conformal blocks and generalized theta functions let yp be the moduli space of rank r vector bundles with trivial determinant on a riemann surface x this space carries a natural line bundle the determinant line bundle s we describe a canonical isomorphism of the space of global sections of sk with the space of conformal blocks defined in terms of representations of the lie algebra 5 c z it follows in particular that the dimension of h yk is given by the verlinde formula

symplectic surgery and the spinc dirac operator abstract letgbe a compact connected lie group and m a compact hamiltoniang space with moment mapj m g under the assumption that these data are pre quantizable one can construct an associated spinc dirac operator formula whose equivariant index yields a virtual representation ofg we prove a conjecture of guillemin and sternberg that if 0 is a regular value ofj the multiplicityn 0 of the trivial representation in the index space formula is equal to the index of the spinc dirac operator for the symplectic quotientm0 j 1 0 g this generalizes previous results for the case thatg tis abelian i e a torus

infinite grassmannians and moduli spaces of g bundles let c be a smooth projective irreducible algebraic curve over c of any genus and g a connected simply connected simple affine algebraic group over c in this paper we elucidate the relationship between 1 the space of vacua conformal blocks defined in conformal field theory using an integrable highest weight representation of the affine kac moody algebra associated to g and 2 the space of regular sections generalised theta functions of a line bundle on the moduli space ta of semistable principal g bundles on c fix a point p in c and let p resp kp be the completion of the local ring p of c at p resp the quotient field of c p let g kp the kp rational points of the algebraic group g be the loop group of g and let g p be the standard maximal parahoric subgroup of then the generalised flag variety x n is an inductive limit of projective varieties in fact of generalised schubert varieties one has a natural r line bundle s on x cf sect 2 2 and the picard group pic x is isomorphic to z which is generated by s proposition 2 3 where f is the universal central extension of by the multiplicative group c cf sect 2 2 by an analogue of the borel weil theorem proved in the kac moody setting by kumar and also by mathieu the space h 162 s of the regular sections of the line bundle y dxo y xo for any d 0 is canonically isomorphic with the full vector space dual v dxo of the integrable highest weight irreducible module v dxo of the affine kacmoody group or of the associated affine kac moody algebra which is a certain one dimensional central extension of the loop algebra lie g with highest weight dxo cf sect 6 1

equivariant dirac operators and differentiable geometric invariant theory in this paper we give a geometric expression for the multiplicities of the equivariant index of a spin c dirac operator

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

the quantization conjecture revisited a strong version of the quantization conjecture of guillemin and sternberg is proved for a reductive group action on a smooth compact polarized variety x l the cohomologies of l over the git quotient x g equal the invariant part of the cohomologies over x this generalizes the theorem of gs on global sections and strengthens its subsequent extensions jk li to riemannroch numbers remarkable by products are the invariance of cohomology of vector bundles over x g under a small change in the defining polarization or under shift desingularization as well as a new proof of boutot s theorem also studied are equivariant holomorphic forms and the equivariant hodgeto de rham spectral sequences for x and its strata whose collapse is shown one application is a new proof of the borel weil bott theorem of ti for the moduli stack of c bundles over a curve and of analogous statements for the moduli stacks and spaces of bundles with parabolic structures collapse of the hodge to de rham sequences for these stacks is also shown

mesh generation using unstructured computational meshes and elliptic partial differential equation smoothing a novel appro ach for generating unstructured meshes using elliptic smoothing is presented like structured mesh generation methods the approach begins with the construction of a computational mesh the computational mesh is used to solve elliptic partial differential equations that control grid point distributions and improve mesh quality two types of elliptic partial differential equations are employed modified linear elastic theory and winslow equation s with or without forcing functions results are included to il lustrate the use of these methods for unstructured mesh generation mesh boundary shape modification mesh untangling and mesh movement

gromov invariants for holomorphic maps from riemann surfaces to grassmannians two compactifications of the space of holomorphic maps of fixed degree from a compact riemann surface to a grassmannian are studied it is shown that the uhlenbeck compactification has the structure of a projective variety and is dominated by the algebraic compactification coming from the grothendieck quot scheme the latter may be embedded into the moduli space of solutions to a generalized version of the vortex equations studied by bradlow this gives an effective way of computing certain intersection numbers known as gromov invariants on the space of holomorphic maps into grassmannians we carry out these computations in the case where the riemann surface has genus one department of mathematics university of utah salt lake city utah 84112 e mail address bertram math utah edu department of mathematics brown university providence rhode island 02912 e mail address daskal gauss math brown edu department of mathematics university of california irvine california 92717 e mail address raw math uci edu license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

