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Open intersection numbers and free fieldsJun 21 2016Jul 05 2016A complete set of the Virasoro and W-constraints for the Kontsevich-Penner model, which conjecturally describes intersections on moduli spaces of open curves, was derived in our previous work. Here we show that these constraints can be described in terms ... More

Cut-and-join description of generalized Brezin-Gross-Witten modelAug 04 2016Aug 17 2016We investigate the Brezin-Gross-Witten model, a tau-function of the KdV hierarchy, and its natural one-parameter deformation, the generalized Brezin-Gross-Witten tau-function. In particular, we derive the Virasoro constraints, which completely specify ... More

Open intersection numbers, Kontsevich-Penner model and cut-and-join operatorsDec 11 2014Jun 22 2016We continue our investigation of the Kontsevich--Penner model, which describes intersection theory on moduli spaces both for open and closed curves. In particular, we show how Buryak's residue formula, which connects two generating functions of intersection ... More

The master T-operator for the Gaudin model and the KP hierarchyJun 05 2013Apr 14 2014Following the approach of [arXiv:1112.3310], we construct the master T -operator for the quantum Gaudin model with twisted boundary conditions and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. We also ... More

Free fermions and tau-functionsDec 25 2012Sep 24 2013We review the formalism of free fermions used for construction of tau-functions of classical integrable hierarchies and give a detailed derivation of group-like properties of the normally ordered exponents, transformations between different normal orderings, ... More

On a differential test of homeomorphism, found by N.V. EfimovOct 18 2010In the year 1968 N.V. Efimov has proven the following remarkable theorem: \textit{Let $f:\mathbb R^2\to\mathbb R^2\in C^1$ be such that $\det f'(x)<0$ for all $x\in\mathbb R^2$ and let there exist a function $a=a(x)>0$ and constants $C_1\geqslant 0$, ... More

A sufficient condition for a polyhedron to be rigidDec 16 2018Dec 26 2018We study oriented connected closed polyhedral surfaces with non-degenerate triangular faces in three-dimensional Euclidean space, calling them polyhedra for short. A polyhedron is called flexible if its spatial shape can be changed continuously by changing ... More

Black holes and higher depth mock modular formsAug 25 2018Oct 01 2018By enforcing invariance under S-duality in type IIB string theory compactified on a Calabi-Yau threefold, we derive modular properties of the generating function of BPS degeneracies of D4-D2-D0 black holes in type IIA string theory compactified on the ... More

Buryak-Okounkov formula for the n-point function and a new proof of the Witten conjectureFeb 08 2019We identify the formulas of Buryak and Okounkov for the n-point functions of the intersection numbers of psi-classes on the moduli spaces of curves. This allows us to combine the earlier known results and this one into a principally new proof of the famous ... More

Attractor flow trees, BPS indices and quiversApr 18 2018Inspired by the split attractor flow conjecture for multi-centered black hole solutions in N=2 supergravity, we propose a formula expressing the BPS index $\Omega(\gamma,z)$ in terms of `attractor indices' $\Omega_*(\gamma_i)$. The latter count BPS states ... More

Classical tau-function for quantum spin chainsDec 14 2011Jul 06 2012For an arbitrary generalized quantum integrable spin chain we introduce a "master T -operator" which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary space. We show ... More

Automating Fault Tolerance in High-Performance Computational Biological Jobs Using Multi-Agent ApproachesMar 03 2014Background: Large-scale biological jobs on high-performance computing systems require manual intervention if one or more computing cores on which they execute fail. This places not only a cost on the maintenance of the job, but also a cost on the time ... More

M-Theory of Matrix ModelsMay 17 2006Small M-theories unify various models of a given family in the same way as the M-theory unifies a variety of superstring models. We consider this idea in application to the family of eigenvalue matrix models: their M-theory unifies various branches of ... More

Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix ModelOct 12 2003Even though matrix model partition functions do not exhaust the entire set of tau-functions relevant for string theory, they seem to be elementary building blocks for many others and they seem to properly capture the fundamental symplicial nature of quantum ... More

Almost Hermitian 6-Manifolds RevisitedMar 08 2004Apr 26 2004A Theorem of Kirichenko states that the torsion 3-form of the characteristic connection of a nearly K\"ahler manifold is parallel. On the other side, any almost hermitian manifold of type $\mathrm{G}_1$ admits a unique connection with totally skew symmetric ... More

