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Explore a one-hour seminar talk that delves into the mathematical concept of calculus of fractions, originally introduced by P. Gabriel and M. Zisman in 1967, and its modern extensions to higher-dimensional mathematics. Learn how the traditional calculus of fractions, while powerful for understanding category localization with weak equivalences, faces limitations in homotopical contexts. Discover new research that bridges classical and homotopical approaches through the development of calculus of fractions for quasicategories, including a practical model for marked quasicategories. Gain insights into this collaborative work between Kapulkin, Carranza, and Lindsey, which opens new possibilities for applications across various mathematical domains.
