The Dixmier-Moeglin equivalence and dynamical properties of automorphisms

我提议的研究涉及代数和动力学之间的相互作用。近年来，人们注意到可以将一个代数对象与给定的几何对象以及某些几何数据联系起来。这些物体被称为扭曲齐次坐标环。有趣的是，许多有趣的代数性质似乎与所谓的“动力学性质”有关。例如，当一个人有一个抽象的空间和这个空间的变换，我们可以迭代这个变换，然后问空间中给定的点随着时间的推移会发生什么，当我们重复迭代的时候。这类问题是动力学的核心，理解其中的一些问题实际上可以让我们深入了解相关的扭曲齐次坐标环。

My proposed research deals with interactions between algebra and dynamics. In recent years, it has been noticed that one can associate an algebraic object to a given geometric object along with certain geometric data. These objects are called twisted homogeneous coordinate rings. What is interesting is that many interesting algebraic properties appear to be linked with what are called "dynamical properties". For example, when one has an abstract space and a transformation of this space, one can iterate the transformation and ask what happens to a given point in the space over time as we repeatedly iterate. These sorts of questions are at the heart of dynamics, and understanding some of these questions actually gives us insight into the associated twisted homogeneous coordinate rings.