Browsing 2018 by Title
Now showing items 14-29 of 29
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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 ... -
The Martin Boundary of Relatively Hyperbolic Groups with Virtually Abelian Parabolic Subgroups
[OWP-2018-03] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-19)Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of the corresponding random walk. We give a complete topological characterization ... -
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 ... -
A McKay Correspondence for Reflection Groups
[OWP-2018-14] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-02)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 ... -
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 ... -
MOSES: A Streaming Algorithm for Linear Dimensionality Reduction
[OWP-2018-12] (Mathematisches Forschungsinstitut Oberwolfach, 2018-06-26)This paper introduces Memory-limited 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 ... -
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 ... -
An Optimal Bound for the Ratio Between Ordinary and Uniform Exponents of Diophantine Approximation
[OWP-2018-15] (Mathematisches Forschungsinstitut Oberwolfach, 2018-07-09)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 ... -
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 ... -
Some Results Related to Schiffer's Problem
[OWP-2018-18] (Mathematisches Forschungsinstitut Oberwolfach, 2018-08-16)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*} ... -
Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D
[OWP-2018-27] (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 ... -
Sur le Minimum de la Fonction de Brjuno
[OWP-2018-26] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-11)The Brjuno function attains a strict global minimum at the golden section. -
The Sylow Structure of Scalar Automorphism Groups
[OWP-2018-05] (Mathematisches Forschungsinstitut Oberwolfach, 2018-03-22)For any locally compact abelian periodic group A its automorphism group contains as a subgroup those automorphisms that leave invariant every closed subgroup of A, to be denoted by SAut(A). This subgroup is again a locally ... -
The Tutte Polynomial of Ideal Arrangements
[OWP-2018-28] (Mathematisches Forschungsinstitut Oberwolfach, 2018-12-21)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 ... -
A Well-Posedness Result for Viscous Compressible Fluids with Only Bounded Density
[OWP-2018-10] (Mathematisches Forschungsinstitut Oberwolfach, 2018-05-28)We are concerned with the existence and uniqueness of solutions with only bounded density for the barotropic compressible Navier-Stokes equations. Assuming that the initial velocity has slightly sub-critical regularity and ...