Spin foam model from canonical quantizationMay 26 2007Feb 22 2008We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found ... More

Reality conditions for Ashtekar gravity from Lorentz-covariant formulationOct 10 2005We show the equivalence of the Lorentz-covariant canonical formulation considered for the Immirzi parameter $\beta=i$ to the selfdual Ashtekar gravity. We also propose to deal with the reality conditions in terms of Dirac brackets derived from the covariant ... More

Continuous deformations of polyhedra that do not alter the dihedral anglesDec 19 2012Jan 03 2013We prove that, both in the hyperbolic and spherical 3-spaces, there exist nonconvex compact boundary-free polyhedral surfaces without selfintersections which admit nontrivial continuous deformations preserving all dihedral angles and study properties ... More

Hyper-Hermitian quaternionic Kaehler manifoldsMay 25 2001Oct 30 2001We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric hyper-Hermitian quaternionic ... More

Enumerative geometry, tau-functions and Heisenberg-Virasoro algebraApr 13 2014May 13 2015In this paper we establish relations between three enumerative geometry tau-functions, namely the Kontsevich-Witten, Hurwitz and Hodge tau-functions. The relations allow us to describe the tau-functions in terms of matrix integrals, Virasoro constraints ... More

2D String Theory as Normal Matrix ModelFeb 14 2003We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted ... More

The set of flexible nondegenerate polyhedra of a prescribed combinatorial structure is not always algebraicAug 17 2015We construct some example of a closed nondegenerate nonflexible polyhedron $P$ in Euclidean 3-space that is the limit of a sequence of nondegenerate flexible polyhedra each of which is combinatorially equivalent to $P$. This implies that the set of flexible ... More

Backgrounds of 2D string theory from matrix modelMar 21 2003In the Matrix Quantum Mechanical formulation of 2D string theory it is possible to introduce arbitrary tachyonic perturbations. In the case when the tachyonic momenta form a lattice, the theory is known to be integrable and, therefore, it can be used ... More

Higher dimensional flexible polyhedraJul 29 1999Sep 02 1999In the previous version of the paper it was announced that ``sphere homeomorphic flexible polyhedra (with self intersections) do really exist in n-dimensional Euclidean, Lobachevskij and spherical spaces for each $n\geq 3$.'' Now the paper has been withdrawn ... More

Around the A.D. Alexandrov's theorem on a characterization of a sphereDec 20 2012This is a survey paper on various results relates to the following theorem first proved by A.D. Alexandrov: \textit{Let $S$ be an analytic convex sphere-homeomorphic surface in $\mathbb R^3$ and let $k_1(\boldsymbol{x})\leqslant k_2(\boldsymbol{x})$ be ... More

Prime number logarithmic geometry on the planeApr 12 2002Feb 14 2003We found a regularity of the behavior of primes that allows to represent both prime and natural numbers as infinite matrices with a common formation rule of their rows. This regularity determines a new class of infinite cyclic groups that permit the proposition ... More

Non-Perturbative Effects in Matrix Models and D-branesJun 18 2003Aug 18 2003The large order growth of string perturbation theory in $c\le 1$ conformal field theory coupled to world sheet gravity implies the presence of $O(e^{-{1\over g_s}})$ non-perturbative effects, whose leading behavior can be calculated in the matrix model ... More

The Geometry of the Master Equation and Topological Quantum Field TheoryFeb 02 1995Feb 07 1995In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a $QP$-manifold, i.e. a super\m equipped with an odd vector field ... More

On weak holonomyMar 27 2004Jul 15 2004We prove that SU(n) (n > 2) and Sp(n)U(1) (n > 1) are the only connected Lie groups acting transitively and effectively on some sphere which can be weak holonomy groups of a Riemannian manifold without having to contain its holonomy group. In both cases ... More

Partition Functions of Matrix Models as the First Special Functions of String Theory. II. Kontsevich ModelNov 17 2008Dec 09 2008In arXiv:hep-th/0310113 we started a program of creating a reference-book on matrix-model tau-functions, the new generation of special functions, which are going to play an important role in string theory calculations. The main focus of that paper was ... More

