Explore the connections between the Helton-Howe Trace, Connes-Chern Character, and Quantization in this 46-minute conference talk delivered by Xiang Tang from Washington University in St. Louis. Presented as part of the Workshop on Operator Algebras and Applications: Non-Commutative Geometry at the Fields Institute, this lecture delves into advanced mathematical concepts within the framework of operator algebras and non-commutative geometry. Gain insights into the speaker's research and its implications for the field, as discussed during the Thematic Program on Operator Algebras and Applications.