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Eliminating dual spacesMar 06 2015Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing dual spaces ... More

Numerical algorithms for detecting embedded componentsMay 30 2014Jan 14 2016We produce algorithms to detect whether a complex affine variety computed and presented numerically by the machinery of numerical algebraic geometry corresponds to an associated component of a polynomial ideal.

Entropy and lowest eigenvalue on evolving manifoldsMay 02 2013Aug 20 2014In this note we determine the first two derivatives of the classical Boltzmann-Shannon entropy of the conjugate heat equation on general evolving manifolds. Based on the second derivative of the Boltzmann-Shannon entropy, we construct Perelman's F and ... More

An entropy formula for the heat equation on manifolds with time-dependent metric, application to ancient solutionsMay 02 2013We introduce a new entropy functional for nonnegative solutions of the heat equation on a manifold with time-dependent Riemannian metric. Under certain integral assumptions, we show that this entropy is non-decreasing, and moreover convex if the metric ... More

Martingales on manifolds with time-dependent connectionMay 02 2013We define martingales on manifolds with time-dependent connection, extending in this way the theory of stochastic processes on manifolds with time-changing geometry initiated by Arnaudon, Coulibaly and Thalmaier (2008). We show that some, but not all ... More

A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metricOct 07 2013Mar 26 2014We first prove stochastic representation formulae for space-time harmonic mappings defined on manifolds with evolving Riemannian metric. We then apply these formulae to derive Liouville type theorems under appropriate curvature conditions. Space-time ... More

New developments in the quantization of supersymmetric solitons (kinks, vortices and monopoles)Apr 28 2004We discuss the one-loop quantum corrections to the mass M and central charge Z of supersymmetric solitons: the kink, the vortex and the monopole. Contrary to previous expectations and published results, in each of these cases there are nonvanishing quantum ... More

Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface termsJan 05 2006Apr 18 2006We calculate the one-loop quantum corrections to the mass and central charge of N=2 and N=4 supersymmetric monopoles in 3+1 dimensions. The corrections to the N=2 central charge are finite and due to an anomaly in the conformal central charge current, ... More

Hilbert series of symmetric ideals in infinite polynomial rings via formal languagesJun 25 2016Let $R$ be the polynomial ring $K[x_{i,j}]$ where $1 \le i \le r$ and $j \in \mathbb{N}$, and let $I$ be an ideal of $R$ stable under the natural action of the infinite symmetric group $S_{\infty}$. Nagel--R\"omer recently defined a Hilbert series $H_I(s,t)$ ... More

Equivariant lattice generators and Markov basesJan 02 2014May 09 2014It has been shown recently that monomial maps in a large class respecting the action of the infinite symmetric group have, up to symmetry, finitely generated kernels. We study the simplest nontrivial family in this class: the maps given by a single monomial. ... More

Polaronic inter-acceptor hopping transport in intrinsically doped nickel oxideMay 09 2019In this work, we revisit the issue of the nature of electronic transport in nickel oxide (NiO) and show that the widely used model of free small polaron hopping, initially raised to characterize transport in high-purity samples, is not appropriate for ... More

Noetherianity for infinite-dimensional toric varietiesJun 04 2013Jun 16 2015We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our class includes many important examples where Noetherianity ... More

High-fidelity entanglement swapping with fully independent sourcesSep 23 2008Jan 23 2009Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. This feature makes it an integral constituent of quantum repeaters. Here, we demonstrate entanglement swapping with time-synchronized ... More

Nonlocal probes of thermalization in holographic quenches with spectral methodsOct 22 2014Apr 22 2015We describe the application of pseudo-spectral methods to problems of holographic thermal quenches of relevant couplings in strongly coupled gauge theories. We focus on quenches of a fermionic mass term in a strongly coupled N=4 supersymmetric Yang-Mills ... More

