Abstract: 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 curves in R^2 and see how the CSF can reshape a curve.