- An asymptotically tight bound on the number of connected components of
realizable sign conditions, with S. Basu, and M.-F. Roy, submitted, (PDF,PS).
- Computing the first Betti number and the connected components of
semi-algebraic sets, with S. Basu, and M-F. Roy, to appear,
Foundations of Computational Mathematics, (PDF, PS).
- The combinatorial encoding of disjoint convex sets, with Goodman, J.E, to
appear, Combinatorica (PDF, PS).
- Convexity in topological affine planes, with
Raghavan Dhandapani, Jacob E. Goodman, Andreas Holmsen, Shakhar Smorodinsky,
Discrete and Computational Geometry, 38:243-257 (2007), (PDF,PS).
- Cremona convexity, frame convexity and a theorem of
Santaló
with Jacob E. Goodman, Andreas Holmsen, K. Ranestad, F. Sottile,
Advances in Geometry, 2006, Volume 6, Issue: 2, 301--321,
(PDF, PS).
- The Hadwiger transversal theorem for pseudolines, with S. Basu, J.E Goodman and A. Holmsen, Current Trends in
Combinatorial and
Computational Geometry: Papers from the Special Program at MSRI, MSRI Publications Volume 52, Cambridge University Press 2005, 87-97, (PDF, PS).
- Computing the Euler-Poincare Characteristic of Sign Conditions,
with S.Basu and M.-F. Roy, Computational Complexity, 14 (2005) 53-71, (PDF, PS).
- On the Betti Numbers of Sign Conditions,with S. Basu, and M.-F.
Roy, Proceedings of the AMS 133 (2005), 965-974, (PDF, PS).
- Interval sequences and the combinatorial encoding of planar
families of convex sets with Raghavan Dhandapani, Jacob E. Goodman,
Andreas Holmsen, Rev. Roumaine Math. Pures Appl. 50 (2005), no. 5-6,
537--553, (PDF, PS).
- On the Realizable Weaving Patterns of Polynomial Curves
in R^{3} with Saugata Basu and Raghavan Dhandapani Proceedings of the 12th International Symposium, Graph Drawing 2004, New York, NY, 30 September 2004, (PDF, PS).
- Computing the Dimension of a Semi-Algebraic Set, with S. Basu and
M.-F. Roy, Zap. Nauchn. Semin. POMI 316, 42-54 (2004), (PDF, PS).
- Computing Roadmaps of Semi-Algeraic Sets on a Variety,
with S.Basu, and M.-F. Roy, Journal of the American Mathematical Society
13 (2000), 55--82, (PDF,PS).