Tiling Theory

REU Program at University of Washington, Bothell 

I worked with two other undergraduate students and Dr. Casey Mann to solve open questions in the field of Tiling Theory through a pure math Research Experience for Undergraduates (REU) program funded by the NSF. 

• Created an algorithm in C++ that provided some of the first examples of 3D solids with finite Heesch numbers. Optimized and parallelized this code to run efficiently on 96 CPUs through the HYAK super-computing cluster at UW Seattle.

• Proved the theorem: “For each n ≥ 3, there exists a tile with the n-enclosing property that admits both a periodic and non-periodic monohedral tiling.”

• Provided a counterexample to the theorem: “The neighborhood of any given tile in a monohedral tiling will be equivalent to the patch generated by that tile.”