Abstract: I will talk about what happened behind the resolution of Talagand's convexity conjecture (with Dongming Merrick Hua and Stefan Tudose) and propose new directions, in particular a Riemannian version of the conjecture for manifolds with nonnegative Ricci curvature.

Brief biography: Antoine Song is a professor at Caltech. He obtained his PhD at Princeton with Fernando Codá Marques, before going to UC Berkeley for a postdoc.

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