Richard M. Pollack
|Richard M. Pollack|
January 25, 1935 |
New York[clarification needed]
|Institutions||Courant Institute, New York|
|Alma mater||Brooklyn College
New York University
|Doctoral advisor||Harold N. Shapiro
Weaving patterns of lines
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. In 1986 he and Jacob E. Goodman were the founding co-editors-in-chief of the journal Discrete and Computational Geometry (Springer-Verlag).
In combinatorics he is known principally for his work with Paul Erdős and János Pach    . In discrete geometry he is known for a number of basic concepts and results[vague]    , joint with his long term collaborator, Jacob E. Goodman; of City College, City University of New York, and some with others      his work with Goodman includes such results as the first nontrivial bounds on the number of order types and polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. In real algebraic geometry he is known principally for a series of papers authored jointly with Saugata Basu and Marie-Françoise Roy  and for their book.
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.
-  http://genealogy.math.ndsu.nodak.edu/id.php?id=33222
-  http://math.nyu.edu/people/
- 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
- 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
- Pach, János; Pollack, Richard; Welzl, Emo (1993), "Weaving patterns of lines and line segments in space", Algorithmica, 9: 561–571, doi:10.1007/bf01190155
- 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
- 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
- Goodman, Jacob E.; Pollack, Richard (1988), "Hadwiger's transversal theorem in higher dimensions", J. Amer. Math. Soc. (1): 301–309
- Goodman, Jacob E.; Pollack, Richard (1983), "Multidimensional sorting", SIAM J. Comput., 12: 484–507, doi:10.1137/0212032
- 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
- Goodman, Jacob E.; Pollack, Richard (1995), "Foundations of a theory of convexity on affine Grassmann manifolds", Mathematika, 42: 305–328, doi:10.1112/s0025579300014613
- 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
- 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
- Basu, Saugata; Pollack, Richard; Roy, Marie-François (2000), "Computing roadmaps of semi-algebraic sets on a variety", J. Amer. Math. Soc., 13: 55–82
- 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
- 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
- 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
- Basu, Saugata; Pollack, Richard; Roy, Marie-François (2003), Algorithms in Real Algebraic Geometry, Algorithms and Computation in Mathematics, 10, Springer-Verlag
- 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.