morse theory for periodic solutions of hamiltonian systems and the maslov index in this paper we prove morse type inequalities for the contractible 1 periodic solutions of time dependent hamiltonian differential equations on those compact symplectic manifolds m for which the symplectic form and the first chern class of the tangent bundle vanish over q m the proof is based on a version of infinite dimensional morse theory which is due to floer the key point is an index theorem for the fredholm operator which plays a central role in floer homology the index formula involves the maslov index of nondegenerate contractible periodic solutions this maslov index plays the same role as the morse index of a nondegenerate critical point does in finite dimensional morse theory we shall use this connection between floer homology and maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every i periodic solution has at least one floquet multiplier which is not equal to 1

the 2 braid group and garside normal form we investigate the relation between the garside normal form for positive braids and the 2 braid group defined by rouquier inspired by work of brav and thomas we show that the garside normal form is encoded in the action of the 2 braid group on a certain categorified left cell module this allows us to deduce the faithfulness of the 2 braid group in finite type we also give a new proof of paris theorem that the canonical map from the generalized braid monoid to its braid group is injective in arbitrary type

parallel detection of groupwise space time codes by predictive soft interference cancellation multiple input multiple output mimo techniques promise huge capacity increase in fading channels groupwise space time coding is a tradeoff between complexity and performance in this letter the structure of particular component space time code trellises is exploited using partial information from a viterbi decoder of the simultaneously decoded interfering component codes we have shown that by calculating the a posteriori probabilities of different states of the encoder at each time and predicting the conditional mean and covariance of interference for the next time index the system performance can be improved by soft interference cancellation the word error rate performance improvement for a system with four transmit and four receive antennas is 1 7 and 1 5 db for two space time codes with 8 and 16 states respectively in addition the parallel structure does not have a decoding delay as in successive interference cancellation and is highly modular for very large scale integration implementation

existence and uniqueness of solution in sobolev space for an unsteady crystal growth problem with zero surface tension abstract we study an initial value problem for a two dimensional dendritic crystal growth model with zero surface tension if the initial data is in sobolev space h 2 r it is proved that an unique local solution exists in proper sobolev space

analyticity and nonexistence of classical steady hele shaw fingers this paper concerns analyticity of a classical steadily translating nger in a hele shaw cell and nonexistence of solutions when the relative nger width is smaller than 1 it is proven that any classical solution to the nger problem if it exists for sufciently small but nonzero surface tension is close to some saffman taylor zero surface tension solution and satises some algebraic decay conditions at 1 must belong to the analytic function space a0 as dened in section 1 and chosen in a previous study 34 of the existence of nger solutions further it is proven that for any x ed 2 0 1 there can be no classical steadynger solution when surface tension is sufciently small which contradicts a previous conclusion based on numerical simulation c 2002 wiley periodicals inc

generators for the hyperelliptic torelli group and the kernel of the burau representation at t 1 we prove that the hyperelliptic torelli group is generated by dehn twists about separating curves that are preserved by the hyperelliptic involution this verifies a conjecture of hain the hyperelliptic torelli group can be identified with the kernel of the burau representation evaluated at t 1 and also the fundamental group of the branch locus of the period mapping and so we obtain analogous generating sets for those one application is that each component in torelli space of the locus of hyperelliptic curves becomes simply connected when curves of compact type are added

a link invariant from the symplectic geometry of nilpotent slices we define an invariant of oriented links in s 3 using the symplectic geometry of certain spaces which arise naturally in lie theory more specifically we present a knot as the closure of a braid which in turn we view as a loop in configuration space fix an affine subspacesm of the lie algebra sl2m c which is a transverse slice to the adjoint action at a nilpotent matrix with two equal jordan blocks the adjoint quotient map restricted to sm gives rise to a symplectic fibre bundle over configuration space an inductive argument constructs a distinguished lagrangian submani

garside families and garside germs garside families have recently emerged as a relevant context for extending results involving garside monoids and groups which themselves extend the classical theory of generalized braid groups here we establish various characterizations of garside families that is equivalently various criteria for establishing the existence of normal decompositions of a certain type

