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• Drawing large pictures at random : Oberwolfach Lecture 2007 ﻿

[OWP-2007-08] (Mathematisches Forschungsinstitut Oberwolfach, 2007)
This lecture is of very introductory nature. The goal will be to describe specific concrete questions, and to use them as a tool to convey some general ideas. Let me therefore skip the general introduction and immediately ...
• Geometric flows and 3-manifolds : Oberwolfach Lecture 2005 ﻿

[OWP-2007-01] (Mathematisches Forschungsinstitut Oberwolfach, 2007)
The current article arose from a lecture1 given by the author in October 2005 on the work of R. Hamilton and G. Perelman on Ricci-flow and explains central analytical ingredients in geometric parabolic evolution equations ...
• The McKay-conjecture for exceptional groups and odd primes ﻿

[OWP-2007-07] (Mathematisches Forschungsinstitut Oberwolfach, 2007)
Let $\mathbf{G}$ be a simply-connected simple algebraic group over an algebraically closed field of characteristic p with a Frobenius map $F:\mathbf{G}→\mathbf{G}$ and $\mathbf{G}:=\mathbf{G}^F$, such that the root system ...
• A 3-local identification of the alternating group of degree 8, the McLaughlin simple group and their automorphism groups ﻿

[OWP-2007-02] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-20)
In this article we give 3-local characterizations of the alternating and symmetric groups of degree 8 and use these characterizations to recognize the sporadic simple group discovered by McLaughlin from its 3-local subgroups.
• Resolution of symplectic cyclic orbifold singularities ﻿

[OWP-2007-03] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-21)
In this paper we present a method to obtain resolutions of symplectic orbifolds arising as quotients of pre-symplectic semi-free S1-actions. This includes, in particular, all orbifolds arising from symplectic reduction of ...
• Vector bundles on degenerations of elliptic curves and Yang-Baxter equations ﻿

[OWP-2007-04] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-22)
In this paper we introduce the notion of a gemetric associative r-matrix attached to a genus one fibration with a section and irreducible fibres. It allows us to study degenerations of solutions of the classical Yang-Baxter ...
• On test sets for nonlinear integer maximization ﻿

[OWP-2007-05] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-23)
A finite test set for an integer maximation problem enables us to verify whether a feasible point atains the global maximum. We establish in this paper several general results that apply to integer maximization problems ...
• Nonlinear matroid optimization and experimental design ﻿

[OWP-2007-06] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-24)
We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial ...
• Self-dual polygons and self-dual curves ﻿

[OWP-2007-09] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-25)
• Zeta functions of 3-dimensional p-adic Lie algebras ﻿

[OWP-2007-10] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-26)
We give an explicit formula for the subalgebra zeta function of a general 3-dimensional Lie algebra over the $p$-adic integers $\mathbb{Z}_p$. To this end, we associate to such a Lie algebra a ternary quadratic form over ...
• Secondary heat flow between confocal ellipses: an application of extended thermodynamics ﻿

[OWP-2007-11] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-27)
Much as non-Newtonian fluids exhibit secondary flows in elliptic pipes, rarefied gases exhibit secondary heat flows between elliptical cylinders. The phenomenon may be called non-Fourierian, because it is not covered by ...
• Slowly oscillating wave solutions of a single species reaction-diffusion equation with delay ﻿

[OWP-2007-12] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-28)
We study positive bounded wave solutions $u(t, x) = \phi(\nu \cdot x+ct)$, $\phi(-\infty)=0$, of equation $u_t(t, x)=\delta u(t,x)−u(t,x) +g(u(t−h,x))$, $x \in \mathbb{R}^m$(*). It is supposed that Eq. (∗) has exactly two ...
• Hölder-Differentiability of Gibbs Distribution Functions ﻿

[OWP-2007-13] (Mathematisches Forschungsinstitut Oberwolfach, 2007-03-29)
In this paper we give non-trivial applications of the thermodynamic formalism to the theory of distribution functions of Gibbs measures (devil’s staircases) supported on limit sets of finitely generated conformal iterated ...
• On the δ=const Collisions of Singularities of Complex Plane Curves ﻿

[OWP-2008-15] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equi-normalizable or ...
• On the Directionally Newton-non-degenerate Singularities of Complex Hypersurfaces ﻿

[OWP-2008-16] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We introduce a minimal generalization of Newton-non-degenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newton-non-degenerate if the local embedded ...
• A note on k[z]-Automorphisms in Two Variables ﻿

[OWP-2008-17] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
We prove that for a polynomial $f \in k[x, y, z]$ equivalent are: (1)$f$ is a $k[z]$-coordinate of $k[z][x,y]$, and (2) $k[x, y, z]/(f)\cong k^[2]$ and $f(x,y,a)$ is a coordinate in $k[x,y]$ for some $a \in k$. This solves ...
• Weyl-Titchmarsh Functions of Vector-Valued Sturm-Liouville Operators on the Unit Interval ﻿

[OWP-2008-13] (Mathematisches Forschungsinstitut Oberwolfach, 2008)
The matrix-valued Weyl-Titchmarsh functions $M(\lambda)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles ...
• Formal punctured ribbons and two-dimensional local fields ﻿

[OWP-2008-01] (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-05)
We investigate formal ribbons on curves. Roughly speaking, formal ribbon is a family of locally linearly compact vector spaces on a curve. We establish a one-to-one correspondence between formal ribbons on curves plus some ...
• Upper tails for intersection local times of random walks in supercritical dimensions ﻿

[OWP-2008-02] (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-06)
We determine the precise asymptotics of the logarithmic upper tail probability of the total intersection local time of $p$ independent random walks in $\mathbb{Z}^d$ under the assumption $p(d-2)>d$. Our approach allows a ...
• Hecke duality relations of Jacobi forms ﻿

[OWP-2008-03] (Mathematisches Forschungsinstitut Oberwolfach, 2008-03-07)
In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished ...