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Generation and manipulation of Schrödinger cat states in Rydberg atom arraysMay 14 2019May 15 2019Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum ... More

The Hausdorff dimension of the boundary of the Lévy dragonJul 22 1999A theoretical approach to computing the Hausdorff dimension of the topological boundary of attractors of iterated function systems is developed. The curve known as the L\'evy Dragon is then studied in detail and the Hausdorff dimension of its boundary ... More

Large-Scale Uniform Optical Focus Array Generation with a Phase Spatial Light ModulatorMar 22 2019We report a new method to generate uniform large-scale optical focus arrays (LOFAs). By identifying and removing undesired phase rotation in the iterative Fourier-transform algorithm (IFTA), our approach rapidly produces computer-generated holograms of ... More

Probing many-body dynamics on a 51-atom quantum simulatorJul 13 2017Nov 30 2017Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on ... More

High-fidelity control and entanglement of Rydberg atom qubitsJun 12 2018Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities ... More

Cold Matter Assembled Atom-by-AtomJul 11 2016The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of individually controlled ... More

The Similarity Boundary of a Self-Similar SetJul 16 1999We define the similarity boundary of a self-similar set and use it to analyze the properties of self-similar sets in the general setting of any complete metric space. The similarity boundary is an attempt at extending the concept of the topological boundary ... More

Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulatorSep 14 2018Apr 01 2019Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics ... More

Fundamental groups of compact Hausdorff spacesJan 26 2005We discuss which groups can be realized as the fundamental groups of compact Hausdorff spaces. In particular, we prove that the claim ``every group can be realized as the fundamental group of a compact Hausdorff space'' is consistent with the Zermelo ... More

Integrating Neural Networks with a Quantum Simulator for State ReconstructionApr 17 2019We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator, by means of a neural network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine ... More

Probing quantum critical dynamics on a programmable Rydberg simulatorSep 14 2018Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics ... More

Generation and manipulation of Schrödinger cat states in Rydberg atom arraysMay 14 2019Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum ... More

Homeomorphisms of unimodal inverse limit spaces with a non-recurrent postcritical pointMar 18 2019In this paper we show that the group of automorphisms of a non-recurrent tent map is very simple by demonstrating that every homeomorphism of such a space is isotopic to a power of the induced shift homeomorphism.

Homeomorphisms of unimodal inverse limit spaces with a non-recurrent postcritical pointMar 18 2019Mar 27 2019In this paper we show that the group of automorphisms of a non-recurrent tent map inverse limit is very simple by demonstrating that every homeomorphism of such a space is isotopic to a power of the induced shift homeomorphism.

A Gröbner basis for Kazhdan-Lusztig idealsSep 03 2009Nov 11 2011Kazhdan-Lusztig ideals, a family of generalized determinantal ideals investigated in [Woo-Yong '08], provide an explicit choice of coordinates and equations encoding a neighbourhood of a torus-fixed point of a Schubert variety on a type A flag variety. ... More

Neutrino energy quantization in rotating mediumSep 30 2008Exact solution of the modified Dirac equation in rotating medium is found in polar coordinates in the limit of vanishing neutrino mass. The solution for the active left-handed particle exhibit properties similar to those peculiar for the charged particle ... More

General Conditions for Lepton Flavour Violation at Tree- and 1-Loop LevelSep 20 2007In this work, we compile the necessary and sufficient conditions a theory has to fulfill in order to ensure general lepton flavour conservation, in the spirit of the Glashow-Weinberg criteria for the absence of flavour-changing neutral currents. At tree-level, ... More

Discrete Uniqueness Sets for Functions with Spectral GapsSep 15 2016It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016Oct 25 2017We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Spectral perturbation theory and the two weights problemJun 08 2013The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs ... More

Mild and viscosity solutions to semilinear parabolic path-dependent PDEsNov 24 2016Nov 14 2018We study and compare two concepts for weak solutions to semilinear parabolic path-dependent partial differential equations (PPDEs). The first is that of mild solutions as it appears, e.g., in the log-Laplace functionals of historical superprocesses. The ... More

Yet again on polynomial convergence for SDEs with a gradient-type driftJun 28 2017Jul 23 2017Bounds on convergence rate to the invariant distribution for a class of stochastic differential equations (SDEs) with a gradient-type drift are obtained.

