Title:
Finding something real in Zilber's field

Abstract:
In 2004, Zilber constructed a class of exponential fields,
known as pseudoexponential fields,
and proved that there is exactly one pseudoexponential field
in every uncountable cardinality up to isomorphism.
He conjectured that the pseudoexponential field of size continuum, K,
is isomorphic to the classic complex exponential field.
Since the complex exponential field contains the real exponential field,
one consequence of this conjecture is the existence
of a real closed exponential subfield of K.
In this talk,
I will sketch the construction of real closed exponential subfields of K
and discuss some of their properties.