gromov witten classes quantum cohomology and enumerative geometry the paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry in particular it contains an axiomatic treatment of gromov witten classes and a discussion of their properties for fano varieties cohomological field theories are defined and it is proved that tree level theories are determined by their correlation functions application to counting rational curves on del pezzo surfaces and projective spaces are given

quasi bezier curves integrating localised information bezier curves bc have become fundamental tools in many challenging and varied applications ranging from computer aided geometric design to generic object shape descriptors a major limitation of the classical bezier curve however is that only global information about its control points cp is considered so there can often be a large gap between the curve and its control polygon leading to large distortion in shape representation while strategies such as degree elevation composite bc refinement and subdivision reduce this gap they also increase the number of cp and hence bit rate and computational complexity this paper presents novel contributions to bc theory with the introduction of quasi bezier curves qbc which seamlessly integrate localised cp information into the inherent global bezier framework with no increase in either the number of cp or order of computational complexity qbc crucially retains the core properties of the classical bc such as geometric continuity and affine invariance and can be embedded into the vertex based shape coding and shape descriptor framework to enhance rate distortion performance the performance of qbc has been empirically tested upon a number of natural and synthetically shaped objects with both qualitative and quantitative results confirming its consistently superior approximation performance in comparison with both the classical bc and other established bc based shape descriptor methods

deligne products of line bundles over moduli spaces of curves we study deligne products for forgetful maps between moduli spaces of marked curves by offering a closed formula for tautological line bundles associated to marked points in particular we show that the deligne products for line bundles on the total spaces corresponding to forgotten marked points are positive integral multiples of the weil petersson bundles on the base moduli spaces

intersection numbers and rank one cohomological field theories in genus one we obtain a simple recursive presentation of the tautological and classes on the moduli space of curves in genus 0 and 1 in terms of boundary strata graphs we derive differential equations for the generating functions for their intersection numbers which allow us to prove a simple relationship between the genus zero and genus one potentials as an application we describe the moduli space of normalized restricted rank one cohomological field theories in genus one in coordinates which are additive under taking tensor products our results simplify and generalize those of kaufmann manin and zagier

the decorated teichmuller space of punctured surfaces a principal 5 bundle over the usual teichmuller space of ans times punctured surface is introduced the bundle is mapping class group equivariant and admits an invariant foliation several coordinatizations of the total space of the bundle are developed there is furthermore a natural cell decomposition of the bundle finally we compute the coordinate action of the mapping class group on the total space the total space is found to have a rich equivariant geometric structure we sketch some connections with arithmetic groups diophantine approximations and certain problems in plane euclidean geometry furthermore these investigations lead to an explicit scheme of integration over the moduli spaces and to the construction of a universal teichmuller space which we hope will provide a formalism for understanding some connections between the teichmuller theory the kp hierarchy and the virasoro algebra these latter applications are pursued elsewhere

periodic stationary patterns governed by a convective cahn hilliard equation we investigate bifurcations of stationary periodic solutions of a convective cahn hilliard equation u t duu x u u 3 u xx xx 0 describing phase separation in driven systems and study the stability of the main family of these solutions for the driving parameter d d 0 the periodic stationary solutions are stable if their wavelength belongs to a certain stability interval it is therefore shown that in a driven phase separating system that undergoes spinodal decomposition the coarsening can be stopped by the driving force and formation of stable periodic structures is possible the modes that destroy the stability at the boundaries of the stability interval are also found

dynamic bezier curves for variable rate distortion bezier curves bc are important tools in a wide range of diverse and challenging applications from computer aided design to generic object shape descriptors a major constraint of the classical bc is that only global information concerning control points cp is considered consequently there may be a sizeable gap between the bc and its control polygon ctrlpoly leading to a large distortion in shape representation while bc variants like degree elevation composite bc and refinement and subdivision narrow this gap they increase the number of cp and thereby both the required bit rate and computational complexity in addition while quasi bezier curves qbc close the gap without increasing the number of cp they reduce the underlying distortion by only a fixed amount this paper presents a novel contribution to bc theory with the introduction of a dynamic bezier curve dbc model which embeds variable localised cp information into the inherently global bezier framework by strategically moving bc points towards the ctrlpoly a shifting parameter sp is defined that enables curves lying within the region between the bc and ctrlpoly to be generated with no commensurate increase in cp dbc provides a flexible rate distortion rd criterion for shape coding applications with a theoretical model for determining the optimal sp value for any admissible distortion being formulated crucially dbc retains core properties of the classical bc including the convex hull and affine invariance and can be seamlessly integrated into both the vertex based shape coding and shape descriptor frameworks to improve their rd performance dbc has been empirically tested upon a number of natural and synthetically shaped objects with qualitative and quantitative results confirming its consistently superior shape approximation performance compared with the classical bc qbc and other established bc based shape descriptor techniques

