Mathematical logic seminar – Oct 17 2017
Time: 3:30pm – 4:30 pm
Room: Wean Hall 8220
Speaker: Vahagn Aslanyan
Department of Mathematical Sciences
Title: Schanuel’s conjecture, pseudo-exponentiation, and Ax’s theorem
Schanuel’s conjecture captures the transcendence properties of the complex exponential function, and is considered out of reach. An interesting, novel approach to it was given by Zilber which led to the construction of pseudo-exponentiation. This gave rise to more conjectures related to Schanuel’s conjecture and the complex exponential field C_exp. One of those, known as Zilber-Pink, is purely number theoretic and generalises many known conjectures (and results) in diophantine geometry such as Mordell-Lang and Andree-Oort. I will describe Zilber’s construction and the Zilber-Pink conjecture. If time permits, I will also discuss a functional analogue of Schanuel’s conjecture proven by Ax in 1971.