measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

multipliers between sobolev spaces and fractional differentiation abstract we characterize the pointwise multipliers which maps a sobolev space h r r d to a sobolev space h s r d in the case s r d 2

on the semi stable coha and its modules arising from smooth models abstract we study a variant of the semi stable cohomological hall algebra which we construct using equivariant chow groups this algebra we call it the semi stable chowha arises as a quotient of the coha smooth models of quiver moduli give rise to modules over the semi stable chowha we prove that these modules are cyclic and we compute a presentation using harder narasimhan methods

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

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

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

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

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

the form boundedness criterion for the laplacian operator abstract in this paper we characterize the class of measurable functions or more generally real or complex valued distributions f such that the commutator operator c f f acting from h 1 r d to h 1 r d in other words we give a complete solution to the problem for the boundedness of the laplacian which is fundamental to quantum mechanics

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

improvement of k 2 entropy calculations by means of dimension scaled distances abstract the k2 entropy is evaluated for experimental time series as well as for numerically simulated ones the conventional calculation procedure leads to results that can be extrapolated to obtain a k2 value for the time series but in the case of experimental systems the outcome is hardly significant for a classification of the states the reason for this is a distortion of distances due to the phase space embedding procedure by time delay coordinates therefore a k2 calculation based on dimension scaled distances dsd is suggested a comparison to the often suggested use of the maximum norm is discussed by the application of dsd the convergence problems are avoided and clear results were obtained in all investigated situations

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

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

estimating correlation dimension from a chaotic time series when does plateau onset occur abstract suppose that a dynamical system has a chaotic attractor a with a correlation dimension d 2 a common technique to probe the system is by measuring a single scalar function of the system state and reconstructing the dynamics in an m dimensional space using the delay coordinate technique the estimated correlation dimension of the reconstructed attractor typically increases with m and reaches a plateau on which the dimension estimate is relatively constant for a range of large enough m values the plateaued dimension value is then assumed to be an estimate of d 2 for the attractor in the original full phase space in this paper we first present rigorous results which state that for a long enough data string with low enough noise the plateau onset occurs at m ceil d 2 where ceil d 2 standing for ceiling of d 2 is the smallest integer greater than or equal to d 2 we then numerical examples illustrating the theoretical prediction in addition we discuss new findings showing how practical factors such as a lack of data and observational noise can produce results that may seem to be inconsistent with the theoretically predicted plateau onset at m ceil d 2

time series and dependent variables we present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series the method is particularly suited to series with broad band spectra such as chaotic series with or without noise we derive quantities j e based on conditional probabilities whose magnitude roughly speaking is an indicator of the extent to which the kth element in the series is a deterministic function of the k j th element to within a measurement uncertainty e we apply our method to a number of deterministic time series generated by chaotic processes such as the tent logistic and h non maps as well as to sequences of quasi random numbers in all cases the 6j correctly indicate the expected dependencies we also show that the j are robust to the addition of substantial noise in a deterministic process in addition we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance e finally we discuss the behavior of the 6i as e approaches zero

fundamental limitations for estimating dimensions and lyapunov exponents in dynamical systems we show that values of the correlation dimension estimated over a decade from the grassberger procaccia algorithm cannot exceed the value 2 log10n if n is the number of points in the time series when this bound is saturated it is thus not legitimate to conclude that low dimensional dynamics is present the estimation of lyapunov exponents is also discussed

stacks of trigonal curves in this paper we study the stack tg of smooth triple covers of a conic when g 5 this stack is embedded mg as the locus of trigonal curves we show that tg is a quotient ug g where g is a certain algebraic group and ug is an open subscheme of a g equivariant vector bundle over an open subscheme of a representation of g using this we compute the integral picard group of tg when g 1 the main tools are a result of miranda that describes a flat finite triple cover of a scheme s as given by a locally free sheaf e of rank two on s with a section of sym 3 e det e and a new description of the stack of globally generated locally free sheaves of fixed rank and degree on a projective line as a quotient stack in moduli theory stacks have often been constructed as quotients by group actions if an algebraic stack f is a quotient stack x g where g is an algebraic group acting on an algebraic variety x the geometry of f is the geometry of the action of g on x and one can apply to f the powerful techniques that have been developed for studying invariants of group actions in algebraic topology and algebraic geometry even just knowing that such a presentation exists even without an explicit description of the action can be useful but it is even better when the variety x and the group g are fairly simple so that this description may be used directly to study f this does not seem possible in many cases for example the stack mg of smooth curves of genus g is of the form x g but when g is large the space x is complicated and to our knowledge no general result about mg has been proved by exploiting this presentation of course in teichmuller theory one represents mg as a quotient of an action of the teichmuller group which is an infinite discrete group acting on a ball in c 3g 3 but this description is topological and it is hard to use it directly to prove algebraic geometric results about mg it has long been known that in characteristic different from 2 and 3 the stack m1 1 of elliptic curves is a quotient x gm where x is the complement of the hypersurface 4x 3 27y 2 0 in a 2 and gm acts with weights 4 and 6 this gives an easy proof of the fact due to mumford mum65 that the picard group of m1 1 is cyclic of order 12 in vis98 the second author gives a presentation of m2 as a quotient x gl2 where x is the scheme of smooth binary forms of degree 6 in two variables the action of gl2 on x is a twist of the customary one as an application he computes the chow ring of m2 this was generalized in av04 to the stack hg of hyperelliptic curves of genus g which has a presentation as a quotient xg gl2 if g is even or xg gmpgl2 if g is odd where x is the space of smooth binary forms of degree 2g 2 in two variables this allows

