Construction of Arithmetic Teichmuller Spaces and applications to Mochizuki's Theory
Algebra and Number Theory Seminar
This talk is intended as an semi-informal introduction to my recent work on Arithmetic Teichmuller Spaces and its relationship to Mochizuki's Inter Universal Teichmuller Theory which is at the center of his work on the abc-conjecture. My work establishes a p-adic analog of classical Teichmuller Theory of Riemann surfaces. Notably in this theory, the etale fundamental group remains fixed (just as in the classical theory of Riemann surfaces) while the holomorphic structure varies. Given the nature of this work and its close relationship to Mochizuki's work, I have intentionally divided this talk into two talks on (10/3/2023) and (10/10/2023) both to provide a gentle introduction to my ideas and also to allow for plenty of questions. [There will be plenty of technical material presented as well but the emphasis will be on providing an introduction to my ideas.] I will also include a discussion of Mochizuki-Scholze-Stix issues in the context of Mochizuki's Theory (and answer any questions in this context).