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Explore the arithmetic properties of power series through advanced mathematical techniques in this 37-minute lecture from the Centre International de Rencontres Mathématiques. Discover a novel approach to proving irrationality of certain periods using rational approximations from existing literature within a newly developed framework. Learn about the key arithmetic holonomy theorem that builds upon foundational work by André, Bost, Charles and others on arithmetic algebraization theorems via Arakelov theory. Examine recent breakthrough results on irrationality measures developed through collaborative research with Frank Calegari and Vesselin Dimitrov. Gain insights into cutting-edge developments in Diophantine approximation and transcendence theory as presented during the thematic meeting at CIRM in Marseille, France.
