a characterization of the finite simple groups abstract in this paper we obtain a quantitative characterization of all finite simple groups let t g denote the set of indices of maximal subgroups of group g and let p g be the smallest number in t g we have the following theorems theorem 2 let n and g be finite simple groups if n divides g p n p g and t n t g then or and 2 11 or 2 and 3 theorem 3 let n be a finite simple and let g be a finite group if g n and t g t n then g n

generalized calabi yau manifolds and the chiral de rham complex abstract we show that the chiral de rham complex of a generalized calabi yau manifold carries n 2 supersymmetry we discuss the corresponding topological twist for this n 2 algebra we interpret this as an algebroid version of the super sugawara or kac todorov construction

applications of homological mirror symmetry to hypergeometric systems duality conjectures abstract homological mirror symmetry for crepant resolutions of gorenstein toric singularities leads to a pair of conjectures on certain hypergeometric systems of pdes we explain these conjectures and verify them in some cases

witt spaces a geometric cycle theory for ko homology at odd primes introduction this paper studies a class of stratified piecewiselinear pseudomanifolds which we call witt spaces characterized by natural local intersection homology conditions 11 we compute the cobordism groups by introducing an invariant taking values in the witt group of symmetric bilinear forms over the rationals w q these pseudomanifolds solve a problem posed by d sullivan 25 to construct a class of p l cycles with signature which represent the connected version of ko homology at odd primes ko 0d z 1 2 the result was one of the first applications of the intersection homology theory of goresky and macpherson 11 specifically the rational intersection homology groups of witt spaces satisfy a poincare duality theorem to each witt space x we associate a p l invariant w x with values in w q this invariant generalizes the signature of manifolds and satisfies cobordism invariance additivity and a product formula adapting classical surgery spherical modification to this setting we prove that w x determines the cobordism class of x and obtain an explicit description of the witt cobordism groups the only nontrivial groups occur in dimensions 4k and for k 0 they are w q sullivan 25 27 has shown that a class of p l pseudomanifolds equipped with such an invariant possesses canonical orientations in ko 0 z 1 2 the orientations induce a natural transformation it of homology theories from witt space bordism to ko 0 z 1 2 the structure of w q is known 14 and we conclude that it is an equivalence at odd primes in this paper we study the cobordism theory of a class of stratified p l pseudomanifolds by means of the recent intersection homology theory of goresky and macpherson 11 goresky and macpherson were interested in finding a class of spaces with cobordism invariant signature for the purpose of extending the hirzebruch l class to the setting of manifolds with

on the rigidity theorems of witten in this paper we prove the rigidity theorems predicted by witten in 1986 about the index of certain elliptic operators on manifolds with an s1 action w witten s insight was the culmination of an interesting interchange of ideas between him and hopkins landweber ochanine and stong for the detailed history we refer the reader to la the present account is essentially a reinterpretation of the second author s taubes t original proof of the theorem the senior author s contribution was solely to notice that the rather densely written arguments of the original manuscript could be formulated in terms of the well known fixed point formulae of equivariant index theory and equivariant cohomology in this context the final proof then appears in direct lineage of the atiyah hirzebruch theorem concerning the vanishing of the a genus of spin manifolds admitting a circle action a h and of the even older idea of lusztig concerning circle actions in the complex case there remains however the beautiful physics inspired novelty of connecting these techniques with elliptic function theory

characteristic classes of symmetric products of complex quasi projective varieties we prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi projective variety more concretely we study homology hirzebruch classes for motivic coefficients as well as for complexes of mixed hodge modules as a special case we obtain a generating series formula for the intersection homology hirzebruch classes of symmetric products in some cases the latter yields a similar formula for twisted homology l classes generalizing results of hirzebruch zagier and moonen our methods also apply to the study of todd classes of complexes of coherent sheaves as well as chern classes of complexes of constructible sheaves generalizing to arbitrary coefficients results of moonen and resp ohmoto

