Die Bedeutung des ökologischen Landbaues für die Gesellschaft

Anlässlich der gemeinsamen Sitzung von Kuratorium und Vorstand der Agrarsozialen Gesellschaft e.V. am 21. März 2002 referierte Dr. Rainer Oppermann zur Bedeutung des Ökologischen Landbaus für die Gesellschaft. Seiner Ansicht nach ist es keine Frage, dass der ökologische Landbau eine feste Größe in der Landwirtschaft ist und dass die Entwicklung eines Wirtschaftsbereichs, der im Jahr 1980 449 Betriebe zählte und heute bei rund 15000 Betrieben angekommen sein dürfte, insgesamt als Erfolgsgeschichte zu bezeichnen ist. (zitiert aus: Oppermann, R (2002) Die Bedeutung des ökologischen Landbaus für die Gesellschaft. Ländlicher Raum 53(2), Agrarsoziale Gesellschaft e.V., 12-16

Dynamical CPA approach to an itinerant fermionic spin glass model

We study a fermionic version of the Sherrington-Kirkpatrick model including nearest-neighbor hopping on a $\infty$-dimensional simple cubic lattices. The problem is reduced to one of free fermions moving in a dynamical effective random medium. By means of a CPA method we derive a set of self-consistency equations for the spin glass order parameter and for the Fourier components of the local spin susceptibility. In order to solve these equations numerically we employ an approximation scheme which restricts the dynamics to a feasible number of the leading Fourier components. From a sequence of systematically improved dynamical approximations we estimate the location of the quantum critical point.Comment: 9 pages, 6 figures, revised versio

Higher dimensional cluster combinatorics and representation theory

Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied. Cyclic polytopes are classical objects of study in convex geometry. In particular, their triangulations have been studied with a view towards generalizing the rich combinatorial structure of triangulations of polygons. In this paper, we demonstrate a connection between these two seemingly unrelated subjects. We study triangulations of even-dimensional cyclic polytopes and tilting modules for higher Auslander algebras of linearly oriented type A which are summands of the cluster tilting module. We show that such tilting modules correspond bijectively to triangulations. Moreover mutations of tilting modules correspond to bistellar flips of triangulations. For any d-representation finite algebra we introduce a certain d-dimensional cluster category and study its cluster tilting objects. For higher Auslander algebras of linearly oriented type A we obtain a similar correspondence between cluster tilting objects and triangulations of a certain cyclic polytope. Finally we study certain functions on generalized laminations in cyclic polytopes, and show that they satisfy analogues of tropical cluster exchange relations. Moreover we observe that the terms of these exchange relations are closely related to the terms occuring in the mutation of cluster tilting objects.Comment: 41 pages. v4: minor corrections throughout the pape