185 results
Search Results
Now showing 1 - 10 of 185
- ItemOn the geometry of regular maps from a quasi-projective surface to a curve(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Parameswaran, A.J.; Tibar, M.We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X.
- 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.
- 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.
- ItemNoncompact harmonic manifolds(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Knieper, Gerhard; Peyerimhoff, NorbertThe Lichnerowicz conjecture asserts that all harmonic manifolds are either flat or locally symmetric spaces of rank 1. This conjecture has been proved by Z.I. Szab´o [Sz] for harmonic manifolds with compact universal cover. E. Damek and F. Ricci [DR] provided examples showing that in the noncompact case the conjecture is wrong. However, such manifolds do not admit a compact quotient. The classification of all noncompact harmonic spaces is still a very difficult open problem. In this paper we provide a survey on recent results on noncompact simply connected harmonic manifolds, and we also prove many new results, both for general noncompact harmonic manifolds and for noncompact harmonic manifolds with purely exponential volume growth.
- ItemG-complete reducibility in non-connected groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, GerhardIn this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of G0 is G0-cr. This essentially reduces the problem of determining G-complete reducibility to the connected case.
- 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.
- ItemOn the derived category of Grassmannians in arbitrary characteristic(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Buchweitz, Ragnar-Olaf; Leuschke, Graham J.; Van den Bergh, MichelIn this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's well-known characteristic-zero results we construct dual exceptional collections on them (which are however not strong) as well as a tilting bundle. We show that this tilting bundle has a quasi-hereditary endomorphism ring and we identify the standard, costandard, projective and simple modules of the latter.
- 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.