Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Bounding nonorthogonality"
In stability theory there is a natural notion for what it means for a complete type $p$ to have significant definable interaction with a definable set $X$: we say that "$p$ is nonorthogonal to $X$”. This notion allows passing to a larger set of parameters, and if we insist on fixing the base parameters we get the stronger, but easier to see, notion of "non-weak-orthogonality”. Last year, Remi Jaoui and I, proved a theorem that, in a certain particular context coming from differential fields, says something like "$p$ is nonorthogonal to $X$ if and only if $p^2$ is not weakly orthogonal to $X$”. This year, Jason Bell, Matt Satriano and I gave the same theorem in another context coming this time from difference fields. The theorems have applications to the bimeromorphic geometry of algebraic vector fields and dynamical systems, but in this talk I will stick to the abstract statement itself, attempt to make it more precise, and maybe convey something about how it is proved (in the differential case).
MC 5479