Mathematics PhD candidate
Department of Mathematics
University of British Columbia
Email: ryano (at) math (dot) ubc (dot) ca
My research interests are in combinatorics. Most specifically in discrete geometry and the use of algebra in combinatorial problems. Lately I have been looking at the possible structure that a collection of lines in the plane can have where each line contains many points of a cartesian product. I have also been looking at a special case of the Erdős unit distance problem. I am also interested in rational distance sets in general position in the plane.
- R. Schwartz, Using the subspace theorem to bound unit distances. Moscow Journal of Combinatorics and Number Theory, 3(1):108-117, 2013.
- R. Schwartz, J. Solymosi and F. de Zeeuw, Extensions of a result of Elekes and Rónyai. Journal of Combinatorial Theory, Series A, 120(7):1695-1713, 2013.
- R. Schwartz, J. Solymosi and F. de Zeeuw, Rational distances with rational angles. Mathematika, 58(2):409-418, 2012.
- R. Schwartz, J. Solymosi and F. de Zeeuw Simultaneous arithmetic progressions on algebraic curves. International Journal of Number Theory, 7(4):921-931, 2011.
- C. Bhika, S. Ewert, R. Schwartz, M. Waruhiu, Table-driven context-free picture grammars. International Journal of Foundations of Computer Science, 18(6):1151-1160, 2007.