gauge theories labelled by three manifolds we propose a dictionary between geometry of triangulated 3 manifolds and physics of three dimensional n 2 gauge theories under this duality standard operations on triangulated 3 manifolds and various invariants thereof classical as well as quantum find a natural interpretation in field theory for example independence of the sl 2 chern simons partition function on the choice of triangulation translates to a statement that s 3 b partition functions of two mirror 3d n 2 gauge theories are equal three dimensional n 2 field theories associated to 3 manifolds can be thought of as theories that describe boundary conditions and duality walls in four dimensional n 2 scfts thus making the whole construction functorial with respect to cobordisms and gluing

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

integrability from 2d n 2 2 dualities we study integrable models in the context of the recently discovered gauge ybe correspondence where the yang baxter equation is promoted to a duality between two su persymmetric gauge theories we study flavored elliptic genus of 2d n 2 2 quiver gauge theories which theories are defined from statistical lattices regarded as quiver diagrams our r matrices are written in terms of theta functions and simplifies considerably when the gauge groups at the quiver nodes are abelian we also discuss the modularity properties of the r matrix reduction of 2d index to 1d witten index and string theory realizations of our theories

crossed products of c correspondences by amenable group actions abstract let x a be a c correspondence with a continuous action by an amenable locally compact group g we will show that if x g a g is the induced c correspondence and is the induced action on o x then o x g o x g as applications we obtain b abadie takai duality for crossed products by hilbert c modules preprint arxiv 0709 1122v1 proposition 4 5 and a kumjian d pask c algebras of directed graphs and group actions ergodic theory dynam systems 19 6 1999 1503 1519 corollary 2 5

equivariant deformations of homogeneous spaces abstract c algebraic deformations of homogeneous spaces g are constructed by completing dense subspaces of c 0 g in a different multiplication and c norm these deformations are equivariant in the sense that they still carry a natural action of g by left translation the motivating examples are the noncommutative heisenberg manifolds of rieffel but the construction given here is based on the authors twisted dual group algebras which are equivariant deformations of c 0 g the procedure is general enough to give other recently studied families of noncommutative spaces and some interesting new examples of simple c algebras

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

elliptic hypergeometry of supersymmetric dualities ii orthogonal groups knots and vortices we consider seiberg electric magnetic dualities for 4d mathcal n 1 sym theories with so n gauge group for all such known theories we construct superconformal indices scis in terms of elliptic hypergeometric integrals equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals in particular we describe a number of new elliptic beta integrals associated with the s confining theories with the spinor matter fields reductions of some dualities from sp 2n to so 2n or so 2n 1 gauge groups are described interrelation of scis and the witten anomaly is briefly discussed possible applications of the elliptic hypergeometric integrals to a two parameter deformation of 2d conformal field theory and related matrix models are indicated connections of the reduced scis with the state integrals of knot theory generalized agt duality for 3 3 d theories and a 2d vortex partition function are described

c algebras generated by stable relations abstract presentations of certain c algebras such as c0 0 1 mn by generators and relations are proven to be stable by the weakest definition of stability a set p1 pn of star polynomials is stable if operators a1 an which almost satisfy these relations meaning pi a1 an can be perturbed within c a1 an to satisfy these relations exactly homotopy and perturbation results for these c algebras are corollaries in particular we prove some new results about the dimension drop c algebras a n c 0 1 m n 0 1 c i we show that an is semiprojective answering a question of effros and kaminker also we show that whenever an b is a homomorphism approximately contained in a sub c algebra b0 b there is a nearby homomorphism of an into b0 this answers a question raised by elliott we prove technical results regarding mn c0 0 1 which should be useful elsewhere first we show this is projective meaning a star homomorphism mn c0 0 1 b j always lifts to a star homomorphism mn c0 0 1 b secondly we show that for a finitely generated m n a m n c 0 0 1 c 0 0 1 a if the amalgamation is done properly