finite groups with biprimary hall subgroups abstract let g be a finite group and let r be a prime divisor of the order of g we prove that if r 5 and g has the e r t property for all t g r then g is r solvable a group g is said to have the e property if g possesses a hall subgroup

projective elliptic genera and elliptic pseudodifferential genera abstract in this paper we construct for the first time the projective elliptic genera for a compact oriented manifold equipped with a projective complex vector bundle such projective elliptic genera are rational q series that have topological definition and also have analytic interpretation via the fractional index theorem in 25 without requiring spin condition we prove the modularity properties of these projective elliptic genera as an application we construct elliptic pseudodifferential genera for any elliptic pseudodifferential operator this suggests the existence of putative s 1 equivariant elliptic pseudodifferential operators on loop space whose equivariant indices are elliptic pseudodifferential genera

superconformal structures on generalized calabi yau metric manifolds we construct an embedding of two commuting copies of the n 2 superconformal vertex algebra in the space of global sections of the twisted chiral anti chiral de rham complex of a generalized calabi yau metric manifold including the case when there is a non trivial h flux and non vanishing dilaton the 4 corresponding brst charges are well defined on any generalized kahler manifold this allows one to consider the half twisted model defining thus the chiral de rham complex of a generalized kahler manifold the classical limit of this result allows one to recover the celebrated generalized kahler identities as the degree zero part of an infinite dimensional lie superalgebra attached to any generalized kahler manifold as a byproduct of our study we investigate the properties of generalized calabi yau metric manifolds in the lie algebroid setting

elliptic genera of singular varieties the notions of orbifold elliptic genus and elliptic genus of singular varieties are introduced and the relation between them is studied the elliptic genus of singular varieties is given in terms of a resolution of singularities and extends the elliptic genus of calabi yau hypersurfaces in fano gorenstein toric varieties introduced earlier the orbifold elliptic genus is given in terms of the fixed point sets of the action we show that the generating function for the orbifold elliptic genus ellorb x 6n p for symmetric groups 6n acting on n fold products coincides with the one proposed by r dijkgraaf g moore e verlinde and h verlinde the two notions of elliptic genera are conjectured to coincide

lagrangian approach to sheaves of vertex algebras we explain how sheaves of vertex algebras are related to mathematical structures encoded by a class of lagrangians the exposition is focused on two examples the wzw model and the 1 1 supersymmetric model we conclude by showing how to construct a family of vertex algebras with base the barannikov kontsevich moduli space thus furnishing the b model moduli for witten s half twisted model

elliptic genera of symmetric products and second quantized strings in this note we prove an identity that equates the elliptic genus partition function of a supersymmetric sigma model on the n fold symmetric product m n sn of a manifold m to the partition function of a second quantized string theory on the space m s 1 the generating function of these elliptic genera is shown to be almost an automorphic form for o 3 2 z in the context of d brane dynamics this result gives a precise computation of the free energy of a gas of d strings inside a higher dimensional brane

topological orbifold models and quantum cohomology rings we discuss the topological sigma model on an orbifold target space we describe the moduli space of classical minima for computing correlation functions involving twisted operators and show through a detailed computation of an orbifold ofcp1 by the dihedral groupd4 how to compute the complete ring of observables through this procedure we compute all the rings of dihedralcp1 orbifolds we then considercp2 d4 and show how the techniques of topologicalanti topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds

elliptic genus of phases of n 2 theories we discuss an algebro geometric description of witten s phases of n 2 theories and propose a definition of their elliptic genus provided some conditions on singularities of the phases are met for landau ginzburg phase one recovers elliptic genus of lg models proposed in physics literature in early 1990s for certain transitions between phases we derive invariance of elliptic genus from an equivariant form of mckay correspondence for elliptic genus as special cases one obtains landau giznburg calabi yau correspondence for elliptic genus of weighted homogeneous potentials as well as certain hybrid cy correspondences

