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Fate of the $η'$ in the Quark Gluon PlasmaMar 13 2019In this paper we study the $\eta'$ mass in $N_f=2+1+1$ lattice QCD simulations at finite temperature. Results are obtained from the analysis of the gluonic defined topological charge density correlator after gradient flow. Our results favour a small dip ... More

Chiral observables and topology in hot QCD with two families of quarksMay 15 2018Nov 08 2018We present results on QCD with four dynamical flavors in the temperature range $150$ MeV $\lesssim T \lesssim 500$ MeV. We have performed lattice simulations with Wilson fermions at maximal twist and measured Polyakov loop, chiral condensate and disconnected ... More

Topology (and axion's properties) from lattice QCD with a dynamical charmMay 04 2017We present results on QCD with four dynamical flavors in the temperature range $0.9 \lesssim T/T_c \lesssim 2$. We have performed lattice simulations with Wilson fermions at maximal twist and measured the topological charge with gluonic and fermionic ... More

Pair ${(bc)}$ diquarks production in high energy proton--proton collisionsJun 13 2016The cross section of pair double heavy diquark production process $pp\to(bc)+(\bar b \bar c)+X$ is calculated in the leading order of gluonic fusion channel with all four possible color and spin combinations $[^1S_0]_{\bar3}$, $[^1S_0]_{6}$, $[^3S_1]_{\bar3}$, ... More

Penetration of Josephson vortices and measurement of the c-axis penetration depth in $Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}$: Interplay of Josephson coupling, surface barrier and defectsJun 23 2000The first penetration field H_{J}(T) of Josephson vortices is measured through the onset of microwave absorption in the locked state, in slightly overdoped $\rm{Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}}$ single crystals (T_{c} ~ 84 K). The magnitude of H_{J}(T) ... More

c-axis penetration depth in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ single crystals measured by ac-susceptibility and cavity perturbation techniqueJun 23 2000The $c$-axis penetration depth $\Delta\lambda_c$ in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) single crystals as a function of temperature has been determined using two techniques, namely, measurements of the ac-susceptibility at a frequency of 100 kHz ... More

Quantum Group as Semi-infinite CohomologyDec 09 2008Apr 15 2010We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is constructed from the ... More

Normal state resistivity of Ba$_{1-x}$K$_x$Fe$_2$As$_2$: evidence for multiband strong-coupling behaviorNov 08 2010Jul 12 2011We present theoretical analysis of the normal state resistivity in multiband superconductors in the framework of Eliashberg theory. The results are compared with measurements of the temperature dependence of normal state resistivity of high-purity Ba$_{0.68}$K$_{0.32}$Fe$_{2}$As$_{2}$ ... More

Dynamics of spatially localized states in transitional plane Couette flowJun 26 2018Jan 16 2019Unsteady spatially localized states such as puffs, slugs or spots play an important role in transition to turbulence. In plane Couette flow, steady versions of these states are found on two intertwined solution branches describing homoclinic snaking (Schneider ... More

On the Riesz basis property of root vectors system for $2 \times 2$ Dirac type operatorsApr 20 2015Apr 26 2015The paper is concerned with the Riesz basis property of a boundary value problem associated in $L^2[0,1] \otimes \mathbb{C}^2$ with the following $2 \times 2$ Dirac type equation $$ L y = -i B^{-1} y' + Q(x) y = \lambda y, \quad B = \begin{pmatrix} b_1 ... More

Completeness property of one-dimensional perturbations of normal and spectral operators generated by first order systemsJul 14 2018The paper is concerned with completeness property of rank one perturbations of unperturbed operators generated by special boundary value problems (BVP) for the following $2 \times 2$ system \begin{equation} L y = -i B^{-1} y' + Q(x) y = \lambda y , \quad ... More

Microwave surface impedance anisotropy of YBa$_2$Cu$_3$O$_x$ single crystals with different oxygen contentFeb 25 2003The linear microwave response of ultra high-quality YBa$_2$Cu$_3$O$_x$ single crystals grown in BaZrO$_3$ crucibles is measured at 9.4 GHz in rf magnetic fields parallel and perpendicular to the $ab$-plane in the temperature range 5$\leq T\leq 200$ K. ... More

On the stability of redundancy modelsMar 11 2019We investigate the stability condition of redundancy-$d$ multi-server systems. Each server has its own queue and implements popular scheduling disciplines such as First-Come-First-Serve (FCFS), Processor Sharing (PS), and Random Order of Service (ROS). ... More

Quantum K-theory of Quiver Varieties and Many-Body SystemsMay 30 2017May 11 2018We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic ... More

Baxter Q-operator from quantum K-theoryDec 27 2016Jan 16 2019We define and study the quantum equivariant $K$-theory of cotangent bundles over Grassmannians. For every tautological bundle in the $K$-theory we define its one-parametric deformation, referred to as quantum tautological bundle. We prove that the spectrum ... More

