Explore the mathematical concepts of Wold decompositions for representations of C∗-algebras associated with noncommutative varieties in this 53-minute lecture by Gelu Popescu from the University of Texas at San Antonio. Delve into topics such as noncommutative domains, multivariable commutative and noncommutative cases, Berezin kernels, and various versions of Wold decomposition. Gain insights into the uniqueness of Wold decomposition, classification, exact sequences of C-algebras, and the relationship between polydomains and varieties. This talk, part of the Focus Program on Analytic Function Spaces and their Applications, offers a comprehensive overview of advanced mathematical concepts in functional analysis and operator theory.