Subgroups and Wicks Forms

Mathematics Research

My undergraduate degree is in mathematics and I also completed an MPhil in pure mathematics. My thesis was in the area of geometric group theory. The main result is a one-to-one correspondence between a subset of the free subgroups of the Modular group of given index (n) and maximal orientable Wicks forms of length n = 12g – 1 (for genus g). The one-to-one correspondence is achieved using tools from graph theory and combinatorics and results in a formula for the number of conjugacy classes of a specific type of free subgroup in the Modular Group with given index. If you are interested, here is my thesis.