chiral de rham complex we define natural sheaves of vertex algebras over smooth manifolds which may be regarded as semi infinite de rham complexes of certain d modules over the loop spaces for calabi yau manifolds they admit n 2 supersymmetry connection with wakimoto modules is discussed

evolution of reaction diffusion patterns in infinite and bounded domains abstract we introduce a semi analytical method to study the evolution of spatial structures in reaction diffusion systems it consists in writing an integral equation for the relevant densities from the propagator of the linear part of the evolution operator in order to test the method we perform an exhaustive study of a one dimensional reaction diffusion model associated to an electrical device the ballast resistor we consider the evolution of step and bubble shaped initial density profiles in free space as well as in a semi infinite domain with dirichlet and neumann boundary conditions the piecewise linear form of the reaction term which preserves the basic ingredients of more complex nonlinear models makes it possible to obtain exact wave front solutions in free space and stationary solutions in the bounded domain short and long time behaviour can also be analytically studied whereas the evolution at intermediate times is analyzed by numerical techniques we paid particular attention to the features introduced in the evolution by boundary conditions

elliptic genera of toric varieties and applications to mirror symmetry the paper contains a proof that elliptic genus of a calabi yau manifold is a jacobi form finds in which dimensions the elliptic genus is determined by the hodge numbers and shows that elliptic genera of a calabi yau hypersurface in a toric variety and its mirror coincide up to sign the proof of the mirror property is based on the extension of elliptic genus to calabi yau hypersurfaces in toric varieties with gorenstein singularities

germs of arcs on singular algebraic varieties and motivic integration we study the scheme of formal arcs on a singular algebraic variety and its images under truncations we prove a rationality result for the poincare series of these images which is an analogue of the rationality of the poincare series associated to p adic points on a p adic variety the main tools which are used are semi algebraic geometry in spaces of power series and motivic integration a notion introduced by m kontsevich in particular we develop the theory of motivic integration for semi algebraic sets of formal arcs on singular algebraic varieties we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of oesterle

motivic characteristic classes in cohomological hall algebras abstract the equivariant chern schwartz macpherson csm class and the equivariant motivic chern mc class are important characteristic classes of singular varieties in cohomology and k theory and their theory overlaps with the theory of okounkov s stable envelopes we study csm and mc classes for the orbits of dynkin quiver representations we show that the problem of computing the csm and mc classes of all these orbits can be reduced to some basic classes c o c o parameterized by positive roots we prove an identity in a deformed version of kontsevich soibelman s cohomological and k theoretic hall algebra coha kha namely that a product of exponentials of c o or c o classes formally depending on a stability function z does not depend on z this identity which encodes infinitely many identities among rational functions in growing number of variables has the structure of donaldson thomas type quantum dilogarithm identities using a wall crossing argument we present the c o c o classes as certain commutators in the coha kha

characters of topological n 2 vertex algebras are jacobi forms on the moduli space of elliptic supercurves abstract we show that trace functions on modules of topological n 2 super vertex algebras give rise to conformal blocks on elliptic supercurves we show that they satisfy a system of linear partial differential equations with respect to the modular parameters of the supercurves under some finiteness condition on the vertex algebra these differential equations can be interpreted as a connection on the vector bundle of conformal blocks we show that this connection is equivariant with respect to a natural action of the jacobi modular group on the modular parameters and the trace functions in the appendix we prove the convergence of the trace functions

a chiral borel weil bott theorem abstract we compute the cohomology of modules over the algebra of twisted chiral differential operators over the flag manifold this is applied to 1 finding the character of g integrable irreducible highest weight modules over the affine lie algebra at the critical level and 2 computing a certain elliptic genus of the flag manifold the main tool is a result that interprets the drinfeld sokolov reduction as a derived functor

sylow numbers and nilpotent hall subgroups let be a set of primes and g a finite group we characterize the existence of a nilpotent hall subgroup of g in terms of the number of sylow subgroups for the primes in

