Splash Biography

If you're interested in math, you might have heard that a type of mathematician called a topologist thinks that a coffee cup and a donut are the same, because we can stretch and squish one into another and back. But how do we know that we can't deform anything into anything else? Are a coffee cup and a donut really the same in some special way, or are they no more similar than a circle and a sphere, or a line and a plane? In this talk we will answer these questions and more by giving a quick and dirty introduction to a powerful tool called homology, which is used in almost all fields of modern mathematics to tell objects apart and prove deep theorems about them.