Geometry/Topology Seminar
James Freitag
UIC
Invariant subvarieties and highly transitive group actions [Joint Geometry/Topology & Logic seminar]
Abstract: Here are two rather different sounding questions: Given variety V and
an algebraic vector field S from V to its tangent bundle, when are
there S-invariant subvarieties of V or V^n for some n? Given an
algebraic group acting regularly on an algebraic variety, what can you
say about the group when the action is 2-transitive?
We'll explain how these two questions are intimately related through
differential Galois theory. The talk won't assume anything except
familiarity with classical algebraic geometry over the complex
numbers.
If time permits, we'll also talk about a version of the problem where
one replaces the vector field with a rational self-map of the variety.
Wednesday March 6, 2024 at 3:00 PM in 636 SEO