Tuesday, November 7, 2017 - 15:00 to 15:50

Thackeray 427

### Abstract or Additional Information

What does a random knot or link look like? If one picks a link "at random", do you expect to get a hyperbolic link? If you do, how big should the hyperbolic volume be? There's a number of different ways of taking random links -- in this talk, I will describe one possible model based on random link diagrams in the plane. The work of Gilles Schaeffer gives us a way to work with these diagrams computationally, so I will present actual data computed in the geometry package *SnapPy*. For the question of hyperbolicity, I'll show how one can prove the following: a random link diagram is typically a satellite, but a random *alternating* link diagram is hyperbolic with volume roughly linear in the number of crossings.