Project description 
In the late 70s, Cherlin and Zilber conjectured that infinite simple groups of finite Morley rank are isomorphic to Chevalley groups over algebraically closed fields. Following the strategy of Ugurlu, we aim to prove that the CherlinZilber conjecture is equivalent to another conjecture, the Principal conjecture: the fixed point subgroup of a generic automorphism of an infinite simple group of finite Morley rank is pseudofinite. Ugurlu defined a tight automorphism A—an automorphism resembling the
nonstandard Frobenius automorphism—of an infinite simple group of finite Morley rank. Recently, the applicant and Ugurlu proved that a "small" infinite simple group of finite Morley rank admitting a tight A whose fixed point subgroup is pseudofinite is isomorphic to a Chevalley group over an algebraically closed field. In the future, we wish to generalise this result with the goal of proving the equivalence between the two conjectures above in mind. 
