Homotopy Theory and Its Applications

Ravenel教授目前的研究集中在稳定同伦理论的望远镜猜想上，这是他20年前提出的几个猜想之一，也是目前唯一不被很好理解的猜想。从那时起，他提出的其他猜想已经演变成Devinatz-Hopkins-Smith的幂零定理、Hopkins-Smith的周期性定理和厚子范畴定理。所有这些都是同伦理论的色方法的一部分，它继续吸引着无数代数拓扑学家的兴趣。更具体地说，Ravenel已经构造并将研究Thomified Eilenberg-Moore谱序列，它包括通常的Eilenberg-Moore谱序列、Adams谱序列和Adams-Novikov谱序列作为特例。他还编制了计算球体循环空间的Morava K理论的程序。稳定同伦理论是代数拓扑学的一个分支，自一个世纪前由Poincare创立以来，一直是纯数学的核心。它一直是代数和几何中新思想的源泉，正如莱夫舍茨在1930年的S关于复代数簇的工作中所看到的那样，在1960年的S和1970年的S中导致证明算术代数几何的韦尔猜想的努力，以及最近的，在1997年沃沃茨基在代数K-理论中成功地将动机上同调应用到Milnor猜想中。它在微分几何、图论和非理论物理中也有许多应用。罗切斯特大学是世界领先的代数拓扑学中心之一。***

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. ***