String center of mass operator and its effect on BRST cohomologyNov 15 1995We consider the theory of bosonic closed strings on the flat background R(25,1). We show how the BRST complex can be extended to a complex where the string center of mass operator, x^mu_0, is well defined. We investigate the cohomology of the extended ... More

An ICT-Based Real-Time Surveillance System for Controlling Dengue in Sri LankaMay 16 2014Dengue is a notifiable communicable disease in Sri Lanka since 1996. Dengue fever spread rapidly among people living in most of the districts of Sri Lanka. The present notification system of dengue communicable diseases which is enforced by law is a passive ... More

Homological projective duality for quadricsFeb 26 2019Mar 01 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019Mar 01 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Approximation of discrete functions and size of spectrumApr 02 2013Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$, then measure($S$)$\geq ... More

Magnetic susceptibility of the quark condensate via holographyFeb 11 2009Jan 13 2010We discuss the holographic derivation of the magnetic susceptibility of the quark condensate. It is found that the susceptibility emerges upon the account of the Chern-Simons term in the holographic action. We demonstrate that Vainshtein's relation is ... More

On Beurling's sampling theorem in $\R^n$Jun 03 2011We present an elementary proof of the classical Beurling sampling theorem which gives a sufficient condition for sampling of multi-dimensional band-limited functions.

Regenerative compositions in the case of slow variation: A renewal theory approachSep 27 2011Sep 01 2012A regenerative composition structure is a sequence of ordered partitions derived from the range of a subordinator by a natural sampling procedure. In this paper, we extend previous studies Barbour and Gnedin (2006), Gnedin, Iksanov and Marynych (2010) ... More

Derived categories of Gushel-Mukai varietiesMay 21 2016We study the derived categories of coherent sheaves on Gushel-Mukai varieties. In the derived category of such a variety, we isolate a special semiorthogonal component, which is a K3 or Enriques category according to whether the dimension of the variety ... More

Mild and viscosity solutions to quasilinear parabolic path-dependent PDEsNov 24 2016We study and compare two different concepts for weak solutions to quasilinear parabolic path-dependent partial differential equations (PPDEs). The first concept is that of a mild solution as it appears, e.g., in the Laplace functionals of historical superprocesses. ... More

Derived categories of cyclic covers and their branch divisorsNov 07 2014Dec 17 2015Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$ and $\mathrm{D^b}(Z)$ ... More

Paramagnetic tunneling state concept of the magnetic anomalies of amorphous insulatorsSep 05 2005A generalized tunneling model of insulating glasses is formulated, considering tunneling states to be paramagnetic centers of spin 1/2. The expression for magnetic field dependent contribution into the free energy is obtained. The derivation is made of ... More

Spherical structures on torus knots and linksAug 02 2010Jul 07 2011The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found ... More

On the Duality between Sampling and InterpolationDec 04 2015We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.

Discrete Translates in Function SpacesDec 02 2016Mar 16 2017We construct a Schwartz function $\varphi$ such that for every exponentially small perturbation of integers $\Lambda$, the set of translates $\{\varphi(t-\lambda), \lambda\in\Lambda\}$ spans the space $L^p(R)$, for every $p > 1$. This result remains true ... More

When is a Schubert variety Gorenstein?Sep 25 2004Nov 21 2005A (normal) variety is Gorenstein if it is Cohen-Macualay and its canonical sheaf is a line bundle. This property, which measures the ``pathology'' of the singularities of a variety, is thus stronger than Cohen-Macualayness, but is also weaker than smoothness. ... More

Evaluation of the Einstein's strength of difference schemes for some chemical reaction-diffusion equationsMar 10 2018In this paper we present a difference algebraic technique for the evaluation of the Einstein's strength of a system of partial difference equations and apply this technique to the comparative analysis of difference schemes for chemical reaction-diffusion ... More

Full exceptional collections on the Lagrangian Grassmannians LG(4,8) and LG(5,10)Oct 13 2009We construct full exceptional collections of vector bundles on the Lagrangian Grassmannians LG(4,8) and LG(5,10).

