Pure Maths Colloquium: A Rational Hilbert-Mumford Theorem
9 March 2015 16:00 in CM221
This talk will be about linear algebraic groups (read "groups of matrices") acting on affine algebraic varieties (read "subsets of linear spaces"). The Hilbert-Mumford Theorem is a very useful tool for studying such actions - since the group and the variety carry a topology, one wants to identify the closed orbits and the Hilbert-Mumford Theorem gives a way to do this.
The study of such actions has a distinguished history (going back to Hilbert, as the name of the theorem suggests) and is very well-developed over algebraically closed fields. However, when one moves to non-algebraically closed fields, the situation is very different. I'll present a new idea for making progress here, illustrated with some straightforward examples. I won't assume any knowledge beyond an idea of what a group action is and some basic concepts from Linear Algebra.
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