A compilation of things I've written for courses and my research.
(All the ones that I like enough to put online, anyway.)
My principal research interest is the theory of F-automatic
sets, as introduced by Jason Bell and Rahim Moosa in
F-sets and finite automata. My
thesis contains an introduction to the
topic and a compilation of my contributions to the area.
My results also appear in two papers:
my work on the general theory of F-automatic sets can be found in
Contributions to the
theory of F-automatic sets, which has been accepted in the
Journal of Symbolic Logic; and some results specific to the case
of the additive group of integers appear in
Automata and tame
expansions of (Z,+), which has been accepted in the Israel
Journal of Mathematics.
In winter 2019, I took PMATH 810, a course in Banach algebras
and operator theory. For the final project, I wrote a paper on
UHF algebras.
I completed my master's essay in spring 2016 under the
supervision of
Rahim Moosa;
I studied applications of model theory to the study of formal
languages.
In winter 2016, I took PMATH 945, a topics course in category
theory and homological algebra. For the final project, I wrote
a paper on monads, algebras over monads, and an interpretation of
the latter via universal algebra.
In fall 2013, I took CS 758, a course in cryptography and
network security. For the final project, Eddie Cheung, Patrick
Lee, and I wrote a paper on secure computations using playing
cards. The paper gives a broad overview of the field, presents a
new perspective on existing techniques, and presents a new
card-based algorithm for computing the AND of two bits.
I did a research term in model theory under the supervision of
Rahim Moosa
during the spring term of 2013.
This resulted in the following documents being
brought into being: