I will overview some important milestones in the development of the Invariant Theory from its classical times to modern days, leading into a discussion of the current progress in theory, computation, and applications. The highlights include Hilbert’s basis theorem, geometric invariant theory, differential algebra of invariants, the moving frame approach, Lie’s work on symmetries of differential equations, and Tresse’s theorem. I will try to emphasize the relationships between the algebraic and differential theories.

This talk is a teaser to the special topic class I will offer in Spring 2022. Students are encouraged to join.

Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact Peter McGrath host to get the link.