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Lattice-induced photon scattering in an optical lattice clockFeb 08 2018Jul 19 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several tens of seconds. Rayleigh scattering does not cause significant decoherence of the ... More

Proof of the Goldbach conjecture in a more stringent formMar 27 2007May 03 2007With an artificial (p', n')-system it has been proved that even numbers > (p(x))^2 are the sum of two p > p(x).

Morita equivalence and dualityMay 07 1998It was shown by Connes, Douglas, Schwarz[1] that one can compactify M(atrix) theory on noncommutative torus. We prove that compactifications on Morita equivalent tori are physically equivalent. This statement can be considered as a generalization of non-classical ... More

Grassmannian and string theoryOct 16 1996Dec 02 1996Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new facts supporting ... More

On the solutions to the string equationSep 10 1991The set of solutions to the string equation $[P,Q]=1$ where $P$ and $Q$ are differential operators is described.It is shown that there exists one-to-one correspondence between this set and the set of pairs of commuting differential operators.This fact ... More

Gauge theories on noncommutative euclidean spacesNov 20 2001Nov 30 2001We consider gauge theories on noncommutative euclidean space . In particular, we discuss the structure of gauge group following standard mathematical definitions and using the ideas of hep-th/0102182.

Theta-functions on noncommutative toriJul 25 2001Ordinary theta-functions can be considered as holomorphic sections of line bundles over tori. We show that one can define generalized theta-functions as holomorphic elements of projective modules over noncommutative tori (theta-vectors). The theory of ... More

Noncommutative instantons: a new approachFeb 26 2001We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field ... More

Equivalences for Morse homologyMay 25 1999An explicit isomorphism between Morse homology and singular homology is constructed via the technique of pseudo-cycles. Given a Morse cycle as a formal sum of critical points of a Morse function, the unstable manifolds for the negative gradient flow are ... More

Structure of the degenerate principal series on symmetric R-spaces and small representationsDec 14 2012Jan 06 2014Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whose nilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We study the degenerate principal series representations of $G$ on $C^\infty(X)$ in the case where $P$ is ... More

Update on String TheoryApr 28 2003The first part of this report gives a very quick sketch of how string theory concepts originated and evolved during its first 25 years (1968-93). The second part presents a somewhat more detailed discussion of the highlights of the past decade. The final ... More

Comments on Born-Infeld TheoryMar 20 2001The low-energy effective action of supersymmetric D-brane systems consists of two terms, one of which is of the Born-Infeld type and one of which is of the Chern-Simons type. I briefly review the status of our understanding of these terms for both the ... More

Remarks on Non-BPS D-BranesAug 12 1999Following Sen's discovery of various stable non-BPS D-branes, K-theory has been shown to be the appropriate mathematical framework for classifying conserved D-brane charges. The classification accounts for known D-branes and predicts some new ones including ... More

Beyond Gauge TheoriesJul 27 1998Sep 01 1998Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality conjectures suggest ... More

From Superstrings to M TheoryDec 08 1998In this talk I will survey some of the basic facts about superstring theories in 10 dimensions and the dualities that relate them to M theory in 11 dimensions. Then I will mention some important unresolved issues.

The Power of M TheoryOct 12 1995A proposed duality between type IIB superstring theory on R^9 X S^1 and a conjectured 11D fundamental theory (``M theory'') on R^9 X T^2 is investigated. Simple heuristic reasoning leads to a consistent picture relating the various p-branes and their ... More

Superstring DualitiesSep 26 1995Oct 09 1995This talk is divided into two parts. The first part reviews some of the duality relationships between superstring theories. These relationships are interpreted as providing evidence for the existence of a unique underlying fundamental theory. The second ... More

On non-overdetermined inverse scattering at zero energy in three dimensionsMay 31 2006We develop the d-bar -approach to inverse scattering at zero energy in dimensions d>=3 of [Beals, Coifman 1985], [Henkin, Novikov 1987] and [Novikov 2002]. As a result we give, in particular, uniqueness theorem, precise reconstruction procedure, stability ... More

Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energyOct 05 2010Jan 24 2011In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sense).

