Complex convexity
Complex convexity is like playing with blocks! Imagine you have a bunch of blocks of different shapes and sizes that you want to stack up neatly. When you start stacking them, you want to make sure that each block is on top of another block, and that they are all pointing in the same direction. This is called being "concave".
Now imagine that you also have some curved blocks that don't fit neatly into your stack. When you try to put them in, they stick out and make your stack look messy. These blocks are "convex".
In the world of math, we use the same ideas to talk about shapes with more than just three dimensions. In a complex space, we use "complex numbers" instead of regular numbers. Complex numbers are like two blocks stuck together- one is the "real" number, and the other is the "imaginary" number.
A "convex shape" in a complex space is one where you can draw a straight line between any two points in the shape and the line will stay inside the shape. Just like with our blocks, a shape is "concave" if it has no curved parts that stick out.
So, in complex convexity, we use the ideas of stacking blocks and drawing straight lines to talk about shapes that are neat and tidy, with no messy bits sticking out.
Now imagine that you also have some curved blocks that don't fit neatly into your stack. When you try to put them in, they stick out and make your stack look messy. These blocks are "convex".
In the world of math, we use the same ideas to talk about shapes with more than just three dimensions. In a complex space, we use "complex numbers" instead of regular numbers. Complex numbers are like two blocks stuck together- one is the "real" number, and the other is the "imaginary" number.
A "convex shape" in a complex space is one where you can draw a straight line between any two points in the shape and the line will stay inside the shape. Just like with our blocks, a shape is "concave" if it has no curved parts that stick out.
So, in complex convexity, we use the ideas of stacking blocks and drawing straight lines to talk about shapes that are neat and tidy, with no messy bits sticking out.