Cauchy independent measures and super-additivity of analytic capacityNov 12 2012We show that, given a family of discs centered at a nice curve, the analytic capacities of arbitrary subsets of these discs add up. However we need that the discs in question would be slightly separated, and it is not clear whether the separation condition ... More

Random "dyadic" lattice in geometrically doubling metric space and $A_2$ conjectureMar 27 2011Apr 21 2011Recently three proofs of the $A_2$-conjecture were obtained. All of them are "glued" to euclidian space and a special choice of one random dyadic lattice. We build a random "dyadic" lattice in any doubling metric space which have properties that are enough ... More

Reachability in Higher-Order-CountersJun 05 2013Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those ... More

Exceptional collections on isotropic GrassmanniansOct 25 2011Sep 13 2015We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the ... More

Paramagnetic tunneling state concept of the low-temperature magnetic anomalies of multicomponent insulating glassesMar 17 2006A generalized tunneling model of multicomponent insulating glasses is formulated, considering tunneling states to be paramagnetic centers of the electronic hole type. The expression for magnetic field dependent contribution into the free energy is obtained. ... More

On multi-dimensional sampling and interpolationApr 02 2013The paper discusses sharp sufficient conditions for interpolation and sampling for functions of n variables with convex spectrum. When n=1, the classical theorems of Ingham and Beurling state that the critical values in the estimates from above (from ... More

Kazhdan-Laumon representations of finite Chevalley groups, character sheaves and some generalization of the Lefschetz-Verdeier trace formulaOct 01 1998In this paper we investigate the representations of reductive groups over a finite field, introduced in 1987 by D.Kazhdan and G.Laumon. We show that generically these representations are irreducible and that their character is equal to the function obtained ... More

Discrete Translates in $L^2(R)$Dec 02 2016A set $\Lambda\subset R$ is called $p$-spectral, if there is a function $\varphi\in L^p(R)$ whose $\Lambda$-translates $\{\varphi(t-\lambda),\lambda\in\Lambda\}$ span $L^p(R)$. We prove that exponentially small non-zero perturbations of the integers are ... More

$L^2-$interpolation with error and size of spectraJun 18 2008Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density ... More

Moments of random sums and Robbins' problem of optimal stoppingJul 17 2011Robbins' problem of optimal stopping asks one to minimise the expected {\it rank} of observation chosen by some nonanticipating stopping rule. We settle a conjecture regarding the {\it value} of the stopped variable under the rule optimal in the sense ... More

Homological projective duality for quadricsFeb 26 2019We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of ... More

Categorical cones and quadratic homological projective dualityFeb 26 2019We introduce the notion of a categorical cone, which provides a categorification of the classical cone over a projective variety, and use our work on categorical joins to describe its behavior under homological projective duality. In particular, our construction ... More

Categorical joinsMar 31 2018Feb 26 2019We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. ... More

Fast gradient descent method for convex optimization problems with an oracle that generates a $(δ,L)$-model of a function in a requested pointNov 07 2017Feb 02 2019In this article we propose a new concept of a $(\delta,L)$-model of a function which generalizes the concept of the $(\delta,L)$-oracle (Devolder-Glineur-Nesterov). Using this concept we describe the gradient descent method and the fast gradient descent ... More

Scattering theory and Banach space valued singular integralsNov 28 2012We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on estimates for the Cauchy ... More

