or $\dim(X)\geq 2$, then the connected component of the identity of $Aut(X[n])$ is isomorphic to the connected ... More

Maximum screening fields of superconducting multilayer structuresJan 07 2015It is shown that a multilayer comprised of alternating thin superconducting and insulating layers on a thick substrate can fully screen the applied magnetic field exceeding the superheating fields $H_s$ of both the superconducting layers and the substrate, ... More

Vacuum Instability in Topologically Massive Gauge TheoryAug 12 1998We find the critical charge for a topologically massive gauge theory for any gauge group, generalising our earlier result for SU(2). The relation between critical charges in TMGT, singular vectors in the WZNW model and logarithmic CFT is investigated. ... More

The Bertini involutionDec 05 2012We summarize and extend E. Moody's results on the explicit equations related to the Bertini involution.

Exponential concentration of cover timesJul 29 2014We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding-Lee-Peres and Ding. The estimate is asymptotically sharp as the ratio of hitting time to cover time goes to zero. ... More

Volumes of line bundlesNov 26 2002Dec 10 2003This paper has been removed by the author due to a misstatement in Theorem 1 and a gap in its proof. A corrected and largely extended successor (a joint work with Thomas Bauer and Tomasz Szemberg) can be found under math.AG/0312211,

Topological AE(0)-groupsJan 04 2000We investigate topological AE(0) -groups class of which contains the class of Polish groups as well as the class of all locally compact groups. We establish the existence of an universal AE(0) -group of a given weight as well as the existence of an universal ... More

Disjoint $n$-amalgamation and pseudofinite countably categorical theoriesOct 13 2015Sep 17 2018Disjoint $n$-amalgamation is a condition on a complete first-order theory specifying that certain locally consistent families of types are also globally consistent. In this paper, we show that if a countably categorical theory $T$ admits an expansion ... More