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Explore the intricate connections between LVM manifolds, toric manifolds, and their quaternionic counterparts in this 53-minute lecture by Alberto Verjovsky from the National Autonomous University of Mexico. Delve into the theory of LVM manifolds and their relationship with toric geometry, while examining the initial steps towards extending these concepts to the quaternionic realm. Gain insights into the intersection of quadrics, moment-angle manifolds, complex and quaternionic manifolds, and convex polytopes as you navigate through this advanced mathematical discourse presented at the University of Miami on October 19, 2020.