the c algebra of a vector bundle and fields of cuntz algebras abstract we study the cuntz pimsner algebra associated with the module of continuous sections of a hilbert bundle and prove that it is a continuous bundle of cuntz algebras furthermore we assign to bundles of cuntz algebras carrying a global circle action a class in the representable kk group of the zero grade bundle we explicitly compute such class for the cuntz pimsner algebra of a vector bundle

vortex partition functions wall crossing and equivariant gromov witten invariants in this paper we identify the problem of equivariant vortex counting in a 2 2 supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant gromov witten invariants of the git quotient target space determined by the quiver we provide new contour integral formulae for the mathcal i and mathcal j functions encoding the equivariant quantum cohomology of the target space its chamber structure is shown to be encoded in the analytical properties of the integrand this is explained both via general arguments and by checking several key cases we show how several results in equivariant gromov witten theory follow just by deforming the integration contour in particular we apply our formalism to compute gromov witten invariants of the mathbb c 3 mathbb z n orbifold of the uhlembeck partial compactification of the moduli space of instantons on mathbb c 2 and of an and dn singularities both in the orbifold and resolved phases moreover we analyse dualities of quantum cohomology rings of holomorphic vector bundles over grassmannians which are relevant to bps wilson loop algebrae

a construction of killing spinors on s n we derive simple general expressions for the explicit killing spinors on the n sphere for arbitrary n using these results we also construct the killing spinors on various ads sphere supergravity backgrounds including ads5 s5 ads4 s7 and ads7 s4 in addition we extend previous results to obtain the killing spinors on the hyperbolic spaces hn

on action angle variables for the second poisson bracket of kdv we prove that on the sobolev spaces h n s 1 n 0 each leaf of the foliation induced by the second poisson bracket of kdv admits global action angle variables the actions with respect to the first bracket raise to the actions with respect to the second bracket the angles for the first bracket are at the same time angles for the second bracket

c algebras and equivalences for c correspondences abstract we study several notions of shift equivalence for c correspondences and the effect that these equivalences have on the corresponding pimsner dilations among others we prove that non degenerate regular full c correspondences which are shift equivalent have strong morita equivalent pimsner dilations we also establish that the converse may not be true these results settle open problems in the literature in the context of c algebras we prove that if two non degenerate regular full c correspondences are shift equivalent then their corresponding cuntz pimsner algebras are strong morita equivalent this generalizes results of cuntz and krieger and muhly tomforde and pask as a consequence if two subshifts of finite type are eventually conjugate then their cuntz krieger algebras are strong morita equivalent our results suggest a natural analogue of the shift equivalence problem in the context of c correspondences even though we do not resolve the general shift equivalence problem we obtain a positive answer for the class of imprimitivity bimodules

quantum heisenberg manifolds as twisted groupoid c algebras abstract the quantum heisenberg manifolds are noncommutative manifolds constructed by m rieffel as strict deformation quantizations of heisenberg manifolds and have been studied by various authors rieffel constructed the quantum heisenberg manifolds as the generalized fixed point algebras of certain crossed product c algebras and they also can be realized as crossed products of c t 2 by hilbert c bimodules in the sense of abadie et al in this paper we describe how the quantum heisenberg manifolds can also be realized as twisted groupoid c algebras in the final section for a transformation groupoid x z with x compact and e p x a locally trivial principal g bundle where g is a compact abelian group we form a groupoid that is a locally trivial principal g bundle over x z which reduces to the twist groupoid of the second author when g t

modules over operator algebras and the maximal c dilation abstract we continue our study of the general theory of possibly nonselfadjoint algebras of operators on a hilbert space and modules over such algebras developing a little more technology to connect nonselfadjoint operator algebra with the c algebraic framework more particularly we make use of the universal or maximal c algebra generated by an operator algebra and c dilations this technology is quite general however it was developed to solve some problems arising in the theory of morita equivalence of operator algebras and as a result most of the applications given here and in a companion paper are to that subject other applications given here are to extension problems for module maps and characterizations of c algebras