The first acquaintance with the tensorNov 26 2013The main concepts of the theory of tensors are presented. The emphasis is on the basic notions of tensor algebra and practical skills in culculations involving the Kronecker delta and Levi-Civita symbol. Sixty routine exercises are included. The article ... More

Flexible polyhedra in the Minkowski 3-spaceNov 01 2001Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape ... More

Open intersection numbers, matrix models and MKP hierarchyOct 07 2014Mar 11 2015In this paper we conjecture that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a tau-function ... More

Algebra versus analysis in the theory of flexible polyhedraFeb 02 2009Jul 06 2010Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used ... More

Immirzi parameter and fermions with non-minimal couplingFeb 08 2008Jun 16 2008We clarify the role played by the Immirzi parameter in classical gravity coupled to fermions. Considering the general non-minimal coupling, we show that, although the torsion depends explicitly on the Immirzi parameter, in a suitable parametrization the ... More

Matrix Quantum Mechanics and Two-dimensional String Theory in Non-trivial BackgroundsNov 28 2003Dec 04 2003String theory is the most promising candidate for the theory unifying all interactions including gravity. It has an extremely difficult dynamics. Therefore, it is useful to study some its simplifications. One of them is non-critical string theory which ... More

The new vertices and canonical quantizationApr 13 2010Jun 25 2010We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the EPRL model leads to the appearance of the Ashtekar-Barbero connection, thus bringing this model even closer ... More

Simplicity and closure constraints in spin foam models of gravityFeb 23 2008Jul 17 2008We revise imposition of various constraints in spin foam models of 4-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on holonomies and together they must be inserted explicitly into the ... More

Sp(n)U(1)-connections with parallel totally skew-symmetric torsionNov 14 2003Jul 08 2004We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the manifold is locally isomorphic ... More

On the total mean curvature of non-rigid surfacesNov 29 2008Using Green's theorem we reduce the variation of the total mean curvature of a smooth surface in the Euclidean 3-space to a line integral of a special vector field and obtain the following well-known theorem as an immediate consequence: the total mean ... More

New manifestations of the Darboux's rotation and translation fields of a surfaceOct 27 2009We show how the rotation and translation fields of a surface, introduced by G. Darboux, may be used to obtain short proofs of a well-known theorem (that reads that the total mean curvature of a surface is stationary under an infinitesimal bending) and ... More

How many times can the volume of a convex polyhedron be increased by isometric deformations?Jul 22 2016We prove that the answer to the question of the title is `as many times as you want.' More precisely, given any constant $c>0$, we construct two oblique triangular bipyramids, $P$ and $Q$, such that $P$ is convex, $Q$ is nonconvex and intrinsically isometric ... More

The first eigenvalue of the Dirac operator on locally reducible Riemannian manifoldsFeb 25 2005We prove a lower estimate for the first eigenvalue of the Dirac operator on a compact locally reducible Riemannian spin manifold with positive scalar curvature. We determine also the universal covers of the manifolds on which the smallest possible eigenvalue ... More

Multiple D3-instantons and mock modular forms IIFeb 17 2017We analyze the modular properties of D3-brane instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In Part I, we found a necessary condition for the existence of an isometric action ... More

Multiple D3-instantons and mock modular forms IMay 19 2016Jul 18 2016We study D3-instanton corrections to the hypermultiplet moduli space in type IIB string theory compactified on a Calabi-Yau threefold. In a previous work, consistency of D3-instantons with S-duality was established at first order in the instanton expansion, ... More

Implicit Function Theorem for systems of polynomial equations with vanishing Jacobian and its application to flexible polyhedra and frameworksJun 19 2000We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient ... More

The Dehn invariants of the Bricard octahedraJan 20 2009We prove that the Dehn invariants of any Bricard octahedron remain constant during the flex and that the Strong Bellows Conjecture holds true for the Steffen flexible polyhedron.

