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Explore a groundbreaking geometric approach to solving a fundamental 40-year-old question in secure computation through this 33-minute conference talk by Hemanta Maji from Purdue University at the Simons Institute. Discover how to determine whether a two-party function can be securely computed in the information-theoretic setting, particularly for functions with randomized output that remained uncharacterized since the 1989 work by Beaver, Chor, and Kushilevitz on deterministic functions. Learn about the innovative finite procedure developed to answer this foundational question by applying geometric methods from information complexity theory. Understand the mathematical breakthrough proving that specific lamination hulls are semi-algebraic, resolving an open problem in geometry while advancing secure computation theory. Examine how lamination hulls generalize convex hulls and their connection to hydrodynamics literature, providing new insights into the geometric structure underlying secure multiparty computation protocols.
