URSP Student Timothy Reid studies the Elements of the Rank 2 Free Group

I am Tim Reid and I am a senior mathematics major. I am doing mathematics research in the field of abstract algebra. Research in pure mathematics is trying to solve unsolved problems that are brought up in previous research literature. In my research project I am studying elements of a set called the rank 2 free group. The elements of the free group are called words, and we are studying how these words can be used to represent deformations of objects in the real projective plane.

I began this project when I started working at the Mason Experimental Geometry Lab (MEGL). At MEGL we study unsolved math problems by using a method called “experimental mathematics.” Experimental mathematics refers to writing computer programs to generate data sets related to the problem, looking for patterns in the data set, using the patterns to form conjectures, and then trying to prove those conjectures. This semester we began investigating how the words can be used to represent the deformations. To assist in understanding how the words can represent the deformations, I am writing a computer program visualize the deformations in the real projective plane. So far I have learned how the deformations work in general but we are still investigating how the words are related to them.

My goal after I graduate is to enter a PhD program in mathematics and then eventually work as a researcher in mathematics. This research project is my first research experience in mathematics and it has only increased my interest in the subject.