Speaker: Steve Trettel

Title: The Many Faces of the Trefoil Knot Complement

 

Some of you may remember last year I gave a talk about the space of lattices in the plane and the trefoil knot.  This talk is not a sequel, but was inspired by that stuff - over the past year I have tracked down a couple of different objects whose "deformation spaces" are homeomorphic to the trefoil complement, including the space of certain cubic equations, SL(2,Z) invariant tilings of H^2 and (at most 3 element) subsets of the circle.  My goal here is to explain some of the cool things that can be gained from taking these different perspectives: for example considering cubic equations will give us a nice description of the trefoil knot group and considering hyperbolic tilings will help us visualize the SL2 geometry of the complement.

 

Mostly, this talk is an excuse for me to show you guys some neat videos I have been producing in Mathematica related to all of this - so even if the trefoil knot is not your thing there should be enough pretty pictures to make it fun!