Recorded 27 September 2024. Stanislav Minsker of the University of Southern California presents "New performance guarantees for Tukey’s median" at IPAM's Analyzing High-dimensional Traces of Intelligent Behavior Workshop. Abstract: Is there a natural way to order data in dimension greater than 1? The approach based on the notion of data depth, often associated with the name of John Tukey, is among the most popular. Tukey’s depth has found applications in robust statistics, graph theory, and the study of elections and social choice. We will give an introduction to the topic, describe the mathematical properties of Tukey’s depth, and explain some remaining open questions as well as our recent progress towards the solutions. The talk is based on a joint work with Yinan Shen. Learn more online at: https://www.ipam.ucla.edu/programs/workshops/workshop-i-analyzing-high-dimensional-traces-of-intelligent-behavior/?tab=overview