Understanding Gravitational Clustering with Non-Linear Perturbation TheoryFeb 21 1997I discuss new results concerning the evolution of the bispectrum due to gravitational instability from gaussian initial conditions using one-loop perturbation theory (PT). Particular attention is paid to the transition from weakly non-linear scales to ... More

Large-Scale Structure in Brane-Induced Gravity I. Perturbation TheoryJun 24 2009Jul 19 2009We study the growth of subhorizon perturbations in brane-induced gravity using perturbation theory. We solve for the linear evolution of perturbations taking advantage of the symmetry under gauge transformations along the extra-dimension to decouple the ... More

Cosmological Perturbations: Entering the Non-Linear RegimeDec 21 1996We consider one-loop corrections to the bispectrum and skewness of cosmological density fluctuations induced by gravitational evolution. As has been established by comparison with numerical simulations, tree-level perturbation theory (PT) describes these ... More

Noncommutative Counterparts of the Springer ResolutionApr 20 2006Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as the (local) ... More

Cohomology of tilting modules over quantum groups and $t$-structures on derived categories of coherent sheavesFeb 28 2004Feb 21 2006The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to a certain t-structure on the derived category of equivariant coherent ... More

Quasi-exceptional sets and equivariant coherent sheaves on the nilpotent coneFeb 06 2001In math.AG/0005152 a certain $t$-structure on the derived category of equivariant coherent sheaves on the nil-cone of a simple complex algebraic group was introduced (the so-called perverse $t$-structure corresponding to the middle perversity). In the ... More

Conservation laws of semidiscrete canonical Hamiltonian equationsFeb 25 2004There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian ... More

Pilot Wave model that includes creation and annihilation of particlesNov 12 2010Nov 16 2010The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing determinism. This has been previously attempted in an article by the same author titled "Incorporating ... More

Spinor fields in Causal Set TheoryAug 21 2008The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar ... More

Universal geometric entanglement close to quantum phase transitionsNov 16 2007Mar 24 2008Under successive Renormalization Group transformations applied to a quantum state $\ket{\Psi}$ of finite correlation length $\xi$, there is typically a loss of entanglement after each iteration. How good it is then to replace $\ket{\Psi}$ by a product ... More

On the solutions of generalized discrete Poisson equationJun 19 2007The set of common numerical and analytical problems is introduced in the form of the generalized multidimensional discrete Poisson equation. It is shown that its solutions with square-summable discrete derivatives are unique up to a constant. The proof ... More

Proving Craig and Lyndon Interpolation Using Labelled Sequent CalculiJan 21 2016We have recently presented a general method of proving the fundamental logical properties of Craig and Lyndon Interpolation (IPs) by induction on derivations in a wide class of internal sequent calculi, including sequents, hypersequents, and nested sequents. ... More

Falsification or Confirmation: From Logic to PsychologyOct 30 2015Corroboration or confirmation is a prominent philosophical debate of the 20th century. Many philosophers have been involved in this debate most notably the proponents of confirmation led by Hempel and its most powerful criticism by the falsificationists ... More

Formulas for phase recovering from phaseless scattering data at fixed frequencyFeb 08 2015Feb 14 2015We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As a corollary, ... More

Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensionsDec 16 2014We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we give also a ... More

Expressing QFT in terms of QM with single extra dimension and classical hidden variable fieldSep 12 2013Oct 30 2015The goal of this paper is to re-express QFT in terms of two "classical" fields living in ordinary space with single extra dimension. The role of the first classical field is to set up an injection from the set of values of extra dimension into the set ... More

Canonical bases for sl(2,C)-modules of spherical monogenics in dimension 3Mar 29 2010Jun 17 2010Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as sl(2,C)-modules. As finite-dimensional irreducible sl(2,C)-modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these ... More

