deconvolution of non gaussian linear processes with vanishing spectral values we consider the problem of estimating the filter generating a non gaussian linear process and the decon voiution of that process when the spectral density of the process has zeros without using a minimum phase assumption we show that often if there are only finitely many zeros there are procedures to effect such an estimation and deconvolution

hadamard products of linear spaces abstract we describe properties of hadamard products of algebraic varieties we show any hadamard power of a line is a linear space and we construct star configurations from products of collinear points tropical geometry is used to find the degree of hadamard products of other linear spaces

grobner geometry of schubert polynomials given a permutation w sn we consider a determinantal ideal iw whose generators are certain minors in the generic n n matrix filled with independent variables using emultidegrees f as simple algebraic substitutes for torus equivariant cohomology classes on vector spaces our main theorems describe for each ideal iw

equivariant quantum schubert polynomials abstract we establish an equivariant quantum giambelli formula for partial flag varieties the answer is given in terms of a specialization of universal double schubert polynomials along the way we give new proofs of the presentation of the equivariant quantum cohomology ring as well as graham positivity of the structure constants in equivariant quantum schubert calculus

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

weight two motivic cohomology of classifying spaces for semisimple groups let f x to y be a torsor for a semisimple group g with y a smooth and geometrically irreducible variety over an arbitrary field we relate the etale motivic cohomology of weight two for x y and g we also compute the etale motivic cohomology groups of degree at most 4 for the classifying space of g this result was used in an another work by the author for the computation of the group of degree 3 cohomological invariants of semisimple groups with coefficients in bbb q bbb z 2

nonabelian localization in equivariant k theory and riemann roch for quotients abstract we prove a localization formula in equivariant algebraic k theory for an arbitrary complex algebraic group acting with finite stabilizer on a smooth algebraic space this extends to nondiagonalizable groups the localization formulas of nielsen diagonalizably linearized coherent sheaves bull soc math france 102 1974 85 97 and thomason une formule de lefschetz en k theorie equivariante algebrique duke math j 68 3 1992 447 462 as an application we give a riemann roch formula for quotients of smooth algebraic spaces by proper group actions this formula extends previous work of toen theoremes de riemann roch pour les champs de deligne mumford k theory 18 1 1999 33 76 and the authors riemann roch for quotients and todd classes of simplicial toric varieties comm algebra 31 2003 3735 3752

modeling non gaussian reflectivities generalizing wiener levinson deconvolution non gaussian modeling is used to generalize wiener levinson wl deconvolution and to obtain a procedure that is more robust to nonstationarities in the reflectivity and to correlated noise this generalization can lead to up to a 60 reduction in the dynamic range of the residual wavelet s amplitude response and in the rms error of phase estimates in addition it reduces to wl deconvolution when the reflectivity is gaussian or when noise masks the nonstationary features of the reflectivity

localization in equivariant intersection theory and the bott residue formula we prove the localization theorem for torus actions in equivariant intersection theory using the theorem we give another proof of the bott residue formula for chern numbers of bundles on smooth complete varieties in addition our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions this class is rather special but it includes some interesting examples such as complete intersections and schubert varieties 1 introduction the purpose of this paper is to prove the localization theorem for torus actions in equivariant intersection theory using the theorem we give another proof of the bott residue formula for chern numbers of bundles on smooth complete varieties in addition our techniques allow us to obtain residue formulas for bundles on a certain class of singular schemes which admit torus actions this class is rather special but it includes some interesting examples such as complete intersections cf bfq and schubert varieties let t be a split torus acting on a scheme x the 7 equivariant chow groups of x are a module over rt sym t where f is the character group of t the localization theorem states that up to torsion the equivariant chow groups of the fixed locus xt are isomorphic to those of x such a theorem is a hallmark of any equivariant theory the earliest version for equivariant cohomology is due to borel bo subsequently it theory versions were proved by segal se in topological a theory quart qu for actions of a cyclic group and thomason th2 for algebraic theory th2 for equivariant chow groups the localization isomorphism is given by the equivariant push forward induced by the inclusion of xt to x an interesting aspect of this theory is that the push forward is naturally defined on the level of cycles even in the singular case the closest topological analogue of this is equivariant borel moore homology see e g3 for a definition and a similar proof establishes localization in that theory for smooth spaces the inverse to the equivariant push forward can be written explicitly it was realized independently by several authors i n a b b v

quantization and the uniqueness of invariant structures we determine and classify certain algebraic structures defined on the space of all complex valued polynomials in 2n real variables which admitaffine contact transformations as automorphisms these are the structures which have the minimum symmetry necessary to define the basic linear and angular momentum observables of classical and quantum mechanics the results relate to the so called dirac problem of finding an appropriate mathematical characterization of the canonical quantization procedure

