Browsing 2017 by MFO Scientific Program "Research in Pairs 2017"
Now showing items 119 of 19

Bredon Cohomology and Robot Motion Planning
[OWP201734] (Mathematisches Forschungsinstitut Oberwolfach, 20171129)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
[OWP201732] (Mathematisches Forschungsinstitut Oberwolfach, 20171030)We study the nonzero composition of n irreducible morphisms between modules lying in coils in relation with the powers of the radical of their module category. 
Detecting Ineffective Features for Pattern Recognition
[OWP201726] (Mathematisches Forschungsinstitut Oberwolfach, 20171017)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 kNearestNeighbor Classification Rule
[OWP201725] (Mathematisches Forschungsinstitut Oberwolfach, 20171016)A binary classification problem is considered. The excess error probability of the knearest neighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the ... 
Experimenting with Zariski Dense Subgroups
[OWP201731] (Mathematisches Forschungsinstitut Oberwolfach, 20171028)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 HType Groups
[OWP201720] (Mathematisches Forschungsinstitut Oberwolfach, 20170724)In this paper we study the extension problem for the sublaplacian on a Htype group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian. 
Freeness of MultiReflection Arrangements via Primitive Vector Fields
[OWP201710] (Mathematisches Forschungsinstitut Oberwolfach, 20170420)In 2002, Terao showed that every reflection multiarrangement 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
[OWP201722] (Mathematisches Forschungsinstitut Oberwolfach, 20170914)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
[OWP201723] (Mathematisches Forschungsinstitut Oberwolfach, 20171002)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
[OWP201735] (Mathematisches Forschungsinstitut Oberwolfach, 20171213)We find new biLipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature. 
The Index of Singular Zeros of Harmonic Mappings of AntiAnalytic Degree One
[OWP201703] (Mathematisches Forschungsinstitut Oberwolfach, 20170202)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
[OWP201714] (Mathematisches Forschungsinstitut Oberwolfach, 20170430)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 pGroups Revisited
[OWP201706] (Mathematisches Forschungsinstitut Oberwolfach, 20170303)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 uptodate ... 
Looking Back on Inverse Scattering Theory
[OWP201724] (Mathematisches Forschungsinstitut Oberwolfach, 20171005)We present an essay on the mathematical development of inverse scattering theory for timeharmonic waves during the past fifty years together with some personal memories of our participation in these events. 
Matrix Elements of Irreducible Representations of SU(n+1) x SU(n+1) and Multivariable MatrixValued Orthogonal Polynomials
[OWP201716] (Mathematisches Forschungsinstitut Oberwolfach, 20170614)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 $\mathbb P^3$
[OWP201721] (Mathematisches Forschungsinstitut Oberwolfach, 20170727)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
[OWP201728] (Mathematisches Forschungsinstitut Oberwolfach, 20171019)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 ... 
Review of the Methods of Reflections
[OWP201727] (Mathematisches Forschungsinstitut Oberwolfach, 20171018)The methods of reflections were invented to obtain approximate solutions of the motion of more than one particle in a given environment, provided that one can represent the solution for one particle rather easily. This ... 
Z2Thurston Norm and Complexity of 3Manifolds, II
[OWP201736] (Mathematisches Forschungsinstitut Oberwolfach, 20171220)In this sequel to earlier papers by three of the authors, we obtain a new bound on the complexity of a closed 3manifold, as well as a characterisation of manifolds realising our complexity bounds. As an application, we ...