mutations and the derived picard group of the brauer star algebra abstract in this paper we show that the derived picard group trpic a of the brauer star algebra of type n t is generated by shift pic a and equivalences h i i 1 n in the case t 1 where h i were shown to satisfy the relations of the braid group on the affine diagram a n 1 by schaps and zakay illouz in the multiplicity free case we show that trpic a is generated by a slightly bigger set

a soergel like category for complex reflection groups of rank one we introduce analogues of soergel bimodules for complex reflection groups of rank one we give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split grothendieck ring by generators and relations this ring turns out to be an extension of the hecke algebra of the reflection group w and a free module of rank w w 1 1 over the base ring we also show that it is a generically semisimple algebra if defined over the complex numbers

braid groups and kleinian singularities we establish faithfulness of braid group actions generated by twists along an ade configuration of 2 spherical objects in a derived category our major tool is the garside structure on braid groups of type ade this faithfulness result provides the missing ingredient in bridgeland s description of a space of stability conditions associated to a kleinian singularity

the burau representation of the braid group b_n is unfaithful for large n two fundamental theorems of classical knot theory by j alexander are that every knot is a closed braid and second that a certain procedure see 1 2 for both results assigns to each knot k a polynomial a k in t which only depends on the topological type of the knot once normalized by a power of t to take a positive value at t 0 with this normalization take t to be a transcendental number since 1926 2 it has been known that the function a knots c is not one to one however it has not become clear whether the composite

categorification of a linear algebra identity and factorization of serre functors we provide a categorical interpretation of a well known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras as a consequence we deduce that the serre functor of a finite dimensional triangular algebra a has always a lift up to shift to a product of suitably defined reflection functors in the category of perfect complexes over the trivial extension algebra of a

the tilting theory of contraction algebras abstract to every minimal model of a complete local isolated cdv singularity donovan wemyss associate a finite dimensional symmetric algebra known as the contraction algebra we construct the first known standard derived equivalences between these algebras and then use the structure of an associated hyperplane arrangement to control the compositions obtaining a faithful group action on the bounded derived category further we determine precisely those standard equivalences which are induced by two term tilting complexes and show that any standard equivalence between contraction algebras up to algebra isomorphism can be viewed as the composition of our constructed functors thus for a contraction algebra we obtain a complete picture of its derived equivalence class and in particular of its derived autoequivalence group

stability conditions on an singularities we study the spaces of locally finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of a n singularities supported at the exceptional sets our main theorem is that they are connected and simply connected the proof is based on the study of spherical objects in a ishii and h uehara autoequivalences of derived categories on the minimal resolutions of a n singularities on surfaces j differential geom 71 3 385 435 2005 and the homological mirror symmetry for a n singularities

a nondisplaceable lagrangian torus in t s2 we show that the lagrangian torus in the cotangent bundles of the 2 sphere obtained by applying the geodesic flow to the unit circle in a fiber is not displaceable by computing its lagrangian floer homology the computation is based on a symmetry argument 2007 wiley periodicals inc

picard groups for derived module categories we introduce in this paper a generalization of picard groups to derived cat egories of algebras we study general properties of those groups and we construct braid group actions on these groups for particular classes of algebras

a note on words in braid monoids abstract the purpose of this note is to give a self contained apart from simple facts about coxeter groups and we hope a bit shorter and more understandable account of some results of c1 c2 on normal forms of braids which are themselves based on the papers d1 t in particular a motivation was to give a proof of proposition 5 1 that we use in b m some proofs and results from section 2 onwards seem to be new i thank several people for improvements from earlier versions of the manuscript m geck for pointing out some errors f digne for pointing out that some results don t need the braid group to be of finite type and j y hee for suggesting and providing further improvements in that direction

disjoinable lagrangian spheres and dilations we consider open symplectic manifolds which admit dilations in the sense previously introduced by solomon and the author we obtain restrictions on collections of lagrangian submanifolds which are pairwise disjoint or pairwise disjoinable by hamiltonian isotopies inside such manifolds this includes the milnor fibres of isolated hypersurface singularities which have been stabilized by adding quadratic terms sufficiently often

