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
--- Probability Theory (more
specifically, Gaussian Radon transforms on infinite-dimensional
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
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
--- Ramsey Theory (in
particular, ultrafilter methods in Ramsey Theory).
--- other topics in standard Probability
Theory, as well as the
probabilistic method applied to combinatorics.
Other 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 Epistemology with a
focus on a priori knowledge.