Hilbert space structure of covariant loop quantum gravityJan 28 2002We investigate the Hilbert space in the Lorentz covariant approach to loop quantum gravity. We restrict ourselves to the space where all area operators are simultaneously diagonalizable, assuming that it exists. In this sector quantum states are realized ... More

Canonical structure of Tetrad Bimetric GravityAug 29 2013Nov 05 2013We perform the complete canonical analysis of the tetrad formulation of bimetric gravity and confirm that it is ghost-free describing the seven degrees of freedom of a massless and a massive gravitons. In particular, we find explicit expressions for secondary ... More

Twistor Approach to String Compactifications: a ReviewNov 12 2011May 09 2013We review a progress in obtaining the complete non-perturbative effective action of type II string theory compactified on a Calabi-Yau manifold. This problem is equivalent to understanding quantum corrections to the metric on the hypermultiplet moduli ... More

Quantum covariant c-mapFeb 26 2007Mar 23 2008We generalize the covariant c-map found in hep-th/0701214 including perturbative quantum corrections. We also perform explicitly the superconformal quotient from the hyperkahler cone obtained by the quantum c-map to the quaternion-Kahler space, which ... More

Hermitian spin surfaces with small eigenvalues of the Dolbeault operatorMar 03 2004We study the compact Hermitian spin surfaces with positive conformal scalar curvature on which the first eigenvalue of the Dolbeault operator of the spin structure is the smallest possible. We prove that such a surface is either a ruled surface or a Hopf ... More

An analytical approach to the Rational Simplex ProblemApr 28 2013May 08 2013In 1973, J. Cheeger and J. Simons raised the following question that still remains open and is known as the Rational Simplex Problem: Given a geodesic simplex in the spherical 3-space so that all of its interior dihedral angles are rational multiples ... More

An analogue of a van der Waerden's theorem and its application to two-distance preserving mappingsApr 15 2015Apr 17 2015The van der Waerden's theorem reads that an equilateral pentagon in Euclidean 3-space $\Bbb E^3$ with all diagonals of the same length is necessarily planar and its vertex set coincides with the vertex set of some convex regular pentagon. We prove the ... More

Indefinite theta series and generalized error functionsJun 17 2016Jul 12 2016Theta series for lattices with indefinite signature $(n_+,n_-)$ arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their modular properties are well understood in the Lorentzian case ($n_+=1$), but have ... More

Sobolev Institute of Mathematics Celebrates its Fiftieth AnniversaryFeb 12 2008This paper describes briefly history and current state of the Sobolev Institute of Mathematics, the biggest research mathematical institute of the Russian Academy of Sciences located east to Ural mountains.

Minkowski-type and Alexandrov-type theorems for polyhedral herissonsNov 19 2002Classical H.Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H.Minkowski uniqueness theorem due to A.D.Alexandrov are extended to a class of nonconvex ... More

c-map as c=1 stringJan 20 2012We show the existence of a duality between the c-map space describing the universal hypermultiplet at tree level and the matrix model description of two-dimensional string theory compactified at a self-dual radius and perturbed by a sine-Liouville potential. ... More

D-instantons and twistors: some exact resultsFeb 16 2009May 09 2013We present some results on instanton corrections to the hypermultiplet moduli space in Calabi-Yau compactifications of Type II string theories. Previously, using twistor methods, only a class of D-instantons (D2-instantons wrapping A-cycles) was incorporated ... More

D-branes and complex curves in c=1 string theoryMar 10 2004Jun 30 2004We give a geometric interpretation for D-branes in the c=1 string theory. The geometric description is provided by complex curves which arise in both CFT and matrix model formulations. On the CFT side the complex curve appears from the partition function ... More

(m,n) ZZ branes and the c=1 matrix modelOct 14 2003Jun 30 2004We argue that the origin of non-perturbative corrections exp(-2\pi R n\mu) in the c=1 matrix model is (1,n) D-branes of Zamolodchikovs. We confirm this identification comparing the flow of these corrections under the Sine--Liouville perturbation in the ... More

On choice of connection in loop quantum gravityJul 22 2001Oct 07 2005We investigate the quantum area operator in the loop approach based on the Lorentz covariant hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz connections giving rise to Wilson lines which are eigenstates ... More

The effective action and quantum gauge transformationsJul 21 1998Jan 12 1999The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass shell, they can ... More

Degenerate Plebanski Sector and Spin Foam QuantizationFeb 22 2012May 18 2012We show that the degenerate sector of Spin(4) Plebanski formulation of four-dimensional gravity is exactly solvable and describes covariantly embedded SU(2) BF theory. This fact ensures that its spin foam quantization is given by the SU(2) Crane-Yetter ... More

Complex curves and non-perturbative effects in c=1 string theoryDec 21 2004We investigate a complex curve in the $c=1$ string theory which provides a geometric interpretation for different kinds of D-branes. The curve is constructed for a theory perturbed by a tachyon potential using its matrix model formulation. The perturbation ... More

On the counting of black hole states in loop quantum gravityAug 11 2004We argue that counting black hole states in loop quantum gravity one should take into account only states with the minimal spin at the horizon.

SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameterMay 19 2000Dec 05 2008An so(4,C)-covariant hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so called Immirzi parameter) is developed. It encompasses the Ashtekar-Barbero gravity which serves as a basis of quantum loop ... More

On the number of solutions of a quadratic equation in a normed spaceJun 08 2015We study an equation $Qu=g$, where $Q$ is a continuous quadratic operator acting from one normed space to another normed space. Obviously, if $u$ is a solution of such equation then $-u$ is also a solution. We find conditions implying that there are no ... More

Dynamic systems with quantum behaviourJan 26 2009Apr 08 2009It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions corresponding to quantum ... More

Area spectrum in Lorentz covariant loop gravityMar 28 2001May 03 2001We use the manifestly Lorentz covariant canonical formalism to evaluate eigenvalues of the area operator acting on Wilson lines. To this end we modify the standard definition of the loop states to make it applicable to the present case of non-commutative ... More

Heat kernel for non-minimal operators on a Kahler manifoldJan 17 1996The heat kernel expansion for a general non--minimal operator on the spaces $C^\infty (\Lambda^k)$ and $C^\infty (\Lambda^{p,q})$ is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the Seeley coefficients ... More

c=1 from c<1: Bulk and boundary correlatorsApr 25 2005Sep 29 2005We study the c_L=25 limit, which corresponds to c=1 string theory, of bulk and boundary correlation functions of Liouville theory with FZZT boundary conditions. This limit is singular and requires a renormalization of vertex operators. We formulate a ... More

TBA for non-perturbative moduli spacesMar 21 2010Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton ... More

Hypermultiplet metric and D-instantonsDec 28 2014Jan 08 2015We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way ... More

Modularity, Quaternion-Kahler spaces and Mirror SymmetryJun 07 2013Feb 13 2014We provide an explicit twistorial construction of quaternion-Kahler manifolds obtained by deformation of c-map spaces and carrying an isometric action of the modular group SL(2,Z). The deformation is not assumed to preserve any continuous isometry and ... More

On Partially Massless Theory in 3 DimensionsOct 10 2014Mar 02 2015We analyze the first-order formulation of the ghost-free bigravity model in three-dimensions known as zwei-dreibein gravity. For a special choice of parameters, it was argued to have an additional gauge symmetry and give rise to a partially massless theory. ... More

A Topology-Preserving Level Set Method for Shape OptimizationMay 07 2004The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level ... More

Wave Propagation in a 3-D Optical WaveguideApr 16 2003In this paper we study the problem of wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open ... More

Theta series, wall-crossing and quantum dilogarithm identitiesNov 09 2015Jul 26 2016Motivated by mathematical structures which arise in string vacua and gauge theories with N=2 supersymmetry, we study the properties of certain generalized theta series which appear as Fourier coefficients of functions on a twisted torus. In Calabi-Yau ... More

Finite Rank Toeplitz Operators: Some Extensions of D.Luecking's TheoremMay 17 2008The recent theorem by D.Luecking about finite rank Bergman-Toeplitz operators is extended to weights being distributions with compact support and to the spaces of harmonic functions.

Deformations of nearly parallel G_2-structuresJan 11 2011We study the infinitesimal deformations of a proper nearly parallel G_2-structure and prove that they are characterized by a certain first order differential equation. In particular we show that the space of infinitesimal deformations modulo the group ... More

Dualities and fivebrane instantonsMay 01 2014Jan 05 2015We derive the fivebrane instanton corrections to the hypermultiplet moduli space $M_H$ of Calabi-Yau string vacua using S-duality symmetry of the type IIB formulation. The result is given in terms of a set of holomorphic functions on the twistor space ... More

S-duality in Twistor SpaceJun 06 2012In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate ... More

Critical Overview of Loops and FoamsSep 22 2010This is a review of the present status of loop and spin foam approaches to quantization of four-dimensional general relativity. It aims at raising various issues which seem to challenge some of the methods and the results often taken as granted in these ... More