A toy model of information retrieval system based on quantum probabilityMay 23 2013Recent numerical results show that non-Bayesian knowledge revision may be helpful in search engine training and optimization. In order to demonstrate how basic assumption about about the physical nature (and hence the observed statistics) of retrieved ... More

Invertibility of symmetric random matricesFeb 01 2011Mar 16 2012We study n by n symmetric random matrices H, possibly discrete, with iid above-diagonal entries. We show that H is singular with probability at most exp(-n^c), and the spectral norm of the inverse of H is O(sqrt{n}). Furthermore, the spectrum of H is ... More

A Model Structure On The Category Of Small Acyclic CategoriesAug 05 2015In this paper, we show that the Thomason model structure restricts to a Quillen equivalent cofibrantly generated model structure on the category of acyclic categories, whose generating cofibrations are the same as those generating the Thomason model structure. ... More

Strongly solvable spherical subgroups and their combinatorial invariantsDec 13 2012Mar 26 2015A subgroup H of an algebraic group G is said to be strongly solvable if H is contained in a Borel subgroup of G. This paper is devoted to establishing relationships between the following three combinatorial classifications of strongly solvable spherical ... More

Variational generalization of free relativistic topJul 25 2014We prove that well known first-order (in spin, momentum, and space-time coordinates) equations of motion of relativistic top are equivalent to the third-order equations of Mathisson on the surface of the Mathisson-Pirani auxiliary constraint. We then ... More

Additive habits with power utility: Estimates, asymptotics and equilibriumAug 14 2011We consider a power utility maximization problem with additive habits in a framework of discrete-time markets and random endowments. For certain classes of incomplete markets, we establish estimates for the optimal consumption stream in terms of the aggregate ... More

On the splitting of polynomial functorsFeb 03 2012Oct 04 2012We develop methods for proving that certain extensions of polynomial functors do not split naturally. As an application we give a functorial description of the third and the fourth stable homotopy groups of the classifying spaces of free abelian groups. ... More

On the homology of the dual de Rham complexJan 18 2010We study the homology of the dual de Rham complex as functors on the category of abelian groups. We give a description of homology of the dual de Rham complex up to degree 7 for free abelian groups and present a corrected version of the proof of Jean's ... More

Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systemsMay 20 2010Sep 20 2010New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate a hierarchy ... More

Affine Grassmannians of group schemes and exotic principal bundles over A^1Aug 14 2013Jan 16 2014Let G be a simple simply-connected group scheme over a regular local scheme U. Let E be a principal G-bundle over A^1_U trivial away from a subscheme finite over U. We show that E is not necessarily trivial and give some criteria of triviality. To this ... More

Perverse sheaves on affine flags and nilpotent cone of the Langlands dual groupJan 27 2002Sep 04 2007In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves on the affine ... More

Perverse coherent sheaves (after Deligne)May 16 2000Jun 23 2010This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category ... More

The Bispectrum: From Theory to ObservationsApr 06 2000Jul 05 2000The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the ... More

Gravitational Clustering from Chi^2 Initial ConditionsFeb 01 2000Jun 13 2001We consider gravitational clustering from primoridal non-Gaussian fluctuations provided by a $\chi^2$ model, as motivated by some models of inflation. The emphasis is in signatures that can be used to constrain this type of models from large-scale structure ... More

Redshift Distortions: Perturbative and N-body ResultsAug 10 1998I discuss the evolution of the redshift-space bispectrum via perturbation theory (PT) and large high-resolution numerical simulations. At large scales, we give the multipole expansion of the bispectrum in PT, which provides a natural way to break the ... More

Exploring corner transfer matrices and corner tensors for the classical simulation of quantum lattice systemsDec 18 2011May 03 2012In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite size. This ... More

Quantum contextuality in classical information retrievalMay 25 2012Document ranking based on probabilistic evaluations of relevance is known to exhibit non-classical correlations, which may be explained by admitting a complex structure of the event space, namely, by assuming the events to emerge from multiple sample ... More

Ph.D. Thesis: Quantum Field Theory and Gravity in Causal SetsMay 14 2009This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time to causal ... More

Novel definition of Grassmann numbers and spinor fieldsAug 06 2008May 25 2009The goal of this paper is to define fermionic field in terms of non-orthonormal vierbeins, where fluctuations away from orthonormality are viewed as fermionic field. Furthermore, Grassmann numbers are defined in a way that makes literal sense.

