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Explore a mathematical seminar lecture examining Hofer's geometry of autonomous flows on the two-sphere, delivered by Egor Shelukhin from the Institute for Advanced Study. Delve into the complex understanding of autonomous Hamiltonian flow growth in Hofer's metric, beginning with Polterovich and Rosen's findings on asymptotically linear growth in generic cases. Learn about the intriguing dichotomy known for open connected surfaces of infinite area, established by Polterovich and Siburg's 2000 research. Discover a novel approach that establishes a robust version of this dichotomy specifically for the two-sphere, developed through collaborative work with Lev Buhovsky, Ben Feuerstein, and Leonid Polterovich.