discrete point spectrum of linear stability operator for saffman taylor bubbles with nonzero surface tension abstract we will study the linear spectral properties of steady saffman taylor bubbles with surface tension in a hele shaw cell it was known 21 that the saffman taylor exact solution without surface tension is linearly unstable and the point spectrum is a continuum set in this paper we rigorously conclude that the point spectrum of the stability operator of any branch of saffman taylor bubbles is a discrete set when surface tension is not zero

the level four braid group by evaluating the burau representation at t 1 we obtain a symplectic representation of the braid group we study the resulting congruence subgroups of the braid group namely the preimages of the principal congruence subgroups of the symplectic group our main result is that the level 4 congruence subgroup is equal to the group generated by squares of dehn twists we also show that the image of the brunnian subgroup of the braid group under the symplectic representation is the level four congruence subgroup

dual braid monoids mikado braids and positivity in hecke algebras we study the rational permutation braids that is the elements of an artin tits group of spherical type which can be written x 1 y where x and y are prefixes of the garside element of the braid monoid we give a geometric characterization of these braids in type a n and b n and then show that in spherical types different from d n the simple elements of the dual braid monoid for arbitrary choice of coxeter element embedded in the braid group are rational permutation braids we conjecture this to hold also in type d n this property implies positivity properties of the polynomials arising in the linear expansion of their images in the iwahori hecke algebra when expressed in the kazhdan lusztig basis in type a n it implies positivity properties of their images in the temperley lieb algebra when expressed in the diagram basis

a relative morse index for the symplectic action the notion of a morse index of a function on a finite dimensional manifold cannot be generalized directly to the symplectic action function a on the loop space of a manifold in this paper we define for any pair of critical points of a a relative morse index which corresponds to the difference of the two morse indices in finite dimensions it is based on the spectral flow of the hessian of a and can be identified with a topological invariant recently defined by viterbo and with the dimension of the space of trajectories between the two critical points

the effect of finiteness in the saffman taylor viscous fingering problem we derive a family of exact time evolving solutions for the the evolution of a finite blob of fluid confined to a channel in a hele shaw cell we show rigorously that for large fluid volume there are solutions for which one of the interfaces approaches the steady saffman taylor finger solution of arbitrary width 0 1 on the basis of this we argue that the far field effects of a displaced second interface do not provide a selection mechanism for the formation of a width frac 1 2 finger when surface tension or any other regularization is ignored

twisted filtrations of soergel bimodules and linear rouquier complexes abstract we consider twisted standard filtrations of soergel bimodules associated to arbitrary coxeter groups and show that the graded multiplicities in these filtrations can be interpreted as structure constants in the hecke algebra this corresponds to the positivity of the polynomials occurring when expressing an element of the canonical basis in a generalized standard basis twisted by a biclosed set of roots in the sense of dyer and comes as a corollary of soergel s conjecture we then show the positivity of the corresponding inverse polynomials in the case where the biclosed set is an inversion set of an element or its complement by generalizing a result of elias and williamson on the linearity of the rouquier complexes associated to lifts of these basis elements in the artin tits group these lifts turn out to be generalizations of mikado braids as introduced in a joint work with digne this second positivity property generalizes a result of dyer and lehrer from finite to arbitrary coxeter groups

pseudoholomorphic curves in symplectizations with applications to the weinstein conjecture in dimension three l in t roduct ion 515 1 1 the weinstein conjecture 515 1 2 the main results 517 1 3 sketch of the proof 522 2 local f redho lm theory 525 2 1 similar i ty principle and consequences 525 2 2 n m as a lmost complex manifold and local fillings 529 2 3 local propert ies of ho lomorphic curves 531 3 bubbl ing off analysis and global fredholm theory 533 3 l grad ien t bounds imply ca bounds 533 3 2 bubbing off analysis of ho lomorphic planes 534 3 3 grad ien t bounds near the boundary 537 4 proof of the main results 544 4 1 set up for a global fredholm theory 544 4 2 bishop s theorem 545 4 3 proof of theorem 5 546 4 4 proof of theorems 8 and 11 547 4 5 uniqueness results for foliations 547 5 appendix 550 5 1 per turbing surfaces 550 5 2 ki l l ing crit ical points of hypersurfaces 552 5 3 adding a thin tube to a sphere 560

