Solving Algebraic Equations, up to Homotopy
by
Michael Hopkins
MIT

The theory of topological modular forms is a hybrid of algebraic topology and the theory of elliptic curves. It offers a rich and surprising relationship between modular forms and the homotopy groups of spheres. This talk will consist of an introduction to this area and to the recent work of Jacob Lurie, who describes the whole structure in the context of "algebraic geometry up to homotopy."

Date received: April 5, 2005