dependent variables in broad band continuous time series in this paper we continue our development of new methods for the analysis of broad band time series by deriving quantities which are able to indicate deterministic dependence of an element in one time series on elements in other time series these methods are very broadly applicable and are particularly well suited to the study of continuous time series in which the value of the function may depend on derivatives of the function itself or on other quantities we apply our methods to a number of mathematical examples including the lorentz equation the h6non heiles equations the forced brusselator and the mackey glass equation we show that our methods are very successful at indicating deterministic dependencies in these systems even if the time series are highly chaotic statistical aspects of our procedure are discussed as are a number of interesting and surprising epistomological implications

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

covariants of binary sextics and vector valued siegel modular forms of genus two we extend igusa s description of the relation between invariants of binary sextics and siegel modular forms of degree 2 to a relation between covariants and vector valued siegel modular forms of degree 2 we show how this relation can be used to effectively calculate the fourier expansions of siegel modular forms of degree 2

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

equivariant cobordism for torus actions abstract we study the equivariant cobordism groups for the action of a split torus t on varieties over a field k of characteristic zero we show that for t acting on a variety x there is an isomorphism t x b t l x as applications we show that for a connected linear algebraic group g acting on a k variety x the forgetful map g x x is surjective with rational coefficients as a consequence we describe the rational algebraic cobordism ring of algebraic groups and flag varieties we prove a structure theorem for the equivariant cobordism of smooth projective varieties with torus action using this we prove various localization theorems and a form of bott residue formula for such varieties as an application we show that the equivariant cobordism of a smooth variety x with torus action is generated by the invariant cobordism cycles in x as b t module

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

state space reconstruction in the presence of noise takens theorem demonstrates that in the absence of noise a multidimensional state space can be reconstructed from a scalar time series this theorem gives little guidance however about practical considerations for reconstructing a good state space we extend takens treatment applying statistical methods to incorporate the effects of observational noise and estimation error we define the distortion matrix which is proportional to the conditional covariance of a state given a series of noisy measurements and the noise amplification which is proportional to root mean square time series prediction errors with an ideal model we derive explicit formulae for these quantities and we prove that in the low noise limit minimizing the distortion is equivalent to minimizing the noise amplification we identify several different scaling regimes for distortion and noise amplification and derive asymptotic scaling laws when the dimension and lyapunov exponents are sufficiently large these scaling laws show that no matter how the state space is reconstructed there is an explosion in the noise amplification from a practical point of view determinism is lost and the time series is effectively a random process in the low noise large data limit we show that the technique of local singular value decomposition is an optimal coordinate transformation in the sense that it achieves the minimum distortion in a state space of the lowest possible dimension however in numerical experiments we find that estimation error complicates this issue for local approximation methods we analyze the effect of reconstruction on estimation error derive a scaling law and suggest an algorithm for reducing estimation errors

gauss composition for p1 and the universal jacobian of the hurwitz space of double covers abstract in this paper we give an explicit description of the moduli space of line bundles on hyperelliptic curves including singular curves we study the universal jacobian j 2 g n of degree n line bundles over the hurwitz stack of double covers of p 1 by a curve of genus g our main results are the construction of a smooth irreducible universally closed but not separated moduli compactification j bd 2 g n of j 2 g n whose points we describe simply and explicitly as sections of certain vector bundles on p 1 a description of the global geometry and moduli properties of these stacks and a computation of the picard groups of j bd 2 g n and j 2 g n in the cases when n g is even an important ingredient of our work is the parametrization of line bundles on double covers by binary quadratic forms this parametrization generalizes the classical number theoretic correspondence between ideal classes of quadratic rings and integral binary quadratic forms which in particular gives the group law on integral binary quadratic forms first discovered by gauss

