## Model Theory Seminar

James Freitag

UIC

Jet spaces and Lascar rank of differential equations

**Abstract:**In various contexts, jet or arc spaces provide a way of studying general geometric objects (varieties, zero sets of differential equations, etc.) by studying associated objects which are more linear. Last week, J. Wolf showed that the zero set of a generic linear differential polynomial has Lascar rank as small as possible (based on differential transcedence degree). This week, we will show how to generalize that result to general differential equations using arc spaces. I'll also talk about the problem which motivated the project: find an interesting analog for the lower bound of the Lascar inequality for so-called minimal Kolchin polynomials.

Tuesday October 24, 2017 at 1:00 PM in SEO 427