Explore outlier-robust clustering techniques for Gaussian mixtures and non-spherical distributions in this 29-minute IEEE conference talk. Delve into robust statistics, focusing on the main result of robustly clustering Gaussian mixtures and its implications for robust covariance estimation. Examine why mean or covariance separation is insufficient, and learn about TV-separation to parameter separation. Investigate simplifying assumptions, anti-concentration, and an inefficient algorithm before diving into Sum-of-Squares relaxation. Gain insights from speakers representing CMU, UW Madison, Berkeley, UCSD, and UT Austin as they outline proofs and discuss high-level Sum of Squares relaxation techniques.