I spent the summer of 2001 at the Research Experiences for Undergraduates (REU) program at Louisiana State University. While there, I worked with William Hoffman and Robert Perlis in a mixture of graph, group and homology theories. At the end of the summer, I wrote a paper "Graph Jacobians and Mackey Functors" which will hopefully be submitted for publication in the near future (see Research > Preprints for an abstract).

In my Ph.D. thesis, "Topological splittings of spectra related to tmf," I give a conjecture regarding the splitting of the Tate spectrum of tmf (the connective spectrum representing topological modular forms) at the prime 2. The main theorem regards the splitting of the spectrum bo ^ tmf, which is analagous to the splitting bo ^ bo into summands related to the integral Brown-Gitler spectra. I use this splitting to provide ample groundwork toward the proof of the conjecture. Furthermore, my interests focused on applications of this splitting to give possible approaches to studying the more complicated structure of the stable cohomology operations of tmf, as well as the structure of MO(8). My advisors were Paul Goerss and Mark Mahowald.