on the geometry of algebraic groups and homogeneous spaces given a connected algebraic group g over an algebraically closed field and a g homogeneous space x we describe the chow ring of g and the rational chow ring of x with special attention to the picard group also we investigate the albanese and the anti affine fibrations of g and x

first steps in tropical intersection theory we establish first parts of a tropical intersection theory namely we define cycles cartier divisors and intersection products between these two without passing to rational equivalence and discuss push forward and pull back we do this first for fans in mathbb r n and then for abstract cycles that are fans locally with regard to applications in enumerative geometry we finally have a look at rational equivalence and intersection products of cycles and cycle classes in mathbb r n

a critique of seismic deconvolution methods different seismic pulse compression methods are evaluated these include several algorithms for computing prediction error filters wiener filtering burg s method the l 1 norm criterion kalman filtering and two time adaptive methods algorithms which do not assume a minimum phase condition for the seismic wavelet include minimum entropy homomorphic and zero phase deconvolution the sensitivity of these algorithms is examined for various earth reflectivity functions source waveforms and signal distortions the results indicate that standard wiener predictive deconvolution is robust under a wide variety of input conditions however a substantial improvement in pulse compression can be obtained by the burg algorithm under conditions of short data segments and by minimum entropy deconvolution for seismograms consisting of mixed phase wavelets combined with sparse reflectivity series

characteristic classes and quadric bundles in this paper we construct stiefel whitney and euler classes in chow cohomology for algebraic vector bundles with nondegenerate quadratic form these classes are not in the algebra generated by the chern classes of such bundles and are new characteristic classes in algebraic geometry on complex varieties they correspond to classes with the same name pulled back from the cohomology of the classifying space bso n c the classes we construct are the only new characteristic classes in algebraic geometry coming from the classical groups t2 eg we begin by using the geometry of quadric bundles to study chern classes of maximal isotropic subbundles if v x is a vector bundle with quadratic form and if e and f are maximal isotropic subbundles of v then we prove theorem 1 that ci e and ci f are equal mod 2 moreover if the rank of v is 2n then cn e cn f proving a conjecture of fulton we define stiefel whitney and euler classes as chow cohomology classes which pull back to chern classes of maximal isotropic subbundles of the pullback bundle using the above theorem we show theorem 2 that these classes exist and are unique even though v need not have a maximal isotropic subbundle these constructions also make it possible to give schubert presentations

moyal dynamics and trajectories we give first an approximation of the operator h f hf h f f h in terms of 2n n 0 where is a hamilton function and denotes the star product the operator which is the generator of time translations in a algebra can be considered as a canonical extension of the liouville operator lh f lhf h f poisson using this operator we investigate the dynamics and trajectories of some examples with a scheme that extends the hamilton jacobi method for classical dynamics to moyal dynamics the examples we have chosen are hamiltonians with a one dimensional quartic potential and two dimensional radially symmetric nonrelativistic and relativistic coulomb potentials and the hamiltonian for a schwarzschild metric we further state a conjecture concerning an extension of the bohr sommerfeld formula for the calculation of the exact eigenvalues for systems with classically periodic trajectories

equivariant cohomology syzygies and orbit structure let x be a nice space with an action of a torus t we consider the atiyah bredon sequence of equivariant cohomology modules arising from the filtration of x by orbit dimension we show that a front piece of this sequence is exact if and only if the h bt module h t x is a certain syzygy moreover we express the cohomology of that sequence as an ext module involving a suitably defined equivariant homology of x one consequence is that the gkm method for computing equivariant cohomology applies to a poincare duality space if and only if the equivariant poincare pairing is perfect

bott s formula and enumerative geometry we outline a strategy for computing intersection numbers on smooth varieties with torus actions using a residue formula of bott as an example gromov witten numbers of twisted cubic and elliptic quartic curves on some general complete intersection in projective space are computed the results are consistent with predictions made from mirror symmetry compu tations we also compute degrees of some loci in the linear system of plane curves of degrees less than 10 like those corresponding to sums of powers of linear forms and curves carrying inscribed polygons mathematical institute university of oslo p 0 box 1053 n 0316 oslo norway e mail address ellingsr0math uio no mathematical institute university of bergen alleg 55 n 5007 bergen norway e mail address strommeti i uib no this content downloaded from 157 55 39 29 on tue 12 apr 2016 10 23 14 utc all use subject to http about jstor org terms

milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs the chromatic polynomial g q of a graph g counts the num ber of proper colorings of g we give an affirmative answer to the conjecture of read and rota heron welsh that the absolute values of the coefficients of the chromatic polynomial form a log concave sequence the proof is obtained by identifying g q with a sequence of numerical invariants of a projective hypersurface analogous to the milnor number of a local analytic hypersurface as a by product of our approach we obtain an analogue of kouchnirenko s