Relativistic corrections to double charmonium production in high energy proton-proton interactionJul 13 2012On the basis of pertubative QCD and the relativistic quark model we calculate relativistic corrections to the process of pair $J/\psi$ production in proton-proton collisions at LHC energy $\sqrt S=7$ TeV. Relativistic terms in the production amplitude ... More

Pair double heavy diquark production in high energy proton-proton collisionsMay 05 2014Oct 21 2014On the basis of perturbative QCD and relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of double heavy diquarks. Relativistic factors in the production amplitude connected with the relative ... More

Relativistic corrections to η_c-pair production in high energy proton-proton collisionsFeb 27 2013On the basis of perturbative QCD and the relativistic quark model we calculate relativistic corrections to the double $\eta_c$ meson production in proton-proton interactions at LHC energies. Relativistic terms in the production amplitude connected with ... More

Relativistic description of the double P-wave charmonium production in e^+e^- annihilationJun 14 2011Aug 10 2011On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of P-wave charmonium states. Relativistic factors in the production amplitude connected with ... More

Fluctuations of the partition function in the GREM with external fieldMay 10 2008We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters. We find that ... More

On Ramond DecorationsSep 19 2017We impose constraints on the odd coordinates of super Teichm\"uller space in the uniformization picture for the monodromies around Ramond punctures, thus reducing the overall odd dimension to be compatible with that of the moduli spaces of super Riemann ... More

Reconstructing the gluonApr 03 2018Nov 07 2018We reconstruct the gluon spectral function in Landau gauge QCD from numerical data for the gluon propagator. The reconstruction relies on two novel ingredients: Firstly we derive analytically the low frequency asymptotics of the spectral function. Secondly ... More

$(SL(N),q)$-opers, the $q$-Langlands correspondence, and quantum/classical dualityNov 25 2018Dec 16 2018A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper, we describe ... More

Anisotropy of microwave conductivity of YBaCuO in superconducting and normal states: Crossover 3D-2DJun 06 2003Imaginary part of the microwave conductivity \sigma''(T<T_c) and the resistivity \rho(T)=1/\sigma(T>T_c) along (\sigma_{ab}'' and \rho_{ab}) and perpendicular to (\sigma_c'' and \rho_c) cuprate ab-planes of YBa_2Cu_3O_{7-x} crystal were measured in the ... More

Relativistic corrections to the pair double heavy diquark production in e^+e^- annihilationAug 19 2013Aug 23 2013On the basis of perturbative QCD and relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of double heavy diquarks. Relativistic factors in the production amplitude connected with the relative ... More

Distributed recovery of jointly sparse signals under communication constraintsNov 08 2016The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed measurements, and ... More

Microwave Response of V3Si Single Crystals: Evidence for Two-Gap SuperconductivitySep 09 2005The investigation of the temperature dependences of microwave surface impedance and complex conductivity of V3Si single crystals with different stoichiometry allowed to observe a number of peculiarities which are in remarkable contradiction with single-gap ... 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.

Optimal Prediction of Stiff Oscillatory MechanicsJan 18 2000We consider many-body problems in classical mechanics where a wide range of time scales limits what can be computed. We apply the method of optimal prediction to obtain equations which are easier to solve numerically. We demonstrate by examples that optimal ... More

A Categorical Construction of Bachmann-Howard Fixed PointsSep 18 2018Sep 19 2018Peter Aczel has given a categorical construction for fixed points of normal functors, i.e. dilators which preserve initial segments. For a general dilator $X\mapsto T_X$ we cannot expect to obtain a well-founded fixed point, as the order type of $T_X$ ... More

$Π^1_1$-Comprehension as a Well-Ordering PrincipleSep 18 2018Sep 19 2018A dilator is a particularly uniform transformation $X\mapsto T_X$ of linear orders that preserves well-foundedness. We say that $X$ is a Bachmann-Howard fixed point of $T$ if there is an almost order preserving collapsing function $\vartheta:T_X\rightarrow ... 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

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.

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

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.

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

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

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

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

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

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

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

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

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

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

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

Steady-state analysis of the Join the Shortest Queue model in the Halfin-Whitt regimeJan 16 2018This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently, Eschenfeldt & Gamarnik ... More

Superfluid density in the underdoped YBa_2Cu_3O_{7-x}: Evidence for d-density wave order of pseudogapDec 22 2003The investigation of the penetration depth \lambda_{ab}(T,p) in YBa_2Cu_3O_{7-x} crystals allowed to observe the following features of the superfluid density n_s(T,p)\propto \lambda_{ab}^{-2}(T,p) as a function of temperature T<Tc/2 and carrier concentration ... More

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.