Timelike surfaces in Lorentz covariant loop gravity and spin foam modelsJan 28 2005Oct 06 2005We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop approach to quantize ... More

End states in a 1-D topological Kondo insulatorMar 26 2014To gain further insight into the properties of interacting topological insulators, we study a 1 dimensional model of topological Kondo insulators which can be regarded as the strongly interacting limit of the Tamm-Shockley model. Treating the model in ... More

Heterotic-type II duality in twistor spaceOct 10 2012Nov 23 2012Heterotic string theory compactified on a K3 surface times T^2 is believed to be equivalent to type II string theory on a suitable Calabi-Yau threefold. In particular, it must share the same hypermultiplet moduli space. Building on the known twistorial ... More

Flexible suspensions with a hexagonal equatorMay 22 2009We construct a flexible (non immersed) suspension with a hexagonal equator in Euclidean 3-space and study its properties related to the Strong Bellows Conjecture which reads as follows: if an immersed polyhedron $\Cal P$ in Euclidean 3-space is obtained ... More

Froehlich Polaron and Bipolaron: Recent DevelopmentsApr 23 2009Apr 27 2009It is remarkable how the Froehlich polaron, one of the simplest examples of a Quantum Field Theoretical problem, as it basically consists of a single fermion interacting with a scalar Bose field of ion displacements, has resisted full analytical or numerical ... More

Prime Number Diffeomorphisms, Diophantine Equations and the Riemann HypothesisNov 22 2004We explicitly construct a diffeomorphic pair (p(x),p^{-1}(x)) in terms of an appropriate quadric spline interpolating the prime series. These continuously differentiable functions are the smooth analogs of the prime series and the prime counting function, ... More

Correlators in 2D string theory with vortex condensationApr 10 2001We calculate one- and two-point correlators of winding operators in the matrix model of 2D string theory compactified on a circle, recently proposed for the description of string dynamics on the 2D black hole background.

Fivebrane instantons in Calabi-Yau compactificationsMar 05 2014We provide the last missing piece of the complete non-perturbative description of the low energy effective action emerging from Calabi-Yau compactifications of type II string theory --- NS5-brane instanton corrections to the hypermultiplet moduli space ... More

Weyl structures with positive Ricci tensorFeb 04 1999Jan 09 2003We prove the vanishing of the first Betti number on compact manifolds admitting a Weyl structure whose Ricci tensor satisfies certain positivity conditions, thus obtaining a Bochner-type vanishing theorem in Weyl geometry. We also study compact Hermitian-Weyl ... More

Vanishing theorems on Hermitian manifoldsJan 21 1999Jan 09 2003We prove the vanishing of the Dolbeault cohomology groups on Hermitian manifolds with $dd^c$-harmonic K\"ahler form and positive (1,1)-part of the Ricci form of the Bismut connection. This implies the vanishing of the Dolbeault cohomology groups on complex ... More

Spin and holographic metalsApr 27 2012May 14 2012In this paper we discuss two-dimensional holographic metals from a condensed matter physics perspective. We examine the spin structure of the Green's function of the holographic metal, demonstrating that the excitations of the holographic metal are "chiral", ... More

The effect of intrinsic point defects on ferroelectric polarization behavior of SrTiO$_3$Sep 14 2016The effect of a variety of intrinsic defects and defect clusters in bulk and thin films of SrTiO$_3$ on ferroelectric polarization and switching mechanism is investigated by means of density-functional-theory (DFT) based calculations and the Berry phase ... More

First order gravity on the light frontDec 18 2014Feb 26 2015We study the canonical structure of the real first order formulation of general relativity on a null foliation. We use a tetrad decomposition which allows to elegantly encode the nature of the foliation in the norm of a vector in the fibre bundle. The ... More

Hamiltonian Analysis of non-chiral Plebanski Theory and its GeneralizationsSep 27 2008We consider non-chiral, full Lorentz group-based Plebanski formulation of general relativity in its version that utilizes the Lagrange multiplier field Phi with "internal" indices. The Hamiltonian analysis of this version of the theory turns out to be ... More

Quantum mirror symmetry and twistorsJun 19 2009Using the twistor approach to hypermultiplet moduli spaces, we derive the worldsheet, D(-1), and D1-instanton contributions to the generalized mirror map, relating Type IIA and Type IIB string theory compactified on generic mirror Calabi-Yau threefolds. ... More

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