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Some Results Related to Schiffer's Problem

[OWP-2018-18] Kawohl, Bernd; Lucia, Marcello (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] 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 ...

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 ...

Deformation Classification of Real Non-Singular Cubic Threefolds with a Marked Line

[OWP-2018-02] Finashin, Sergey; Kharlamov, Viatcheslav (Mathematisches Forschungsinstitut Oberwolfach, 2018-02-21)

We prove that the space of pairs

$(X,l)$ formed by a real non-singular cubic hypersurface

$X\subset P^4$ with a real line

$l\subset X$ has 18 connected components and give for them several quite explicit interpretations. ...

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 ...

The Sylow Structure of Scalar Automorphism Groups

[OWP-2018-05] Herfort, Wolfgang; Hofmann, Karl Heinrich; Kramer, Linus; Russo, Francesco G. (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 ...

MOSES: A Streaming Algorithm for Linear Dimensionality Reduction

[OWP-2018-12] Eftekhari, Armin; Hauser, Raphael A.; Grammenos, Andreas (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 ...

The Tutte Polynomial of Ideal Arrangements

[OWP-2018-28] Randriamaro, Hery (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 ...

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 ...