on the de rham cohomology of differential and algebraic stacks abstract we introduce the notion of cofoliation on a stack a cofoliation is a change of the differentiable structure which amounts to giving a full representable smooth epimorphism cofoliations are uniquely determined by their associated lie algebroids cofoliations on stacks arise from flat connections on groupoids connections on groupoids generalize connections on gerbes and bundles in a natural way a flat connection on a groupoid is an integrable distribution of the morphism space compatible with the groupoid structure and complementary to both source and target fibres a cofoliation of a stack determines the flat groupoid up to etale equivalence we show how a cofoliation on a stack gives rise to a refinement of the hodge to de rham spectral sequence where the e 1 term consists entirely of vector bundle valued cohomology groups our theory works for differentiable holomorphic and algebraic stacks

on differential operators on complete symmetric varieties of type a1 and a2 abstract in this paper we consider the algebra of global differential operators d x on wonderful compactifications x of symmetric spaces g h of type a 1 and a 2 we will first construct a global differential operator on these varieties that does not come from the infinitesimal action of the lie algebra of g we will then focus on type a 2 where we will show that d x is an algebra of finite type and that for any invertible sheaf l on x h 0 x l is either 0 or a simple left d x l module finally we will show with the help of local cohomology that this still holds for higher cohomology groups h i x l

parabolic higgs bundles and representations of the fundamental group of a punctured surface into a real group abstract we study parabolic g higgs bundles over a compact riemann surface with fixed punctures when g is a real reductive lie group and establish a correspondence between these objects and representations of the fundamental group of the punctured surface in g with arbitrary holonomy around the punctures this generalizes simpson s results for gl n c to arbitrary complex and real reductive lie groups three interesting features are the relation between the parabolic degree and the tits geometry of the boundary at infinity of the symmetric space the treatment of the case when the logarithm of the monodromy is on the boundary of a weyl alcove and the correspondence of the orbits encoding the singularity via the kostant sekiguchi correspondence we also describe some special features of the moduli spaces when g is a split real form or a group of hermitian type

the yang mills heat flow on the moduli space of framed bundles on a surface we study the analog of the yang mills heat flow on the moduli space of framed bundles on a cut surface existence and convergence of the heat flow give a stratification of morse type invariant under the action of the loop group we use the stratification to prove versions of kahler quantization commutes with reduction and kirwan surjectivity

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

the strong macdonald conjecture and hodge theory on the loop grassmannian we prove the strong macdonald conjecture of hanlon and feigin for reductive groups g in a geometric reformulation we show that the dolbeault cohomology hq x op of the loop grassmannian x is freely generated by de rham s forms on the disk coupled to the indecomposables of h bg equating the two euler characteristics gives an identity independently known to macdonald m which generalises ramanujan s 1 1 sum for simply laced root systems at level 1 we also find a strong form of bailey s 4 4 sum failure of hodge decomposition implies the singularity of x and of the algebraic loop groups some of our results were announced in t2

a model for competitiveness level analysis in sports competitions application to basketball abstract the degree of overall competitiveness of a sport league is a complex phenomenon it is difficult to assess and quantify all elements that yield the final standing in this paper we analyze the general behavior of the result matrices of each season and we use the corresponding results as a probably density thus the results of previous seasons are a way to investigate the probability that each team has to reach a certain number of victories we developed a model based on shannon entropy using two extreme competitive structures a hierarchical structure and a random structure and applied this model to investigate the competitiveness of two of the best professional basketball leagues the nba usa and the acb spain both leagues entropy levels are high nba mean 0 983 acb mean 0 980 indicating high competitiveness although the entropy of the acb from 0 986 to 0 972 demonstrated more seasonal variability than that of the nba from 0 985 to 0 990 a possible result of greater sporting gradients in the acb the use of this methodology has proven useful for investigating the competitiveness of sports leagues as well as their underlying variability across time

numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh a finite difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two dimensional poisson equation s 0 where is a function of or its derivatives sis a function of position and or its normal derivative is specified on the boundary the finite difference equations are solved by successive overrelaxation the triangle mesh which is constructed numerically by solving laplace s equation is easily adapted to nonrectangular boundaries and interfaces examples of numerical results are given for the magnetostatic problem with iron and other possible applications are mentioned

moduli of parabolic higgs bundles and atiyah algebroids in this paper we study the geometry of the moduli space of non strongly parabolic higgs bundles over a riemann surface with marked points we show that this space possesses a poisson structure extending the one over the dual of an atiyah al gebroid over the moduli space of parabolic vector bundles by con sidering the case of full flags we get a grothendieck springer reso lution for all other flag types in particular for the moduli spaces of twisted higgs bundles as studied by markman and bottacin and used in the recent work of laumon ngo we discuss the hitchin system and demonstrate that all these moduli spaces are inte grable systems in the poisson sense

