This page is old and unmaintained, preserved as a historical curiosity.
Please visit my current page.
It's hard to write generalities about mathematics, other than that
it's been very important to me throughout my life, both as a tool, and as a
discipline. Nowadays, mathematics classes, assignments, and research
take up most of my time. Eventually, I hope to add a section about enjoying mathematics
(instead of seeing it as difficult, scary, and remote, as seems to be the case
for most people). Coming sooner are links to detailed papers on my recent work.
In the meantime, here are brief descriptions:
Senior Thesis
I hope to derive a number of results concerning the spectral densities of sparse
random matrices. I have found some interesting results already.
Second Junior Paper
Spring semester ended up being two scout missions -- one involving numerics that
led up to my senior thesis, and the other attempting to solve the 4-dimensional
version of Dean Hoffman's cube puzzle. In 3D, the puzzle is: take 27
axbxc
blocks; how can you put together an (a+b+c)-sided cube (with holes) out
of them?
First Junior Paper
Fall semester, I independently (without searching for appropriate literature) tackled two
somewhat tricky graph theory problems. Both turned out to be solved when I checked them out
after completing my work. The first amounted to proving that the graphs with the maximum
possible girth of 2d+1 (given a fixed diameter d) are exactly the Moore graphs.
The second was to classify the self-dual, self-complement graphs embeddable in the plane and torus.
