## Yibo Gao

Research and Innovation Scholar

Computer Search for Finite Saturated Pure Partial Planes of Certain Orders

2015–2016

Henry Cohn

Whether a finite projective plane of certain order exists has been a famous open problem for a long time. In this project, I will focus on another related mathematical object, saturated pure partial planes, which have not been studied before. Computers will be used to search for all saturated pure partial planes of small orders whose intrinsic geometric properties will be studied afterwards. The next step will be finding regular patterns in them and generalizing the results to higher orders. The application of computers to mathematics has become a trend and with stronger and stronger computational power of modern computers, interesting results are guaranteed to appear.

My project is categorized into either theoretical computer science or applied math. My primary major is math and I have a decent background in algorithms and complexity so I think I am prepared. What I hope to learn most is the correct way of doing research. My supervisor gave me a general topic and I came up with the project myself so I am quite unsure whether interesting things will show up, but I have a chance since computers these days are powerful.