Geometric Invariant Theory and Moduli Problems

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• Joshua Jackson (Oxford)
• Friday 19 October 2018, 15:00-16:00
• MR13.

If you have a question about this talk, please contact Ben Morley.

Geometric Invariant Theory, which one may characterise as ‘the art of quotienting algebraic varieties by group actions’, has long been a central tool in algebraic geometry. In particular, it is of tremendous use in the construction and study of moduli spaces: perhaps most notably the Deligne-Mumford moduli space of stable curves, and the moduli space of semistable coherent sheaves over a projective scheme. Less well known, however, is the recent generalisation of GIT to actions of non-reductive groups, due to Berczi-Doran-Hawes-Kirwan. I will attempt to explain why non-reductive GIT is much harder, what results are known about it, and some of the cool things we can do with it- including joint work generalising the two moduli spaces mentioned above.

This talk is part of the Junior Geometry Seminar series.

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