wave block in excitable media due to regions of depressed excitability we study propagation failure using the one dimensional scalar bistable equation with a passive gap region by applying comparison principles for this type of equation the problem of finding conditions for block is reduced to finding conditions for the existence of steady state solutions we present a geometrical method that allows one to easily compute the critical gap length above which a steady state solution and thus block first occurs the method also helps to uncover the general bifurcation structure of the problem including the stability of the steady state solutions in obtaining these results we characterize the relationship between the properties of the system and propagation failure the method can easily be extended to other gap dynamics we use it to show that block associated with any local inhomogeneity must be associated with a limit point bifurcation

hodge elliptic genera and how they govern k3 theories the complex hodge elliptic genus and its conformal field theoretic counterpart were recently introduced by kachru and tripathy refining the traditional complex elliptic genus we construct a different so called chiral hodge elliptic genus which is expected to agree with the generic conformal field theoretic hodge elliptic genus in contrast to the complex hodge elliptic genus as originally defined for k3 surfaces x the chiral hodge elliptic genus is shown to be independent of all moduli moreover employing kapustin s results on infinite volume limits it is shown that it agrees with the generic conformal field theoretic hodge elliptic genus of k3 theories while the complex hodge elliptic genus does not this new invariant governs part of the field content of k3 theories supporting the idea that all their spaces of states have a common subspace which underlies the generic conformal field theoretic hodge elliptic genus and thereby the complex elliptic genus mathematically this space is modelled by the sheaf cohomology of the chiral de rham complex of x it decomposes into irreducible representations of the n 4 superconformal algebra such that the multiplicity spaces of all massive representations have precisely the dimensions required in order to furnish the representation of the mathieu group m 24 that is predicted by mathieu moonshine this is interpreted as evidence in favour of the ideas of symmetry surfing which have been proposed by taormina and the author along with the claim that the sheaf cohomology of the chiral de rham complex is a natural home for mathieu moonshine these investigations also imply that the generic chiral algebra of k3 theories is precisely the n 4 superconformal algebra at central charge c 6 if the usual predictions on infinite volume limits from string theory hold true

canonical desingularization in characteristic zero by blowing up the maximum strata of a local invariant this article contains an elementary constructive proof of resolution of singularities in characteristic zero our proof applies in particular to schemes of finite type and to analytic spaces so we recover the great theorems of hironaka we introduce a discrete local invariant rm inv x a whose maximum locus determines a smooth centre of blowing up leading to desingularization to define rm inv x we need only to work with a category of local ringed spaces x x cal o x satisfying certain natural conditions if a in x then rm inv x a depends only on widehat cal o x a more generally rm inv x is defined inductively after any sequence of blowings up whose centres have only normal crossings with respect to the exceptional divisors and lie in the constant loci of rm inv x cdot the paper is self contained and includes detailed examples one of our goals is that the reader understand the desingularization theorem rather than simply know it is true

chern numbers for singular varieties and elliptic homology a fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones intersection homology for example directly produces groups associated to any variety which have almost all the properties of the usual homology groups of a smooth variety minimal model theory suggests the possibility of working more indirectly by relating any singular variety to a variety which is smooth or nearly so here we use ideas from minimal model theory to define some characteristic numbers for singular varieties generalizing the chern numbers of a smooth variety this was suggested by goresky and macpherson as a next natural problem after the definition of intersection homology 11 we find that only a subspace of the chern numbers can be defined for singular varieties a convenient way to describe this subspace is to say that a smooth variety has a fundamental class in complex bordism whereas a singular variety can at most have a fundamental class in a weaker homology theory elliptic homology we use this idea to give an algebro geometric definition of elliptic homology complex bordism modulo flops equals elliptic homology this paper was inspired by some questions asked by jack morava the descriptions of elliptic homology given by gerald hohn 13 were also an important influence thanks to dave bayer mike stillman john stembridge sheldon katz and stein stromme for their computer algebra programs macaulay sf and schubert which helped in guessing the right answer

