Professor Ravenel's current research is focused on the telescope conjecture of stable homotopy theory, one of several conjectures he formulated 20 years ago, and the only one that is not well understood at this time. Other conjectures he made then have since evolved into the nilpotence theorem of Devinatz-Hopkins-Smith, the periodicity theorem of Hopkins-Smith, and the the thick subcategory theorem. All of these are part of the chromatic approach to homotopy theory, which continues to attract the interest of numerous algebraic topologists. More specifically, Ravenel has constructed and will study the Thomified Eilenberg-Moore spectral sequence, which includes the usual Eilenberg-Moore spectral sequence, the Adams spectral sequence, and the Adams-Novikov spectral sequence as special cases. He also has a program for the computation of the Morava K-theory of interated loop spaces of spheres. Stable homotopy theory is a branch of algebraic topology, which has been central to pure mathematics since its founding by Poincare a century ago. 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 the 1930's, the efforts leading to the proof of the Weil conjectures of arithmetic algebraic geometry in the 1960's and 1970's, and most recently, in the successful application of motivic cohomology to the Milnor conjecture in algebraic K-theory by Voevodsky in 1997. It has also found numerous applications in differential geometry, in graph theory, and in theoretical physics. The University of Rochester is one of the leading centers of algebraic topology in the world. ***