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

stability conditions on text cy _n categories associated to a_n quivers and period maps in this paper we study the space of stability conditions on a certain n calabi yau mathrm cy n category associated to an a n quiver recently bridgeland and smith constructed stability conditions on some mathrm cy 3 categories from meromorphic quadratic differentials with simple zeros generalizing their results to higher dimensional calabi yau categories we describe the space of stability conditions as the universal cover of the space of polynomials of degree n 1 with simple zeros in particular central charges of stability conditions on mathrm cy n categories are constructed as the periods of quadratic differentials with zeros of order n 2 which are associated to polynomials

witten s complex and infinite dimensional morse theory we investigate the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space the results are applied to an infinite dimensional problem involving the symplect c action function

on weyl groups and artin groups associated to orbifold projective lines abstract we associate a generalized root system in the sense of kyoji saito to an orbifold projective line via the derived category of finite dimensional representations of a certain bound quiver algebra we generalize results by saito and takebayashi and yamada for elliptic weyl groups and elliptic artin groups to the weyl groups and the fundamental groups of the regular orbit spaces associated to the generalized root systems moreover we study the relation between this fundamental group and a certain subgroup of the autoequivalence group of a triangulated subcategory of the derived category of 2 calabi yau completion of the bound quiver algebra

analyticity of classical steady needle crystals abstract this paper is a continuation of our previous work rigorous results in selection of steady needle crystals j differential equations 197 2004 349 426 it concerns analyticity of a classical steadily translating needle crystal it is proved that any classical solution to the needle crystal problem with sufficiently small but nonzero surface tension if its slope deviation is close to some ivantsov zero surface tension solution and if its curvature satisfies some algebraic decay conditions at must belong to the analytic function space a 0 defined in 1 and chosen in the previous study mentioned above the analyticity result implies that there can be no classical steady needle crystal solution when anisotropy is zero

quivers floer cohomology and braid group actions we consider the derived categories of modules over a certain family a m of graded rings and floer cohomology of lagrangian intersections in the symplectic manifolds which are the milnor fibres of simple singularities of type a m we show that each of these two rather different objects encodes the topology of curves on an m 1 punctured disc we prove that the braid group b m 1 acts faithfully on the derived category of a m modules and that it injects into the symplectic mapping class group of milnor fibers the philosophy behind our results is as follows using floer cohomology one should be able to associate to the milnor fibre a triangulated category its construction has not been carried out in detail this triangulated category should contain a full subcategory which is equivalent up to a slight difference in the grading to the derived category of a m modules the full embedding would connect the two occurrences of the braid group thus explaining the similarity between them

nonexistence of classical steady hele shaw bubble this paper concerns nonexistence of steadily translating bubbles in a hele shaw cell for small but nonzero surface tension it is proved that for any fixed bubble velocity u relative to the fluid velocity at infinity in the interval 2 there can be no classical steady bubble solution

transversality in elliptic morse theory for the symplectic action our goal in this paper is to settle some transversality question for the perturbed nonlinear cauchy riemann equations on the cylinder these results play a central role in the denition of symplectic floer homology and hence in the proof of the arnold conjecture there is currently no other reference to these transversality results in the open literature our approach does not require aronszajn s theorem instead we derive the unique continuation theorem from a generalization of the carleman similarity principle

weil restriction of noncommutative motives abstract the weil restriction functor introduced in the late fifties was recently extended by karpenko to the category of chow motives with integer coefficients in this article we introduce the noncommutative nc analogue of the weil restriction functor where schemes are replaced by dg algebras and extend it to kontsevich s categories of nc chow motives and nc numerical motives instead of integer coefficients we work more generally with coefficients in a binomial ring along the way we extend karpenko s functor to the classical category of numerical motives and compare this extension with its nc analogue as an application we compute the nc chow motive of the weil restriction of every smooth projective scheme whose category of perfect complexes admits a full exceptional collection finally in the case of central simple algebras we describe explicitly the nc analogue of the weil restriction functor using solely the degree of the field extension this leads to a categorification of the classical corestriction homomorphism between brauer groups

relative singularity categories i auslander resolutions abstract let r be an isolated gorenstein singularity with a non commutative resolution a end r r m in this paper we show that the relative singularity category r a of a has a number of pleasant properties such as being hom finite moreover it determines the classical singularity category d s g r of buchweitz and orlov as a certain canonical quotient category if r has finite cm type which includes for example kleinian singularities then we show the much more surprising result that d s g r determines r aus r where aus r is the corresponding auslander algebra the proofs of these results use dg algebras a koszul duality and the new concept of dg auslander algebras which may be of independent interest

derived automorphism groups of k3 surfaces of picard rank 1 we give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a k3 surface of picard rank 1 we do this by proving that a distinguished connected component of the space of stability conditions is preserved by all autoequivalences and is contractible

koszul duality patterns in representation theory the aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of koszul duality to repre sentation theory the paper consists of three parts relatively independent of each other the first part gives a reasonably selfcontained introduction to koszul rings and koszul duality koszul rings are certain z graded rings with particularly nice homological properties which involve a kind of duality thus to a koszul ring one associates naturally the dual koszul ring the second part is devoted to an application to representation theory of semisimple lie algebras we show license or copyright restrictions may apply to redistribution see http www ams org journal terms of use koszul duality patterns 527 that the block of the bernstein gelfand gelfand category o that corresponds to any fixed central character is governed by the koszul ring moreover the dual of that ring governs a certain subcategory of the category o again this generalizes the selfduality theorem conjectured by beilinson and ginsburg in 1986 and proved by soergel in 1990 in the third part we study certain cate gories of mixed perverse sheaves on a variety stratified by affine linear spaces we provide a general criterion for such a category to be governed by a koszul ring in the flag variety case this reduces to the setup of part two in the more general case of affine flag manifolds and affine grassmannians the criterion should yield interesting results about representations of quantum groups and affine lie algebras department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address sasha math mit edu department of mathematics the university of chicago chicago illinois 60637 e mail address ginzburg math uchicago edu max planck institut fur mathematik gottfried claren strase 26 d 53 bonn 3 germany current address mathematisches institut universitat freiburg albertstrase 23b d 79104 freiburg germany e mail address soergel sun1 mathematik uni freiburg de license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

exchange graphs and ext quivers abstract we study the oriented exchange graph eg n q of reachable hearts in the finite dimensional derived category d n q of the cy n ginzburg algebra n q associated to an acyclic quiver q we show that any such heart is induced from some heart in the bounded derived category d q via some lagrangian immersion l d q d n q we build on this to show that the quotient of eg n q by the seidel thomas braid group is the exchange graph ceg n 1 q of cluster tilting sets in the higher cluster category c n 1 q as an application we interpret buan thomas coloured quiver for a cluster tilting set in terms of the ext quiver of any corresponding heart in d n q

cohomologie des varietes de deligne lusztig abstract we study the cohomology of deligne lusztig varieties with aim the construction of actions of hecke algebras on such cohomologies as predicted by the conjectures of broue malle and michel ultimately aimed at providing an explicit version of the abelian defect conjecture we develop the theory for varieties associated to elements of the braid monoid and partial compactifications of them we are able to compute the cohomology of varieties associated to possibly twisted rank 2 groups and powers of the longest element w 0 some indeterminacies remain for g 2 we use this to construct hecke algebra actions on the cohomology of varieties associated to w 0 or its square for groups of arbitrary rank in the subsequent work f digne j michel endomorphisms of deligne lusztig varieties nagoya j math 183 2006 we construct actions associated to more general regular elements and we study their traces on cohomology

two block springer fibers of types c and d a diagrammatic approach to springer theory we explain an elementary topological construction of the springer representation on the homology of topological springer fibers of types c and d in the case of nilpotent endomorphisms with two jordan blocks the weyl group and component group actions admit a diagrammatic description in terms of cup diagrams which appear in the definition of arc algebras of types b and d we determine the decomposition of the representations into irreducibles and relate our construction to classical springer theory as an application we obtain presentations of the cohomology rings of all two block springer fibers of types c and d moreover we deduce explicit isomorphisms between the kazhdan lusztig cell modules attached to the induced trivial module and the irreducible specht modules in types c and d

decorated marked surfaces spherical twists versus braid twists we are interested in the 3 calabi yau categories mathcal d arising from quivers with potential associated to a triangulated marked surface mathbf s without punctures we prove that the spherical twist group mathrm st of mathcal d is isomorphic to a subgroup generated by braid twists of the mapping class group of the decorated marked surface mathbf s bigtriangleup here mathbf s bigtriangleup is the surface obtained from mathbf s by decorating with a set of points where the number of points equals the number of triangles in any triangulations of mathbf s for instance when mathbf s is an annulus the result implies that the corresponding spaces of stability conditions on mathcal d are contractible

khovanov seidel quiver algebras and ozsvath szabo s bordered theory abstract in the 2016 preprint kauffman states bordered algebras and a bigraded knot invariant ozsvath and szabo introduced a set of algebraic constructions in the spirit of bordered heegaard floer homology their constructions can be used to compute knot floer homology algebraically for knots in the 3 sphere in this paper we investigate a relationship between ozsvath szabo s bordered theory and the algebras and bimodules constructed by khovanov and seidel in quivers floer cohomology and braid group actions 2002 specifically we show that the khovanov seidel quiver algebras are isomorphic to quotients of idempotent truncations of some of ozsvath szabo s algebras furthermore we show that the dg bimodule associated to a braid generator by khovanov seidel with the right action restricted using the quotient map is homotopy equivalent to ozsvath szabo s da bimodule with the left action induced using the quotient map

quasi hereditary algebras and generalized koszul duality abstract we present an easily applicable sufficient condition for standard koszul algebras to be koszul with respect to if a quasi hereditary algebra is koszul with respect to then and the yoneda extension algebra of are koszul dual in a sense explained below implying in particular that their bounded derived categories of finitely generated graded modules are equivalent we also prove that the extension algebra of is koszul in the classical sense

stability conditions and quantum dilogarithm identities for dynkin quivers abstract we study the fundamental groups of the exchange graphs for the bounded derived category d q of a dynkin quiver q and the finite dimensional derived category d n q of the calabi yau n ginzburg algebra associated to q in the case of d q we prove that its space of stability conditions in the sense of bridgeland is simply connected as an application we show that the donaldson thomas type invariant associated to q can be calculated as a quantum dilogarithm function on its exchange graph in the case of d n q we show that the faithfulness of the seidel thomas braid group action which is known for q of type a or n 2 implies the simply connectedness of the space of stability conditions

equivariant split generation and mirror symmetry of special isogenous tori abstract we prove a version of equivariant split generation of fukaya category when a symplectic manifold admits a free action of a finite group g combining this with some generalizations of seidel s algebraic frameworks from 35 we obtain new cases of homological mirror symmetry for some symplectic tori with non split symplectic forms which we call special isogenous tori this extends the work of abouzaid smith 2 we also show that derived fukaya categories are complete invariants of special isogenous tori

rigorous results in selection of steady needle crystals abstract this paper concerns the existence of solutions to a steady needle crystal growth problem in a one sided model we rigorously prove that for small nonzero anisotropy analytic symmetric needle crystal solutions exist in the limit of surface tension e 2 if only if the stokes constant s for a relatively simple nonlinear differential equation is zero this stokes constant s depends on the parameter 2 9 7 e 8 7 and earlier numerical calculations by a number of investigators have shown this to be zero for a discrete set of values of it is also proven that for 0 there can be no symmetric needle crystal solution in the considered space the methodology consists of two steps first the original problem is reduced to a weak half strip problem for any in a compact set of 0 1 by relaxation of the symmetry condition the weak problem is shown to have a unique solution in the function space considered for any 0 m for some m 0 when a symmetry is invoked the weak problem is shown equivalent to the original needle crystal problem next by considering the behavior of the solution in neighborhood of an appropriate complex turning point for 0 m we extract an exponentially small term in e as e 0 that generally violates the symmetric condition we prove that the symmetry condition is satisfied for small e when the parameter is constrained appropriately

the hodge theory of soergel bimodules we prove soergel s conjecture on the characters of indecomposable soergel bimodules we deduce that kazhdan lusztig polynomials have positive coecients for arbitrary coxeter systems using results of soergel one may deduce an algebraic proof of the kazhdan lusztig conjecture

turbo space time processing to improve wireless channel capacity by deriving a generalized shannon capacity formula for multiple input multiple output rayleigh fading channels and by suggesting a layered space time architecture concept that attains a tight lower bound on the capacity achievable foschini see wireless pers commun vol 6 no 3 p 311 35 1998 has shown a potential enormous increase in the information capacity of a wireless system employing multiple element antenna arrays at both the transmitter and receiver the layered space time architecture allows signal processing complexity to grow linearly rather than exponentially with the promised capacity increase this paper includes two important contributions first we show that foschini s lower bound is in fact the shannon bound when the output signal to noise ratio snr of the space time processing in each layer is represented by the corresponding matched filter bound this proves the optimality of the layered space time concept second we present an embodiment of this concept for a coded system operating at a low average snr and in the presence of possible intersymbol interference this embodiment utilizes the already advanced space time filtering coding and turbo processing techniques to provide yet a practical solution to the processing needed performance results are provided for quasi static rayleigh fading channels with no channel estimation errors we see for the first time that the shannon capacity for wireless communications can be both increased by n times where n is the number of the antenna elements at the transmitter and receiver and achieved within about 3 db in average snr about 2 db of which is a loss due to the practical coding scheme we assume the layered space time processing itself is nearly information lossless

action du groupe des tresses sur une categorie we describe how to define by generators and relations an action of the braid group on a category more generally how to define a functor from a generalized positive braids monoid corresponding to a finite coxeter group to a monoidal category applications to constructions of bondal exceptional systems and of broue michel correspondences on flag manifolds are given

floer cohomology and pencils of quadrics there is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces we investigate symplectic aspects of this relationship with a view to applications in low dimensional topology

mimo ofdm for wireless communications signal detection with enhanced channel estimation multiple transmit and receive antennas can be used to form multiple input multiple output mimo channels to increase the capacity by a factor of the minimum number of transmit and receive antennas in this paper orthogonal frequency division multiplexing ofdm for mimo channels mimo ofdm is considered for wideband transmission to mitigate intersymbol interference and enhance system capacity the mimo ofdm system uses two independent space time codes for two sets of two transmit antennas at the receiver the independent space time codes are decoded using prewhitening followed by minimum euclidean distance decoding based on successive interference cancellation computer simulation shows that for four input and four output systems transmitting data at 4 mb s over a 1 25 mhz channel the required signal to noise ratios snrs for 10 and 1 word error rates wer are 10 5 db and 13 8 db respectively when each codeword contains 500 information bits and the channel s doppler frequency is 40 hz corresponding normalized frequency 0 9 increasing the number of the receive antennas improves the system performance when the number or receive antennas is increased from four to eight the required snrs for 10 and 1 wer are reduced to 4 db and 6 db respectively therefore mimo ofdm is a promising technique for highly spectrally efficient wideband transmission

cuspidal sln modules and deformations of certain brauer tree algebras we show that the algebras describing blocks of the category of cuspidal weight resp generalized weight sln modules are one parameter resp multi parameter deformations of certain brauer tree algebras we explicitly determine these deformations both graded and ungraded the algebras we deform also appear as special centralizer subalgebras of temperley lieb algebras or as generalized khovanov algebras they show up in the context of highest weight representations of the virasoro algebra in the context of rational representations of the general linear group and schur algebras and in the study of the milnor fiber of kleinian singularities

enhanced gauge symmetry and braid group actions enhanced gauge symmetry appears in type ii string theory as well as f and m theory compactified on calabi yau manifolds containing exceptional divisors meeting in dynkin configurations it is shown that in many such cases at enhanced symmetry points in moduli a braid group acts on the derived category of sheaves of the variety this braid group covers the weyl group of the enhanced symmetry algebra which itself acts on the deformation space of the variety in a compatible way extensions of this result are given for nontrivial b fields on k3 surfaces explaining physical restrictions on the b field as well as for elliptic fibrations the present point of view also gives new evidence for the enhanced gauge symmetry content in the case of a local a 2n configuration in a threefold having global 2 monodromy

normalisateur et groupe d artin de type spherique abstract let a s be an artin group and x a subset of s denote by ax the subgroup of a generated by x when a is of spherical type we prove that the normalizer and the commensurator of ax in a are equal and are the product of ax by the quasi centralizer of ax in a looking the associated monoids a and ax we described the quasi centralizer of ax in a thanks to results in coxeter groups these two results generalize earlier results of paris j algebra 196 1997 369 399 finally we compare in the spherical case the normalizer of a parabolic subgroup in the artin group and in the coxeter group

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

existence and uniqueness of analytic solution for unsteady crystals with zero surface tension abstract we study the initial value problem for two dimensional dendritic crystal growth with zero surface tension if the initial data is analytic and close to ivantsov steady solution it is proved that unique analytic solution exists locally in time the analysis is based on a nirenberg theorem on abstract cauchy kovalevsky problem in properly chosen banach spaces

exact lagrangians in a_n surface singularities in this paper we classify lagrangian spheres in a n surface singularities up to hamiltonian isotopy combining with a result of ritter geom funct anal 20 3 779 816 2010 this yields a complete classification of exact lagrangians in a n surface singularities our main new tool is the application of a technique which we call ball swappings and its relative version

a categorification of the jones polynomial author s khovanov mikhail abstract we construct a bigraded cohomology theory of links whose euler characteristic is the jones polynomial

classification of two term tilting complexes over brauer graph algebras using only the combinatorics of its defining ribbon graph we classify the two term tilting complexes as well as their indecomposable summands of a brauer graph algebra as an application we determine precisely the class of brauer graph algebras which are tilting discrete

the weyl extension algebra of gl2 f p abstract we compute the yoneda extension algebra of the collection of weyl modules for g l 2 over an algebraically closed field of characteristic p 0 by developing a theory of generalised koszul duality for certain 2 functors one of which controls the rational representation theory of g l 2 over such a field

the symplectic arc algebra is formal this is the author accepted manuscript the final version is available from duke university press via http dx doi org 10 1215 00127094 3449459

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

stability conditions via spherical objects an object in the bounded derived category db x of coherent sheaves on a complex projective k3 surface x is spherical if it is rigid and simple although spherical objects form only a discrete set in the moduli stack of complexes they determine much of the structure of x and db x here we show that a stability condition on db x is determined by the stability of spherical objects

existence and selection of steady bubbles in a hele shaw cell abstract this paper concerns the existence of a steadily translating bubble in a hele shaw cell for small but non zero surface tension 2 we rigorously conclude that for bubble velocity u relative to the fluid velocity at infinity in the interval 1 2 analytic symmetric solutions exist in the asymptotic limit of surface tension 2 0 if and only if the stokes constant for a relatively simple nonlinear differential equation is zero this stokes constant s depends on the parameter 0 1 corresponding to bubble size and a u 1 2 2 u 1 2 2 2 1 2 4 3 earlier calculations have shown s to be zero for a discrete set of values of a

rigorous results in steady finger selection in viscous fingering this paper concerns the existence of a steadily translating finger solution in a hele shaw cell for small but non zero surface tension 2 though there are numerous numerical and formal asymptotic results for this problem we know of no mathematically rigorous results that address the selection problem we rigorously conclude that for relative finger width in the range with small analytic symmetric finger solutions exist in the asymptotic limit of surface tension if and only if the stokes constant for a relatively simple nonlinear differential equation is zero this stokes constant s depends on the parameter and earlier calculations by a number of authors have shown it to be zero for a discrete set of values of a the methodology consists of proving the existence and uniqueness of analytic solutions for a weak half strip problem for any in a compact subset of 0 1 the weak problem is shown to be equivalent to the original finger problem in the function space considered provided we invoke a symmetry condition next we consider the behavior of the solution in a neighborhood of an appropriate complex turning point for the restricted case for some this turning point accounts for exponentially small terms in as 0 that generally violate the symmetry condition we prove that the symmetry condition is satisfied for small when the parameter a is constrained appropriately