Geometric invariant theory

Have you ever played with shapes like triangles, circles or squares? Imagine you have some different shapes like these and you want to group them based on their properties. For example, you might group all the shapes that have three sides together, or all the shapes that have a curved edge together.

Now, let's say you have a special kind of shape called a "cone." A cone is a shape that looks like an ice cream cone or a party hat. You might notice that no matter how you turn the cone, it always looks the same. This is what we call an "invariant" - something that stays the same no matter what you do to it.

Geometric Invariant Theory is all about studying the properties of shapes and finding invariants. In other words, Geometric Invariant Theory helps us figure out which properties of a shape will always stay the same no matter how we move or transform it.

So, if you have a group of shapes and you want to know which ones will always look the same no matter what, you can use Geometric Invariant Theory to help you group them. It's kind of like playing a puzzle game where you have to match shapes based on their unique properties!