log concavity of characteristic polynomials and the bergman fan of matroids in a recent paper the first author proved the log concavity of the coefficients of the characteristic polynomial of a matroid realizable over a field of characteristic 0 answering a long standing conjecture of read in graph theory we extend the proof to all realizable matroids making progress towards a more general conjecture of rota heron welsh our proof follows from an identification of the coefficients of the reduced characteristic polynomial as answers to particular intersection problems on a toric variety the log concavity then follows from an inequality of hodge type

motivic decompositions of twisted flag varieties and representations of hecke type algebras motivated by the motivic galois group and the kostant kumar results on equivariant cohomology of flag varieties we provide a uniform de scription of motivic direct sum decompositions with integer coefficients of versal flag varieties in terms of integer representations of the associated affine nil hecke algebra h more generally we establish an equivalence between the h motivic subcat egory generated by the motive of e b and the category of projective modules of the associated rational algebra d of push pull operators where e is a tor sor for a split semisimple linear algebraic group g over a field k b is a borel subgroup of g h is an algebraic oriented cohomology theory in the sense of levine morel e g chow ring ch or an algebraic cobordism the algebra d can be think of as an integer analogue of the hopf algebra of the h motivic galois group of e b as an application taking h ch and specializing the coefficients to the finite field fp we obtain that p modular projective representations of d h are generated by an irreducible h module corresponding to the generalized rost voevodsky motive for g p

deformation of algebras and related quantizations weak bose and fermi type quantizations are defined via deformations of algebras generated by characters from linear topological spaces into commutative or grassmann algebras respectively this yields an inherent symmetrization and antisymmetrization respectively of deformed products with respect to undeformed products combining both quantizations one obtains a weak supersymmetric quantization of a 2 graded algebra for bose type quantizations a hilbert space representation based on quasi invariant measures is outlined

gromov witten theory of deligne mumford stacks given a smooth complex deligne mumford stack cal x with a projective coarse moduli space we introduce gromov witten invariants of cal x and prove some of their basic properties including the wdvv equation

cohomological donaldson thomas theory of a quiver with potential and quantum enveloping algebras this paper concerns the cohomological aspects of donaldson thomas theory for jacobi algebras and the associated cohomological hall algebra introduced by kontsevich and soibelman we prove the hodge theoretic categorification of the integrality conjecture and the wall crossing formula and furthermore realise the isomorphism in both of these theorems as poincare birkhoff witt isomorphisms for the associated cohomological hall algebra we do this by defining a perverse filtration on the cohomological hall algebra a result of the hidden properness of the semisimplification map from the moduli stack of semistable representations of the jacobi algebra to the coarse moduli space of polystable representations this enables us to construct a degeneration of the cohomological hall algebra for generic stability condition and fixed slope to a free supercommutative algebra generated by a mixed hodge structure categorifying the bps invariants as a corollary of this construction we furthermore obtain a lie algebra structure on this mixed hodge structure the lie algebra of bps invariants for which the entire cohomological hall algebra can be seen as the positive part of a yangian type quantum group

riemann roch for equivariant k theory abstract we show that for a linear algebraic group g acting on a smooth quasi projective scheme x over a field there is a chern character map k i g x r g r g c h x g ch g x i s g s g with rational coefficients which is an isomorphism this establishes the equivariant version of the riemann roch isomorphism between the higher algebraic k theory and the higher chow groups of smooth quasi projective schemes

chern classes of deligne mumford stacks and their coarse moduli spaces let x be a complex projective algebraic variety with gorenstein quotient singularities and mathcal x a smooth deligne mumford stack having x as its coarse moduli space we show that the csm class c sm x coincides with the pushforward to x of the total chern class c t i mathcal x of the inertia stack i mathcal x we also show that the stringy chern class c str x of x whenever it is defined coincides with the pushforward to x of the total chern class c t ii mathcal x of the double inertia stack ii mathcal x some consequences concerning stringy orbifold hodge numbers are deduced

compactifications of subvarieties of tori we study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non archimedean amoebas these compactifications have many nice properties for example any k boundary divisors intersect in codimension k we consider some examples including m 0 n subset overline m 0 n and more generally log canonical models of complements of hyperplane arrangements and compact quotients of grassmannians by a maximal torus