unstructured mesh manipulation in response to surface deformation the winslow elliptic smoothing equations have been shown to be effective for smoothing structured and unstructured computational meshes used in computational fluid dynamics applications although an implicit computational space is readily available for structured meshes an explicitly constructed space is required for unstructured meshes for a three dimensional mesh a method is presented where the original physical space is manipulated to generate virtual control volumes that can be employed as an effective computational space a two phase volume deformation scheme is implemented to effectively address mesh requirements for the viscous region near a no slip slip surface region limited smoothing is employed to fine tune the mesh smoothing to specific areas of interest and greatly increase the efficiency of the overall process a tool called meshgrind is used to demonstrate elliptic mesh manipulation and smoothing on practical engineering applications several test cases demonstrate winslow elliptic smoo

groupe de picard des varietes de modules de fibres semi stables sur les courbes algebriques soient x une courbe algebrique projective lisse de genre g 2 sur r d des entiers avec r 2 on note u r d la variete de modules des fibres algebriques semi stables sur x de rang r et de degre d us r d l ouvert de u r d correspondant aux fibres stables on sait que u r d est une variete algebrique projective irreductible et normale si r et d ne sont pas premiers entre eux u r d n est pas lisse sauf dans une exception le cas ou g 2 r 2 et d est pair on supposera dans cet article qu on n est pas dans ce cas on a alors codimu r d u r d us r d 2 et u r d us r d est le lieu des points singuliers de u r d si l est un fibre en droites de degre d sur x on note u r l la sous variete fermee de u r d correspondant aux fibres vectoriels de determinant isomorphe a l on etudie dans cet article les groupes de picard pic u r d et pic u r l on montre d abord que les varietes u r d et u r l sont localement factorielles on calcule ensuite pic u r d et pic u r l qui sont decrits au moyen des diviseurs thetas generalises

formality in an equivariant setting we define and discuss g formality for certain spaces endowed with an action by a compact lie group this concept is essentially formality of the borel construction of the space in a category of commutative differential graded algebras over r h bg these results may be applied in computing the equivariant cohomology of their loop spaces

the multiplicative eigenvalue problem and deformed quantum cohomology abstract we construct deformations of the small quantum cohomology rings of homogeneous spaces g p and obtain an irredundant set of inequalities determining the multiplicative eigen polytope for the compact form k of g

the index formula for the moduli of g bundles on a curve we prove the formulae conjectured by the first author for the index of k theory classes over the moduli stack of algebraic g bundles on a smooth projective curve the formulae generalize e verlinde s for line bundles and have witten s integrals over the moduli space of stable bundles as their large level limits as an application we prove the newstead ramanan conjecture on the vanishing of high chern classes of certain moduli spaces of semi stable g bundles

borel weil bott theory on the moduli stack of g bundles over a curve let g be a semi simple group and m the moduli stack of g bundles over a smooth complex projective curve using representation theoretic methods i prove the pure dimensionality of sheaf cohomology for certain evaluation vector bundles over m twisted by powers of the fundamental line bundle this result is used to prove a borel weil bott theorem conjectured by g segal for certain generalized flag varieties of loop groups along the way the homotopy type of the group of algebraic maps from an affine curve to g and the homotopy type the hodge theory and the picard group of m are described one auxiliary result in appendix a is the alexander cohomology theorem conjectured in gro2 a self contained account of the uniformization theorem of ls for the stack m is given including a proof of a key result of drinfeld and simpson in characteristic 0 a basic survey of the simplicial theory of stacks is outlined in appendix b

the poisson model limits in nba basketball complexity in team sports abstract team sports are frequently studied by researchers there is presumption that scoring in basketball is a random process and that can be described using the poisson model basketball is a collaboration opposition sport where the non linear local interactions among players are reflected in the evolution of the score that ultimately determines the winner in the nba the outcomes of close games are often decided in the last minute where fouls play a main role we examined 6130 nba games in order to analyze the time intervals between baskets and scoring dynamics most numbers of baskets n over a time interval t follow a poisson distribution but some e g t 10 s n 3 behave as a power law the poisson distribution includes most baskets in any game in most game situations but in close games in the last minute the numbers of events are distributed following a power law the number of events can be adjusted by a mixture of two distributions in close games both teams try to maintain their advantage solely in order to reach the last minute a completely different game for this reason we propose to use the poisson model as a reference the complex dynamics will emerge from the limits of this model

