Shayan Oveis Gharan - University of Washington I will talk about three applications of a particular class of stability preserver operators, 1-partial_x partial_y. First, I use it to prove that matching polynomial is real rooted, then I use it to generalize the main theorem of Interlacing Families II to strongly Rayleigh distributions, and lastly I use it to generalize Gurvits's machinery on the van-der-Waerden conjecture. Based on joint works with Nima Anari.