Department of Mathematics

University of British Columbia

Vancouver, Canada

Email: ryano (at) math (dot) ubc (dot) ca

Office: AA125

Here is a link to my Curriculum Vitae.

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.