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- 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.
- 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.
- 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.
- ItemOn the autonomous metric on the groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Brandenbursky, MichaelLet g be a closed hyperbolic surface of genus g and let Ham g be the group of Hamiltonian diffeomorphisms of g. The most natural word metric on this group is the autonomous metric. It has many interesting properties, most important of which is the bi-invariance of this metric. In this work we show that Ham g is unbounded with respect to this metric
- ItemGeneralized killing spinors and Lagrangian graphs(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Moroianu, Andrei; Semmelmann, UweWe study generalized Killing spinors on the standard sphere S3, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold S3×S3 and to great circle flows on S3. Using our methods we generalize a well known result of Gluck and Gu [6] concerning divergence-free geodesic vector fields on the sphere and we show that the space of Lagrangian submanifolds of S3×S3 has at least three connected components.
- ItemNear critical density irregular sampling in Bernstein spaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Olevskii, Alexander; Ulanovskii, AlexanderWe obtain sharp estimates for the sampling constants in Bernstein spaces when the density of the sampling set is near the critical value.
- ItemCentral limit theorems for the radial spanning tree(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Schulte, Matthias; Thäle, ChristophConsider a homogeneous Poisson point process in a compact convex set in d- dimensional Euclidean space which has interior points and contains the origin. The radial spanning tree is constructed by connecting each point of the Poisson point process with its nearest neighbour that is closer to the origin. For increasing in- tensity of the underlying Poisson point process the paper provides expectation and variance asymptotics as well as central limit theorems with rates of convergence for a class of edge functionals including the total edge length.
- ItemMesh ratios for best-packing and limits of minimal energy configurations(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Bondarenko, A.V.; Hardin, D.P.; Saff, E.B.For N-point best-packing configurations ωN on a compact metric space (A,ρ), we obtain estimates for the mesh-separation ratio γ(ρN,A), which is the quotient of the covering radius of ωN relative to A and the minimum pairwise distance between points in ωN . For best-packing configurations ωN that arise as limits of minimal Riesz s-energy configurations as s→∞, we prove that γ(ωN,A)≤1 and this bound can be attained even for the sphere. In the particular case when N=5 on S1 with ρ the Euclidean metric, we prove our main result that among the infinitely many 5-point best-packing configurations there is a unique configuration, namely a square-base pyramid ω∗5, that is the limit (as s→∞) of 5-point s-energy minimizing configurations. Moreover, γ(ω∗5,S2)=1.