Weights (non-negative locally integrable functions) satisfying a reverse H"older condition are important in the study of harmonic measure and boundary value problems for elliptic and parabolic partial differential equations. In this talk, I will discuss a quantitative version of a Carleson measure characterization of reverse H"older weights (originally found by Fefferman, Kenig and Pipher in the 90s) and its application to elliptic measure. In addition, I will explain extensions and modifications of the results needed in the analogous theory for parabolic measures. This is based on joint work (and work in progress) with Simon Bortz and Moritz Egert.

The video of this talk is available on the IISc Math Department channel.