Fourier expansion along geodesicsJul 11 2006Sep 01 2017For an eigenfunction of the Laplacian on a hyperbolic Riemann surface, the coefficients of the Fourier expansion are described as intertwining functionals. All intertwiners are classified. A refined growth estimate for the coefficients is given and a ... More

SLE martingales in coset conformal field theoryMay 28 2012Aug 08 2012Scharmm-Loewner evolution (SLE) and conformal field theory (CFT) are popular and widely used instruments to study critical behavior of two-dimensional models, but they use different objects. While SLE has natural connection with lattice models and is ... More

Duality in a stability problem for some functionals arising in interpolation theoryFeb 22 2019By using duality, it is shown that there exist near-minimizers for the distance functionals for the couple $(L^\infty, L^p)$, $1<p<\infty$, that are stable under the action of singular integral operators.

Computable Aspects of the Bachmann-Howard PrincipleSep 18 2018Sep 19 2018We have previously established that $\Pi^1_1$-comprehension is equivalent to the statement that every dilator has a well-founded Bachmann-Howard fixed point, over $\mathbf{ATR_0}$. In the present paper we show that the base theory can be lowered to $\mathbf{RCA_0}$. ... More

A Note on Iterated Consistency and Infinite ProofsSep 05 2017Jul 16 2018Schmerl and Beklemishev's work on iterated reflection achieves two aims: It introduces the important notion of $\Pi^0_1$-ordinal, characterizing the $\Pi^0_1$-theorems of a theory in terms of transfinite iterations of consistency; and it provides an innovative ... More

Minimax and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations for Time-Delay SystemsJan 15 2019The paper deals with a Bolza optimal control problem for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional in this problem, the ... More

Alexandrov meets Lott--Villani--SturmMar 30 2010Apr 10 2015Here I show compatibility of two definition of generalized curvature bounds --- the lower bound for sectional curvature in the sense of Alexandrov and lower bound for Ricci curvature in the sense of Lott--Villani--Sturm.

Space of isospectral periodic tridiagonal matricesMar 30 2018Dec 14 2018A periodic tridiagonal matrix is a tridiagonal matrix with additional two entries at the corners. We study the space $X_{n,\lambda}$ of Hermitian periodic tridiagonal $n\times n$-matrices with a fixed simple spectrum $\lambda$. Using the discretized Shr\"{o}dinger ... More

A note on relative equilibria of multidimensional rigid bodyFeb 18 2012It is well known that a rotation of a free generic three-dimensional rigid body is stationary if and only if it is a rotation around one of three principal axes of inertia. As it was noted by many authors, the analogous result is true for a multidimensional ... More

Toric manifolds over 3-polytopesJul 12 2016Dec 01 2016In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes, that do not ... More

Factorizations of Rational Matrix Functions with Application to Discrete Isomonodromic Transformations and Difference Painlevé EquationsApr 13 2009Feb 13 2013We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given ... More

Expanders are order diameter non-hyperbolicJan 30 2015Feb 25 2015We show that expander graphs must have Gromov-hyperbolicity at least proportional to their diameter, with a constant of proportionality depending only on the expansion constant and maximal degree. In other words, expanders contain geodesic triangles which ... More

Dimensions of multi-fan algebrasJul 13 2016Dec 01 2016Given an arbitrary non-zero simplicial cycle and a generic vector coloring of its vertices, there is a way to produce a graded Poincare duality algebra associated with these data. The procedure relies on the theory of volume polynomials and multi-fans. ... More

Pseudogap in the microwave response of YBa_2Cu_3O_{7-x}Dec 23 2003The in-plane and out-of-plane surface impedance and microwave conductivity components of one and the same YBa_2Cu_3O_{7-x} (0.07\le x\le 0.47) single crystal are determined in the wide ranges of temperature T and carrier concentration p in CuO_2 planes. ... 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.

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

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

Definitive Computation of Bernstein-Sato PolynomialsMar 24 2000Let n and d be positive integers, let k be a field and let P(n,d;k) be the space of the polynomials in n variables of degree at most d with coefficients in k. Let B(n,d) be the set of the Bernstein-Sato polynomials of all polynomials in P(n,d;k) as k ... More

Puzzles in geometry that I know and loveJun 01 2009Oct 06 2018Problems for the graduate students who want to improve problem solving skills in geometry. Every problem has a short elegant solution --- this gives a hint which was not available when it was solved for the first time.

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

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 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

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

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

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.

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

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

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

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

Locally standard torus actions and sheaves over Buchsbaum posetsJan 20 2015Feb 24 2015We consider a sheaf of exterior algebras on a simplicial poset $S$ and introduce a notion of homological characteristic function. Two natural objects are associated with these data: a graded sheaf $\mathcal{I}$ and a graded cosheaf $\widehat{\Pi}$. When ... 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

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

The first detections of the key prebiotic molecule PO in star-forming regionsAug 23 2018Phosphorus is a crucial element in prebiotic chemistry, especially the P$-$O bond, which is key for the formation of the backbone of the deoxyribonucleic acid. So far, PO had only been detected towards the envelope of evolved stars, and never towards ... More