Zoom link: https://huji.zoom.us/j/81000212562?pwd=5VinYS2zbLuCHJDbAhCiOC3pLyqhha.1
Meeting ID: 810 0021 2562
Passcode: 901314
Title: Invariant rings and fields in o-minimal structures
Abstract: Jana Marikova in 2007, studied automorphism-invariant groups in o-minimal structures and showed that they can be endowed with a group topology, similarly to the case of definable groups. In this talk I will describe results on invariant rings and fields. While 0-dimensional invariant fields may include the fields of rational or algebraic numbers (clearly not definable), we show that a positive dimensional type-definable or Ind-definable field must be definable, as is any invariant positive dimensional sub-field of a definable ring.
In addition, while an arbitrary invariant field of positive dimension might not be definable we conjecture that it is isomorphic, via an invariant map, to a definable one.
The proofs are “soft” and could probably be generalized to similar geometric settings.
This is joint work with Mirvat Mhameed and incorporates parts of her MSc thesis.