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

an attractor in a solar time series a time series analysis of observed solar radio pulsations suggests that there must be a low dimensional attractor the power spectrum cannot be interpreted as a superposition of periodic components estimates of the maximum lyapunov exponent and of the kolmogorov entropy give some indications for a deterministic chaos in order to study the limitations inherent in small data samples we include data from the lorenz model and an artificial noise record consequences for the physical modelling of the pulsation event are discussed

characterization of spatiotemporal chaos from time series the analysis of time series generated by spatiotemporal chaotic systems is discussed we find that a grassberger procaccia algorithm with a suitable normalisation for the correction of systematic errors caused by the shape of the attractor is a reliable method for distinguishing between high dimensional chaos and noise we show that even a quantitative description of the attractor is possible by means of dimension densities the results obtained from the time series are in good agreement with values calculated directly from the generating equations of motion

the integral orbifold chow ring of toric deligne mumford stacks in this paper we study the integral chow ring of toric deligne mumford stacks we prove that the integral chow ring of a semi projective toric deligne mumford stack is isomorphic to the stanley reisner ring of the associated stacky fan the integral orbifold chow ring is also computed our results are illustrated with several examples

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

correlation integral as a tool for distinguishing between dynamics and statistics in time series data abstract we propose a new test for time series data for proper choice of processing technique dynamical or statistical it is based upon the normalized slope of the correlation integral m m 1 d ln c d ln where m is the embedding dimension it is shown that when does not tend to 0 on the resolved range of scales as m grows then there will be serious limitations for dynamical methods even if the data are dynamical by nature in the latter case it means that the length of time series does not allow to resolve small scales and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques such as estimating lyapunov exponents or predicting time series

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

framed sheaves on root stacks and supersymmetric gauge theories on ale spaces we develop a new approach to the study of supersymmetric gauge theories on ale spaces using the theory of framed sheaves on root toric stacks which illuminates relations with gauge theories on r 4 and with two dimensional conformal field theory we construct a stacky compactification of the minimal resolution xk of the ak 1 toric singularity c 2 zk which is a projective toric orbifold xk such that xknxk is a zk gerbe we construct moduli spaces of tor sion free sheaves on xk which are framed along the compactification gerbe we prove that this moduli space is a smooth quasi projective variety compute its dimension and classify its fixed points under the natural induced toric action we use this construction to compute the partition functions and correlators of chiral bps operators forn 2 quiver gauge theories on xk with nontrivial holonomies at infinity the partition functions are computed with and without cou plings to bifundamental matter hypermultiplets and expressed in terms of toric blowup formulas which relate them to the corresponding nekrasov partition functions on the affine toric subsets of xk we compare our new partition functions with previous computations explore their con nections to the representation theory of affine lie algebras and find new constraints on fractional instanton charges in the coupling to fundamental matter we show that the partition functions in the low energy limit are characterised by the seiberg witten curves and in some cases also by suitable blowup equations involving riemann theta functions on the seiberg witten curve with characteristics related to the nontrivial holonomies

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

distinguishing between low dimensional dynamics and randomness in measured time series the success of current attempts to distinguish between low dimensional chaos and random behavior in a time series of observations is considered first we discuss stationary stochastic processes which produce finite numerical estimates of the correlation dimension and k2 entropy under naive application of correlation integral methods we then consider several straightforward tests to evaluate whether correlation integral methods reflect the global geometry or the local fractal structure of the trajectory this determines whether the methods are applicable to a given series if they are we evaluate the significance of a particular result for example by considering the results of the analysis of stochastic signals with statistical properties similar to those of observed series from the examples considered it is clear that the correlation integral should not be used in isolation but as one of a collection of tools to distinguish chaos from stochasticity

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

modular compactifications of the space of marked trigonal curves abstract we construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent beginning with the standard admissible cover compactification the sequence first proceeds through contractions of the boundary divisors and then through flips of the so called maroni strata culminating in a fano model for even genera and a fano fibration for odd genera while the sequence of divisorial contractions arises from a more general construction the sequence of flips uses the particular geometry of triple covers we explicitly describe the mori chamber decomposition given by this sequence of flips

statistical tests for deterministic effects in broad band time series we derive a normalized version of the indicators of savit and green and prove that these normalized statistics have asymptotically a normal distribution with a mean of zero and standard deviation of one if the time series is random in the sense of being lid independent and identically distributed we verify this result numerically and study the magnitude of the finite size effects we also show that these statistics are very sensitive to the existence of deterministic effects in the series even if the underlying deterministic structure is complex such as those generated by a chaotic system we show that with moderate amounts of data the statistics can easily indicate the presence of an underlying attractor even in the presence of iid noise which is as large as or greater than the signal finally we discuss the generalization of our approach to include 1 other null hypotheses besides lid which express assumptions of specific dependencies and 2 the study of deterministic effects between more than one time series

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

geometric representations of the formal affine hecke algebra abstract for any formal group law there is a formal affine hecke algebra defined by hoffnung malagon lopez savage zainoulline coming from this formal group law there is also an oriented cohomology theory we identify the formal affine hecke algebra with a convolution algebra coming from the oriented cohomology theory applied to the steinberg variety as a consequence this algebra acts on the corresponding cohomology of the springer fibers this generalizes the action of classical affine hecke algebra on the k theory of the springer fibers constructed by lusztig we also give a residue interpretation of the formal affine hecke algebra which generalizes the residue construction of ginzburg kapranov vasserot when the formal group law comes from a 1 dimensional algebraic group