Event Series
Event Type
Seminar
Friday, October 25, 2019 2:00 PM
Shintaro Fushida-Hardy

The uniformization theorem, dating back to the 19th century, provides a classification of surfaces up to conformal equivalence. Classical proofs rely on harmonic analysis techniques, but with the advent of Ricci flow, spicy new proofs have been created. In this talk we’ll introduce the relevant notions from Riemannian geometry, define Ricci flow, and use it to prove (modulo details) the uniformization theorem for closed oriented surfaces. The large genus cases are the easiest to work with, but uniformization on the sphere turns out to require a clever trick. You guessed it, the trick is entropy.