Browsing 1 - Oberwolfach Preprints (OWP) by MFO Scientific Program "Research in Pairs 2018"
Now showing items 1-20 of 25
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Affine Space Fibrations
[OWP-2018-19] (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] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-13) -
Cataland: Why the Fuß?
[OWP-2019-01] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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] (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 ... -
Reflective Prolate-Spheroidal Operators and the KP/KdV Equations
[OWP-2019-24] (Mathematisches Forschungsinstitut Oberwolfach, 2019-11-05)Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and ...