Browsing 2009 by Title
Now showing items 625 of 27

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 ... 
Geometric quantization of integrable systems with hyperbolic singularities
[OWP200901] (Mathematisches Forschungsinstitut Oberwolfach, 2009)We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. ... 
HeisenbergWeyl algebra revisited: combinatorics of words and paths
[OWP200902] (Mathematisches Forschungsinstitut Oberwolfach, 2009)The Heisenberg–Weyl algebra, which underlies virtually all physical representations of Quantum Theory, is considered from the combinatorial point of view. We provide a concrete model of the algebra in terms of paths on a ... 
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 ... 
An introduction to heavytailed and sibexponential distributions
[OWP200913] (Mathematisches Forschungsinstitut Oberwolfach, 20090307)This text studies heavytailed distributions in probability theory, and especially convolutions of such distributions. The mail goal is to provide a complete and comprehensive introduction to the theory of longtailed ... 
Minimal Riesz energy on the sphere for axissupported external fields
[OWP200904] (Mathematisches Forschungsinstitut Oberwolfach, 2009)Abstract. We investigate the minimal Riesz $s$energy problem for positive measures on the ddimensional unit sphere $\mathbb{S}^d$ in the presence of an external field induced by a point charge, and more generally by ... 
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 Siegel modular forms of level p and their properties mod p
[OWP200923] (Mathematisches Forschungsinstitut Oberwolfach, 20090316)Using theta series we construct Siegel modular forms of level p which behave well modulo $p$ in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 ... 
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 ... 
On the nonanalyticity locus of an arcanalytic function
[OWP200903] (Mathematisches Forschungsinstitut Oberwolfach, 20090221)A function is called arcanalytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arcanalytic functions that are not real analytic. Arc analytic functions appear ... 
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 ... 
Pointwise hyperbolicity implies uniform hyperbolicity
[OWP200906] (Mathematisches Forschungsinstitut Oberwolfach, 20090223)We provide a general mechanism for obtaining uniform information from pointwise data. A sample result is that if a diffeomorphism of a compact Riemannian manifold has pointwise expanding and contracting continuous invariant ... 
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 ... 
Proof mining in metric fixed point theory and ergodic theory
[OWP200905] (Mathematisches Forschungsinstitut Oberwolfach, 2009)In this survey we present some recent applications of proof mining to the fixed point theory of (asymptotically) nonexpansive mappings and to the metastability (in the sense of Terence Tao) of ergodic averages in uniformly ... 
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 ... 
Singer quadrangles
[OWP200907] (Mathematisches Forschungsinstitut Oberwolfach, 20090301) 
Stein's method for dependent random variables occuring in statistical mechanics
[OWP200909] (Mathematisches Forschungsinstitut Oberwolfach, 20090303)We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the ... 
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 ...