Richard M. Pollack

Richard M. Pollack
Born(1935-01-25)January 25, 1935
New York City, New York, U.S.
DiedSeptember 18, 2018(2018-09-18) (aged 83)
Montclair, New Jersey, U.S.
Alma materBrooklyn College
New York University
Scientific career
FieldsMathematics
InstitutionsCourant Institute of Mathematical Sciences, New York
Doctoral advisorHarold N. Shapiro[1]

Richard M. Pollack (January 25, 1935 – September 18, 2018[2][3]) was an American geometer who spent most of his career at the Courant Institute of Mathematical Sciences at New York University, where he was Professor Emeritus until his death.

Contributions

In combinatorics, Pollack published several papers with Paul Erdős and János Pach.[4][5][6][7]

Pollack also published papers in discrete geometry.[8][9][10][11][12][13][14][15][16][17][18] His work with Jacob E. Goodman includes the first nontrivial bounds on the number of order types and polytopes,[8] and a generalization of the Hadwiger transversal theorem to higher dimensions.[9] He and Goodman were the founding editors of the journal Discrete & Computational Geometry.[19]

In real algebraic geometry, Pollack wrote a series of papers with Saugata Basu and Marie-Françoise Roy,[13][14][15][16] as well as a book.[20]

Awards and honors

In 2003, a collection of original research papers in discrete and computational geometry entitled Discrete and Computational Geometry: The Goodman–Pollack Festschrift was published as a tribute to Jacob E. Goodman and Richard Pollack on the occasion of their 2/3 × 100 birthdays.[21]

In 2012, he became a fellow of the American Mathematical Society.[22]

A special memorial 556-page issue of Discrete & Computational Geometry for Pollack was published in October 2020.[23]

References

  1. ^ Richard M. Pollack at the Mathematics Genealogy Project
  2. ^ "Richard M. Pollack". Prout Funeral Home. Retrieved November 17, 2021.
  3. ^ "Ricky Pollack", sent by Joseph S. B. Mitchell on behalf of the Computational Geometry steering committee to the compgeom-announce mailing list, September 19, 2018
  4. ^ Erdős, Paul; Pach, János; Pollack, Richard; Tuza, Zsolt (1989), "Radius, diameter, and minimum degree", Journal of Combinatorial Theory, Series B, 47: 73–79, doi:10.1016/0095-8956(89)90066-x
  5. ^ de Fraysseix, Hubert; Pach, János; Pollack, Richard (1990), "How to draw a planar graph on a grid", Combinatorica, 10: 41–51, doi:10.1007/BF02122694, S2CID 6861762
  6. ^ Pach, János; Pollack, Richard; Welzl, Emo (1993), "Weaving patterns of lines and line segments in space", Algorithmica, 9 (6): 561–571, doi:10.1007/bf01190155, S2CID 28034074
  7. ^ Agarwal K., Pankaj; Aronov, Boris; Pach, János; Pollack, Richard; Sharir, Micha (1997), "Quasi-planar graphs have a linear number of edges", Combinatorica, 17: 1–9, CiteSeerX 10.1.1.696.1596, doi:10.1007/bf01196127, S2CID 8092013
  8. ^ a b Goodman, Jacob E.; Pollack, Richard (1986), "There are asymptotically far fewer polytopes than we thought", Bulletin of the American Mathematical Society, 46: 127–129, doi:10.1090/s0273-0979-1986-15415-7
  9. ^ a b Goodman, Jacob E.; Pollack, Richard (1988), "Hadwiger's transversal theorem in higher dimensions", Journal of the American Mathematical Society, 1 (2): 301–309, doi:10.1090/S0894-0347-1988-0928260-1
  10. ^ Goodman, Jacob E.; Pollack, Richard (1983), "Multidimensional sorting", SIAM Journal on Computing, 12 (3): 484–507, doi:10.1137/0212032
  11. ^ Goodman, Jacob E.; Pollack, Richard (1984), "Semispaces of configurations, cell complexes of arrangements", Journal of Combinatorial Theory, Series A, 37 (3): 257–293, doi:10.1016/0097-3165(84)90050-5
  12. ^ Goodman, Jacob E.; Pollack, Richard (1995), "Foundations of a theory of convexity on affine Grassmann manifolds", Mathematika, 42 (2): 305–328, CiteSeerX 10.1.1.48.3232, doi:10.1112/s0025579300014613
  13. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (1996), "On the number of cells defined by a family of polynomials on a variety", Mathematika, 43: 120–126, doi:10.1112/s0025579300011621
  14. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (1996), "On the combinatorial and algebraic complexity of quantifier elimination", Journal of the ACM, 43 (6): 1002–1045, CiteSeerX 10.1.1.49.3736, doi:10.1145/235809.235813, S2CID 9536962
  15. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (2000), "Computing roadmaps of semi-algebraic sets on a variety", Journal of the American Mathematical Society, 13: 55–82, doi:10.1090/S0894-0347-99-00311-2
  16. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (2009), "An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions", Combinatorica, 29 (5): 523–546, arXiv:math/0603256, doi:10.1007/s00493-009-2357-x
  17. ^ Goodman, Jacob E.; Pollack, Richard; Sturmfels, Bernd (1990), "The intrinsic spread of a configuration in R^d", Journal of the American Mathematical Society, 3 (3): 639–651, doi:10.1090/s0894-0347-1990-1046181-2
  18. ^ Cappell, Sylvain; Goodman, Jacob E.; Pach, János; Pollack, Richard; Sharir, Micha; Wenger, Rephael (1994), "Common tangents and common transversals", Advances in Mathematics, 106 (2): 198–215, doi:10.1006/aima.1994.1056
  19. ^ "Discrete & Computational Geometry". Discrete & Computational Geometry. Springer Science+Business Media. Retrieved November 17, 2021.
  20. ^ Basu, Saugata; Pollack, Richard; Roy, Marie-Françoise (2003), Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics, vol. 10, Springer-Verlag
  21. ^ Discrete and Computational Geometry: The Goodman-Pollack Festschrift. Algorithms and Combinatorics. Springer. 2003. ISBN 9783540003717.
  22. ^ List of Fellows of the American Mathematical Society, retrieved 2013-05-26.
  23. ^ "Discrete & Computational Geometry | Volume 64, issue 3". SpringerLink. Retrieved 2020-11-26.
  • Pollack, Richard (1962), Some Tauberian theorems in elementary prime number theory (Ph.D. Thesis), New York University.
  • Goodman, Jacob E.; Pach, János; Pollack, Richard, eds. (2008), Surveys on Discrete and Computational Geometry: Twenty Years Later, Contemporary Mathematics, vol. 453, American Mathematical Society.