a change of coordinates on the large phase space of quantum cohomology the gromov witten invariants of a smooth projective variety v when twisted by the tautological classes on the moduli space of stable maps give rise to a family of cohomological field theories and endow the base of the family with coordinates we prove that the potential functions associated to the tautological classes the large phase space and the classes are related by a change of coordinates which generalizes a change of basis on the ring of symmetric functions our result is a generalization of the work of manin zograf who studied the case where v is a point we utilize this change of variables to derive the topological recursion relations associated to the classes from those associated to the classes

higher weil petersson volumes of moduli spaces of stable n pointed curves moduli spaces of compact stablen pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the weil petersson volume forms and constitute a version of mumford classes we give various new formulas for the integrals of these forms and their generating functions

new results of intersection numbers on moduli spaces of curves we present a series of results we obtained recently about the intersection numbers of tautological classes on moduli spaces of curves including a simple formula of the n point functions for witten s classes an effective recursion formula to compute higher weil petersson volumes several new recursion formulae of intersection numbers and our proof of a conjecture of itzykson and zuber concerning denominators of intersection numbers we also present virasoro and kdv properties of generating functions of general mixed and intersections

dynamics of domain walls governed by the convective cahn hilliard equation the convective cahn hilliard cch equation ut uxx u u 3 xx d 2 u 2 x 0 has been suggested recently for the description of several physical phenomena including spinodal decomposition of driven phase separating systems in an external field instability of steps moving on a crystal surface and faceting of growing thermodynamically unstable surfaces in this paper the dynamics of domain walls kinks governed by the convective cahn hilliard equation is studied by means of asymptotic and numerical methods a special attention is paid to the dynamics of kink pairs and triplets that play crucial role in the coarsening ostwald ripening process for the driving parameter d d 0 2 3 and large distance between the kinks l 1 analytical formulas are found that describe the motion of the kink pairs and triplets the analytical formulas are in excellent agreement with the results of direct numerical simulations of cch equation they explain the logarithmically slow coarsening observed for the kink dynamics governed by cch equation when the distances between the kinks become large unlike the fast coarsening for moderate distances between the kinks at intermediate stages 2005 elsevier b v all rights reserved

intersection theory on the moduli space of curves and the matrix airy function we show that two natural approaches to quantum gravity coincide this identity is nontrivial and relies on the equivalence of each approach to kdv equations we also investigate related mathematical problems

growth of weil petersson volumes and random hyperbolic surfaces of large genus in this paper we investigate the geometric properties of random hyperbolic surfaces of large genus we describe the relationship between the behavior of lengths of simple closed geodesics on a hyperbolic surface and properties of the moduli space of such surfaces first we study the asymptotic behavior of weil petersson volume vg n of the moduli spaces of hyperbolic surfaces of genus g with n punctures as g then we discuss basic geometric properties of a random hyperbolic surface of genus g with respect to the weil petersson measure as g

on a higher order convective cahn hilliard type equation a higher order convective cahn hilliard type equation that describes the faceting of a growing surface is considered with periodic boundary conditions by using a galerkin approach the existence

asymptotic solutions for the equilibrium crystal shape with small corner energy regularization dynamic models for facet formation often employ a regularization of the surface energy based on a corner energy term here we consider the effect of this regularization on the equilibrium shape of a solid particle in two dimensions using matched asymptotic expansions we determine the explicit solution for the corner shape in the presence of the regularization our results show that for a class of surface energy anisotropy models the regularized solution approaches the classic sharp corner results as the regularization approaches zero the results validate the use of the regularization in numerical calculations for the equilibrium problem finally a byproduct of the analysis is an exact solution for the equilibrium shape of a semi infinite wedge in the presence of the regularization

how covariant closed string theory solves a minimal area problem for a given genusg riemann surface withn 0 punctures n 3 forg 0 we consider the problem of finding the metric of minimal area under the condition that the length of any nontrivial closed curve be greater or equal to 2 the minimal area metrics are found for the case of all punctured genus zero surfaces and for many of the higher genus surfaces both with and without punctures these metrics are induced by jenkins strebel quadratic differentials they arise from the string diagrams corresponding to restricted feynman graphs of a closed string field theory action containing classical and quantum restricted polyhedra