Edge-Disjoint Node-Independent Spanning Trees in Dense Gaussian NetworksJan 26 2016Jan 27 2016Independent trees are used in building secure and/or fault-tolerant network communication protocols. They have been investigated for different network topologies including tori. Dense Gaussian networks are potential alternatives for 2-dimensional tori. ... More

Automated Search for new Quantum ExperimentsSep 09 2015Feb 20 2016Quantum mechanics predicts a number of at first sight counterintuitive phenomena. It is therefore a question whether our intuition is the best way to find new experiments. Here we report the development of the computer algorithm Melvin which is able to ... More

Twisted Photons: New Quantum Perspectives in High DimensionsAug 21 2017Quantum information science and quantum information technology have seen a virtual explosion world-wide. It is all based on the observation that fundamental quantum phenomena on the individual particle or system-level lead to completely novel ways of ... More

Improving Variational Quantum Optimization using CVaRJul 10 2019Hybrid quantum/classical variational algorithms can be implemented on noisy intermediate-scale quantum computers and can be used to find solutions for combinatorial optimization problems. Approaches discussed in the literature minimize the expectation ... More

Unstable analogues of the Lichtenbaum-Quillen conjectureNov 07 2012This survey is mostly concerned with unstable analogues of the Lichtenbaum-Quillen Conjecture. The Lichtenbaum-Quillen Conjecture (now implied by the Voevodsky-Rost Theorem) attempts to describe the algebraic K-theory of rings of integers in number fields ... More

Quantum entanglement of angular momentum states with quantum numbers up to 10010Jul 04 2016Photons with a twisted phase front carry a quantized amount of orbital angular momentum (OAM) and have become important in various fields of optics, such as quantum and classical information science or optical tweezers. Because no upper limit on the OAM ... More

Crossed crystal scheme for fs-pulsed entangled photon generation in ppKTPApr 28 2014We demonstrate a novel scheme for femto-second pulsed spontaneous parametric down-conversion in periodically poled KTP crystals. Our scheme is based on a crossed crystal configuration with collinear quasi-phase-matching. The non-degenerate photon pairs ... More

Quantum Entanglement of High Angular MomentaJul 10 2012Jun 06 2014Single photons with helical phase structures may carry a quantized amount of orbital angular momentum (OAM) and their entanglement is important for quantum information science and fundamental tests of quantum theory. Because there is no theoretical upper ... More

Divergence of an orbital-angular-momentum-carrying beam upon propagationOct 31 2014There is recent interest in the use of light beams carrying orbital angular momentum (OAM) for creating multiple channels within free-space optical communication systems. One limiting issue is that, for a given beam size at the transmitter, the beam divergence ... More

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

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

Molecular motors govern liquid-like ordering and fusion dynamics of bacterial coloniesFeb 06 2019Bacteria can adjust the structure of colonies and biofilms to enhance their survival rate under external stress. Here, we explore the link between bacterial interaction forces and colony structure. We show that the activity of extracellular pilus motors ... More

Design considerations and sensitivity estimates for an acoustic neutrino detectorSep 15 2005We present a Monte Carlo study of an underwater neutrino telescope based on the detection of acoustic signals generated by neutrino induced cascades. This provides a promising approach to instrument large detector volumes needed to detect the small flux ... More

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

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

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

Face rings of cycles, associahedra, and standard Young tableauxMar 20 2015Aug 22 2016We show that J_n, the Stanley-Reisner ideal of the n-cycle, has a free resolution supported on the (n-3)-dimensional simplicial associahedron A_n. This resolution is not minimal for n > 5; in this case the Betti numbers of J_n are strictly smaller than ... More

Topological model for h"-vectors of simplicial manifoldsFeb 19 2015Any manifold with boundary gives rise to a Poincare duality algebra in a natural way. Given a simplicial poset $S$ whose geometric realization is a closed orientable homology manifold, and a characteristic function, we construct a manifold with boundary ... More

K-stability of relative flag varietiesJul 29 2013Nov 10 2015We generalise partial results about the Yau-Tian-Donaldson correspondence on ruled manifolds to bundles whose fibre is a classical flag variety. This is done using Chern class computations involving the combinatorics of Schur functors. The strongest results ... More

A prime geodesic theorem for higher rank II: singular geodesicsOct 26 2004A prime geodesic theorem for singular geodesics in a locally symmetric space is proved. As an application, an asymptotic formula for units in number fields is given.