football goal distributions and extremal statistics we analyse the distributions of the number of goals scored by home teams away teams and the total scored in the match in domestic football games from 169 countries between 1999 and 2001 the probability density functions pdfs of goals scored are too heavy tailed to be fitted over their entire ranges by poisson or negative binomial distributions which would be expected for uncorrelated processes log normal distributions cannot include zero scores and here we find that the pdfs are consistent with those arising from extremal statistics in addition we show that it is sufficient to model english top division and fa cup matches in the seasons of 1970 71 2000 01 on poisson or negative binomial distributions as reported in analyses of earlier seasons and that these are not consistent with extremal statistics

dimension of zero weight space an algebro geometric approach abstract let g be a connected adjoint simple algebraic group over the complex numbers with a maximal torus t and a borel subgroup b containing t the study of zero weight spaces in irreducible representations of g has been a topic of considerable interest there are many works which study the zero weight space as a representation space for the weyl group in this paper we study the variation on the dimension of the zero weight space as the highest weight of the irreducible representation varies over the set of dominant integral weights of t which are lattice points in a certain polyhedral cone the theorem proved here asserts that the zero weight spaces have dimensions which are piecewise quasi polynomial functions on the polyhedral cone of dominant integral weights the main tool we use are the geometric invariant theory and the riemann roch theorem

scaling of conformal blocks and generalized theta functions over overline mathcal m _ g n by way of intersection theory on overline mathcal m g n we show that geometric interpretations for conformal blocks as sections of ample line bundles over projective varieties do not have to hold at points on the boundary we show such a translation would imply certain recursion relations for first chern classes of these bundles while recursions can fail geometric interpretations are shown to hold under certain conditions

adaptive optimization based improvement of tetrahedral meshes a tetrahedral mesh improvement method is presented that uses an optimization based node perturbation technique to minimize a cost function the cost function for each tetrahedron is based on the element condition number this condition number incorporates a weight matrix that transforms the element from physical space to a reference space the condition number is a measure of the conformity of the physical element with respect to the reference element feature based adaptation is incorporated into the element weight matrix to influence the node perturbation scheme to favor nonunit aspect ratio elements the mesh improvement scheme produces meshes that cluster grid nodes in high gradient regions of the selected adaptation function results for several inviscid three dimensional cases are included

der kanonische modul eines invariantenrings abstract we calculate the canonical module of a ring of invariants r of a reductive group acting on an affine variety from that we derive a criterion for the gorenstein property to hold for r in case r is the ring of invariants of a graded ring we obtain lower and upper bounds for the degree of the generating function of r

trace functionals on noncommutative deformations of moduli spaces of flat connections abstract we describe an efficient construction of a canonical noncommutative deformation of the algebraic functions on the moduli spaces of flat connections on a riemann surface the resulting algebra is a variant of the quantum moduli algebra introduced by alekseev grosse and schomerus and buffenoir and roche we construct a natural trace functional on this algebra and show that it is related to the canonical trace in the formal index theory of fedosov and nest and tsygan via verlinde s formula

gauged gromov witten theory for small spheres we relate the genus zero gauged gromov witten invariants of a smooth projective variety for sufficiently small area with equivariant gromov witten invariants as an application we deduce a gauged version of abelianization for gromov witten invariants in the small area chamber in the symplectic setting we prove that any sequence of genus zero symplectic vortices with vanishing area has a subsequence that converges after gauge transformation to a holomorphic map with zero average moment map

geometric proof of a conjecture of fulton we give a geometric proof of a conjecture of fulton on the multiplicities of irreducible representations in a tensor product of irreducible representations for gl r

on the variation in the cohomology of the symplectic form of the reduced phase space is called the momentum mapping of the hamiltonian t action given 1 1 the condition 1 2 just means that t acts along the fibers of j for the basic definitions and properties of non commutative hamiltonian group actions see am the results of this paper can easily be extended to hamiltonian actions of arbitrary compact connected lie groups by applying our results to the action of its maximal toms and using the equivariance of the momentum mapping for some more details see the remarks at the end of sect 2 we will assume throughout this paper that the momentum map is proper that is j i u is compact for each compact subset u of t now let r be a regular value of j that is t j tmm t is surjective for all meye j 1 4 then ye is a smooth submanifold of m compact because

descent of coherent sheaves and complexes to geometric invariant theory quotients abstract fix a scheme x over a field of characteristic zero that is equipped with an action of a reductive algebraic group g we give necessary and sufficient conditions for a g equivariant coherent sheaf on x or a bounded above complex of g equivariant coherent sheaves on x to descend to a good quotient x g this gives a description of the coherent derived category of x g as an admissible subcategory of the equivariant derived category of x

