# Grayson Y

- Research Program Mentor

## MS Master of Science candidate

Expertise

Computer Science theory, particularly complexity theory or algorithms. Also interested in game theory, especially applications of computational methods to microeconomic theory and political science.

### Project ideas

#### Literature Review of Recent Work in Tiling Theory

Tiling theory is a fascinating field of mathematics with applications to DNA computing. Problems essentially relate to which pictures can be created by jigsaw puzzle pieces which can connect in different ways. This field is moving fast, and a lot of interesting work is being done, but a lot of loose ends are left behind that need to be tied up, and a lot of existing work needs to be made more accessible. This project would start with a crash course on complexity theory and methods in theoretical computer science, and then move into reading primary literature in tiling theory and compiling that work into a literature review describing current methods of computing with DNA.

#### A Study on the Mathematical Properties of Elections

In recent years, there has been a lot of discussion about which election mechanism is most effective at achieving various goals. Proposed mechanisms in united states elections include majority elections, the electoral college, approval voting, and ranked choice voting. All of these mechanisms have benefits and drawbacks, and it turns out that no perfect election mechanism can exist. In this project we will look at the work being done by political scientists, economists, mathematicians, and computer scientists to understand when elections fail, and what can be done to improve them.