Explore the intricacies of Belavin-Drinfeld quantum groups in this 46-minute conference talk delivered by Tim Hodges at the Canada-Mexico-US Conference on Representation Theory, Noncommutative Algebra, and Categorification. Delve into the deformations of the algebra of functions of semi-simple algebraic Poisson groups, focusing on Poisson structures derived from factorizable Lie bialgebra structures on (semi-)simple Lie algebras. Gain insights into the current state of knowledge in this field, examine key conjectures, and discover potential future research directions. Enhance your understanding of quantum groups and their applications in mathematical physics and representation theory.