• Affine Space Fibrations 

      [OWP-2018-19] Gurjar, Rajendra V.; Masuda, Kayo; Miyanishi, Masayoshi (Mathematisches Forschungsinstitut Oberwolfach, 2018-09-05)
      We discuss various aspects of affine space fibrations. Our interest will be focused in the singular fibers, the generic fiber and the propagation of properties of a given smooth special fiber to nearby fibers.
    • Applications of BV Type Spaces 

      [OWP-2019-04] Appell, Jürgen; Bugajewska, Daria; Kasprzak, Piotr; Merentes, Nelson; Reinwand, Simon; Sánchez, José Luis (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-13)
    • Cataland: Why the Fuß? 

      [OWP-2019-01] Stump, Christian; Thomas, Hugh; Williams, Nathan (Mathematisches Forschungsinstitut Oberwolfach, 2019-01-21)
      The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. ...
    • Categorical Linearly Ordered Structures 

      [OWP-2018-08] Downey, Rod; Melnikov, Alexander; Ng, Keng Meng (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-26)
      We prove that for every computable limit ordinal $\alpha$ there exists a computable linear ordering $\mathcal{A}$ which is $\Delta^0_\alpha$-categorical and $\alpha$ is smallest such, but nonetheless for every isomorphic ...
    • Computing Congruence Quotients of Zariski Dense Subgroups 

      [OWP-2018-22] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-26)
      We obtain a computational realization of the strong approximation theorem. That is, we develop algorithms to compute all congruence quotients modulo rational primes of a finitely generated Zariski dense group $H \leq ...
    • Criteria for Algebraicity of Analytic Functions 

      [OWP-2018-25] Bochnak, Jacek; Gwoździewicz, Janusz; Kucharz, Wojciech (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-12)
      We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend ...
    • Experimenting with Symplectic Hypergeometric Monodromy Groups 

      [OWP-2019-15] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-22)
      We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results ...
    • 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.
    • 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 ...
    • 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 ...
    • Hölder Continuity of the Spectra for Aperiodic Hamiltonians 

      [OWP-2019-05] Beckus, Siegfried; Bellissard, Jean; Cornean, Horia (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-26)
      We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, ...
    • The Magic Square of Reflections and Rotations 

      [OWP-2018-13] Buchweitz, Ragnar-Olaf; Faber, Eleonore; Ingalls, Colin (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-01)
      We show how Coxeter’s work implies a bijection between complex reflection groups of rank two and real reflection groups in 0(3). We also consider this magic square of reflections and rotations in the framework of Clifford ...
    • Max-Linear Models on Infinite Graphs Generated by Bernoulli Bond Percolation 

      [OWP-2018-09] Klüppelberg, Claudia; Sönmez, Ercan (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-17)
      We extend previous work of max-linear models on finite directed acyclic graphs to infinite graphs, and investigate their relations to classical percolation theory. We formulate results for the oriented square lattice graph ...
    • Metric Connections with Parallel Skew-Symmetric Torsion 

      [OWP-2018-16] Cleyton, Richard; Moroianu, Andrei; Semmelmann, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-16)
      A geometry with parallel skew-symmetric torsion is a Riemannian manifold carrying a metric connection with parallel skew-symmetric torsion. Besides the trivial case of the Levi-Civita connection, geometries with non-vanishing ...
    • On a Group Functor Describing Invariants of Algebraic Surfaces 

      [OWP-2019-08] Dietrich, Heiko; Moravec, Primož (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-01)
      Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of ...
    • On the Gauss Algebra of Toric Algebras 

      [OWP-2018-07] Herzog, Jürgen; Jafari, Raheleh; Nasrollah Nejad, Abbas (Mathematisches Forschungsinstitut Oberwolfach, 2018-04-25)
      Let $A$ be a $K$-subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\mathbb{G}(A)$ of $A$ is generated by monomials of ...
    • On the Invariants of the Cohomology of Complements of Coxeter Arrangements 

      [OWP-2018-21] Douglass, J. Matthew; Pfeiffer, Götz; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2018-10-22)
      We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit ...
    • Real Analyticity is Concentrated in Dimension 2 

      [OWP-2018-23] Bochnak, Jacek; Kucharz, Wojciech (Mathematisches Forschungsinstitut Oberwolfach, 2018-11-05)
      We prove that a real-valued function on a real analytic manifold is analytic whenever all its restrictions to $2$-dimensional analytic submanifolds are analytic functions. We also obtain analogous results in the framework ...
    • Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D 

      [OWP-2018-27] Beckus, Siegfried; Bellissard, Jean; De Nittis, Giuseppe (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-17)
      The existence and construction of periodic approximations with convergent spectra is crucial in solid state physics for the spectral study of corresponding Schrödinger operators. In a forthcoming work [9] this task was ...