Title: The Story of the Figure-Eight Knot: A journey through hyperbolic geometry, algebraic number theory, and beyond.
Speaker: Jeff Meyer
Speaker Info: University of Oklahoma
During this hour we will discuss the figure-eight knot. This seemingly mild mannered knot, regularly used by sailors and climbers as long as anyone can remember, is actually incredibly mathematically rich. In the early 1970's, Robert Riley showed that the complement of the figure-eight knot is in fact a hyperbolic 3-manifold. Its fundamental group, an interesting finitely presented group with two generators, is an arithmetic lattice in PSL(2,C) whose entries lie in a certain imaginary quadratic extension of Q. The use of algebraic number theoretic tools gives deep insight into the geometry of the knot complement as well as the figure-eight knot itself. This talk will be accessible to a general audience and there will be many pictures.Date: Friday, May 22, 2015