Gauge Fields in Causal Set TheoryJul 13 2008This is the second paper in a series on the dynamics of matter fields in the causal set approach to quantum gravity. We start with the usual expression for the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field, in which the gauge ... More

Use of sphere and curves to define Berezin integralAug 18 2009Sep 09 2015In this paper we will describe various ways of describing Berezin integral as a literal limit of the sum taken either over a surface (in our case, a sphere) or a curve.

Mountain Peak Detection in Online Social MediaAug 12 2015We present a system for the classification of mountain panoramas from user-generated photographs followed by identification and extraction of mountain peaks from those panoramas. We have developed an automatic technique that, given as input a geo-tagged ... More

On the Grothendieck-Serre conjecture on principal bundles in mixed characteristicJan 17 2015Nov 13 2016Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. ... More

On the energy of inviscid singular flowsMar 13 2008It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space $B^{1/3}_{3,\infty}$. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various $L^p$-space ... More

Variationality with second derivatives, relativistic uniform acceleration, and the 'spin'-curvature interaction in two-dimensional space-timeOct 20 2015Apr 23 2016A variational formulation for the geodesic circles in two-dimensional Riemannian manifold is discovered. Some relations with the uniform relativistic acceleration and the one-dimensional 'spin'-curvature interaction is investigated.

Four lectures on probabilistic methods for data scienceDec 20 2016Nov 04 2017Methods of high-dimensional probability play a central role in applications for statistics, signal processing theoretical computer science and related fields. These lectures present a sample of particularly useful tools of high-dimensional probability, ... More

Market selection with learning and catching up with the JonesesJun 15 2011Jan 15 2012We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and learning mechanism, ... More

Twisted de Rham cohomology, homological definition of the integral and "Physics over a ring"Aug 30 2008We define the twisted de Rham cohomology and show how to use it to define the notion of an integral of the form $\int g(x) e^{f(x)}dx$ over an arbitrary ring. We discuss also a definition of a family of integrals and some properties of the homological ... More

Algebraic structure of Yang-Mills theoryApr 23 2004In the present paper we analyze algebraic structures arising in Yang-Mills theory. The paper should be considered as a part of a project started with a paper "On maximally supersymmetric Yang-Mills theories" devoted to maximally supersymmetric Yang-Mills ... More

Some remarks on Gopakumar-Vafa invariantsDec 12 2004Sep 23 2005We show that Gopakumar-Vafa invariants can be expressed in terms of the cohomology ring of moduli space of D-branes without reference to the sl_2 \times sl_2 action. We also give a simple construction of this action.

Geometry of N=1 Super Yang-Mills Theory in Curved SuperspaceSep 10 1996Sep 12 1996We give a new description of N=1 super Yang-Mills theory in curved superspace. It is based on the induced geometry approach to a curved superspace in which it is viewed as a surface embedded into C(4|2). The complex structure on C(4|2) supplied with a ... More

Lifting automorphisms of quotients of adjoint representationsJan 26 2013Nov 24 2013Let $\mathfrak g_i$ be a simple complex Lie algebra, $1\leq i \leq d$, and let $G=G_1\times...\times G_d$ be the corresponding adjoint group. Consider the $G$-module $V=\oplus r_i\mathfrak g_i$ where $r_i\geq 1$ for all $i$. We say that $V$ is \emph{large} ... More

Measurement of Multijet Production in DIS and Determination of the Strong Coupling ConstantJul 07 2011Inclusive jet, dijet and trijet differential cross sections have been measured in neutral current deep-inelastic scattering for exchanged boson virtualities $150 < Q^2 < 15000$ GeV$^2$ with the H1 detector at HERA using an integrated luminosity of 351 ... More