wave blocking phenomena in bistable reaction diffusion systems the following bistable reaction variable diffusion systems including a parameter sigma is considered u 1 d x u x x frac 1 sigma f u v u 1 d x u x x sigma g u v traveling wave blocking problems are the motivation for studying the dependency of the heterogeneity of d x on the existence of stationary solutions which play the role of variers of traveling front or back waves

front dynamics in heterogeneous diffusive media abstract we herein consider two component reaction diffusion systems with a specific bistable and odd symmetric nonlinearity which have the bifurcation structure of pitchfork type traveling front solutions with opposite velocities we introduce a spatial heterogeneity for example a heaviside like abrupt change at the origin in the space into diffusion coefficients numerically the responses of traveling fronts via the heterogeneity can be classified into four types of behavior depending on the strength of the heterogeneity which in the present paper is represented by the height of the jump passage stoppage and two types of reflection the goal of the present paper is to reduce the pde dynamics to finite dimensional ode systems on a center manifold and show the mathematical mechanism for producing the four types of response in the pde systems using finite dimensional ode systems the reduced ode systems include the terms referred to as heterogeneous perturbations originating from the interaction between traveling front solutions and the heterogeneity which is very important for determining the dynamics of the ode systems in the present paper we succeed in calculating these heterogeneous perturbations exactly and explicitly

an extension of a theorem by cheeger and muller to spaces with isolated conical singularities the aim of this article is to extend a theorem by cheeger and muller to spaces with isolated conical singularities by generalizing the proof of bismut and zhang to the singular setting the main tools in this approach are the witten deformation and local index techniques

computing twisted signatures and l classes of stratified spaces this paper establishes an atiyah type characteristic class formula for both the twisted signature and the twisted l classes of a singular space the result in its present form applies to coefficient systems that satisfy a transversality condition near the singularities this condition is frequently automatically satisfied e g on supernormal spaces or for local systems arising in certain geometric mapping situations we obtain applications to stratified maps by combining our formula with the cappell shaneson signature formula

toric varieties and modular forms let n r be a lattice and let deg n be a piecewise linear function that is linear on the cones of a complete rational polyhedral fan under certain conditions on deg the data n deg determines a function f that is a holomorphic modular form of weight r for the congruence subgroup 1 l moreover by considering all possible pairs n deg we obtain a natural subring l of modular forms with respect to 1 l we construct an explicit set of generators for l and show that l is stable under the action of the hecke operators finally we relate l to the hirzebruch elliptic genera that are modular with respect to 1 l

berglund hubsch mirror symmetry via vertex algebras we give a vertex algebra proof of the berglund hubsch duality of nondegenerate invertible potentials we suggest a way to unify it with the batyrev borisov duality of reflexive gorenstein cones

superperverse intersection cohomology stratification in dependence within its traditional range of perversity parameters intersection cohomology is a topological invariant of pseudomanifolds this is no longer true once one allows superperversities perversities with open image in new window in this case intersection cohomology may depend on the choice of the stratification by which it is defined topological invariance also does not hold if one allows stratifications with codimension one strata nonetheless both errant situations arise in important situations the former in the cappell shaneson superduality theorem and the latter in any discussion of pseudomanifold bordism we show that while full invariance of intersection cohomology under restratification does not hold in this generality it does hold up to restratifications that fix the the top stratum

on the number of classes of conjugate hall subgroups in finite simple groups abstract in this paper we find the number of classes of conjugate hall subgroups in all finite almost simple groups we also complete the classification of hall subgroups in finite simple groups and correct some mistakes from our previous paper

