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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Pure Maths Colloquium: A Rational Hilbert-Mumford Theorem

Presented by Michael Bate, University of York

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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