On the Grothendieck-Serre conjecture on principal bundles in mixed characteristicJan 17 2015Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. ... More

A New Angle on Gravitational ClusteringAug 17 2000We describe a new approach to gravitational instability in large-scale structure, where the equations of motion are written and solved as in field theory in terms of Feynman diagrams. The basic objects of interest are the propagator (which propagates ... More

Homological properties of representations of p-adic groups related to geometry of the group at infinityJun 10 2004Geometry of buildings is used to prove some homological properties of the category of smooth representations of a reductive p-adic group (Kazhdan's "pairing conjecture", Bernstein's description of homological duality in terms of Deligne-Lusztig duality). ... More

On two geometric realizations of an affine Hecke algebraSep 03 2012Sep 04 2015The article is a contribution to the local theory of geometric Langlands correspondence. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra, thought of as an algebra of Iwahori bi-invariant functions on ... More

"Classical" model of discrete QFT: Klein Gordon and electromagnetic fieldsOct 10 2011Feb 04 2013The purpose of this paper is to propose a "classical" model of "quantum" fields which is local. Yet it admittedly violates relativity as we know it and, instead, it fits within a bimetric model with one metric corresponding to speed of light and another ... More

Pilot wave model without configuration or Fock spacesNov 15 2010Dec 06 2010The goal of this article is to come up with interpretation of quantum phenomena that is both local and deterministic. This is done by the means of envoking two different metrics, $g_o$ and $g_s$. These two metrics give very different "speeds of light": ... More

Bosonic Fields in Causal Set TheoryJul 29 2008In this paper I will define a Lagrangian for scalar and gauge fields on causal sets, based on the selection of an Alexandrov set in which the variation of appropriate expressions in terms of either scalar field or the gauge field holonomies around suitable ... More

Non-linear corrections to Lagrangians predicted by causal set theory: Flat space bosonic toy modelJan 27 2012A while ago a proposal have been made regarding Klein Gordon and Maxwell Lagrangians for causal set theory. These Lagrangian densities are based on the statistical analysis of the behavior of field on a sample of points taken throughout some "small" region ... More

Incorporating particle creation and annihilation into Bohm's Pilot Wave modelMar 01 2010May 12 2010The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing causality. In some sense, this work echoes the work of Nikoli\'c (I call "visibility" what ... More

Causal set as a discretized phase spacetimeOct 13 2009Apr 30 2010The first goal of this paper is to show that discreteness, locality, and relativistic covariance can peacefully coexist if the ordinary spacetime (OST) is replaced with phase spacetime (PST) as a geometric background of a Poisson process, where PST is ... More

Semiclassical behaviour of expectation values in time evolved Lagrangian states for large timesFeb 03 2004We study the behaviour of time evolved quantum mechanical expectation values in Lagrangian states in the limit $\hbar\to 0$ and $t\to\infty$. We show that it depends strongly on the dynamical properties of the corresponding classical system. If the classical ... More

Combining low-dimensional ensemble postprocessing with reordering methodsDec 17 2015State-of-the-art weather forecasts usually rely on ensemble prediction systems, accounting for the different sources of uncertainty. As ensembles are typically uncalibrated, they should get statistically postprocessed. Several multivariate ensemble postprocessing ... More

l2-Betti numbers of discrete and non-discrete groupsSep 17 2015This survey is an extended version of a talk during the Arbeitsgemeinschaft on totally disconnected locally compact groups, held in Oberwolfach in October 2014. We explain the definition of l2-Betti numbers of locally compact groups -- both discrete and ... More

IMF Lending and Economic Growth: An Empirical Analysis of UkraineSep 05 2015This study uses Vector Autoregression (VAR) Methodology as well as Vector Error Correction (VEC) Methodology to examine the existence and direction of causality between economic growth and IMF lending for Ukraine. The paper examines the IMF lending data ... More