the yang mills functional and laplace s equation on quantum heisenberg manifolds in this paper we discuss the yang mills functional and a certain family of its critical points on quantum heisenberg manifolds using noncommutative geometrical methods developed by a connes and m rieffel in our main result we construct a certain family of connections on a projective module over a quantum heisenberg manifold that gives rise to critical points of the yang mills functional moreover we show that there is a relationship between this particular family of critical points of the yang mills functional and laplace s equation on multiplication type skew symmetric elements of quantum heisenberg manifolds recall that laplacian is the leading term for the coupled set of equations making up the yang mills equation

yang mills connections on quantum heisenberg manifolds abstract we investigate critical points and minimizers of the yang mills functional ym on quantum heisenberg manifolds d c where the yang mills functional is defined on the set of all compatible linear connections on finitely generated projective modules over d c a compatible linear connection which is both a critical point and minimizer of ym is called a yang mills connection in this paper we investigate yang mills connections with constant curvature we are interested in yang mills connections on the following classes of modules over d c i abadie s module of trace 2 and its submodules ii modules of trace 2 iii tensor product modules of the form p e c where e c is morita equivalent to d c and p is a projection in e c we present a characterization of critical points and minimizers of ym and provide a class of new yang mills connections with constant curvature on over d c via concrete examples in particular we show that every yang mills connection on over d c with constant curvature should have a certain form of the curvature such as x y x z 0 and y z i id e also we show that these yang mills connections with constant curvature do not provide global minima but only local minima we do this by constructing a set of compatible connections that are not critical points but their values are smaller than those of yang mills connections with constant curvature our other results include i an example of a compatible linear connection with constant curvature on d c such that the corresponding connection on an isomorphic projective module does not have constant curvature and ii the construction of a compatible linear connection with constant curvature which neither attains its minimum nor is a critical point of ym on d c consequently the critical points and minimizers of ym depend crucially on the geometric structure of d c and of the projective modules over d c furthermore we construct the grassmannian connection on the projective modules with trace 2 over d c and compute its corresponding curvature finally we construct tensor product connections on p e c whose coupling constant is 2 and characterize the critical points of ym for this projective module

partition functions of n 2 2 gauge theories on s 2 and vortices we apply localization techniques to compute the partition function of a two dimensional mathcal n 2 2 r symmetric theory of vector and chiral multiplets on s2 the path integral reduces to a sum over topological sectors of a matrix integral over the cartan subalgebra of the gauge group for gauge theories which would be completely higgsed in the presence of a fayet iliopoulos term in flat space the path integral alternatively reduces to the product of a vortex times an antivortex partition functions weighted by semiclassical factors and summed over isolated points on the higgs branch for applications we evaluate the partition function for some u n gauge theories showing equality of the path integrals for theories conjectured to be dual by hori and tong and deriving new expressions for vortex partition functions

gap estimates of the spectrum of hill s equation and action variables for kdv consider the schrodinger equation y v y y for a potential v of period 1 in the weighted sobolev space n z 0 r 0 h s c f x k f k e f n where f k k z denote the fourier coefficients of f when considered as a function of period 1

crossed products by endomorphisms and reduction of relations in relative cuntz pimsner algebras abstract starting from an arbitrary endomorphism of a unital c algebra a we construct a crossed product it is shown that the natural construction depends not only on the c dynamical system a but also on the choice of an ideal j orthogonal to ker the article gives an explicit description of the internal structure of this crossed product and in particular discusses the interrelation between relative cuntz pimsner algebras and partial isometric crossed products we present a canonical procedure that reduces any given c correspondence to the smallest c correspondence yielding the same relative cuntz pimsner algebra as the initial one in the context of crossed products this reduction procedure corresponds to the reduction of c dynamical systems and allows us to establish a coincidence between relative cuntz pimsner algebras and crossed products introduced

