Now showing items 1-20 of 22

• #### 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, ...
• #### 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.
• #### Deformation Classification of Real Non-Singular Cubic Threefolds with a Marked Line ﻿

[OWP-2018-02] (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-21)
We prove that the space of pairs $(X,l)$ formed by a real non-singular cubic hypersurface $X\subset P^4$ with a real line $l\subset X$ has 18 connected components and give for them several quite explicit interpretations. ...
• #### 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.
• #### Homogenization of a nonlinear monotone problem with nonlinear Signorini boundary conditions in a domain with highly rough boundary ﻿

[OWP-2018-06] (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-16)
We consider a domain $\Omega_\varepsilon\subset\mathbb{R}^N$, $N\geq2$, with a very rough boundary depending on~$\varepsilon$. For instance, if $N=3$ the domain $\Omega_\varepsilon$ has the form of a brush with an ...
• #### 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 ...
• #### 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 ...
• #### Looking Back on Inverse Scattering Theory ﻿

[OWP-2017-24] (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-05)
We present an essay on the mathematical development of inverse scattering theory for time-harmonic waves during the past fifty years together with some personal memories of our participation in these events.
• #### The Martin Boundary of Relatively Hyperbolic Groups with Virtually Abelian Parabolic Subgroups ﻿

[OWP-2018-03] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-19)
Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of the corresponding random walk. We give a complete topological characterization ...
• #### Matrix Elements of Irreducible Representations of SU(n+1) x SU(n+1) and Multivariable Matrix-Valued Orthogonal Polynomials ﻿

[OWP-2017-16] (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 ...
• #### The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$ ﻿

[OWP-2017-21] (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-27)
Mustaţă has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in $\mathbb P^3$ this conjecture ...
• #### On an Effective Variation of Kronecker’s Approximation Theorem Avoiding Algebraic Sets ﻿

[OWP-2017-28] (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 ...