Richard M. Pollack

From Wikipedia, the free encyclopedia
Jump to: navigation, search
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
[1]
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]

Contributions[edit]

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]

References[edit]

  1. ^ [1] http://genealogy.math.ndsu.nodak.edu/id.php?id=33222
  2. ^ [2] http://math.nyu.edu/people/
  3. ^ http://www.springer.com/journal/454
  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. ^ http://math.sci.ccny.cuny.edu/person/list
  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. ^ http://www.springer.com/mathematics/geometry/book/978-3-540-00371-7
  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. .