inverse problem and the trace formula for the hill operator ii consider the hill operator t d 2 dx 2 q x on l 2 mathbb r where q in l 2 0 1 is a 1 periodic real potential and int 0 1q x dx 0 the spectrum of t is absolutely continuous and consists of intervals separated by gaps gamma n a n a n n geq 1 let mu n n geq 1 be the dirichlet eigenvalue of the equation y qy ly on the interval 0 1 introduce the vector g n g cn g sn in mathbb r 2 with components g cn a n a n 2 mu n and g sn gamma n 2 4 g cn 2 s n where the sign s n or s n for all n geq 1 using nonlinear functional analysis in hilbert spaces we show that the mapping g q to g q g n 1 iy in ell 2 oplus ell 2 is a real analytic isomorphism in the second part a trace formula for q in l 2 0 1 is proved

killing spinors on spheres and hyperbolic manifolds properties of killing spinors on spheres and hyperbolic manifolds are investigated with an emphasis on the relations to killing vectors conformal killing vectors and solutions of maxwell s equations

elliptic genera of 2d mathcal n 2 gauge theories we compute the elliptic genera of general two dimensional mathcal n 2 2 and mathcal n 0 2 gauge theories we find that the elliptic genus is given by the sum of jeffrey kirwan residues of a meromorphic form representing the one loop determinant of fields on the moduli space of flat connections on t2 we give several examples illustrating our formula with both abelian and non abelian gauge groups and discuss some dualities for u k and su k theories this paper is a sequel to the authors previous paper benini et al lett math phys 104 465 493 2014

singularities of bi hamiltonian systems we study the relationship between singularities of bi hamiltonian systems and algebraic properties of compatible poisson brackets as the main tool we introduce the notion of linearization of a poisson pencil from the algebraic viewpoint a linearized poisson pencil can be understood as a lie algebra with a fixed 2 cocycle in terms of such linearizations we give a criterion for non degeneracy of singular points of bi hamiltonian systems and describe their types

integrating over higgs branches we develop some useful techniques for integrating over higgs branches in supersymmetric theories with 4 and 8 supercharges in particular we define a regularized volume for hyperkahler quotients we evaluate this volume for certain ale and alf spaces in terms of the hyperkahler periods we also reduce these volumes for a large class of hyperkahler quotients to simpler integrals these quotients include complex coadjoint orbits instanton moduli spaces on 4 and ale manifolds hitchin spaces and moduli spaces of parabolic higgs bundles on riemann surfaces in the case of hitchin spaces the evaluation of the volume reduces to a summation over solutions of bethe ansatz equations for the non linear schrodinger system we discuss some applications of our results

operator algebras of monomial ideals in noncommuting variables abstract we study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables through the apparatus of subproduct systems and c correspondences we provide a full comparison amongst the related operator algebras for our analysis we isolate a partially defined dynamical system to which we refer as the quantised dynamics of the monomial ideal in addition we revisit several previously considered constructions these include matsumoto s subshift c algebras as well as the tensor and the pimsner algebras associated with dynamical systems or graphs we sort out the various relations by giving concrete conditions and counterexamples that orientate the operator algebras of our context it appears that the boundary c algebras do not arise as the quotient with the compact operators unconditionally we establish a dichotomy to this effect by examining the resulting tensor algebras we identify their boundary representations we analyse their c envelopes and we give criteria for hyperrigidity moreover we completely classify them in terms of the data provided by the monomial ideals for tensor algebras of c correspondences and bounded isomorphisms this is achieved up to the level of local conjugacy in the sense of davidson and roydor for the quantised dynamics for tensor algebras of subproduct systems and algebraic isomorphisms this is achieved up to the level of equality of monomial ideals modulo permutations of the variables in the process we accomplish more in different directions most notably we show that tensor algebras form a complete invariant for isomorphic resp similar subproduct systems of homogeneous ideals up to isometric resp bounded isomorphisms the results on local conjugacy are obtained via an alternative proof of the breakthrough result of davidson and katsoulis on piecewise conjugate systems for our purposes we use appropriate compressions of the fock representation we then apply this alternative proof locally for the partially defined quantised dynamics in this way we avoid the topological graphs machinery and pave the way for further applications these include operator algebras of dynamical systems over commuting contractions or over row commuting contractions

