Filters

2010 - 20153

More filters

2019 - 20203
Reset filters

Settings

Type: Text × Subject: rationality ×

Search Results

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Cocharacter-closure and spherical buildings
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2015) Bate, Michael; Herpel, Sebastian; Benjamin, Martin; Röhrle, Gerhard
    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 rationality condition on the point stabilizer of a G-orbit to prove Galois ascent/descent and Levi ascent/descent results concerning cocharacter-closure for the corresponding G(k)-orbit in V . In the present paper we employ building-theoretic techniques to derive analogous results.
  • Thumbnail Image
    Item
    Risk, rationality, and resilience
    (Beijing : Beijing Normal University Press, 2010) Jaeger, C.
    Improving our ability to cope with large risks is one of the key challenges for humankind in this century. This article outlines a research program in this perspective. Starting with a concrete example of a relatively small disaster, it questions simplistic ideas of rationality. It then proposes a fresh look at the concepts of probability and utility in the context of socio-ecological systems. This leads first to an emphasis on the problem of equilibrium selection, and then to a distinction between three kinds of resilience that matter both for theory and practice of risk management. They can be investigated by paying attention to the transitions into and out of actual disasters.
  • Thumbnail Image
    Item
    Cocharacter-Closure and the Rational Hilbert-Mumford Theorem
    (Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2014) Bate, Michael; Herpel, Sebastian; Martin, Benjamin; Röhrle, Gerhard
    For a field k, let G be a reductive k-group and V an affine k-variety on which G acts. Using the notion of cocharacter-closed G(k)-orbits in V , we prove a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We initiate a study of applications stemming from this rationality tool. A number of examples are discussed to illustrate the concept of cocharacter-closure and to highlight how it differs from the usual Zariski-closure.