Richard M. Pollack

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Richard M. Pollack
Richard M. Pollack.jpg
Born (1935-01-25) January 25, 1935 (age 81)
New York[clarification needed]
Nationality  United States
Fields Mathematics
Institutions Courant Institute, New York
Alma mater Brooklyn College
New York University
Doctoral advisor Harold N. Shapiro
Known for

Weaving patterns of lines
Geometric transversal theory
Roadmaps of semi-algebraic sets
Algorithms in real algebraic geometry

Discrete & Computational Geometry (journal)

Richard M. Pollack is a geometer who has spent most of his career at the Courant Institute of New York University, where he is now Professor Emeritus.[2] In 1986 he and Jacob E. Goodman were the founding co-editors-in-chief of the journal Discrete and Computational Geometry (Springer-Verlag).[3]


In combinatorics he is known principally for his work with Paul Erdős and János Pach [4] [5] [6] .[7] In discrete geometry he is known for a number of basic concepts and results[vague][8] [9] [10] [11] ,[12] joint with his long term collaborator, Jacob E. Goodman;[13] of City College, City University of New York, and some with others [14] [15] [16] [17] [18][19] his work with Goodman includes such results as 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] In real algebraic geometry he is known principally for a series of papers authored jointly with Saugata Basu and Marie-Françoise Roy [14][15][16][17] and for their 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[21] was published as a tribute to Jacob E. Goodman and Richard Pollack on the occasion of their 2/3 × 100 birthdays.

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


  1. ^ [1]
  2. ^ [2]
  3. ^
  4. ^ Erdős, Paul; Pach, János; Pollack, Richard; Tuza, Zsolt (1989), "Radius, diameter, and minimum degree", J. Combin. Theory Ser. 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 
  6. ^ Pach, János; Pollack, Richard; Welzl, Emo (1993), "Weaving patterns of lines and line segments in space", Algorithmica, 9: 561–571, doi:10.1007/bf01190155 
  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, doi:10.1007/bf01196127 
  8. ^ a b Goodman, Jacob E.; Pollack, Richard (1986), "There are asymptotically far fewer polytopes than we thought", Bull. Amer. Math. Soc., 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", J. Amer. Math. Soc. (1): 301–309 
  10. ^ Goodman, Jacob E.; Pollack, Richard (1983), "Multidimensional sorting", SIAM J. Comput., 12: 484–507, doi:10.1137/0212032 
  11. ^ Goodman, Jacob E.; Pollack, Richard (1984), "Semispaces of configurations, cell complexes of arrangements", J. Combinatorial Theory Ser. A, 37: 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: 305–328, doi:10.1112/s0025579300014613 
  13. ^
  14. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-François (1996), "On the number of cells defined by a family of polynomials on a variety", Mathematika, 43: 120–126, doi:10.1112/s0025579300011621 
  15. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-François (1996), "On the combinatorial and algebraic complexity of quantifier elimination", J. ACM, 43: 1002–1045, doi:10.1145/235809.235813 
  16. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-François (2000), "Computing roadmaps of semi-algebraic sets on a variety", J. Amer. Math. Soc., 13: 55–82 
  17. ^ a b Basu, Saugata; Pollack, Richard; Roy, Marie-François (2009), "An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions", Combinatorica, 29: 523–546, doi:10.1007/s00493-009-2357-x 
  18. ^ Goodman, Jacob E.; Pollack, Richard; Sturmfels, Bernd (1990), "The intrinsic spread of a configuration in R^d", J. Amer. Math. Soc., 3: 639–651, doi:10.1090/s0894-0347-1990-1046181-2 
  19. ^ Cappell, Sylvain; Goodman, Jacob E.; Pach, János; Pollack, Richard; Sharir, Micha; Wenger, Rephael (1994), "Common tangents and common transversals", Advances in Math., 106: 198–215, doi:10.1006/aima.1994.1056 
  20. ^ Basu, Saugata; Pollack, Richard; Roy, Marie-François (2003), Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics, 10, Springer-Verlag 
  21. ^
  22. ^ List of Fellows of the American Mathematical Society, retrieved 2013-05-26.
  • 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, 453, Amer. Math. Soc. .