quiver text w _ boldsymbol epsilon _ mathbf 1 boldsymbol epsilon _ mathbf 2 algebras of 4d boldsymbol mathcal n mathbf mathbf 2 gauge theories we construct an e deformation of w algebras corresponding to the additive version of quiver w q t algebras which feature prominently in the 5d version of the bps cft correspondence and refined topological strings on toric calabi yau s this new type of algebras fill in the missing intermediate level between q deformed and ordinary w algebras we show that e deformed w algebras are spectral duals of conventional w algebras in particular the e deformed conformal blocks manifestly reproduce instanton partition functions of 4d n 2 quiver gauge theories in the full background and give dual integral representations of ordinary w conformal blocks

a bethe ansatz type formula for the superconformal index inspired by recent work by closset kim and willett we derive a new formula for the superconformal or supersymmetric index of 4d mathcal n 1 theories such a formula is a finite sum over the solution set of certain transcendental equations that we dub bethe ansatz equations of a function evaluated at those solutions

the jiang su algebra revisited we give a number of new characterizations of the jiang su algebra z both intrinsic and extrinsic in terms of c algebraic dynamical topological and k theoretic conditions along the way we study divisibility properties of c algebras we give a precise characterization of those unital c algebras of stable rank one that admit a unital embedding of the dimensiondrop c algebra zn n 1 and we prove a cancellation theorem for the cuntz semigroup of c algebras of stable rank one

crossed products by hilbert pro c bimodules versus tensor products abstract we show that if x a and y b are two isomorphic hilbert pro c bimodules then the crossed product a x z of a by x and the crossed product b y z of b by y are isomorphic as pro c algebras we also prove a property of associativity between min and x as well as max and x

circle actions on c algebras partial automorphisms and a generalized pimsner voiculescu exact sequence abstract we introduce a method to study c algebras possessing an action of the circle group from the point of view of their internal structure and their k theory under relatively mild conditions our structure theorem shows that any c algebra where an action of the circle is given arises as the result of a construction that generalizes crossed products by the group of integers such a generalized crossed product construction is carried out for any partial automorphism of a c algebra where by a partial automorphism we mean an isomorphism between two ideals of the given algebra our second main result is an extension to crossed products by partial automorphisms of the celebrated pimsner voiculescu exact sequence for k groups the representation theory of the algebra arising from our construction is shown to parallel the representation theory for c dynamical systems in particular we generalize several of the main results relating to regular and covariant representations of crossed products

noncommutative finite dimensional manifolds ii moduli space and structure of noncommutative 3 spheres this paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3 spheres we develop the notion of central quadratic form for quadratic algebras and a general theory which creates a bridge between noncommutative differential geometry and its purely algebraic counterpart it allows to construct a morphism from an involutive quadratic algebra to a c algebra constructed from the characteristic variety and the hermitian line bundle associated to the central quadratic form we apply the general theory in the case of noncommutative 3 spheres and show that the above morphism corresponds to a natural ramified covering by a noncommutative 3 dimensional nilmanifold we then compute the jacobian of the ramified covering and obtain the answer as the product of a period of an elliptic integral by a rational function we describe the real and complex moduli spaces of noncommutative 3 spheres relate the real one to root systems and the complex one to the orbits of a birational cubic automorphism of three dimensional projective space we classify the algebras and establish duality relations between them

