Seminar

A lot of good math starts by taking an existence theorem and asking ``How many?'' or ``How big?'' or ``How fast''. The best-known example may be the Riemann hypothesis. Euclid proved that infinitely many primes exist, and the Riemann hypothesis describes how quickly they grow.

I'll discuss what happens when you apply the same idea to simple connectivity. In a simply-connected space, any closed curve is the boundary of some disc, but how big is that disc? And what can that tell you about the geometry of the space?