Torus actions of complexity one and their local propertiesFeb 24 2018We consider an effective action of a compact (n-1)-torus on a smooth 2n-manifold with isolated fixed points. We prove that under certain conditions the orbit space is a closed topological manifold. In particular, this holds for certain torus actions with ... More

Numerical Algebraic Geometry for Macaulay2Nov 09 2009May 22 2011Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic geometry. We present ... More

Irreducible Ulrich bundles on isotropic GrassmanniansApr 06 2016May 13 2016We classify irreducible equivariant Ulrich vector bundles on isotropic Grassmannians.

Area minimizing polyhedral surfaces are saddleMar 15 2014May 20 2014We show that area minimizing polyhedral surfaces are saddle.

Spherical parking functions, uprooted trees, and yet another way to count $n^n$Jun 12 2018Parking functions are a widely studied class of combinatorial objects, with connections to several branches of mathematics. The number of parking functions of length $n$ is given by $(n+1)^{n-1}$, which by Cayley's formula is equal to the number of spanning ... More

One-skeleta of $G$-parking function ideals: resolutions and standard monomialsAug 15 2017Jun 15 2018Given a graph $G$, the $G$-parking function ideal $M_G$ is an artinian monomial ideal in the polynomial ring $S$ with the property that a linear basis for $S/M_G$ is provided by the set of $G$-parking functions. It follows that the dimension of $S/M_G$ ... More

A search for an optimal start system for numerical homotopy continuationMay 22 2011We use our recent implementation of a certified homotopy tracking algorithm to search for start systems that minimize the average complexity of finding all roots of a regular system of polynomial equations. While finding optimal start systems is a hard ... More

Quadratic Algebras arising from Hopf operads generated by a single elementJul 12 2019The operads of Poisson and Gerstenhaber algebras are generated by a single binary element if we consider them as Hopf operads (i.e. as operads in the category of cocommutative coalgebras). In this note we discuss in details the Hopf operads generated ... More

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

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

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

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

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

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

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

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

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

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

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

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

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

Reduced zeta functions of Lie algebrasOct 01 2007Apr 12 2010We define reduced zeta functions of Lie algebras, which can be derived from motivic zeta functions using the Euler characteristic. We show that reduced zeta functions of Lie algebras possessing a suitably well-behaved basis are easy to analyse. We prove ... More

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

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

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

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

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

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

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

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

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

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

Holomorphic torsion for Hermitian locally symmetric spacesMar 05 1996Sep 27 1996The holomorphic torsion of a compact locally symmetric manifold is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.

A Lefschetz formula for flowsDec 01 1995For the geodesic flow of an odd dimensional hyperbolic manifold we prove a Lefschetz type formula. The local terms are Fuller indices of the closed orbits. The global "Frobenius operator" is the generator of the flow and its action on tangential cohomology. ... More

Schemes over $F_1$Apr 08 2004Jul 26 2006Using the approach of Kurokawa, Ochiai, and Wakayama to 'absolute mathematics' we define a corresponding notion of schemes.

Euler-Poincar'e functionsJan 24 2002A new construction of Euler-Poincar\'e functions for real reductive groups is given. This construction also works for non-connected groups and representations that do not lift.

Differential operators on equivariant vector bundles over symmetric spacesMay 19 2000Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with respect to the larger ... More

On the growth of modular symbolsFeb 09 2007It is shown that the modular symbol of a cusp form of weight two has logarithmic growth.

Lefschetz formulae for p-adic groupsMay 19 2005Lefschetz formulae for torus actions on p-adic groups are proven.