on the morita equivalence of tensor algebras our objective is two fold first we want to develop a notion of morita equivalence for c correspondences that guarantees that if two c correspondences e and f are morita equivalent then the tensor algebras of e and f taoeu and taofu are strongly morita equivalent in the sense of 8 the toeplitz algebras toeu and tofu are strongly morita equivalent in the sense of rieffel 32 see 33 also and the cuntz pimsner algebras 28 ooeu and oofu are strongly morita equivalent in the same sense we were inspired by earlier work of curto williams and the first author in 15 and combes 14 these papers investigate conditions implying that the crossed product of two c dynamical systems are strongly morita equivalent given that the coefficient algebras are strongly morita equivalent abadie eilers and exel 1 were similarly inspired and developed a theory of morita equivalence for special c correspondences our analysis extends theirs but our arguments are different see example 2 5 and remarks 3 3 and 3 6 for a comparison of their results and ours second we want to investigate the converse implication that is we study the following question if taoeu and taofu are strongly morita equivalent in the sense of 8 when are e and f morita equivalent in the sense we define for this converse direction we focus on the tensor algebras rather than the toeplitz and cuntz pimsner algebras because very little can be said in the self adjoint setting here we were inspired by arveson s paper 2 in which it is proved that two ergodic measure preserving transformations are conjugate if and only if certain non self adjoint crossed products associated with the transformations are algebraically isomorphic see 3 also his analysis was further extended by k saito and the first author to cover non self adjoint crossed products built from automorphisms of general von neumann algebras they showed that non self adjoint crossed products built from properly outer automorphisms of von neumann algebras are isomorphic if and only if the automorphisms are conjugate see 22 and 23 our principal result in the converse direction theorem 7 2 asserts that if e and f are two aperiodic correspondences and if taoeu is strongly morita equivalent to taofu in the sense of 8 then e and f are morita equivalent as we shall see in 5 the notion of aperiodicity is an exact analogue for correspondences of the concept of free action in ergodic theory free action was a central hypothesis in arveson s

convergence to normal forms of integrable pdes in an infinite dimensional hilbert space we consider a family of commuting analytic vector fields vanishing at the origin and which are nonlinear perturbations of some fundamental linear vector fields we prove that one can construct by the method of poincar e normal form a local analytic coordinate transformation near the origin transforming the family into a normal form the result applies to the kdv and nls equations and to the toda lattice with periodic boundary conditions one gets existence of birkhoff coordinates in a neighbourhood of the origin the proof is obtained by directly estimating in an iterative way the terms of the poincar e normal form and of the transformation to it through a rapid convergence algorithm

convexity properties of the moment mapping ii be its associated momen t mapping see w for definitions the set x is the union of co adjoint orbits the main result of this paper is a description of the orbit structure of this set to describe this result we first note that the coadjoint orbits in q can be parametr ized as follows let t be a caf tan subalgebra of g and let b be a positive definite g invariant bilinear form on by means of b we get a g equivariant identification q let t be the subspace of q corresponding to t then every co adjoint orbit intersects i in a weyl group orbit so there is a one one correspondence between co adjoint orbits in q and weyl group orbits in t to get an even sharper parametrization let t be a weyl chamber in then every weyl group orbit intersects t in a single point so t is a modul i space for the co adjoint orbits two orbits in x are said to be of the same type if they are isomorphic as homogeneous g spaces since x is compact there are at most a finite number of different types of orbits see 1113 let h be a closed subgroup of t of codimension r and let cit be the set of all orbits in x of type g h

topological aperiodicity for product systems over semigroups of ore type we prove a version of uniqueness theorem for cuntz pimsner algebras of discrete product systems over semigroups of ore type to this end we introduce doplicher roberts picture of cuntz pimsner algebras and the semigroup dual to a product system of regular c correspondences under a certain aperiodicity condition on the latter we obtain the uniqueness theorem and a simplicity criterion for the algebras in question these results generalize the corresponding ones for crossed products by discrete groups due to archbold and spielberg and for exel s crossed products due to exel and vershik they also give interesting conditions for topological higher rank graphs and p graphs and apply to the new cuntz c algebra qn arising from the ax b semigroup over n

on the korteweg de vries equation convergent birkhoff normal form abstract the korteweg de vries equation kdv formula is a completely integrable hamiltonian system of infinite dimension with phase space the sobolev spacehn s1 r n 1 hamiltonian h q s1 1 2 xq x 2 q x 3 dx and poisson structure x the functionq 0 is an elliptic fixed point we prove that for anyn 1 the korteweg de vries equation and thus the entire kdv hierarchy admits globally defined real analytic action angle variables as a consequence it follows that in a neighborhood ofq 0 inh1 s1 r the kdv hamiltonian h and similarly any hamiltonian in the kdv hierarchy admits a convergent birkhoff normal form to the best of our knowledge this is the first such example in infinite dimension moreover using the constructed action angle variables we analyze the regularity properties of the hamiltonian vectorfield of kdv

