2018
Recent Submissions

The Tutte Polynomial of Ideal Arrangements
[OWP201828] (Mathematisches Forschungsinstitut Oberwolfach, 20181221)The Tutte polynomial is originally a bivariate polynomial enumerating the colorings of a graph and of its dual graph. But it reveals more of the internal structure of the graph like its number of forests, of spanning ... 
Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D
[OWP201827] (Mathematisches Forschungsinstitut Oberwolfach, 20181217)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 ... 
Sur le Minimum de la Fonction de Brjuno
[OWP201826] (Mathematisches Forschungsinstitut Oberwolfach, 20181211)The Brjuno function attains a strict global minimum at the golden section. 
Criteria for Algebraicity of Analytic Functions
[OWP201825] (Mathematisches Forschungsinstitut Oberwolfach, 20181112)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 ... 
Global Variants of Hartogs' Theorem
[OWP201824] (Mathematisches Forschungsinstitut Oberwolfach, 20181106)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 ... 
Real Analyticity is Concentrated in Dimension 2
[OWP201823] (Mathematisches Forschungsinstitut Oberwolfach, 20181105)We prove that a realvalued 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 ... 
Computing Congruence Quotients of Zariski Dense Subgroups
[OWP201822] (Mathematisches Forschungsinstitut Oberwolfach, 20181026)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 ... 
On the Invariants of the Cohomology of Complements of Coxeter Arrangements
[OWP201821] (Mathematisches Forschungsinstitut Oberwolfach, 20181022)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 ... 
Demailly’s Notion of Algebraic Hyperbolicity: Geometricity, Boundedness, Moduli of Maps
[OWP201820] (Mathematisches Forschungsinstitut Oberwolfach, 20181008)Demailly's conjecture, which is a consequence of the GreenGriffithsLang conjecture on varieties of general type, states that an algebraically hyperbolic complex projective variety is Kobayashi hyperbolic. Our aim is to ... 
Affine Space Fibrations
[OWP201819] (Mathematisches Forschungsinstitut Oberwolfach, 20180905)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. 
Some Results Related to Schiffer's Problem
[OWP201818] (Mathematisches Forschungsinstitut Oberwolfach, 20180816)We consider the following semilinear overdetermined problem on a two dimensional bounded or unbounded domain $\Omega$ with analytic boundary $\partial\Omega$ having at least one bounded connected component \begin{eqnarray*} ... 
Generalized Vector Cross Products and Killing Forms on Negatively Curved Manifolds
[OWP201817] (Mathematisches Forschungsinstitut Oberwolfach, 20180717)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 ... 
Metric Connections with Parallel SkewSymmetric Torsion
[OWP201816] (Mathematisches Forschungsinstitut Oberwolfach, 20180716)A geometry with parallel skewsymmetric torsion is a Riemannian manifold carrying a metric connection with parallel skewsymmetric torsion. Besides the trivial case of the LeviCivita connection, geometries with nonvanishing ... 
An Optimal Bound for the Ratio Between Ordinary and Uniform Exponents of Diophantine Approximation
[OWP201815] (Mathematisches Forschungsinstitut Oberwolfach, 20180709)We provide a lower bound for the ratio between the ordinary and uniform exponents of both simultaneous Diophantine approximation to n real numbers and Diophantine approximation for one linear form in n variables. This ... 
A McKay Correspondence for Reflection Groups
[OWP201814] (Mathematisches Forschungsinstitut Oberwolfach, 20180702)We construct a noncommutative desingularization of the discriminant of a finite reflection group $G$ as a quotient of the skew group ring $A=S*G$. If $G$ is generated by order two reflections, then this quotient identifies ... 
The Magic Square of Reflections and Rotations
[OWP201813] (Mathematisches Forschungsinstitut Oberwolfach, 20180701)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 ... 
MOSES: A Streaming Algorithm for Linear Dimensionality Reduction
[OWP201812] (Mathematisches Forschungsinstitut Oberwolfach, 20180626)This paper introduces Memorylimited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of data and reducing its dimension. More specifically, consider a scenario where the data vectors ... 
A Deformed Quon Algebra
[OWP201811] (Mathematisches Forschungsinstitut Oberwolfach, 20180625)The quon algebra is an approach to particle statistics in order to provide a theory in which the Pauli exclusion principle and Bose statistics are violated by a small amount. The quons are particles whose annihilation and ... 
A WellPosedness Result for Viscous Compressible Fluids with Only Bounded Density
[OWP201810] (Mathematisches Forschungsinstitut Oberwolfach, 20180528)We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible NavierStokes equations. Assuming that the initial velocity has slightly subcritical regularity and ... 
MaxLinear Models on Infinite Graphs Generated by Bernoulli Bond Percolation
[OWP201809] (Mathematisches Forschungsinstitut Oberwolfach, 20180517)We extend previous work of maxlinear 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 ...