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Explore a mathematics lecture from Harvard CMSA's Math Science Lectures series honoring Raoul Bott, focusing on fibered knots and the slice-ribbon conjecture. Delve into the 1962 Fox conjecture which suggests that knots bounding smooth disks into B^4 must also bound ribbon disks. Learn about Casson-Gordon's work providing obstruction evidence for fibered knots being ribbon, and examine the 2022 findings by Dai-Kong-Mallick-Park-Stoffregen demonstrating that many potential counterexample knots don't actually bound smooth disks into B^4. Discover a simplified proof showing why the (2,1)-cable of the figure eight knot isn't slice, and investigate ongoing questions in the field through collaborative research presented by Maggie Miller, Paolo Aceto, Nickolas Castro, JungHwan Park, and Andras Stipsicz.