characteristic classes of singular toric varieties in this paper we compute the motivic chern classes and homology hirzebruch characteristic classes of possibly singular toric varieties which in the context of complete toric varieties fit nicely with a generalized hirzebruch riemann roch theorem as important special cases we obtain new or recover well known formulae for the baum fulton macpherson todd or macpherson s chern classes of toric varieties as well as for the thom milnor l classes of simplicial projective toric varieties we present two different perspectives for the computation of these characteristic classes of toric varieties first we take advantage of the torus orbit decomposition and the motivic properties of the motivic chern and respectively homology hirzebruch classes to express the latter in terms of dualizing sheaves and respectively the dual todd classes of closures of orbits this method even applies to torus invariant subspaces of a given toric variety the obtained formula is then applied to weighted lattice point counting in lattice polytopes and their subcomplexes yielding generalized pick type formulae second in the case of simplicial toric varieties we compute our characteristic classes by using the lefschetz riemann roch theorem of edidin graham in the context of the geometric quotient description of such varieties in this setting we define mock hirzebruch classes of simplicial toric varieties which specialize to the mock chern mock todd and mock l classes of such varieties and investigate the difference between the actual homology hirzebruch class and the mock hirzebruch class we show that this difference is localized on the singular locus and we obtain a formula for it in which the contribution of each singular cone is identified explicitly finally the two methods of computing characteristic classes are combined for proving several characteristic class formulae originally obtained by cappell and shaneson in the early 1990s 2015 wiley periodicals inc

vertex algebras and mirror symmetry mirror symmetry for calabi yau hypersurfaces in toric varieties is by now well established however previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror we are able to calculate explicitly vertex algebras that correspond to holomorphic parts of a and b models of calabi yau hypersurfaces and complete intersections in toric varieties we establish the relation between these vertex algebras for mirror calabi yau manifolds this should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra as well as some basic results of the theory of vertex algebras ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties

stringy chern classes of singular varieties motivic integration m kontsevich motivic integration lecture at orsay 1995 and macpherson s transformation r macpherson chern classes for singular varieties ann of math 100 1974 423 432 are combined in this paper to construct a theory of stringy chern classes for singular varieties these classes enjoy strong birational invariance properties and their definition encodes data coming from resolution of singularities the singularities allowed in the theory are those typical of the minimal model program examples are given by quotients of manifolds by finite groups for the latter an explicit formula is proven assuming that the canonical line bundle of the manifold descends to the quotient this gives an expression of the stringy chern class of the quotient in terms of chern schwartz macpherson classes of the fixed point set data

global bifurcation phenomena of traveling wave solutions for some bistable reaction diffusion systems on considere le systeme bistable e u t e 2 u xx f u v v t v xx g u v ou e est petit on etudie les solutions onde de propagation qui tendent vers deux etats stables quand x

confirmation for wielandt s conjecture abstract let be a set of primes by h wielandt s definition sylow theorem holds for a finite group g if all maximal subgroups of g are conjugate in the paper the following statement is proven assume that is a union of disjoint subsets and and a finite group g possesses a hall subgroup which is a direct product of a subgroup and a subgroup furthermore assume that both the sylow theorem and theorem hold for g then the sylow theorem holds for g this result confirms a conjecture posed by h wielandt in 1959

chiral rings of vertex algebras of mirror symmetry we calculate chiral rings of the n 2 vertex algebras constructed from the combinatorial data of toric mirror symmetry and show that they coincide with the description of stringy cohomology conjectured previously in a joint work with a mavlyutov this constitutes an important reality check of the vertex algebra approach to mirror symmetry

nerve impulse propagation in a branching nerve system a simple model abstract local spatial changes of nerve axon geometry such as diameter increase and branching may cause that action potential waves approaching a region of geometric change fail to propagate beyond it in this paper this effect will be examined for a special kind of nonuniformity within the framework of a simple model an initial value problem for a single nonlinear diffusion equation on an unbounded domain

