Browsing 2009 by MFO Scientific Program "Research in Pairs 2009"
Now showing items 114 of 14

Approximation of discrete functions and size of spectrum
[OWP200917] (Mathematisches Forschungsinstitut Oberwolfach, 20090311)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 PaleyWiener space $PW_s$, which approximates ... 
The contact polytope of the leech lattice
[OWP200918] (Mathematisches Forschungsinstitut Oberwolfach, 20090312)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 noncommutative integrability: the proof of a conjecture by M. Kontsevich
[OWP200924] (Mathematisches Forschungsinstitut Oberwolfach, 20090317)We prove a conjecture of Kontsevich regarding the solutions of rank two recursion relations for noncommutative variables which, in the commutative case, reduce to rank two cluster algebras of affine type. The conjecture ... 
Homological properties of piecewise hereditary algebras
[OWP200911] (Mathematisches Forschungsinstitut Oberwolfach, 20090305)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 ... 
A new counting function for the zeros of holomorphic curves
[OWP200925] (Mathematisches Forschungsinstitut Oberwolfach, 20090318)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 $\mathbb{CP}^{p1}$. We introduce a new and more careful notion of counting the order of the ... 
On the distribution of a second class particle in the asymmetric simple exclusion process
[OWP200922] (Mathematisches Forschungsinstitut Oberwolfach, 20090315)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
[OWP200915] (Mathematisches Forschungsinstitut Oberwolfach, 20090309)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
[OWP200927] (Mathematisches Forschungsinstitut Oberwolfach, 20090320)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 Tsystem cluster algebra
[OWP200921] (Mathematisches Forschungsinstitut Oberwolfach, 20090314)We give the path model solution for the cluster algebra variables of the $A_r$ Tsystem with generic boundary conditions. The solutions are partition functions of (strongly) nonintersecting paths on weighted graphs. The ... 
Simple graded commutative algebras
[OWP200912] (Mathematisches Forschungsinstitut Oberwolfach, 20090306)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
[OWP200920] (Mathematisches Forschungsinstitut Oberwolfach, 20090313)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 ... 
A study on gradient blow up for viscosity solutions of fully nonlinear, uniformly elliptic equations
[OWP200910] (Mathematisches Forschungsinstitut Oberwolfach, 20090304)We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear, uniformly elliptic equations under Dirichlet boundary conditions. When these conditions are ... 
Tilting on noncommutative rational projective curves
[OWP200914] (Mathematisches Forschungsinstitut Oberwolfach, 20090308)In this article we introduce a new class of noncommutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex. In particular, we prove that the right ... 
Weighted Fourier inequalities for radial functions
[OWP200926] (Mathematisches Forschungsinstitut Oberwolfach, 20090319)Weighted $L^p(\mathbb{R}^n) \to L^q(\mathbb{R}^n)$ Fourier inequalities are studied. We prove PittBoas type results on integrability with power weights of the Fourier transform of a radial function.