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Explore a categorical proposal for constructing a web of spherical functors associated with toric configurations in this hour-long lecture. Delve into an expansion of Aspinwall, Plesser, and Wang's conjecture from string theory, examining numerical and mirror symmetric evidence supporting the proposal. Learn about the collaborative research conducted with Ludmil Katzarkov, focusing on the intricate connections between spherical functors and toric birational geometry.