On known and less known relations of Leonhard Euler with PolandMay 10 2015Feb 04 2016Leonhard Euler was working for the St. Petersburg Academy of Sciences (Russia) and Prussian Academy of Sciences during various periods of his life. It is not a popular knowledge about Euler's contacts with Polish scientists of his era and Poland in general. ... More

Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and HolographyJul 24 2014Oct 18 2014This is a short review on selected theory developments on Tensor Network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from ... More

Conjugacy classes in discrete Heisenberg groupsMay 21 2014We study some extension of a discrete Heisenberg group coming from the theory of loop-groups and find invariants of conjugacy classes in this group. In some cases including the case of the integer Heisenberg group we make these invariants more explicit. ... More

Lecture Script: Introduction to Computational Quantum MechanicsMar 27 2014Jun 05 2015This document is the lecture script of a one-semester course taught at the University of Basel in the Fall semesters of 2012 and 2013 and in the Spring semester of 2015. It is aimed at advanced students of physics who are familiar with the concepts and ... More

A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair StatesJun 10 2013Jun 10 2014This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas ... More

Connection between GRW "spontaneous collapse" and Mensky's "restricted path integral" modelsMay 26 2013Aug 10 2016In this paper we will show how Mensky's model of "restricted path integrals" can be derived from GRW "spontaneous collapse" model.

Recent Belle results in quarkonium physicsMar 01 2013Mar 25 2013We review selected recent Belle results in quarkonium physics, that include precision measurement of the eta_b(1S) parameters, evidence for the eta_b(2S); evidence for the psi_2(1D); observation of the psi(4040) and psi(4160) transitions to J/psi eta ... More

A brief Introduction to Dispersion Relations and AnalyticityOct 19 2016In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the K\"all\'en-Lehmann and general dispersion relations. The ... More

Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundlesMay 07 2015Dec 26 2015Consider the holomorphic bundle with connection on $\mathbb P^1-\{0,1,\infty\}$ corresponding to the regular hypergeometric differential operator \[ \prod_{j=1}^h(D-\alpha_j)-z\prod_{j=1}^h(D-\beta_j), \qquad D=z\frac{d}{dz}. \] If the numbers $\alpha_i$ ... More

On the S-matrix conjectureJun 28 2013Sep 06 2013Motivated with a problem in spectroscopy, Sloane and Harwit conjectured in 1976 what is the minimal Frobenius norm of the inverse of a matrix having all entries from the interval [0, 1]. In 1987, Cheng proved their conjecture in the case of odd dimensions, ... More

Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroupJun 28 2011Jan 14 2013For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if ... More

The next variational prolongation of the Euclidean spaceJul 17 2014The unique third-order invariant variational equation in three-dimensional (pseudo)Euclidean space is derived.

A new proof of the Larman-Rogers upper bound for the chromatic number of the Euclidean spaceOct 10 2016Dec 04 2018The chromatic number $\chi(\mathbb{R}^n)$ of the Euclidean space $\mathbb{R}^n$ is the smallest number of colors sufficient for coloring all points of the space in such a way that any two points at the distance 1 have different colors. In 1972 Larman--Rogers ... More

Canonical systems and de Branges spacesAug 26 2014This is an exposition of the inverse spectral theory of canonical systems based on de Branges spaces of entire functions

Exterior Distance FunctionJun 26 2017We introduce and study exterior distance function (EDF) and correspondent exterior point method (EPM) for convex optimization. The EDF is a classical Lagrangian for an equivalent problem obtained from the initial one by monotone transformation of both ... More

On tensor categories attached to cells in affine Weyl groupsOct 10 2000Dec 31 2011We prove a conjecture by Lusztig, which describes the tensor categories of perverse sheaves on affine flag manifolds, with tensor structure provided by truncated convolution, in terms of the Langlands dual group. We also give a geometric (categorical) ... More

Koszul Property and Frobenius Splitting of Schubert VarietiesFeb 20 1995We show how the Frobenius splitting method of Mehta-Ramanathan implies the Koszul property of projective coordinate rings of Schubert varieties.