William A. Veech

William A. Veech is the Edgar O. Lovett Professor of Mathematics at Rice University.[1] His research concerns dynamical systems; he is particularly known for his work on interval exchange transformations, and is the namesake of the Veech surface.

Education

Veech graduated from Dartmouth College in 1960,[1] and earned his Ph.D. in 1963 from Princeton University under the supervision of Salomon Bochner.[1][2]

Contributions

An interval exchange transformation is a dynamical system defined from a partition of the unit interval into finitely many smaller intervals, and a permutation on those intervals. Veech and Howard Masur independently discovered that, for almost every partition and every irreducible permutation, these systems are uniquely ergodic, and also made contributions to the theory of weak mixing for these systems.[3] The Rauzy–Veech–Zorich induction map, a function from and to the space of interval exchange transformations is named in part after Veech: Rauzy defined the map, Veech constructed an infinite invariant measure for it, and Zorich strengthened Veech's result by making the measure finite.[4]

The Veech surface and the related Veech group are named after Veech, as is the Veech dichotomy according to which geodesic flow on the Veech surface is either periodic or ergodic.[5]

Veech played a role in the Nobel-prize-winning discovery of buckminsterfullerene in 1985 by a team of Rice University chemists including Richard Smalley. At that time, Veech was chair of the Rice mathematics department, and was asked by Smalley to identify the shape that the chemists had determined for this molecule. Veech answered, "I could explain this to you in a number of ways, but what you've got there, boys, is a soccer ball."[6][7]

Veech is the author of A Second Course in Complex Analysis (W. A. Benjamin, 1967; Dover, 2008, ISBN 9780486462943).[8][9][10]

Awards and honors

In 2012, Veech became one of the inaugural fellows of the American Mathematical Society.[11]

References

  1. 1 2 3 Faculty profile, Rice University, retrieved 2015-03-01.
  2. ↑ William A. Veech at the Mathematics Genealogy Project
  3. ↑ Hunt, B. R.; Kaloshin, V. Yu. (2010), "Prevalence", in Broer, H.; Takens, F.; Hasselblatt, B., Handbook of Dynamical Systems, Volume 3, Elsevier, pp. 43–88, ISBN 9780080932262. See in particular p. 51.
  4. ↑ Bufetov, Alexander I. (2006), "Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of abelian differentials", Journal of the American Mathematical Society 19 (3): 579–623, doi:10.1090/S0894-0347-06-00528-5, MR 2220100.
  5. ↑ Smillie, John; Weiss, Barak (2008), "Veech's dichotomy and the lattice property", Ergodic Theory and Dynamical Systems 28 (6): 1959–1972, doi:10.1017/S0143385708000114, MR 2465608.
  6. ↑ Edelson, Edward (August 1991), "Buckyball: the magic molecule", Popular Science: 52–57, 87. The quote is on p. 55.
  7. ↑ Ball, Philip (1996), Designing the Molecular World: Chemistry at the Frontier, Princeton Science Library, Princeton University Press, p. 46, ISBN 9780691029009.
  8. ↑ Review of A Second Course in Complex Analysis by E. Hille, MR 0220903.
  9. ↑ Wenzel, H., "W. A. Veech, A Second Course in Complex Analysis", Book Reviews, Journal of Applied Mathematics and Mechanics 48 (7): 502–503, doi:10.1002/zamm.19680480725.
  10. ↑ Stenger, Allen (April 24, 2008), "A Second Course in Complex Analysis, William A. Veech", MAA Reviews (Mathematical Association of America).
  11. ↑ List of Fellows of the American Mathematical Society, retrieved 2015-03-01.
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