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Explore equivariant birational geometry in this 53-minute conference talk delivered by Yuri Tschinkel from the Courant Institute at NYU and Simons Foundation. Presented at the WIMSA Inaugural Conference 2022, hosted by the University of Miami, delve into advanced mathematical concepts and their applications in this specialized field of algebraic geometry. Gain insights from Tschinkel's expertise as he discusses the interplay between group actions and birational transformations, providing a comprehensive overview of current research and developments in equivariant birational geometry.