Oberwolfach Preprints (OWP)
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- Item2-Minimal subgroups in classical groups: Linear and unitary groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Parker, Chris; Rowley, Peter[no abstract available]
- ItemA 3-Local characterization of Co2(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2008) Parker, Christopher; Rowley, PeterConway's second largest simple group, Co2, is characterized by the centralizer of an element of order 3 and certain fusion data.
- ItemA 3-local identification of the alternating group of degree 8, the McLaughlin simple group and their automorphism groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2007) Parker, Christopher; Rowley, PeterIn this article we give 3-local characterizations of the alternating and symmetric groups of degree 8 and use these characterizations to recognize the sporadic simple group discovered by McLaughlin from its 3-local subgroups.
- ItemAbstract bivariant Cuntz semigroups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Antoine, Ramon; Perera, Francesc; Thiel, HannesWe show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups S and T, there is another Cuntz semigroup JS, TK playing the role of morphisms from S to T. Applied to C*-algebras A and B, the semigroup JCu(A),Cu(B)K should be considered as the target in analogues of the UCT for bivariant theories of Cuntz semigroups. Abstract bivariant Cuntz semigroups are computable in a number of interesting cases. We explore its behaviour under the tensor product with the Cuntz semigroup of strongly self-absorbing C*-algebras and the Jacelon-Razak algebra. We also show that order-zero maps between C*-algebras naturally define elements in the respective bivariant Cuntz semigroup.
- ItemAbundance of 3-planes on real projective hypersurfaces(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Finashin, S.; Kharlamov, V.We show that a generic real projective n-dimensional hypersurface of odd degree d , such that 4(n - 2) = (d + 3 3), contains "many" real 3-planes, namely, in the logarithmic scale their number has the same rate of growth, d3 log d, as the number of complex 3-planes. This estimate is based on the interpretation of a suitable signed count of the 3-planes as the Euler number of an appropriate bundle.
- ItemAlexander r-tuples and Bier complexes(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Jojic, Dusko; Nekrasov, Ilya; Panina, Gaiane; Zivaljevic, RadeWe introduce and study Alexander r-tuples K = Kiir i=1 of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable complexes of [BFZ-1]. In the same vein, the Bier complexes, defined as the deleted joins K delta of Alexander r-tuples, include both standard Bier spheres and optimal multiple chessboard complexes (Section 2.2) as interesting, special cases. Our main results are Theorem 4.3 saying that (1) the r-fold deleted join of Alexander r-tuple is a pure complex homotopy equivalent to a wedge of spheres, and (2) the r-fold deleted join of a collective unavoidable r-tuple is (n - r - 1)-connected, and a classification theorem (Theorem 5.1 and Corollary 5.2) for Alexander r-tuples and Bier complexes.
- ItemThe algebra of differential operators for a Gegenbauer weight matrix(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2015) Zurrián, Ignacio NahuelIn this work we study in detail the algebra of differential operators D(W) associated with a Gegenbauer matrix weight. We prove that two second order operators generate the algebra, indeed D(W) is isomorphic to the free algebra generated by two elements subject to certain relations. Also, the center is isomorphic to the affine algebra of a singular rational curve. The algebra D(W) is a finitely-generated torsion-free module over its center, but it is not at and therefore neither projective. After [Tir11], this is the second detailed study of an algebra D(W) and the first one coming from spherical functions and group representation theory.
- ItemThe algebraic combinatorial approach for low-rank matrix completion(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Király, Franz J.; Theran, Louis; Tomioka, Ryota; Uno, TakeakiWe propose an algebraic combinatorial framework for the problem of completing partially observed low-rank matrices. We show that the intrinsic properties of the problem, including which entries can be reconstructed, and the degrees of freedom in the reconstruction, do not depend on the values of the observed entries, but only on their position. We associate combinatorial and algebraic objects, differentials and matroids, which are descriptors of the particular reconstruction task, to the set of observed entries, and apply them to obtain reconstruction bounds. We show how similar techniques can be used to obtain reconstruction bounds on general compressed sensing problems with algebraic compression constraints. Using the new theory, we develop several algorithms for low-rank matrix completion, which allow to determine which set of entries can be potentially reconstructed and which not, and how, and we present algorithms which apply algebraic combinatorial methods in order to reconstruct the missing entries.
- ItemAlgebraic geometric comparison of probability distributions(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Király, Franz J.; von Bünau, Paul; Meinecke, Frank C.; Blythe, Duncan A.J.; Müller, Klaus-RobertWe propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding the subspace on which several probability distributions agree. Instead of minimizing an objective function involving the estimated cumulants, we show that by treating the cumulants as elements of the polynomial ring we can directly solve the problem, at a lower computational cost and with higher accuracy. Moreover, the algebraic viewpoint on probability distributions allows us to invoke the theory of Algebraic Geometry, which we demonstrate in a compact proof for an identifiability criterion.
- ItemAlgebraic matroids with graph symmetry(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Király, Franz J.; Rosen, Zvi; Theran, LouisThis paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a) algebraic matroids, we expose cryptomorphisms making them accessible to techniques from commutative algebra. This allows us to introduce for each circuit in an algebraic matroid an invariant called circuit polynomial, generalizing the minimal polynomial in classical Galois theory, and studying the matroid structure with multivariate methods. For (b) matroids with symmetries we introduce combinatorial invariants capturing structural properties of the rank function and its limit behavior, and obtain proofs which are purely combinatorial and do not assume algebraicity of the matroid; these imply and generalize known results in some specific cases where the matroid is also algebraic. These results are motivated by, and readily applicable to framework rigidity, low-rank matrix completion and determinantal varieties, which lie in the intersection of (a) and (b) where additional results can be derived. We study the corresponding matroids and their associated invariants, and for selected cases, we characterize the matroidal structure and the circuit polynomials completely.
