Mathematical Sciences: Topology and Its Connections to Geometry and Modular Representation Theory

点击翻译按钮获取中文摘要

This project deals with homotopy theory and its applications to several related areas. Friedlander works on the homotopy type of certain algebraic varieties, and also studies the representation theory of mod-p Lie algebras and the cohomology of groups of Lie type. Additionally, he plans to continue his study of algebraic K-theory. Mahowald works on intrinsic questions in stable and unstable homotopy theory. His main emphasis is on periodic structures in the homotopy groups of spheres. Priddy studies relations between modular representation theory and the stable homotopy type of finite and infinite groups. The cohomology of groups and stable splittings of classifying spaces are central to his work. In short, all three investigators are working with highly sophisticated algebraic tools for studying geometric structures. On the one hand, they improve our understanding of the tools. On the other hand, they apply the tools to answer geometric questions about spaces.