Quasiminimality of complex powers

by Dr Francesco Gallinaro (Albert-Ludwigs-Universität Freiburg)

Thursday 23 Nov 2023, 11:00 → 12:00 Europe/Rome

Aula Riunioni (Dipartimento di Matematica)

A conjecture due to Zilber predicts that the complex exponential field is quasiminimal: that is, that all subsets of the complex numbers that are definable in the language of rings expanded by a symbol for the complex exponential function are countable or cocountable. Zilber showed that this conjecture would follow from Schanuel's Conjecture and an existential closedness type property, asserting that certain systems of exponential-polynomial equations can be solved in the complex numbers. Bays and Kirby removed the dependence on Schanuel's Conjecture, shifting the focus to the solvability of systems of equations. In this talk, I will discuss joint work with Jonathan Kirby on the quasiminimality of a reduct of the complex exponential field, that is, the complex field equipped with multivalued power functions.