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http://publications.mfo.de:8080/handle/mfo/1295
News on quadratic polynomials
Pottmeyer, Lukas
Bruschi, David Edward; Niediek, Johannes; Cederbaum, Carla
Many problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning quadratic polynomials, which uses a bridge between algebra and analysis. We study the iterations of quadratic polynomials, obtained by computing the value of a polynomial for a given number and feeding the outcome into the exact same polynomial again. These iterations of polynomials have interesting applications, such as in fractal theory.
Tue, 18 Jul 2017 00:00:00 GMThttp://publications.mfo.de:8080/handle/mfo/12952017-07-18T00:00:00ZInductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements
http://publications.mfo.de:8080/handle/mfo/1293
Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements
Hoge, Torsten; Röhrle, Gerhard
Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the
restriction $A''$ of $A$ to any hyperplane endowed with the natural
multiplicity is then a free multiarrangement. We initiate a study of the
stronger freeness property of inductive freeness for these canonical free
multiarrangements and investigate them for the underlying class of reflection
arrangements.
<br />More precisely, let $A = A(W)$ be the reflection arrangement of a complex
reflection group $W$. By work of Terao, each such reflection arrangement is
free. Thus so is Ziegler's canonical multiplicity on the restriction $A''$ of
$A$ to a hyperplane. We show that the latter is inductively free as a
multiarrangement if and only if $A''$ itself is inductively free.
MSC: 20F55; 51F15; 52C35; 14N20; 32S22; 51D20
Sun, 30 Apr 2017 00:00:00 GMThttp://publications.mfo.de:8080/handle/mfo/12932017-04-30T00:00:00ZOn Unipotent Radicals of Pseudo-Reductive Groups
http://publications.mfo.de:8080/handle/mfo/1292
On Unipotent Radicals of Pseudo-Reductive Groups
Bate, Michael; Martin, Benjamin; Röhrle, Gerhard; Stewart, David I.
We establish some results on the structure of the geometric unipotent
radicals of pseudo-reductive k-groups. In particular, let k' be a purely
inseparable field extension of k of degree p^e and let G denote the Weil
restriction of scalars \R_{k'/k}(G') of a reductive k'-group G'. We prove that
the unipotent radical R_u(G_{\bar k}) of the extension of scalars of G to the
algebraic closure \bar k of k has exponent e. Our main theorem is to give
bounds on the nilpotency class of geometric unipotent radicals of standard
pseudo-reductive groups, which are sharp in many cases.
MSC: 20G15
Thu, 27 Apr 2017 00:00:00 GMThttp://publications.mfo.de:8080/handle/mfo/12922017-04-27T00:00:00ZOn Vietoris-Rips Complexes of Ellipses
http://publications.mfo.de:8080/handle/mfo/1291
On Vietoris-Rips Complexes of Ellipses
Adamaszek, Michal; Adams, Henry; Reddy, Samadwara
MSC: 05E45; 55U10; 68R05
Tue, 25 Apr 2017 00:00:00 GMThttp://publications.mfo.de:8080/handle/mfo/12912017-04-25T00:00:00Z