Browsing 2017 by Title
Now showing items 1-20 of 36
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Abstract Bivariant Cuntz Semigroups
[OWP-2017-04] (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 ... -
Analysis and Simulation of a New Multi-Component Two-Phase Flow Model with Phase Transitions and Chemical Reactions
[OWP-2017-08] (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-15)A class-II model for multi-component mixtures recently introduced in D. Bothe, W. Dreyer, Continuum thermodynamics of chemically reacting fluid mixtures, Acta Mech., 226 (2015), 1757–1805 is investigated for simple mixtures. ... -
Bredon Cohomology and Robot Motion Planning
[OWP-2017-34] (Mathematisches Forschungsinstitut Oberwolfach, 2017-11-29)In this paper we study the topological invariant ${\sf {TC}}(X)$ reflecting the complexity of algorithms for autonomous robot motion. Here, $X$ stands for the configuration space of a system and ${\sf {TC}}(X)$ is, roughly, ... -
Cocycle Superrigidity and Group Actions on Stably Finite C*-Algebras
[OWP-2017-01] (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 ... -
The Colored Jones Polynomial and Kontsevich-Zagier Series for Double Twist Knots
[OWP-2017-29] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-20)Using a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots $K_{(-m,-p)}$ and $K_{(-m,p)}$ where $m$ and $p$ are positive integers. In the $(-m,-p)$ case, this leads to new ... -
Composition of Irreducible Morphisms in Coils
[OWP-2017-32] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-30)We study the non-zero composition of n irreducible morphisms between modules lying in coils in relation with the powers of the radical of their module category. -
Counting Curves on Toric Surfaces Tropical Geometry & the Fock Space
[OWP-2017-18] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-17)We study the stationary descendant Gromov–Witten theory of toric surfaces by combining and extending a range of techniques – tropical curves, floor diagrams, and Fock spaces. A correspondence theorem is established between ... -
Detecting Ineffective Features for Pattern Recognition
[OWP-2017-26] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-17)For a binary classification problem, the hypothesis testing is studied, that a component of the observation vector is not effective, i.e., that component carries no information for the classification. We introduce nearest ... -
Exact Rate of Convergence of k-Nearest-Neighbor Classification Rule
[OWP-2017-25] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-16)A binary classification problem is considered. The excess error probability of the k-nearest neighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the ... -
Experimenting with Zariski Dense Subgroups
[OWP-2017-31] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-28)We give a method to describe all congruence images of a finitely generated Zariski dense group $H\leq SL(n, \mathbb{R})$. The method is applied to obtain efficient algorithms for solving this problem in odd prime degree ... -
An Extension Problem and Trace Hardy Inequality for the Sublaplacian on H-Type Groups
[OWP-2017-20] (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. -
Freeness of Multi-Reflection Arrangements via Primitive Vector Fields
[OWP-2017-10] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-20)In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ... -
GAP Functionality for Zariski Dense Groups
[OWP-2017-22] (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] (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 ... -
Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants
[OWP-2017-35] (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-13)We find new bi-Lipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature. -
Holonomy Groups of $G_2^*$-Manifolds
[OWP-2017-07] (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 ... -
The Index of Singular Zeros of Harmonic Mappings of Anti-Analytic Degree One
[OWP-2017-03] (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-02)We study harmonic mappings of the form $f(z) = h(z) - \overline{z}$, where $h$ is an analytic function. In particular we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the ... -
Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements
[OWP-2017-14] (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-30)Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger ... -
Linear Syzygies, Hyperbolic Coxeter Groups and Regularity
[OWP-2017-15] (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. ... -
Locally Compact Abelian p-Groups Revisited
[OWP-2017-06] (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-03)Even though the structure of locally compact abelian groups is generally considered to be rather thoroughly known through a wealth of publications, one keeps encountering corners that are not elucidated in up-to-date ...