Definable Holomorphic Continuations in O-minimal Structures

This conference talk by Adele Padgett explores definable holomorphic continuations in o-minimal structures, presenting joint work with P. Speissegger. Discover how real analytic functions can always be continued holomorphically to some domain, while holomorphic continuations of definable functions in an o-minimal structure may not be definable. Learn about the study of holomorphic continuations of functions definable in two o-minimal expansions of the real field, and see applications to the complex Gamma function and Riemann zeta function. The talk was recorded during the thematic meeting "Tame geometry" on February 10, 2025, at the Centre International de Rencontres Mathématiques in Marseille, France. Access this 54-minute video and other talks by worldwide mathematicians on CIRM's Audiovisual Mathematics Library, featuring helpful functionalities like chapter markers, keywords, abstracts, bibliographies, and multi-criteria search options.