title: William Floyd (mathematician)
text: # William Floyd (mathematician)
  
  William J. Floyd is an American mathematician specializing in topology. He is currently a professor at Virginia Polytechnic Institute and State University. Floyd received a PhD in mathematics from Princeton University 1978 under the direction of William Thurston.
  
  ## Mathematical contributions
  
  Most of Floyd's research is in the areas of geometric topology and geometric group theory.
  
  Floyd and Allen Hatcher classified all the incompressible surfaces in punctured-torus bundles over the circle.
  
  In a 1980 paper Floyd introduced a way to compactify a finitely generated group by adding to it a boundary which came to be called the Floyd boundary. Floyd also wrote a number of joint papers with James W. Cannon and Walter R. Parry exploring a combinatorial approach to the Cannon conjecture using finite subdivision rules. This represents one of the few plausible lines of attack of the conjecture.
  
  