Mathematical Sciences: Manifolds and Algebraic Topology

该项目涉及四名高级教员，一名 初级教员，和几个先进的研究生在 各种各样的拓扑学研究。 William P. 瑟斯顿将继续研究低维流形， 计算几何和几何群论。 比如说， 他将自动群体定义为一个在某种意义上 它可以被精确地处理，可以被有限状态处理 自动机 此外，他还证明了， 任何负弯曲的流形都是自动的。 其它几何 有趣的群体也符合这一观点，计算机 可以编写算法来利用这种情况。 John N.马瑟和维克托·J·唐奈，还有瑟斯顿， 将解决动力学和叶理理论中的问题。 Donnay发现了遍历测地线流的第一个例子， 一个二维的球体， 公制 这件事的后果需要一段时间来 明白 威廉·布劳德和吴忠祥从事广泛的- 微分拓扑与变换的研究 群论，同伦理论，代数簇， topology. Hsiang的工作也延伸到微分几何。

This project involves four senior faculty members, one junior faculty member, and several advanced graduate students in a wide variety of topological investigations. William P. Thurston will continue research on low-dimensional manifolds, computational geometry and geometric group theory. For example, he has defined an automatic group as one that can, in a sense that can be made quite precise, be treated by a finite state automaton. Moreover, he has shown that the fundamental group of any negatively curved manifold is automatic. Other geometrically interesting groups also fit this viewpoint, and computer algorithms may be written to exploit the situation. John N. Mather and Victor J. Donnay, as well as Thurston, will attack problems in dynamics and the theory of foliations. Donnay has found the first example of an ergodic geodesic flow on a two-dimensional sphere equipped with an appropriately chosen metric. The ramifications of this will take some time to understand. William Browder and Wu-chung Hsiang are engaged in wide- ranging research in differential topology and transformation group theory, homotopy theory, and algebraic varieties and topology. Hsiang's work also extends into differential geometry.