- ItemAlternative iterative methods for nonexpansive mappings, rates of convergence and applications(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Colao, Vittorio; Laurent¸iu Leu¸stean, Laurent¸iu Leu¸stean; Genaro L´opez, Genaro L´opez; Mart´ın-M´arquez, VictoriaAlternative iterative methods for a nonexpansive mapping in a Banach space are proposed and proved to be convergent to a common solution to a fixed point problem and a variational inequality. We give rates of asymptotic regularity for such iterations using proof-theoretic techniques. Some applications of the convergence results are presented.
- ItemAnalysis and simulation of a new multi-component two-phase flow model with phase transitions and chemical reactions(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Hantke, Maren; Müller, SiegfriedA class-II model for multi-component mixtures recently introduced in D. Bothe, W. Dreyer, Continuum thermodynamics of chemically reacting uid mixtures, Acta Mech., 226 (2015), 1757{1805 is investigated for simple mixtures. Bothe and Dreyer were aiming at deriving physically admissible closure conditions. Here the focus is on mathematical properties of this model. In particular, hyperbolicity of the inviscid ux Jacobian is veried for non-resonance states. Although the eigenvalues cannot be determined explicitly but have to be computed numerically an eigenvector basis is constructed depending on the eigenvectors. This basis is helpful to apply standard numerical solvers for the discretization of the model. This is veried by numerical computations for two- and three-component mixtures with and without phase transition and chemical reactions.
- ItemAnalytic structure in fibers(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Aron, Richard M.; Falcó, Javier; García, Domingo; Maestre, ManuelLet BX be the open unit ball of a complex Banach space X, and let H∞(BX) and Au(BX) be, respectively, the algebra of bounded holomorphic functions on BX and the subalgebra of uniformly continuous holomorphic functions on BX. In this paper we study the analytic structure of fibers in the spectrum of these two algebras. For the case of H∞(BX), we prove that the fiber in M(H∞(Bc0)) over any point of the distinguished boundary of the closed unit ball B¯ℓ∞ of ℓ∞ contains an analytic copy of Bℓ∞. In the case of Au(BX) we prove that if there exists a polynomial whose restriction to the open unit ball of X is not weakly continuous at some point, then the fiber over every point of the open unit ball of the bidual contains an analytic copy of D.
- 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.
- ItemApproximation of discrete functions and size of spectrum(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2009) Olevskii, Alexander; Ulanovskii, AlexanderLet Λ⊂R be a uniformly discrete sequence and S⊂R a compact set. We prove that if there exists a bounded sequence of functions in Paley-Wiener space PWs, which approximates δ-functions on Λ with l2-error d, then measure(S)≥2π(1−d2)D+(Λ). This estimate is sharp for every d. Analogous estimate holds when the norms of approximating functions have a moderate growth, and we find a sharp growth restriction.
- ItemAsymptotic behavior of the eigenvalues and eigenfunctions to a spectral problem in a thick cascade junction with concentrated masses(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Chechkin, Gregory A.; Mel'nyk, Taras A.The asymptotic behavior (as ε→0) of eigenvalues and eigenfunctions of a boundaryvalue problem for the Laplace operator in a thick cascade junction with concentrated masses is investigated. This cascade junction consists of the junction's body and great number 5N=O(ε−1) of ε-alternating thin rods belonging to two classes. One class consists of rods of finite length and the second one consists of rods of small length of order O(ε). The density of the junction is order O(ε−α) on the rods from the second class (the concentrated masses if α>0) and O(1) outside of them. In addition, we study the influence of the concentrated masses on the asymptotic behavior of these magnitudes in the case α=1 and α∈(0,1).
- ItemAverages of shifted convolutions of d3(n)(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Baier, S.; Browning, T.D.; Marasingha, G.; Zhao, L.We investigate the first and second moments of shifted convolutions of the generalised divisor function d3(n).
- ItemThe Berry-Keating operator on a lattice(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Bolte, Jens; Egger, Sebastian; Keppeler, StefanWe construct and study a version of the Berry-Keating operator with a built-in truncation of the phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating.
- ItemBoundary representations of operator spaces, and compact rectangular matrix convex sets(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2016) Fuller, Adam H.; Hartz, Michael; Lupini, MartinoWe initiate the study of matrix convexity for operator spaces. We dene the notion of compact rectangular matrix convex set, and prove the natural analogs of the Krein-Milman and the bipolar theorems in this context. We deduce a canonical correspondence between compact rectangular matrix convex sets and operator spaces. We also introduce the notion of boundary representation for an operator space, and prove the natural analog of Arveson's conjecture: every operator space is completely normed by its boundary representations. This yields a canonical construction of the triple envelope of an operator space.
- ItemBraid equivalences and the L-moves(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2011) Lambropoulou, SofiaIn this survey paper we present the L–moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot complements, in c.c.o. 3–manifolds and in handlebodies, as well as for virtual knots, for flat virtuals, for welded knots and for singular knots. The L–moves are local and they provide a uniform ground for formulating and proving braid equivalence theorems for any diagrammatic setting where the notion of braid and diagrammatic isotopy is defined, the statements being first geometric and then algebraic.