Now showing items 1-20 of 24

• #### Approximation of discrete functions and size of spectrum ﻿

[OWP-2009-17] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-11)
Let $\Lambda \subset \mathbb{R}$ be a uniformly discrete sequence and $S \subset \mathbb{R}$ a compact set. We prove that if there exists a bounded sequence of functions in Paley-Wiener space $PW_s$, which approximates ...
• #### Asymptotic behavior of the eigenvalues and eigenfunctions to a spectral problem in thick cascade junction with concentrated masses ﻿

[OWP-2011-12] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-14)
The asymptotic behavior (as $\varepsilon \to 0$) of eigenvalues and eigenfunctions of a boundaryvalue problem for the Laplace operator in a thick cascade junction with concentrated masses is investigated. This cascade ...
• #### The contact polytope of the leech lattice ﻿

[OWP-2009-18] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-12)
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we classify the facets of the contact polytope of the Leech lattice up to symmetry. There are 1, 197, 362, 269, 604, 214, 277, 200 ...
• #### Discrete non-commutative integrability: the proof of a conjecture by M. Kontsevich ﻿

[OWP-2009-24] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-17)
We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for non-commutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture ...
• #### Fibonacci-like unimodal inverse limit spaces ﻿

[OWP-2010-03] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-9)
We study the structure of inverse limit space of so-called Fibonacci-like tent maps. The combinatorial constraints implied by the Fibonacci-like assumption allows us to introduce certain chains that enable a more detailed ...
• #### Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: the Rank Theorem ﻿

[OWP-2011-05] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-8)
We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in a noncommutative isotropic absolutely almost simple group $\mathcal{G}$ over a global function field is one less than the sum of the local ranks ...
• #### Homological properties of piecewise hereditary algebras ﻿

[OWP-2009-11] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-05)
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We will investigate homological properties of piecewise hereditary algebras $\Lambda$. In particular we give lower and upper bounds of ...
• #### An Identification Therorem for PSU6(2) and its Automorphism Groups ﻿

[OWP-2011-08] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-10)
We identify the groups PSU6(2), PSU6(2):2, PSU6(2):3 and Aut(PSU6(2)) from the structure of the centralizer of an element of order 3.
• #### The ingram conjecture ﻿

[OWP-2010-02] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-8)
We prove the Ingram Conjecture, i.e., we show that the inverse limit spaces of every two tent maps with different slopes in the interval [1,2] are non-homeomorphic. Based on the structure obtained from the proof, we also ...
• #### A new counting function for the zeros of holomorphic curves ﻿

[OWP-2009-25] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-18)
Let $f_1,..., f_p$ be entire functions that do not all vanish at any point, so that $(f_1,..., f_p)$ is a holomorphic curve in $\mathbb{CP}^{p-1}$. We introduce a new and more careful notion of counting the order of the ...
• #### On Generalizations of Kac-Moody Groups ﻿

[OWP-2010-06] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-10)
In [7] we define a Curtis-Tits group as a certain generalization of a Kac-Moody group. We distinguish between orientable and non-orientable Curtis-Tits groups and identify all orientable Curtis-Tits groups as Kac-Moody ...
• #### On the complement of the dense orbit for a quiver of type A ﻿

[OWP-2010-11] (Mathematisches Forschungsinstitut Oberwolfach, 2010)
Let $\mathbb{A}_t$ be the directed quiver of type $A$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank ...
• #### On the Complement of the Richardson Orbit ﻿

[OWP-2010-09] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-13)
We consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ ...
• #### On the distribution of a second class particle in the asymmetric simple exclusion process ﻿

[OWP-2009-22] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-15)
We give an exact expression for the distribution of the position $X(t)$ of a single second class particle in the asymmetric simple exclusion process (ASEP) where initially the second class particle is located at the origin ...
• #### On the geometry of the space of fibrations ﻿

[OWP-2009-15] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-09)
We study geometrical aspects of the space of fibrations between two given manifolds $M$ and $B$, from the point of view of Fréchet geometry. As a first result, we show that any connected component of this space is the ...
• #### Optimal bounds for the colored Tverberg Problem ﻿

[OWP-2009-27] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-20)
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color ...
• #### Positivity of the T-system cluster algebra ﻿

[OWP-2009-21] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-14)
We give the path model solution for the cluster algebra variables of the $A_r$ T-system with generic boundary conditions. The solutions are partition functions of (strongly) non-intersecting paths on weighted graphs. The ...
• #### Representation Theory of Non-Commutative Association Schemes of Order ﻿

[OWP-2010-07] (Mathematisches Forschungsinstitut Oberwolfach, 2010-03-11)
In this note, we investigate association schemes of order 6. We prove that non-normal closed subsets of such schemes have order 2 and that normal closed subsets of non-commutative schemes have order 2 or 3. After that, ...
• #### Simple graded commutative algebras ﻿

[OWP-2009-12] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-06)
We study the notion of $\Gamma$-graded commutative algebra for an arbitrary abelian group $\Gamma$. The main examples are the Clifford algebras already treated in [2]. We prove that the Clifford algebras are the only ...
• #### Simple vector bundles on plane degenerations of an elliptic curve ﻿

[OWP-2009-20] (Mathematisches Forschungsinstitut Oberwolfach, 2009-03-13)
In 1957 Atiyah classified simple and indecomposable vector bundles on an elliptic curve. In this article we generalize his classification by describing the simple vector bundles on all reduced plane cubic curves. Our main ...