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.[1]

Dr. Floyd discusses languages over the integer lattice.

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.[2]

In a 1980 paper[3] Floyd introduced a way to compactify a finitely generated group by adding to it a boundary which came to be called the Floyd boundary.[4][5] Floyd also wrote a number of joint papers with James W. Cannon and Walter R. Parry exploring a combinatorial approach to the Cannon conjecture[6][7][8] using finite subdivision rules. This represents one of the few plausible lines of attack of the conjecture.[9]

gollark: If you're a political activist or something, they can dredge up old data to discredit you.
gollark: Perhaps nobody there *does* care now. That's probably true, even. But let's imagine you become somewhat important some day, somehow?
gollark: Once they have your data, you can't revoke it.
gollark: And would.
gollark: They're also a giant company, so if it becomes profitable to just randomly sell data to anyone who pays £50, they could do that.

References
  1. William J. Floyd. Mathematics Genealogy Project. Accessed February 6, 2010
  2. Floyd, W.; Hatcher, A. Incompressible surfaces in punctured-torus bundles. Topology and its Applications, vol. 13 (1982), no. 3, pp. 263–282
  3. Floyd, William J., Group completions and limit sets of Kleinian groups. Inventiones Mathematicae, vol. 57 (1980), no. 3, pp. 205–218
  4. Karlsson, Anders, Free subgroups of groups with nontrivial Floyd boundary. Communications in Algebra, vol. 31 (2003), no. 11, pp. 5361–5376.
  5. Buckley, Stephen M.; Kokkendorff, Simon L., Comparing the Floyd and ideal boundaries of a metric space. Transactions of the American Mathematical Society, vol. 361 (2009), no. 2, pp. 715–734
  6. J. W. Cannon, W. J. Floyd, W. R. Parry. Sufficiently rich families of planar rings. Annales Academiæ Scientiarium Fennicæ. Mathematica. vol. 24 (1999), no. 2, pp. 265–304.
  7. J. W. Cannon, W. J. Floyd, W. R. Parry. Finite subdivision rules. Conformal Geometry and Dynamics, vol. 5 (2001), pp. 153–196.
  8. J. W. Cannon, W. J. Floyd, W. R. Parry. Expansion complexes for finite subdivision rules. I. Conformal Geometry and Dynamics, vol. 10 (2006), pp. 63–99.
  9. Ilya Kapovich, and Nadia Benakli, in Boundaries of hyperbolic groups, Combinatorial and geometric group theory (New York, 2000/Hoboken, NJ, 2001), pp. 39–93, Contemporary Mathematics, 296, American Mathematical Society, Providence, RI, 2002, ISBN 0-8218-2822-3 MR1921706; pp. 63–64


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