Recorded 03 April 2025. Rafael Oliveira of the University of Waterloo presents "Scaling problems and entropic optimal transport" at IPAM's Optimal Transport for Density Operators: Theory and Numerics Workshop. Abstract: In this talk, we will talk about two scaling problems — in particular the matrix scaling and its quantum generalization: operator scaling — and we will see how invariant theory can be used to rigorously analyze the convergence of the natural alternate minimization algorithms for these problems (and obtain different efficient algorithms for these). Then, time permitting, we will also see how operator scaling can be viewed as the dual of a natural entropic optimal transport problem. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-optimal-transport-for-density-operators-theory-and-numerics/?tab=schedule