In this talk, we will discuss two examples of scaling problems (matrix scaling and operator scaling), which have recently been used to solve problems in a wide variety of areas, ranging from non-commutative algebra and invariant theory to functional analysis. These scaling problems have very simple and deterministic algorithms which give (1+epslion) multiplicative approximation to compute Gurvits' capacity, as well as the Brascamp-Lieb constant (whenever the latter is finite).

This talk is based on joint work with Ankit Garg, Leonid Gurvits and Avi Wigderson.