Explore the fascinating world of Quantum Toric Geometry (QTG) and its impact on Hodge numbers in non-algebraic complex manifolds in this 58-minute lecture by Ernesto Lupercio from CINVESTAV. Begin with an introduction to QTG as a natural non-commutative analog of classical toric geometry. Delve into the enriching aspects of QTG in the study of Hodge numbers, particularly in the context of non-algebraic complex manifolds. Gain insights from this collaborative research effort involving Lupercio, Katzarkov, Lee, Meersseman, and Verjovsky, presented at the University of Miami.