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Large orbits in finite group actions

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GR2W01 - Counting conjectures and beyond

We present a survey on results and open problems centering around the question of the existence of ”large” orbits in finite linear group actions. If a finite group G acts linearly on a finite vector space V, one is often interested in finding a large orbit in this action. The most extreme case is the existence of an orbit of size |G|. Such an orbit is called a regular orbit. In general, regular orbits need not exist, but they often do. Existence results forr egular orbits are very important, but when they do not exist, it is still interesting to study what can be said about the largest orbit in the action.

This talk is part of the Isaac Newton Institute Seminar Series series.

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