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

continuous fields of c algebras arising from extensions of tensor c categories abstract the notion of extension of a given c category c by a c algebra a is introduced in the commutative case a c the objects of the extension category are interpreted as fiber bundles over of objects belonging to the initial category it is shown that the doplicher roberts algebra dr algebra in the following associated to an object in the extension of a strict tensor c category is a continuous field of dr algebras coming from the initial one in the case of the category of the hermitian vector bundles over the general result implies that the dr algebra of a vector bundle is a continuous field of cuntz algebras some applications to pimsner c algebras are given

topological freeness for c correspondences abstract we study conditions that ensure uniqueness theorems of cuntz krieger type for relative cuntz pimsner algebras o j x associated to a c correspondence x over a c algebra a we give general sufficient conditions phrased in terms of a multivalued map x acting on the spectrum a of a when x j is of type i we construct a directed graph dual to x and prove a uniqueness theorem using this graph when x j is liminal we show that topological freeness of this graph is equivalent to the uniqueness property for o j x as well as to an algebraic condition which we call j acyclicity of x as an application we improve the fowler raeburn uniqueness theorem for the toeplitz algebra t x we give new simplicity criteria for o x we generalize and enhance uniqueness results for relative quiver c algebras of muhly and tomforde we also discuss applications to crossed products by endomorphisms

deformation quantization of heisenberg manifolds form a smooth manifold equipped with a poisson bracket we formulate ac algebra framework for deformation quantization including the possibility of invariance under a lie group of diffeomorphisms preserving the poisson bracket we then show that the much studied non commutative tori give examples of such deformation quantizations invariant under the usual action of ordinary tori going beyond this the main results of the paper provide a construction of invariant deformation quantizations for those poisson brackets on heisenberg manifolds which are invariant under the action of the heisenberg lie group and for various generalizations suggested by this class of examples interesting examples are obtained of simplec algebras on which the heisenberg group acts ergodically

two sphere partition functions and gromov witten invariants many n 2 2 two dimensional nonlinear sigma models with calabi yau target spaces admit ultraviolet descriptions as n 2 2 gauge theories gauged linear sigma models we conjecture that the two sphere partition function of such ultraviolet gauge theories recently computed via localization by benini et al and doroud et al yields the exact kahler potential on the quantum kahler moduli space for calabi yau threefold target spaces in particular this allows one to compute the genus zero gromov witten invariants for any such calabi yau threefold without the use of mirror symmetry more generally when the infrared superconformal fixed point is used to compactify string theory this provides a direct method to compute the spacetime kahler potential of certain moduli e g vector multiplet moduli in type iia exactly in we compute these quantities for the quintic and for rodland s pfaffian calabi yau threefold and find agreement with existing results in the literature we then apply our methods to a codimension four determinantal calabi yau threefold in p 7 recently given a nonabelian gauge theory description by the present authors for which no mirror calabi yau is currently known we derive predictions for its gromov witten invariants and verify that our predictions satisfy nontrivial geometric checks

quantum sheaf cohomology on grassmannians in this paper we study the quantum sheaf cohomology of grassmannians with deformations of the tangent bundle quantum sheaf cohomology is a 0 2 deformation of the ordinary quantum cohomology ring realized as the ope ring in a 2 twisted theories quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models glsms here we study 0 2 deformations of nonabelian glsms for which previous methods have been intractable combined with the classical result the quantum ring structure is derived from the one loop effective potential we also utilize recent advances in supersymmetric localization to compute a 2 correlation functions and check the general result in examples in this paper we focus on physics derivations and examples in a companion paper we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring