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- ItemMehler-Heine asymptotics of a class of generalized hypergeometric polynomials(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Bracciali, Cleonice F.; Moreno-Balcázar, Juan JoséWe obtain a Mehler–Heine type formula for a class of generalized hypergeometric polynomials. This type of formula describes the asymptotics of polynomials scale conveniently. As a consequence of this formula, we obtain the asymptotic behavior of the corresponding zeros. We illustrate these results with numerical experiments and some figures.
- ItemFibonacci-like unimodal inverse limit spaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Bruin, H.; Štimac, S.We study the structure of inverse limit space of so-called Fibonacci-like tent maps. The combinatorial constraints implied by the Fibonacci-like assumption allows us to introduce certain chains that enable a more detailed analysis of symmetric arcs within this space than is possible in the general case. We show that link-symmetric arcs are always symmetric or a well-understood concatenation of quasi-symmetric arcs. This leads to simplification of some existing results, including the Ingram Conjecture for Fibonacci-like unimodal inverse limits.
- ItemDominance and transmissions in supertropical valuation theory(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Izhakian, Zur; Knebusch, Manfred; Rowen, LouisThis paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring R and studied a dominance relation Φ>=v between supervaluations φ and υ on R, aiming at an enrichment of the algebraic tool box for use in tropical geometry. A supervaluation φ:R→U is a multiplicative map from R to a supertropical semiring U, cf. [IR1], [IR2], [IKR1], with further properties, which mean that φ is a sort of refinement, or covering, of an m-valuation (= monoid valuation) υ:R→M. In the most important case, that R is a ring, m-valuations constitute a mild generalization of valuations in the sense of Bourbaki [B], while φ>=υ means that υ:R→V is a sort of coarsening of the supervaluation φ. If φ(R) generates the semiring U, then φ>=υ if there exists a "transmission" α:U→V with φ=α∘φ. Transmissions are multiplicative maps with further properties, cf. [IKR1, §55]. Every semiring homomorphism α:U→V is a transmission, but there are others which lack additivity, and this causes a major difficulty. In the main body of the paper we study surjective transmissions via equivalence relations on supertropical semirings, often much more complicated than congruences by ideals in usual commutative algebra.
- ItemGhost algebras of double Burnside algebras via Schur functors(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Boltje, Robert; Danz, SusanneFor a finite group G, we introduce a multiplication on the Q-vector space with basis SG×G, the set of subgroups of G × G. The resulting Q-algebra A˜ can be considered as a ghost algebra for the double Burnside ring B(G,G) in the sense that the mark homomorphism from B(G,G) to A˜ is a ring homomorphism. Our approach interprets QB(G,G) as an algebra eAe, where A is a twisted monoid algebra and e is an idempotent in A. The monoid underlying the algebra A is again equal to SG×G with multiplication given by composition of relations (when a subgroup of G × G is interpreted as a relation between G and G). The algebras A and A˜ are isomorphic via Mo¨bius inversion in the poset SG×G. As an application we improve results by Bouc on the parametrization of simple modules of QB(G,G) and also of simple biset functors, by using results by Linckelmann and Stolorz on the parametrization of simple modules of finite category algebras. Finally, in the case where G is a cyclic group of order n, we give an explicit isomorphism between QB(G,G) and a direct product of matrix rings over group algebras of the automorphism groups of cyclic groups of order k, where k divides n.
- ItemPolynomiality, wall crossings and tropical geometry of rational double Hurwitz cycles(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Bertram, Aaron; Cavalieri, Renzo; Markwig, HannahWe study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon observed for double Hurwitz numbers, such cycles are piecewise polynomial in the entries of the special ramification; the chambers of polynomiality and wall crossings have an explicit and “modular” description. A main goal of this paper is to simultaneously carry out this investigation for the corresponding objects in tropical geometry, underlining a precise combinatorial duality between classical and tropical Hurwitz theory.
- ItemAnalytic varieties with finite volume amoebas are algebraic(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Madani, Farid; Nisse, MounirIn this paper, we study the amoeba volume of a given k-dimensional generic analytic variety V of the complex algebraic torus (C∗)n. When n>=2k, we show that V is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the k-linear spaces will be given.
- ItemAn inductive approach to Coxeter arrangements and Solomon’s descent algebra(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Douglass, J.Matthew; Pfeiffer, Götz; Röhrle, GerhardIn our recent paper [3], we claimed that both the group algebra of a finite Coxeter group W as well as the Orlik-Solomon algebra of W can be decomposed into a sum of induced one-dimensional representations of centralizers, one for each conjugacy class of elements of W, and gave a uniform proof of this claim for symmetric groups. In this note we outline an inductive approach to our conjecture. As an application of this method, we prove the inductive version of the conjecture for nite Coxeter groups of rank up to 2.
- ItemProducts of pairs of Dehn twists and maximal real Lefschetz fibrations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Loos, Alex; Neher, NerminWe address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic Lefschetz bration is algebraic.
- ItemSome combinatorial identities related to commuting varieties and Hilbert schemes(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Bellamy, Gwyn; Ginzburg, VictorIn this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane.
- ItemSemi-invertible extensions of C*-algebras(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Manuilov, Vladimir; Thomsen, KlausWe prolonge the list of C*-algebras for which all extensions by any stable separable C*-algebra are semi-invertible. In particular, we handle certain amalgamations, both of C*-algebras and of groups. Concerning groups we consider both reduced and full group C*-algebras.