What numerical characteristics do geometric shapes have? You will probably think of the length of a curve, or the volume of a 3-dimensional shape, or an angle between two directions in space. In this talk we will discuss a characteristic of curves called curvature, which measures the sharpness of a turn while moving along a path.
It turns out that this characteristic controls the process of curve evolution, called the CSF, ``curve shortening flow". We will talk about some important work that was done in the 80s on embedded curves in $\mathbb{R}^2$ and see how the CSF can reshape a curve.