Title: Arithmetic holonomy bounds in transcendence proofs and effective Diophantine approximation.

Abstract: The method of arithmetic holonomy bounds, developed presently in a collaboration with Calegari and Tang, encodes some Diophantine problems of a traditional interest into suitable generating functions with good analytic and Diophantine properties. I will present a completely explicit Ansatz and explain its fairly straightforward proof. The challenge is then to cook up holonomy template setups where the Ansatz has interesting consequences. Nevertheless, already the simplest “infinite dihedral orbifold” setup has applications including the transcendence of Pi (in a particularly simple way) and a new effective solution of the two-variable S-unit equation, but also some explicit irrationality measures for logarithms that seem to enter into a blind spot of the literature.

New room: Seminarraum 00.002, Rheinsprung 21