Time:  3:30pm  4:30 pm 
Room: 
Wean Hall 8220

Speaker: 
Vahagn Aslanyan Department of Mathematical Sciences CMU 
Title: 
Schanuel's conjecture, pseudoexponentiation, and Ax's theorem

Abstract: 
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 pseudoexponentiation. This gave rise to more conjectures related to Schanuel's conjecture and the complex exponential field C_{exp}. One of those, known as ZilberPink, is purely number theoretic and generalises many known conjectures (and results) in diophantine geometry such as MordellLang and AndreeOort. I will describe Zilber's construction and the ZilberPink conjecture. If time permits, I will also discuss a functional analogue of Schanuel's conjecture proven by Ax in 1971. 