The intersection of the division group of a finitely generated subgroup of a torus with an algebraic sub-variety has been understood for some time (Lang, Laurent). After a brief review of some of the tools in the analysis and their recent extensions (André-Oort conjectures), we give some old and new applications; periodicity of Betti numbers, algebraicity of Painlevé equations, and the additive structure of the spectra of quantum graphs.
This is the first of a two-part lecture, the second of which is here.
This video is part of Harvard University‘s two-part Alfors lecture 2019.