Subtle Characteristic ClassesJan 26 2014We construct new subtle Stiefel--Whitney classes of quadratic forms. These classes are much more informative than the ones introduced by Milnor. In particular, they see all the powers of the fundamental ideal of the Witt ring, contain the Arason invariant ... More

Governing Singularities of Schubert VarietiesMar 12 2006Jun 29 2006We present a combinatorial and computational commutative algebra methodology for studying singularities of Schubert varieties of flag manifolds. We define the combinatorial notion of *interval pattern avoidance*. For "reasonable" invariants P of singularities, ... More

Diagonalization of the Finite Hilbert Transform on two adjacent intervalsNov 06 2015We study the interior problem of tomography. The starting point is the Gelfand-Graev formula, which converts the tomographic data into the finite Hilbert transform (FHT) of an unknown function $f$ along a collection of lines. Pick one such line, call ... More

Time-periodic Néel wall motionsJun 24 2010In thin ferromagnetic films, the predominance of the magnetic shape anisotropy leads to in-plane magnetizations. The simplest domain wall in this geometry is the one-dimensional Neel wall that connects two magnetizations of opposite sign by a planar 180 ... More

Stars and singularities: Stellar phenomena near a massive black holeFeb 12 2002This is a pedagogical review of recent results on the interactions of central massive black holes with stars very near them, focused on the black hole in the center of the Milky Way. Table of contents: [1] Introduction [2] Stellar dynamics near a black ... More

The Galactic Center as a laboratory for extreme mass ratio gravitational wave source dynamicsJul 11 2008Jul 16 2008The massive Galactic black hole and the stars around it are a unique laboratory for studying how relaxation processes lead to close interactions of stars and compact remnants with the central massive black hole, in particular those leading to the emission ... More

Analysis of energetic models for rate-independent materialsMay 01 2003We consider rate-independent models which are defined via two functionals: the time-dependent energy-storage functional $\calI:[0,T]\ti X\to [0,\infty]$ and the dissipation distance $\calD:X\ti X\to[0,\infty]$. A function $z:[0,T]\to X$ is called a solution ... More

Expander Graphs in Pure and Applied MathematicsMay 12 2011Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing ... More

Rayleigh-Bénard Convection as a Nambu-metriplectic problemMar 31 2008May 14 2008The traditional Hamiltonian structure of the equations governing conservative Rayleigh-B\'enard convection (RBC) is singular, i.e. it's Poisson bracket possesses nontrivial Casimir functionals. We show that a special form of one of these Casimirs can ... More

A modular analogue of Morozov's theorem on maximal subalgebras of simple Lie algebrasDec 17 2015Jan 23 2016Let $G$ be a simple algebraic group over an algebraically closed field of characteristic $p>0$ and suppose that $p$ is a very good prime for $G$. We prove that any maximal Lie subalgebra $M$ of $\mathfrak{g} = {\rm Lie}(G)$ with ${\rm rad}(M) \ne 0$ has ... More

Magnetic Behavior of the Cuprate SuperconductorsMay 17 1995I review recent work on magnetic dynamics of the high temperature superconductors using a model that combines two weakly interacting species of low-energy excitations: the antiferromagnetic spin waves which carry spin-1 and no charge, and Fermi-liquid-like ... More

Some Interesting Integer Polynomial MapsJan 03 2013We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.

