Work
Here are a few things that I have written in the past.
Surface classification and geography. This is an essay on surface classification, geography and moduli spaces of surfaces with given Chern invariants; set by Prof. Pelham Wilson. It contains a very general review of the basic setting of the birational geometry of surfaces.; as well as a proof of Bombieri's result on the birationality of the canonical maps, and a sketch of Gieseker's theorem stating that there is a moduli space parametrizing classes of surfaces with given Chern invariants.
Maximal non-commuting subsets of groups . This is the result of my one-term project at UCLA . I was introduced to this problem by Ergun Yalcin. Terence Tao at UCLA was kind help me on this project. The report contains a few results that I came upon during the project as well as the classification of extraspecial p-groups as explained by Peter Cameron. (The nice trick used to show the maximality of the known non-commuting subset for S(2,n) is Tao's).
Computational Problems in the Braid Group with Applications to Cryptography. This is the expository essay I wrote as the final project for Olga Radko's knot theory class. It contains a quick introduction to computational complexity, links and braids, as well as some computational considerations concerning braids, including the word and conjgacy problems, cryptography and the non-minimal braids problem.