weil petersson volumes and intersection theory on the moduli space of curves in this paper we establish a relationship between the weil petersson volume vgin b of the moduli space mg n b of hyperbolic riemann surfaces with geodesic boundary components of lengths b bn and the intersection numbers of tauto logical classes on the moduli space mg n of stable curves as a result by using the recursive formula for vg n b obtained in 22 we derive a new proof of the virasoro constraints for a point this result is equivalent to the witten kontsevich formula 14

correlation functions of the kdv hierarchy and applications to intersection numbers over m g n we derive an explicit generating function of correlations functions of an arbitrary tau function of the kdv hierarchy in particular applications our formulation gives closed formulae of a new type for the generating series of intersection numbers of classes as well as of mixed and classes in full genera

perturbative series and the moduli space of riemann surfaces on utilise des techniques de la theorie quantique des champs pour calculer des quantites reliees aux groupes de symetrie de paires f g ou f est une surface et g une epine de f

intersection theory of moduli space of stable n pointed curves of genus zero we give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the chow ring

matrix integration and combinatorics of modular groups integration over gaussian matrix ensembles was used to obtain the virtual euler characteristics of mapping class groups we present some simplifications in the combinatorial part of the calculation

automatic outline capture of arabic fonts this paper presents an algorithm for automatic outline capture of digital character images particularly suitable for non roman languages like arabic in most of the desktop publishing systems the shapes of the characters are stored in the computer memory in terms of their outlines and the outlines are expressed as cubic bezier curves the process of producing outlines includes various steps detection of boundary discovering corner points and break points and fitting the curve this process becomes slow and inaccurate if there is any involvement of humans in any of the above steps the work done in this paper fully automates the process and produces the best optimal results

estimates of weil petersson volumes via effective divisors we study the asymptotics of the weil petersson volumes of the moduli spaces of compact riemann surfaces of genus g with n punctures for fixed n as g

coarsening dynamics of a one dimensional driven cahn hilliard system we study the one dimensional cahn hilliard equation with an additional driving term representing say the effect of gravity we find that the driving field e has an asymmetric effect on the solution for a single stationary domain wall or kink the direction of the field determining whether the analytic solutions found by leung j stat phys 61 345 1990 are unique the dynamics of a kink antikink pair bubble is then studied the behavior of a bubble is dependent on the relative sizes of a characteristic length scale mathit e mathrm ensuremath 1 where e is the driving field and the separation l of the interfaces for el ensuremath gg 1 the velocities of the interfaces are negligible while in the opposite limit a traveling wave solution is found with a velocity v ensuremath propto e l for this latter case el ensuremath ll 1 a set of reduced equations describing the evolution of the domain lengths is obtained for a system with a large number of interfaces and implies a characteristic length scale growing as et 1 2 numerical results for the domain size distribution and structure factor confirm this behavior and show that the system exhibits dynamical scaling from very early times textcopyright 1996 the american physical society

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

computing top intersections in the tautological ring of mg we derive effective recursion formulae of top intersections in the tautological ring r mathcal m g of the moduli space of curves of genus g 2 as an application we prove a convolution type tautological relation in r g 2 mathcal m g and some interesting bernoulli number identities

coarsening dynamics of the convective cahn hilliard equation abstract we characterize the coarsening dynamics associated with a convective cahn hilliard equation cch in one space dimension first we derive a sharp interface theory through a matched asymptotic analysis two types of phase boundaries kink and anti kink arise due to the presence of convection and their motions are governed to leading order by a nearest neighbors interaction coarsening dynamical system cds theoretical predictions on cds include the characteristic length l m for coarsening exhibits the temporal power law scaling t1 2 provided l m is appropriately small with respect to the peclet length scale l p binary coalescence of phase boundaries is impossible ternary coalescence only occurs through the kink ternary interaction two kinks meet an anti kink resulting in a kink direct numerical simulations performed on both cds and cch confirm each of these predictions a linear stability analysis of cds identifies a pinching mechanism as the dominant instability which in turn leads to kink ternaries we propose a self similar period doubling pinch ansatz as a model for the coarsening process from which an analytical coarsening law for the characteristic length scale l m emerges it predicts both the scaling constant c of the t1 2 regime i e l m ct 1 2 as well as the crossover to logarithmically slow coarsening as l m crosses l p our analytical coarsening law stands in good qualitative agreement with large scale numerical simulations that have been performed on cch

higher order cahn hilliard equations with dynamic boundary conditions abstract our aim in this paper is to study the well posedness and the dissipativity of higher order cahn hilliard equations with dynamic boundary conditions more precisely we prove the existence and uniqueness of solutions and the existence of the global attractor