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In this 36-minute conference talk, David Gao from the University of California, San Diego introduces the concept of sofic actions of groups on sets and graphs at IPAM's Free Entropy Theory and Random Matrices Workshop. Explore how this new notion of sofic actions extends beyond previous work on pmp actions by Elek, Lippner, and Paunescu to address discrete objects. Discover how this framework generalizes the work of Hayes and Sale, demonstrating that a broad class of generalized wreath product and graph wreath product groups are sofic. Learn about fascinating examples of sofic actions, including transitive actions of sofic groups on graphs with amenable stabilizers, arbitrary actions of amenable groups and free groups on graphs, and arbitrary actions of LERF groups on sets. The presentation primarily covers joint research with Srivatsav Kunnawalkam Elayavalli and Gregory Patchell, recorded on February 26, 2025, at the Institute for Pure & Applied Mathematics (IPAM) at UCLA.
