Browsing 2017 by Issue Date
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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 ... 
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 ... 
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. 
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 ... 
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 ... 
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 ... 
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 ... 
The Colored Jones Polynomial and KontsevichZagier Series for Double Twist Knots
[OWP201729] (Mathematisches Forschungsinstitut Oberwolfach, 20171020)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 ... 
NonExtendability of Holomorphic Functions with Bounded or Continuously Extendable Derivatives
[OWP201730] (Mathematisches Forschungsinstitut Oberwolfach, 20171021)We consider the spaces $H_{F}^{\infty}(\Omega)$ and $\mathcal{A}_{F}(\Omega)$ containing all holomorphic functions $f$ on an open set $\Omega \subseteq \mathbb{C}$, such that all derivatives $f^{(l)}$, $l\in F \subseteq ... 
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 ... 
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. 
The Varchenko Determinant of a Coxeter Arrangement
[OWP201733] (Mathematisches Forschungsinstitut Oberwolfach, 20171124)The Varchenko determinant is the determinant of a matrix defined from an arrangement of hyperplanes. Varchenko proved that this determinant has a beautiful factorization. It is, however, not possible to use this factorization ... 
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, ... 
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. 
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 ...