My senior thesis was entitled: "Optimal topological generators of U(1) and short paths in Xp,q and SU(2)." I was fortunate to be advised by Peter Sarnak.
Chapter 1 appears as "Optimal topological generators of U(1)" in Journal of Number Theory. Chapter 2.1 describes related papers of Sardari and Carvalho Pinto and Petit. Chapter 2.2 appears as "Short paths in PU(2)" in Quantum Information and Computation.
Click here for a PDF of the slides I used for my defense. Click here for a Haskell implementation of the main algorithm of Chapter 2.2, and click here for a Mathematica implementation of the same.
This thesis was honored with the Middleton Miller '29 Prize for best independent work.