Main mathematical interests:
My current research interests lie
in the applications of Nonstandard Analysis. In particular, I have been working on applications to:
--- Combinatorial Number Theory (more specifically, different measures of
density of subsets of natural numbers, and structural properties such as
existence of arithmetic/geometric progressions of prescribed lengths,
etc., of those subsets).
--- Probability Theory (more specifically, Gaussian Radon transforms on infinite-dimensional spaces).
Though these two areas may seem unrelated at first (and they
really are, for the most part), there are some common themes when
studying them using "nonstandard tools." For example, the general
construction of a Loeb measure space
is a tool that can be made useful in both these situations
(and in many other situations).
Other interests that I am NOT actively working on right now:
Aside from these topics, I enjoy exploring other related areas such as:
--- Model Theory (nonstandard analysis can actually be described as applied model theory).
Ergodic Theory (I am mainly interested in its number theoretic
applications, though I am also interested in the "nonstandard
formulations" of many purely ergodic theoretic concepts).
--- Ramsey Theory (in particular, ultrafilter methods in Ramsey Theory).
--- other topics in standard Probability Theory, as well as the probabilistic method applied to combinatorics.
than being generally philosophically minded (and a sceptic of sorts),
my interest in philosophy grew out of working in mathematical logic
(model theory) and being curious to understand how philosophers
study/view the same topics in logic. Being
a dual mathematics-philosophy student, it is natural for me to care
about the history and philosophy of mathematics as well. Here
is a research article on the history and epistemology of infinitesimals
(and infinites) that I wrote for a Philosophy course named "Scientific
Knowledge" in 2016. I hope to polish on this and work more along this
line in future. This semester, I am taking a course on Kant, and will
hopefully be trying to learn the Neo-Kantian stance on infinitesimals as a personal project.