• Freeness of Multi-Reflection Arrangements via Primitive Vector Fields 

      [OWP-2017-10] Hoge, Torsten; Mano, Toshiyuki; Röhrle, Gerhard; Stump, Christian (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 ...
    • A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables 

      [OWP-2019-02] Falcó, Javier; Gauthier, Paul Montpetit; Manolaki, Myrto; Nestoridis, Vassili (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-11)
      For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.
    • Fundamental Theorem of Projective Geometry over Semirings 

      [OWP-2021-09] Tewari, Ayush Kumar (Mathematisches Forschungsinstitut Oberwolfach, 2021-10-11)
      We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail ...
    • G-complete reducibility in non-connected groups 

      [OWP-2013-09] Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2013-04-10)
      In this paper we present an algorithm for determining whether a subgroup $H$ of a non-connected reductive group $G$ is $G$-completely reducible. The algorithm consists of a series of reductions; at each step, we perform ...
    • 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 ...
    • A Generalization of the Discrete Version of Minkowski’s Fundamental Theorem 

      [OWP-2014-17] González Merino, Bernardo; Henze, Matthias (Mathematisches Forschungsinstitut Oberwolfach, 2014)
      One of the most fruitful results from Minkowski’s geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume of an o-symmetric convex body whose only ...
    • Generalized Entropy Method for the Renewal Equation with Measure Data 

      [OWP-2016-07] Gwiazda, Piotr; Wiedemann, Emil (Mathematisches Forschungsinstitut Oberwolfach, 2016-06-17)
      We study the long-time asymptotics for the so-called McKendrick-Von Foerster or renewal equation, a simple model frequently considered in structured population dynamics. In contrast to previous works, we can admit a bounded ...
    • Generalized Killing spinors and Lagrangian graphs 

      [OWP-2014-11] Moroianu, Andrei; Semmelmann, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 2014-08-20)
      We study generalized Killing spinors on the standard sphere $\mathbb{S}^3$, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold $S^3 \times S^3$ and to great circle flows on $\mathbb{S}^3$. ...
    • Generalized Vector Cross Products and Killing Forms on Negatively Curved Manifolds 

      [OWP-2018-17] Barberis, María Laura; Moroianu, Andrei; Semmelmann, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-17)
      Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using ...
    • Generating Finite Coxeter Groups with Elements of the Same Order 

      [OWP-2020-07] Hart, Sarah; Kelsey, Veronica; Rowley, Peter (Mathematisches Forschungsinstitut Oberwolfach, 2020-03-16)
      Supposing $G$ is a group and $k$ a natural number, $d_k(G)$ is defined to be the minimal number of elements of $G$ of order $k$ which generate $G$ (setting $d_k(G) = 0$ if $G$ has no such generating sets). This paper ...
    • Geometric flows and 3-manifolds : Oberwolfach Lecture 2005 

      [OWP-2007-01] Huisken, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2007)
      The current article arose from a lecture1 given by the author in October 2005 on the work of R. Hamilton and G. Perelman on Ricci-flow and explains central analytical ingredients in geometric parabolic evolution equations ...
    • Geometric quantization of integrable systems with hyperbolic singularities 

      [OWP-2009-01] Hamilton, Mark D.; Miranda, Eva (Mathematisches Forschungsinstitut Oberwolfach, 2009)
      We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. ...
    • 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 ...
    • Getzler rescaling via adiabatic deformation and a renormalized local index formula 

      [OWP-2016-18] Bohlen, Karsten; Schrohe, Elmar (Mathematisches Forschungsinstitut Oberwolfach, 2016-10)
      We prove a local index theorem of Atiyah-Singer type for Dirac operators on manifolds with a Lie structure at infinity (Lie manifolds for short). After introducing a renormalized supertrace on Lie manifolds with spin ...
    • Ghost Algebras of Double Burnside Algebras via Schur Functors 

      [OWP-2012-09] Boltje, Robert; Danz, Susanne (Mathematisches Forschungsinstitut Oberwolfach, 2012-07-03)
      For a finite group $G$, we introduce a multiplication on the $\mathbb{Q}$-vector space with basis $\mathscr{S}_{G\times G}$, the set of subgroups of ${G \times G}$. The resulting $\mathbb{Q}$-algebra $\tilde{A}$ can be ...
    • Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation 

      [OWP-2015-04] Genovese, Giuseppe; Lucatti, Renato; Valeri, Daniele (Mathematisches Forschungsinstitut Oberwolfach, 2015-05-18)
      We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion $\int ...
    • Global Solutions to Stochastic Wave Equations with Superlinear Coefficients 

      [OWP-2019-26] Millet, Annie; Sanz-Solé, Marta (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-13)
      We prove existence and uniqueness of a random field solution $(u(t,x);(t,x)\in [0,T]\times \mathbb{R}^d)$ to a stochastic wave equation in dimensions $d=1,2,3$ with diffusion and drift coefficients of the form $|x| ...
    • Global Variants of Hartogs' Theorem 

      [OWP-2018-24] Bochnak, Jacek; Kucharz, Wojciech (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-06)
      Hartogs' theorem asserts that a separately holomorphic function, defined on an open subset of $\mathbb{C}^n$, is holomorphic in all the variables. We prove a global variant of this theorem for functions defined on an open ...
    • Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants 

      [OWP-2017-35] Paunescu, Laurentiu; Tibăr, Mihai-Marius (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.
    • Graphical constructions for the sl(3), C2 and G2 invariants for virtual knots, virtual braids and free knots 

      [OWP-2015-13] Kauffman, Louis H.; Manturov, Vassily Olegovich (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-31)
      We construct graph-valued analogues of the Kuperberg sl(3) and $G_2$ invariants for virtual knots. The restriction of the sl(3) and $G_2$ invariants for classical knots coincides with the usual Homflypt sl(3) invariant and ...