Strength is an algebraic measure of nondegeneracy for multivariate polynomials. Motivated by questions in additive combinatorics, Green and Tao proved that polynomials over finite fields with high strength have equidistributed values. This result led to a flurry of various extensions and improvements by many others. I will survey what is known both qualitatively and quantitatively and then introduce an equidistribution result for polynomials with inputs restricted to lie on a variety.
Joint work with Tamar Ziegler.