Explore nonrational toric geometry through a lecture that establishes a correspondence between simplicial fans and foliated complex manifolds called LVMB manifolds. Delve into toric quasifolds as leaf spaces, examining how the interplay between toric geometry and combinatorics extends to nonrational contexts. Investigate a one-parameter family of toric quasifolds containing Hirzebruch surfaces from a foliation perspective. Learn about Stanley's g-Theorem proof reformulation for simple polytope combinatorics and discover the rich connections between convex geometry, Gale duality, and holomorphic foliations in this advanced mathematical exploration.