Geometrically Nilpotent SubvarietiesMay 13 2015We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteration of the map, while the whole subvariety is not. Several related open questions ... More

Recursive Definitions of Monadic FunctionsDec 22 2010Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's imperative programming ... More

Function Weighted Metric Discovery for Unreliable FunctionsOct 31 2016Nov 02 2016We consider building a function adapted diffusion operator high dimensional data $X$ when the function $F$ can only be evaluated on large subsets of the data, and possibly only depends on a small subset of the features. Our method breaks $X$ up into hierarchical ... More

Intrinsic time in Friedmann-Robertson-Walker universeJan 04 2016A global intrinsic time in Friedmann - Robertson - Walker models is proportional to a scaling factor of the spatial metric. The aim of the paper is to study an applicability of the intrinsic global time chosen to nearest non-symmetric cases by taking ... More

Magnetoconductivity in the presence of Bychkov-Rashba spin-orbit interactionJun 24 2006A closed-form analytic formula for the magnetoconductivity in the diffusive regime is derived in the presence of Bychkov-Rashba spin-orbit interaction in two dimensions. It is shown that at low fields B << B_{so}, where B_{so} is the characteristic field ... More

A derived category approach to Kempf's vanishing theoremNov 30 2016We give a proof of the property of the Steinberg character that implies Kempf's vanishing theorem. Our argument is based on the structure of derived categories of coherent sheaves on flag varieties.

A quantum measure of the multiverseDec 03 2013Dec 11 2013It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an extension of this ... More

On cosmic natural selectionOct 04 2006Nov 27 2006The rate of black hole formation can be increased by increasing the value of the cosmological constant. This falsifies Smolin's conjecture that the values of all constants of nature are adjusted to maximize black hole production.

On the factor ordering problem in stochastic inflationFeb 01 1999The stochastic approach to inflation suffers from ambiguities due to the arbitrary choice of the time variable and due to the choice of the factor ordering in the corresponding Fokker-Planck equation. Here it is shown that both ambiguities can be removed ... More

Predictions from Quantum CosmologyJun 06 1994Oct 27 1994The world view suggested by quantum cosmology is that inflating universes with all possible values of the fundamental constants are spontaneously created out of nothing. I explore the consequences of the assumption that we are a `typical' civilization ... More

Quantum cosmology and eternal inflationApr 18 2002This contribution consists of two parts. In the first part, I review the tunneling approach to quantum cosmology and comment on the alternative approaches. In the second part, I discuss the relation between quantum cosmology and eternal inflation. In ... More

Quantum Cosmology and the Constants of NatureDec 15 1995In models where the constants of Nature can take more than one set of values, the cosmological wave function $\psi$ describes an ensemble of universes with different values of the constants. The probability distribution for the constants can be determined ... More

Predictions from Quantum CosmologyJul 07 1995Nov 20 1995After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt equation, boundary conditions, interpretation of $\psi$), I discuss how these ideas can be tested observationally. Observational predictions differ for different choices of boundary ... More

Extended Deligne-Lusztig varieties for general and special linear groupsNov 24 2009Sep 30 2010We give a generalisation of Deligne-Lusztig varieties for general and special linear groups over finite quotients of the ring of integers in a non-archimedean local field. Previously, a generalisation was given by Lusztig by attaching certain varieties ... More

Representations of reductive groups over finite rings and extended Deligne-Lusztig varietiesMar 28 2004In a previous paper it was shown that a certain family of varieties suggested by Lusztig, is not enough to construct all irreducible complex representations of reductive groups over finite rings coming from the ring of integers in a local field, modulo ... More

Infinitesimal Hecke algebras of so_NJun 06 2013Aug 05 2014In this article we classify all infinitesimal Hecke algebras of so_N. We establish isomorphism of their universal versions and the W-algebras of so_{N+2m+1} with a 1-block nilpotent element of the Jordan type (1,...,1,2m+1). This should be considered ... More

Remarks on a Categorical Definition of Degeneration in Triangulated CategoriesJun 08 2015This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety and isomorphism ... More

QCD Sum Rules for Heavy Flavour PhysicsAug 24 2001Uses of QCD sum rules for heavy flavoured hadrons are discussed. "Standard" applications such as the determination of the $b$, $c$ quark masses, the calculation of $f_B$, $f_D$ and of the heavy-to-light form factors are overviewed. Furthermore, a new ... More