the entropic discriminant abstract the entropic discriminant is a non negative polynomial associated to a matrix it arises in contexts ranging from statistics and linear programming to singularity theory and algebraic geometry it describes the complex branch locus of the polar map of a real hyperplane arrangement and it vanishes when the equations defining the analytic center of a linear program have a complex double root we study the geometry of the entropic discriminant and we express its degree in terms of the characteristic polynomial of the underlying matroid singularities of reciprocal linear spaces play a key role in the corank one case the entropic discriminant admits a sum of squares representation derived from the discriminant of a characteristic polynomial of a symmetric matrix

quantum riemann roch lefschetz and serre given a holomorphic vector bundle e over a compact kahler manifold x one defines twisted gromov witten invariants of x to be intersection numbers in moduli spaces of stable maps f x with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle h 0 f e h 1 f e using the formalism of quantized quadratic hamiltonians 25 we express the descendant potential for the twisted theory in terms of that for x this result theorem 1 is a consequence of mumford s grothendieck riemann roch theorem applied to the universal family over the moduli space of stable maps it determines all twisted gromov witten invariants of all genera in terms of untwisted invari ants when e is concave and the c equivariant inverse euler class is chosen as the characteristic class the twisted invariants of x give gromov witten invariants of the total space of e nonlinear serre duality 21 23 expresses gromov witten invariants of e in terms of those of the super manifold e it relates gromov witten invariants of x twisted by the inverse euler class and e to gromov witten invariants of x twisted by the euler class and e we derive from theorem 1 nonlinear serre duality in a very general form corollary 2 when the bundle e is convex and a submanifold y x is defined by a global section of e the genus zero gromov witten invariants of e coin cide with those of y we establish a quantum lefschetz hyperplane section principle theorem 2 expressing genus zero gromov witten invariants of a complete intersection y in terms of those of x this extends earlier results 4 9 18 29 33 and yields most of the known mirror formulas for toric complete intersections

functorial reconstruction theorems for stacks abstract we study the circumstances under which one can reconstruct a stack from its associated functor of isomorphism classes this is possible surprisingly often we show that many of the standard examples of moduli stacks are determined by their functors our methods seem to exhibit new anabelian style phenomena in the form of structures in the category of schemes that encode automorphism data in groupoids

the picard group of the universal moduli space of vector bundles on stable curves abstract we construct the moduli stack of properly balanced vector bundles on semistable curves and we determine explicitly its picard group as a consequence we obtain an explicit description of the picard groups of the universal moduli stack of vector bundles on smooth curves and of the schmitt s compactification over the stack of stable curves we prove some results about the gerbe structure of the universal moduli stack over its rigidification by the natural action of the multiplicative group in particular we give necessary and sufficient conditions for the existence of poincare bundles over the universal curve of an open substack of the rigidification generalizing a result of mestrano ramanan

the kazhdan lusztig polynomial of a matroid abstract we associate to every matroid m a polynomial with integer coefficients which we call the kazhdan lusztig polynomial of m in analogy with kazhdan lusztig polynomials in representation theory we conjecture that the coefficients are always non negative and we prove this conjecture for representable matroids by interpreting our polynomials as intersection cohomology poincare polynomials we also introduce a q deformation of the mobius algebra of m and use our polynomials to define a special basis for this deformation analogous to the canonical basis of the hecke algebra we conjecture that the structure coefficients for multiplication in this special basis are non negative and we verify this conjecture in numerous examples

autocorrelation estimation using constrained iterative spectral deconvolution computing an autocorrelation conventionally produces a biased estimate especially for a short data sequence windowing the autocorrelation can remove the bias but at the expense of violating the nonnegativity of the corresponding power spectrum constrained iterative deconvolution provides a basis for improving an autocorrelation estimate by reducing the bias while guaranteeing nonnegative definiteness the length of the autocorrelation is increased in order to satisfy the nonnegativity constraints on the power spectral estimate the constraints can also have significant effects on small poorly determined values of the autocorrelation the technique is applied to synthetic and real examples to show the improvements in the autocorrelation and power spectrum which are possible the method is reasonably stable in the presence of noise and it approximately preserves the area of the power spectrum comparison to the maximum entropy technique shows that the iterative method gives power spectral resolution whi

picard group of moduli of hyperelliptic curves the main subject of this work is the difference between the coarse moduli space and the stack of hyperelliptic curves we compute their picard groups giving explicit description of the generators we get an application to the non existence of a tautological family over the coarse moduli space

h vectors of matroids and logarithmic concavity abstract let m be a matroid on e representable over a field of characteristic zero we show that h vectors of the following simplicial complexes are log concave 1 the matroid complex of independent subsets of e 2 the broken circuit complex of m relative to an ordering of e the first implies a conjecture of colbourn on the reliability polynomial of a graph and the second implies a conjecture of hoggar on the chromatic polynomial of a graph the proof is based on the geometric formula for the characteristic polynomial of denham garrousian and schulze