Delve into the second part of a comprehensive lecture on Quantum Toric Geometry, presented by Ernesto Lupercio at the University of Miami. Explore this cutting-edge generalization of toric geometry, which extends the concept in a manner analogous to how the quantum torus generalizes the conventional torus. Gain insights into the moduli spaces of quantum toric varieties, a key focus of this 57-minute talk. Discover the collaborative research efforts of Lupercio, Katzarkov, Meersseman, and Verjovsky in this fascinating field. Part of the "Geometry, Topology, Group Actions, and Singularities in the Americas" conference, this lecture bridges algebraic topology, algebraic geometry, and mathematical physics, fostering interdisciplinary connections across the Americas.