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A Rational Hilbert-Mumford Theorem

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If you have a question about this talk, please contact David Craven.

The classical Hilbert-Mumford Theorem gives a way of identifying closed orbits for algebraic groups acting on varieties (think groups of matrices acting on vector spaces and you won’t go far wrong). Identifying the closed orbits is very important if you want to form a quotient, for example. The theory is highly developed and works very well over algebraically closed fields, but problems arise as soon as you move to other fields (even the transition from complex to real numbers throws up some difficulties). In this talk I’ll describe a new approach to such problems which works over arbitrary fields. I’ll illustrate some of the key features using simple examples which shouldn’t need much more than a bit of linear algebra to understand.

This talk is part of the Algebra seminar series.

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