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Explore the foundations of noncommutative stochastic calculus in this 26-minute lecture delivered by Evangelos Nikitopoulos from the University of California, San Diego. Presented on November 15, 2023, as part of the Workshop on Operator Algebras and Applications: Free Probability at the Fields Institute, this talk delves into the intricacies of a cutting-edge mathematical field. Gain insights into the intersection of operator algebras and probability theory, and discover how these concepts apply to complex systems in quantum mechanics and financial mathematics. For a more comprehensive understanding, refer to the abstract and consider exploring the broader context of the Thematic Program on Operator Algebras and Applications.