Yunqing TangAffiliation: UC Berkeley Title Of Talk: The arithmetic of power series and applications to irrationality Abstract: We will first briefly discuss our approach to prove irrationality of certain periods such as certain product of two log values. Our method uses rational approximations from the literature such as the work of Alladi and Robinson inspired by the work of Apéry; we develop a new framework to make use of these approximations. The key ingredient is an arithmetic holonomy theorem built upon earlier work by André, Bost, Charles (and others) on arithmetic algebraization theorems via Arakelov theory; a version of our arithmetic holonomy theorem was also used in our proof of the unbounded denominators conjecture. We will then discuss our recent result on irrationality measures. This is joint work with Frank Calegari and Vesselin Dimitrov.
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