gromov witten gauge theory we introduce a modular completion of the stack of maps from stable marked curves to the quotient stack pt c x and use this stack to construct some gauge theoretic analogues of the gromov witten invariants we also indicate the generalization of these invariants to the quotient stacks x c x where x is a smooth proper complex algebraic variety

the witten reshetikhin turaev invariant for links in finite order mapping tori i abstract we state asymptotic expansion and growth rate conjectures for the witten reshetikhin turaev invariants of arbitrary framed links in 3 manifolds and we prove these conjectures for the natural links in mapping tori of finite order automorphisms of marked surfaces our approach is based upon geometric quantisation of the moduli space of parabolic bundles on the surface which we show coincides with the construction of the witten reshetikhin turaev invariants using conformal field theory as was recently completed by andersen and ueno

q exponential weibull and q weibull distributions an empirical analysis abstract in a comparative study the q exponential and weibull distributions are employed to investigate frequency distributions of basketball baskets cyclone victims brand name drugs by retail sales and highway length in order to analyze the intermediate cases a distribution the q weibull one which interpolates the q exponential and weibull ones is introduced it is verified that the basketball baskets distribution is well described by a q exponential whereas the cyclone victims and brand name drugs by retail sales ones are better adjusted by a weibull distribution on the other hand for highway length the q exponential and weibull distributions do not give satisfactory adjustment being necessary to employ the q weibull distribution furthermore the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law q exponential with q 1 controversy

properness for scaled gauged maps we prove properness of moduli stacks of gauged maps satisfying a stability conditition introduced by mundet 42 schmitt 48 and ziltener 59 the proof combines a git construction of schmitt 48 properness for twisted stable maps by abramovich vistoli 1 a variation of a boundedness argument due to ciocan fontanine kim maulik 13 and a removal of singularities for bundles on surfaces in colliot thelene sansuc 14

an analytic proof of the geometric quantization conjecture of guillemin sternberg we present a direct analytic approach to the guillemin sternberg conjecture gs that geometric quantization commutes with symplectic reduction which was proved recently by meinrenken m1 m2 and vergne v1 v2 et al besides providing a new proof of this conjecture our methods also lead immediately to further extensions in various contexts

moduli of vector bundles frobenius splitting and invariant theory let x be an irreducible projective curve of genus g over an algebraically closed field of positive characteristic 2 3 in part i we prove adapting the degeneration arguments of n tr that moduli spaces of rank two parabolic bundles on x are frobenius split m r for generic smooth x a similar result holds for x nodal a consequence is the verlinde formula in positive characteristic in part ii we give a direct proof of the fact that the local rings of the moduli spaces are f split and further that they are cohen macaulay this involves showing that the ring of invariants of g copies of 2 x 2 matrices under the adjoint action of sl 2 is f split and cohen macaulay

vibro acoustic radiation of rigid bodies oscillating at large amplitude and low mach number modelling and experiments the acoustic radiation of vibrating bodies can usually be considered as a linear phenomenon as in most cases the vibration amplitudes of oscillating bodies are small compared to their dimension however in case of large amplitude and small mach number the large displacement amplitude of a vibrating body gives rise to geometric nonlinear acoustic effects in this paper it is shown that the nonlinearity causes an asymmetry in the time signal of the radiated pressure as observed at a fixed position resulting in harmonic distortion of the radiated sound field these nonlinear effects can be analysed by the finite element method using a linear fluid behaviour in combination with a moving mesh approach this approach is implemented and used to predict the nonlinear sound radiation of lithographic stages oscillating at large amplitude and low mach number acoustic experiments prove the validity of the analysis technique for the geometrical nonlinear phenomena in addition the structural response of a nearby body excited by the nonlinear acoustic radiation of the stage is calculated and verified experimentally

multiplicities formula for geometric quantization part ii 1 introduction let p be a compact manifold let h be a compact lie group acting on the right on p we assume that the stabilizer of each element y e p is a finite subgroup of h the space m p h is an orbifold and every orbifold can be presented this way if h acts freely then m is a manifold if ae graded space of h invariant solutions of the h horizontal dirac operator on p twisted by the line bundle let m o 9 be the moment map for the g action assume 0 is a regular value of let mred be the reduced orbifold of m that is mred o g consider the reduced orbifold line bundle rd lu lto g on m oa in the ease where both g andh are torus we prove here the formula

on the equivariant formality of kahler manifolds with torus group actions we consider simply connected compact kahler manifolds which have a holomorphic action of a torus group we use the existing equivariant models for rational homotopy to show that these spaces satisfy an equivariant formality condition over the complex numbers