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Explore a 50-minute lecture from Institut des Hautes Etudes Scientifiques (IHES) examining the computation of multiplicity automata behavior through matrix star operations with noncommutative coefficients in semirings. Delve into various applications including Sweedler's duals, Topological algebras, and Infinite iterated integrals, while discovering extensions of holomorphic-valued shuffle characters such as polylogarithms. Learn about a groundbreaking two-state transducer that generates the Collatz function, which forms the foundation of an award-winning paper. The presentation represents collaborative research with Didier Caucal, Nihar Gargava, and Pierre Simonnet, delivered by Gérard Duchamp from LIPN, Université Paris Nord.
