I was a graduate student in the Mathematics department of the State University of New York at Stony Brook. Miraculously, my dissertation was accepted by the Graduate School. Feel free to read it if you have particularly masochistic tendencies. My advisor was Professor Scott Sutherland.

The project was in complex dynamics (yeah, chaos is cool): we investigated whether the Mandelbrot set is locally connected at the Feigenbaum point. What does this mean? It means if one were to look at the Mandelbrot set in an arbitrarily small neighborhood of the parameter value (roughly) equal to 1.401155, would one be able to connect any two point in this neighborhood by a path lying entirely in the Mandelbrot set. We used renormalization techniques and computers to investigate, and pretty much showed that, indeed the Mandelbrot set is locally connected at the Feigenbaum point (admittedly there are two small gaps in my proof). The picture on the right is the first picture the computer drew. Check out some cooler ones. Some final pictures are available in the dissertation itself.