CalcHEP 2.3: MSSM, structure functions, event generation, batchs, and generation of matrix elements for other packagesDec 14 2004Oct 21 2009CalcHEP is a package for computation of Feynman diagrams and integration over multi-particle phase space. The main idea prescribed into CalcHEP is to make available passing on from Lagrangians to the final distributions effectively with a high level of ... More

Space functions of groupsOct 31 2010Dec 09 2010We consider space functions $s(n)$ of finitely presented groups $G =< A\mid R> .$ (These functions have a natural geometric analog.) To define $s(n)$ we start with a word $w$ over $A$ of length at most $n$ equal to 1 in $G$ and use relations from $R$ ... More

Tilting bundles via the Frobenius morphismApr 08 2009Jan 24 2010We show how to construct tilting bundles for a class of smooth projective varieties using characteristic $p$ methods. Given such a variety $X$, reduce it modulo a prime number and consider the direct image of the structure sheaf under the Frobenius morphism. ... More

Volumes of hyperbolic manifolds and mixed Tate motivesJan 19 1996Jan 24 1996Two different constructions of an invariant of an odd dimensional hyperbolic manifold in the K-group $K_{2n-1}(\bar \Bbb Q)\otimes \Bbb Q$ are given. The volume of the manifold is equal to the value of the Borel regulator on that element. The scissor ... More

Lagrangian Formalism Over Graded AlgebrasJul 06 1994Apr 01 1995This paper provides a description of an algebraic setting for the Lagrangian formalism over graded algebras and is intended as the necessary first step towards the noncommutative C-spectral sequence (variational bicomplex). A noncommutative version of ... More

Function Weighted Metric Discovery for Unreliable FunctionsOct 31 2016We consider building a function adapted diffusion operator high dimensional data $X$ when the function $F$ can only be evaluated on large subsets of the data, and possibly only depends on a small subset of the features. Our method breaks $X$ up into hierarchical ... More

On the equivariant K-homology of PSL\_2 of the imaginary quadratic integersJun 12 2015Jan 21 2016We establish formulae for the part due to torsion of the equivariant K-homology of all the Bianchi groups (PSL\_2 of the imaginary quadratic integers), in terms of elementary number-theoretic quantities. To achieve this, we introduce a novel technique ... More

Constructive description of Hardy-Sobolev spaces in $\mathbb{C}^n$Jan 13 2016In this paper we study the polynomial approximations in Hardy-Sobolev spaces on for convex domains. We use the method of pseudoanalytical continuation to obtain the characterization of these spaces in terms of polynomial approximations.

Tensor Lagrangians, Lagrangians equivalent to the Hamilton-Jacobi equation and relativistic dynamicsJan 17 2016We deal with Lagrangians which are not the standard scalar ones. We present a short review of tensor Lagrangians, which generate massless free fields and the Dirac field, as well as vector and pseudovector Lagrangians for the electric and magnetic fields ... More

What is a Young tableau?Nov 02 2006Young tableaux are classical combinatorial objects playing recurring and varied roles in representation theory, algebraic geometry and commutative algebra. This article is a short exposition on Young tableaux, written for the "WHAT IS...?" series of the ... More

Efficient Kernel Convolution for Smooth Surfaces without Edge EffectsJan 13 2016One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be processed in ... More

Essén Lectures: Representation Theory of Symmetric GroupsJan 23 2014These are partial lecture notes from the fifteen Ess\'en Lectures for graduate students at Uppsala University given (in four days!) in June 2013.

Continuous time Ehrenfest process in term structure modellingMar 29 2010In this paper, a finite-state mean-reverting model for the short-rate, based on the continuous time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and the special symmetric cases. ... More

Edge spin accumulation in 2D electron and hole systems in a quasi-ballistic regimeJan 29 2014We consider a two-dimensional structure with spin-orbit-related splitting of the electron (hole) spectrum and calculate the edge spin density which appears due to the intrinsic mechanism of spin-orbit interaction in the presence of a charge current through ... More