## The William P. Thurston Lecture Colloquium: Michael Hutchings (University of California, Berkeley)

**Talk title:** Two or Infinitely Many Reeb Orbits

**Abstract:** What is the minimum number of periodic orbits of a vector field on a three-manifold? In general the answer is zero. However on (closed) three-manifolds, Reeb vector fields, which are important in connection with Hamiltonian dynamics, always have at least one periodic orbit. We discuss a theorem proved with Dan Cristofaro-Gardiner and Dan Pomerleano asserting that under mild assumptions, every Reeb vector field on a (closed, connected) three-manifold has either two or infinitely many Reeb orbits.

**Date:** Tuesday, March 13

**Time:** 4:00 pm

**Room:** 135 TMCB