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Abstract Bivariant Cuntz Semigroups

[OWP-2017-04] Antoine, Ramon; Perera, Francesc; Thiel, Hannes (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-13)

We show that abstract Cuntz semigroups form a closed symmetric monoidal category. Thus, given Cuntz semigroups

$S$ and

$T$ , there is another Cuntz semigroup

$((S,T))$ playing the role of morphisms from

$S$ to

$T$ . Applied ...

On Vietoris-Rips Complexes of Ellipses

[OWP-2017-11] Adamaszek, Michal; Adams, Henry; Reddy, Samadwara (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-25)

For

$X$ a metric space and

$r > 0$ a scale parameter, the Vietoris–Rips complex

$VR_<(X; r)$ (resp.

$VR_≤(X; r)$ ) has

$X$ as its vertex set, and a finite subset

$\sigma \subseteq X$ as a simplex whenever the diameter of ...

Linear Syzygies, Hyperbolic Coxeter Groups and Regularity

[OWP-2017-15] Constantinescu, Alexandru; Kahle, Thomas; Varbaro, Matteo (Mathematisches Forschungsinstitut Oberwolfach, 2017-05-24)

We build a new bridge between geometric group theory and commutative algebra by showing that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. ...

An Extension Problem and Trace Hardy Inequality for the Sublaplacian on H-Type Groups

[OWP-2017-20] Roncal, Luz; Thangavelu, Sundaram (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-24)

In this paper we study the extension problem for the sublaplacian on a H-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian.

Cocycle Superrigidity and Group Actions on Stably Finite C*-Algebras

[OWP-2017-01] Gardella, Eusebio; Lupini, Martino (Mathematisches Forschungsinstitut Oberwolfach, 2017-01-17)

Let

$\Lambda$ be a countably infinite property (T) group, and let

$D$ be UHF-algebra of infinite type. We prove that there exists a continuum of pairwise non (weakly) cocycle conjugate, strongly outer actions of $\Lambda ...

Matrix Elements of Irreducible Representations of SU(n+1) x SU(n+1) and Multivariable Matrix-Valued Orthogonal Polynomials

[OWP-2017-16] Koelink, Erik; van Pruijssen, Maarten; Román, Pablo Manuel (Mathematisches Forschungsinstitut Oberwolfach, 2017-06-14)

In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are ...

GAP Functionality for Zariski Dense Groups

[OWP-2017-22] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2017-09-14)

In this document we describe the functionality of GAP [4] routines for Zariski dense or arithmetic groups that are developed in [1, 2, 3]. The research underlying the software was supported through the programme "Research ...

Geometry of Free Loci and Factorization of Noncommutative Polynomials

[OWP-2017-23] Helton, J. William; Klep, Igor; Volčič, Jurij; Helton, J. William (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)

The free singularity locus of a noncommutative polynomial f is defined to be the sequence

$Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ...

Holonomy Groups of $G_2^*$ -Manifolds

[OWP-2017-07] Fino, Anna; Kath, Ines (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-07)

We classify the holonomy algebras of manifolds admitting an indecomposable torsion free

$G_2^*$ -structure, i.e. for which the holonomy representation does not leave invariant any proper non-degenerate subspace. We realize ...

On an Effective Variation of Kronecker’s Approximation Theorem Avoiding Algebraic Sets

[OWP-2017-28] Fukshansky, Lenny; German, Oleg; Moshchevitin, Nikolay (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-19)

Let

$\Lambda \subset \mathbb R^n$ be an algebraic lattice, coming from a projective module over the ring of integers of a number field

$K$ . Let

$\mathcal Z \subset \mathbb R^n$ be the zero locus of a finite collection of ...