# Mathematics Colloquia and Seminars

I will describe what I mean by the "gradient push" and then I will discuss some of its applications. Here is a sample application: If $M$ is an almost non-negatively curved manifold, then $\pi_1(M)$ acts on $\pi_k(M,R)$ for $k\ge 2$ by transformations such that the absolute value of each eigenvalue is one.