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- ItemResolution of symplectic cyclic orbifold singularities(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Niederkrüger, Klaus; Pasquotto, FedericaIn this paper we present a method to obtain resolutions of symplectic orbifolds arising as quotients of pre-symplectic semi-free S1–actions. This includes, in particular, all orbifolds arising from symplectic reduction of Hamiltonian S1–manifolds at regular values, as well as all isolated cyclic orbifold singularities. As an application, we show that pre-quantisations of symplectic orbifolds are symplectically fillable by a smooth manifold.
- ItemWie steuert man einen Kran?(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Altmann, Robert; Heiland, JanDie Steuerung einer Last an einem Kran ist ein technisch und mathematisch schwieriges Problem, da die Bewegung der Last nur indirekt beeinflusst werden kann. Anhand eines Masse-Feder-Systems illustrieren wir diese Schwierigkeiten und zeigen wie man mit einem zum konventionellen Lösungsweg alternativen Optimierungsansatz die auftretenden Komplikationen teilweise umgehen kann.
- ItemThe McKay conjecture for exceptional groups and odd primes(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Späth, BrittaLet G be a simply-connected simple algebraic group over an algebraically closed field of characteristic p with a Frobenius map F : G ! G and G := GF , such that the root system is of exceptional type or G is a Suzuki-group or Steinberg’s triality group. We show that all irreducible characters of CG(S), the centraliser of S in G, extend to their inertia group in NG(S), where S is any F-stable Sylow torus of (G, F). Together with the work in [17] this implies that the McKay-conjecture is true for G and odd primes ` different from the defining characteristic. Moreover it shows important properties of the associated simple groups, which are relevant for the proof that the associated simple groups are good in the sense of Isaacs, Malle and Navarro, as defined in [15].
- ItemGeometric quantization of integrable systems with hyperbolic singularities(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Hamilton, Mark D.; Miranda, EvaWe construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we compute the effect of hyperbolic singularities, which make an infinite-dimensional contribution to the quantization, thus showing that this quantization depends strongly on polarization.
- ItemCocycle superrigidity and group actions on stably finite C*-algebras(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Gardella, Eusebio; Lupini, MartinoLet be a countably innite property (T) group, and let A be UHF-algebra of innite type. We prove that there exists a continuum of pairwise non (weakly) cocycle conjugate, strongly outer actions of on A. The proof consists in assigning, to any second countable abelian pro-p group G, a strongly outer action of on A whose (weak) cocycle conjugacy class completely remembers the group G. The group G is reconstructed from the action via its (weak) 1-cohomology set endowed with a canonical pairing function. The key ingredient in this computation is Popa's cocycle superrigidity theorem for Bernoulli shifts on the hypernite II1 factor. Our construction also shows the following stronger statement: the relations of conjugacy, cocycle conjugacy, and weak cocycle conjugacy of strongly outer actions of on A are complete analytic sets, and in particular not Borel. The same conclusions hold more generally when is only assumed to contain an innite subgroup with relative property (T), and A is a (not necessarily simple) separable, nuclear, UHF-absorbing, self-absorbing C*-algebra with at least one trace.
- 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.
- ItemRandom sampling of domino and lozenge tilings(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Fusy, ÉricA grid region is (roughly speaking) a collection of “elementary cells” (squares, for example, or triangles) in the plane. One can “tile” these grid regions by arranging the cells in pairs. In this snapshot we review different strategies to generate random tilings of large grid regions in the plane. This makes it possible to observe the behaviour of large random tilings, in particular the occurrence of boundary phenomena that have been the subject of intensive recent research.
- 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.
- ItemRational approximation on products of planar domains(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Aron, Richard M.; Gauthier, Paul M.; Maestre, Manuel; Nestoridis, Vassili; Falcó, JavierWe consider A(Ω), the Banach space of functions f from Ω¯¯¯¯=∏i∈IUi¯¯¯¯¯ to C that are continuous with respect to the product topology and separately holomorphic, where I is an arbitrary set and Ui are planar domains of some type. We show that finite sums of finite products of rational functions of one variable with prescribed poles off Ui¯¯¯¯¯ are uniformly dense in A(Ω). This generalizes previous results where Ui=D is the open unit disc in C or Ui¯¯¯¯¯c is connected.
- ItemEstimating the volume of a convex body(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Baldin, NicolaiSometimes the volume of a convex body needs to be estimated, if we cannot calculate it analytically. We explain how statistics can be used not only to approximate the volume of the convex body, but also its shape.