chiral differential operators on supermanifolds the first part of this paper provides a new description of chiral differential operators cdos in terms of global geometric quantities the main result is a recipe to define all sheaves of cdos on a smooth cs manifold its ingredients consist of an affine connection and an even 3 form that trivializes p1 with fixed two suitable 3 forms define isomorphic sheaves of cdos if and only if their difference is exact moreover conformal structures are in one to one correspondence with even 1 forms that trivialize c1 applying our work in the first part we then construct what may be called chiral dolbeault complexes of a complex manifold m and analyze conditions under which these differential vertex superalgebras admit compatible conformal structures or extra gradings by fermion numbers when m is compact their cohomology computes in various cases the witten genus the two variable elliptic genus and a spinc version of the witten genus this part contains some new results as well as provides a geometric formulation of certain known facts from the study of holomorphic cdos and models

orbifold genera product formulas and power operations we generalize the definition of orbifold elliptic genus and introduce orbifold genera of chromatic level h using h tuples rather than pairs of commuting elements we show that our genera are in fact orbifold invariants and we prove integrality results for them if the genus arises from an h8 map into the morava lubin tate theory eh then we give a formula expressing the orbifold genus of the symmetric powers of a stably almost complex manifold m in terms of the genus of m itself our formula is the p typical analogue of the dijkgraaf moore verlinde verlinde formula for the orbifold elliptic genus r dijkgraaf et al elliptic genera of symmetric products and second quantized strings comm math phys 185 1 1997 197 209 it depends only on h and not on the genus

models of unidirectional propagation in heterogeneous excitable media two differential equation models of excitable media threshold and recovery kinetics with solutions that exhibit unidirectional propagation are presented it is shown that unidirectional propagation in heterogeneous excitable media with non oscillatory kinetics can be initiated from homogeneous initial data simulations on a reaction diffusion model with fitzhugh nagumo kinetics and spatially heterogeneous parameters yields a rotating wave on a one dimensional circular spatial domain an ordinary differential equation model with four semi coupled excitable cells and heterogeneous parameters is analyzed to determine a critical parameter region over which unidirectional propagation may occur

on the geometry of a siegel modular threefold introduction 317 1 compactifications 318 2 humbert surfaces 324 3 the chern numbers of s n 331 4 symmetric quartic threefolds 334 5 the modular threefold of level 2 335 6 kummer surfaces 338 7 prym surfaces 340 8 humbert surfaces again 345

mckay correspondence for elliptic genera we establish a correspondence between orbifold and singular elliptic genera of a global quotient while the former is defined in terms of the fixed point set of the action the latter is defined in terms of the resolution of singularities as a byproduct the second quantization formula of dijkgraaf moore verlinde and verlinde is extended to arbitrary kawamata log terminal pairs

small intersections of principal blocks abstract in this note it is shown that a finite group g is solvable if for each odd prime divisor p of g irr b 0 g 2 irr b 0 g p 2 where irr b 0 g p is the set of complex irreducible characters of the principal p block b 0 g p of g also the structure of such groups is investigated examples show that the bound 2 is best possible

elliptic classes of schubert varieties we introduce new notions in elliptic schubert calculus the twisted borisov libgober classes of schubert varieties in general homogeneous spaces g p while these classes do not depend on any choice they depend on a set of new variables for the definition of our classes we calculate multiplicities of some divisors in schubert varieties which were only known for full flag varieties before our approach leads to a simple recursions for the elliptic classes comparing this recursion with r matrix recursions of the so called elliptic weight functions of rimanyi tarasov varchenko we prove that weight functions represent elliptic classes of schubert varieties

on the elliptic genus of generalised kummer varieties borisov and libgober 2 recently proved a conjecture of dijkgraaf moore verlinde and verlinde see 6 on the elliptic genus of a hilbert scheme of points on a surface we show how their result can be used together with our work on complex genera of generalised kummer varieties 17 to deduce the following formula conjectured by kawai and yoshioka 15 on the elliptic genus of a generalised kummer variety a n of dimension 2 n 1 here is the weak jacobi form of weight 1 and index and v n is the hecke operator sending jacobi forms of index r to jacobi forms of index nr see 7