Alfred P. Sloan Research Fellowship for Nathaniel Stapleton in Mathematics

Algebraic topologists are in the business of constructing and understanding lossy computable invariants of topological spaces. In searching for such invariants, algebraic topologists were led to the notion of a cohomology theory. This notion is an axiomatization of properties held by some of the most important known invariants: singular cohomology (built out of simplices), topological K-theory (built out of vector bundles), and bordism cohomology theories (built out of compact manifolds). My work is centered around understanding and exploiting an in?nite family of cohomology theories called the “Morava E- theories.” These are built out of Lubin-Tate theory, which is a fundamental piece of arithmetic geometry.