Richard M. Pollack

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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[edit]

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[edit]

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[edit]

  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.
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