Mellin transforms of p-adic Whittaker functionsSep 18 2001It is shown that Mellin transforms of p-adic Whittaker functions exist for generic characters. For good choices of vectors they are rational functions. For class one vectors they can be calculated explicitly. It turns out that they are automorphic L-factors ... More

Pentagrams, inscribed polygons, and Prym varietiesJul 13 2016Sep 19 2016The pentagram map is a discrete integrable system on the moduli space of planar polygons. The corresponding first integrals are so-called monodromy invariants $E_1, O_1, E_2, O_2,\dots$ By analyzing the combinatorics of these invariants, R.Schwartz and ... More

Measurable versions of the Lovász Local Lemma and measurable graph coloringsApr 25 2016Aug 07 2016In this paper we investigate the extent to which the Lov\'asz Local Lemma (an important tool in probabilistic combinatorics) can be adapted for the measurable setting. In most applications, the Lov\'asz Local Lemma is used to produce a function $f \colon ... More

Trident pair production in strong laser pulsesNov 17 2010Jan 14 2011We calculate the trident pair production amplitude in a strong laser background. We allow for finite pulse duration, while still treating the laser fields nonperturbatively in strong-field QED. Our approach reveals explicitly the individual contributions ... More

Weak-coupling techniques for the thermodynamics of the quark-gluon plasmaApr 04 2005Apr 08 2005We describe some of the recent progress in the calculation of thermodynamic quantities in QCD at high temperatures and densities by weak-coupling techniques and extrapolation to realistic coupling strength. We argue that a (mostly) weakly coupled quark-gluon ... More

Comment on ``Damping of energetic gluons and quarks in high-temperature QCD''Mar 16 1992Burgess and Marini have recently pointed out that the leading contribution to the damping rate of energetic gluons and quarks in the QCD plasma, given by $\gamma=c g^2\ln(1/g)T$, can be obtained by simple arguments obviating the need of a fully resummed ... More

HTL-resummed thermodynamics of hot and dense QCD: An updateJan 17 2003Apr 04 2003We review the proposal to resum the physics of hard thermal loops in the thermodynamics of the quark-gluon plasma through nonperturbative expressions for entropy and density obtained from a Phi-derivable two-loop approximation. A comparison with the recently ... More

Profiles of spectral lines from failed and decelerated winds from neutron stars and black holesFeb 10 2011We calculate profiles of spectral lines from an extended outflow from the compact object (a black hole or a neutron star). We assume that the bulk velocity of the flow increases during a short phase of acceleration and then rapidly decreases forming a ... More

Combinatorics of Matrix Factorizations and Integrable SystemsFeb 13 2013We study relations between the eigenvectors of rational matrix functions on the Riemann sphere. Our main result is that for a subclass of functions that are products of two elementary blocks it is possible to represent these relations in a combinatorial-geometric ... More

Intersections of conjugate solvable subgroups in classical groups of Lie typeMar 01 2017In this paper we obtain a partial solution to Problem 17.41 from "Kourovka notebook": if $S$ is a solvable subgroup of a finite group $G$ with trivial solvable radical, do there exist five conjugate of $S$ with trivial intersection. We consider the case, ... More

The universality of Hom complexesFeb 16 2007It is shown that if T is a connected nontrivial graph and X is an arbitrary finite simplicial complex, then there is a graph G such that the complex Hom(T,G) is homotopy equivalent to X. The proof is constructive, and uses a nerve lemma. Along the way ... More

The problem of Buchstaber number and its combinatorial aspectsMar 02 2010For any simplicial complex on m vertices a moment-angle complex Z_K embedded in C^m can be defined. There is a canonical action of a torus T^m on Z_K, but this action fails to be free. The Buchstaber number is the maximal integer s(K) for which there ... More

Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebrasJul 23 2011Aug 08 2012In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry. The most important ... More

