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- ItemExtremal configurations of polygonal linkages(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Khimshiashvili, G.; Panina, G.; Siersma, D.; Zhukova, A.[no abstract available]
- ItemInfeasibility certificates for linear matrix inequalities(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Klep, Igor; Schweighofer, MarkusFarkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix inequalities. We provide nonlinear algebraic certificates for all infeasible linear matrix inequalities in the spirit of real algebraic geometry. More precisely, we show that a linear matrix inequality L(x)⪰0 is infeasible if and only if −1 lies in the quadratic module associated to L. We prove exponential degree bounds for the corresponding algebraic certificate. In order to get a polynomial size certi cate, we use a more involved algebraic certificate motivated by the real radical and Prestel's theory of semiorderings. Completely different methods, namely complete positivity from operator algebras, are employed to consider linear matrix inequality domination.
- ItemA series of algebras generalizing the octonions and Hurwitz-Radon identity(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Morier-Genoud, Sophie; Ovsienko, ValentinWe study non-associative twisted group algebras over (Z2)n with cubic twisting functions. We construct a series of algebras that extend the classical algebra of octonions in the same way as the Clifford algebras extend the algebra of quaternions. We study their properties, give several equivalent definitions and prove their uniqueness within some natural assumptions. We then prove a simplicity criterion. We present two applications of the constructed algebras and the developed technique. The first application is a simple explicit formula for the following famous square identity: (a21+...+a2N)(b21+...+b2ρ(N))=c21+...+c2N, where ck are bilinear functions of the ai and bj and where ρ(N) is the Hurwitz-Radon function. The second application is the relation to Moufang loops and, in particular, to the code loops. To illustrate this relation, we provide an explicit coordinate formula for the factor set of the Parker loop.
- ItemA construction of hyperbolic coxeter groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Osajda, DamianWe give a simple construction of Gromov hyperbolic Coxeter groups of arbitrarily large virtual cohomological dimension. Our construction provides new examples of such groups. Using this one can construct e.g. new groups having some interesting asphericity properties.
- ItemA new counting function for the zeros of holomorphic curves(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Anderson, J.M.; Hinkkanen, AimoLet f1, . . . , fp be entire functions that do not all vanish at any point, so that (f1, . . . , fp) is a holomorphic curve in CPp−1. We introduce a new and more careful notion of counting the order of the zero of a linear combination of the functions f1, . . . , fp at any point where such a linear combination vanishes, and, if all the f1, . . . , fp are polynomials, also at infinity. This enables us to formulate an inequality, which sometimes holds as an identity, that sharpens the classical results of Cartan and others.
- ItemLocally conformally Kähler manifolds admitting a holomorphic conformal flow(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2010) Ornea, Liviu; Verbitsky, MishaAbstract A manifold M is locally conformally Kähler (LCK) if it admits a Kähler covering ˜M with monodromy acting by holomorphic homotheties. Let M be an LCK manifold admitting a holomorphic conformal flow of diffeomorphisms, lifted to a non-isometric homothetic flow on ˜M . We show that M admits an automorphic potential, and the monodromy group of its conformal weight bundle is Z.
- ItemThe contact polytope of the Leech lattice(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Dutour Sikiri´c, Mathieu; Schürmann, Achill; Vallentin, FrankThe contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1, 197, 362, 269, 604, 214, 277, 200 many facets in 232 orbits.
- ItemWeakly complex homogeneous spaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Moroianu, Andrei; Semmelmann, UweWe complete our recent classification [GMS11] of compact inner symmetric spaces with weakly complex tangent bundle by filling up a case which was left open, and extend this classification to the larger category of compact homogeneous spaces with positive Euler characteristic. We show that a simply connected compact equal rank homogeneous space has weakly complex tangent bundle if and only if it is a product of compact equal rank homogeneous spaces which either carry an invariant almost complex structure (and are classified by Hermann [H56]), or have stably trivial tangent bundle (and are classified by Singhof and Wemmer [SW86]), or belong to an explicit list of weakly complex spaces which have neither stably trivial tangent bundle, nor carry invariant almost complex structures.
- ItemOn test sets for nonlinear integer maximization(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Lee, Jon; Onn, Shmuel; Weismantel, RobertA finite test set for an integer maximization problem enables us to verify whether a feasible point attains the global maximum. We estabish in the paper several general results that apply to integer maximization problems wthe monlinear objective functions.
- ItemContractive idempotents on locally compact quantum groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2012) Neufang, Matthias; Salmi, Pekka; Skalski, Adam; Spronk, Nicogeneral form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established.