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Virtual Polytopes
[OWP-2015-02] (Mathematisches Forschungsinstitut Oberwolfach, 2015-04-10)
Originating in diverse branches of mathematics, from polytope algebra and toric varieties to the theory of stressed graphs, virtual polytopes represent a natural algebraic generalization of convex polytopes. Introduced as ...
Euler Reflexion Formulas for Motivic Multiple Zeta Functions
[OWP-2015-17] (Mathematisches Forschungsinstitut Oberwolfach, 2015-11-18)
We introduce a new notion of *-product of two integrable series with coeficients in distinct Grothendieck rings of algebraic varieties, preserving the integrability and commuting with the limit of rational series. In the ...
Cocharacter-closure and spherical buildings
[OWP-2015-12] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)
Let $k$ be a field, let $G$ be a reductive $k$-group and $V$ an affine $k$-variety on which $G$ acts. In this note we continue our study of the notion of cocharacter-closed $G(k)$-orbits in $V$. In earlier work we used a ...
Composition of Irreducible Morphisms in Quasi-Tubes
[OWP-2015-03] (Mathematisches Forschungsinstitut Oberwolfach, 2015-04-09)
We study the composition of irreducible morphisms between indecomposable modules lying in quasi-tubes of the Auslander-Reiten quivers of artin algebras $A$ in relation with the powers of the radical of their module category ...
Realizing Spaces as Classifying Spaces
[OWP-2015-01] (Mathematisches Forschungsinstitut Oberwolfach, 2015-04-10)
Which spaces occur as a classifying space for fibrations with a given fibre? We address this question in the context of rational homotopy theory. We construct an infinite family of finite complexes realized (up to rational ...
The algebra of differential operators for a Gegenbauer weight matrix
[OWP-2015-07] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)
In this work we study in detail the algebra of differential operators $\mathcal{D}(W)$ associated with a Gegenbauer matrix weight. We prove that two second order operators generate the algebra, indeed $\mathcal{D}(W)$ is ...
Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
[OWP-2015-04] (Mathematisches Forschungsinstitut Oberwolfach, 2015-05-18)
We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite sequence of formal integrals of motion $\int ...
A nested family of k-total effective rewards for positional games
[OWP-2015-21] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
We consider Gillette's two-person zero-sum stochastic games with perfect information. For each $k \in \mathbb{Z}_+$ we introduce an effective reward function, called $k$-total. For $k = 0$ and $1$ this function is known ...
A potential reduction algorithm for two-person zero-sum mean payoff stochastic games
[OWP-2015-19] (Mathematisches Forschungsinstitut Oberwolfach, 2015)
We suggest a new algorithm for two-person zero-sum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$-ergodic, if its values from any ...
Instability of point defects in a two-dimensional nematic liquid crystal model
[OWP-2015-05] (Mathematisches Forschungsinstitut Oberwolfach, 2015-07-29)
We study a class of symmetric critical points in a variational 2$D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3 \times 3$ matrices. These critical points play ...