Homotopy Theory and Its Applications

9802516拉文埃尔 Ravenel教授目前的研究集中在稳定同伦理论的望远镜投影上，这是他20年前提出的几个理论之一，也是目前唯一一个没有得到很好理解的理论。 他的其他理论后来发展成Devinatz-Hopkins-Smith的周期性定理、Hopkins-Smith的周期性定理和厚子范畴定理。 所有这些都是同伦论的色方法的一部分，它继续吸引着众多代数拓扑学家的兴趣。 此外，Ravenel还构造并研究了简化的Eilenberg-Moore谱序列，其中包括通常的Eilenberg-Moore谱序列、亚当斯谱序列和作为特例的亚当斯-诺维科夫谱序列。 他也有一个程序计算的摩拉瓦K-理论的相互循环空间的领域。 稳定同伦理论是代数拓扑学的一个分支，自一个世纪前由庞加莱创立以来一直是纯数学的核心。 它一直是一个持续的来源，新的想法，在代数和几何，如工作中看到的莱夫谢茨复杂的代数品种在20世纪30年代，努力导致证明的韦尔代数几何在20世纪60年代和70年代，最近，在成功应用motivic上同调的Milnorconceptuation代数K理论Voevodsky在1997年。 它也发现了许多应用在微分几何，图论和理论物理。 罗切斯特大学是世界上代数拓扑学的主要研究中心之一。***

9802516Ravenel Professor Ravenel's current research is focused on the telescopeconjecture of stable homotopy theory, one of several conjectures heformulated 20 years ago, and the only one that is not well understood atthis time. Other conjectures he made then have since evolved into thenilpotence theorem of Devinatz-Hopkins-Smith, the periodicity theorem ofHopkins-Smith, and the the thick subcategory theorem. All of these arepart of the chromatic approach to homotopy theory, which continues toattract the interest of numerous algebraic topologists. Morespecifically, Ravenel has constructed and will study the ThomifiedEilenberg-Moore spectral sequence, which includes the usualEilenberg-Moore spectral sequence, the Adams spectral sequence, and theAdams-Novikov spectral sequence as special cases. He also has a programfor the computation of the Morava K-theory of interated loop spaces ofspheres. Stable homotopy theory is a branch of algebraic topology, which hasbeen central to pure mathematics since its founding by Poincare a centuryago. It has been a continuing source of new ideas in algebra and geometry,as seen in the work of Lefschetz on complex algebraic varieties in the1930's, the efforts leading to the proof of the Weil conjectures ofarithmetic algebraic geometry in the 1960's and 1970's, and most recently,in the successful application of motivic cohomology to the Milnorconjecture in algebraic K-theory by Voevodsky in 1997. It has also foundnumerous applications in differential geometry, in graph theory, and intheoretical physics. The University of Rochester is one of the leadingcenters of algebraic topology in the world. ***