Infinite energy solutions for critical wave equation with fractional damping in unbounded domainsNov 14 2015This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of $\mathbb{R}^3$ with fractional damping of the form $(-\Delta_x+1)^\frac{1}{2}\partial_t u$. The work extends previously known results for bounded ... More

Integrating by Spheres: Summary of Blaschke-Petkantschin FormulasApr 24 2019In some applications, like some areas in stochastic geometry, a convenient change of variables involves spheres. In this review we summarize formulas of Blaschke-Petkantschin type, that help to pass from integration over $k$-tuples of points in space ... More

Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentialsNov 01 2010Moduli spaces of Abelian and quadratic differentials are stratified by multiplicities of zeroes; connected components of the strata correspond to ergodic components of the Teichmuller geodesic flow. It is known that the strata are not necessarily connected; ... More

Exposed circuits, linear quotients, and chordal cluttersDec 19 2018Feb 25 2019A graph $G$ is said to be chordal if it has no induced cycles of length four or more. In a recent preprint Culbertson, Guralnik, and Stiller give a new characterization of chordal graphs in terms of sequences of what they call `edge-erasures'. We show ... More

Homology of torus spaces with acyclic proper faces of the orbit spaceMay 19 2014Let $X$ be 2n-dimensional compact manifold with a locally standard action of a compact torus. The orbit space $X/T$ is a manifold with corners. Suppose that all proper faces of $X/T$ are acyclic. In the paper we study the homological spectral sequence ... More

Predicative collapsing principlesJun 18 2019We show that arithmetical transfinite recursion is equivalent to a suitable formalization of the following: For every ordinal $\alpha$ there exists an ordinal $\beta$ such that $1+\beta\cdot(\beta+\alpha)$ (ordinal arithmetic) admits an almost order preserving ... More

Slow ReflectionJan 29 2016Jun 29 2017We describe a "slow" version of the hierarchy of uniform reflection principles over Peano Arithmetic ($\mathbf{PA}$). These principles are unprovable in Peano Arithmetic (even when extended by usual reflection principles of lower complexity) and introduce ... More

Bi-Lipschitz extension from boundaries of certain hyperbolic spacesDec 12 2011Tukia and Vaisala showed that every quasi-conformal map of $\R^n$ extends to a quasi-conformal self-map of $\R^{n+1}$. The restriction of the extended map to the upper half-space $\R^n \times \R^+$ is, in fact, bi-Lipschitz with respect to the hyperbolic ... More

$p$-adic quantum hyperenveloping algebra for $\mathfrak{sl}_{2}$Dec 16 2013Dec 26 2013We construct an example of quantum hyperenveloping algebra over discretely valued field for the Lie algebra $\mathfrak{sl}_{2}$.

Non-Elitist Genetic Algorithm as a Local Search MethodJul 12 2013Mar 28 2014Sufficient conditions are found under which the iterated non-elitist genetic algorithm with tournament selection first visits a local optimum in polynomially bounded time on average. It is shown that these conditions are satisfied on a class of problems ... More

Strichartz Inequalities for Lipschitz Metrics on Manifolds and Nonlinear Schrodinger Equation on DomainsDec 29 2005We prove wellposedness of the Cauchy problem for the nonlinear Schrodinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on ... More

On a conjecture of Kuznetsov and PolishchukMay 12 2015We prove a conjecture by A. Kuznetsov and A. Polishchuk on the existence of some particular full exceptional collections in bounded derived categories of coherent sheaves on Grassmannian varieties.

The first-order deviation of superpolynomial in an arbitrary representation from the special polynomialNov 19 2012Dec 29 2012Like all other knot polynomials, the superpolynomials should be defined in arbitrary representation R of the gauge group in (refined) Chern-Simons theory. However, not a single example is yet known of a superpolynomial beyond symmetric or antisymmetric ... More

Geometric zeta-functions of locally symmetric spacesNov 10 1995Apr 21 1997The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential ... More