Mathematics

I am a mathematician... [Page last updated 2025-05-09]

Here is an ever-expanding always-incomplete list of things I have done, or possibly will do, that pertain to mathematics. This page will always be "under construction".

2025

• First author: Node2binary: Compact Graph Node Embeddings using Binary Vectors (accepted in WWW 2025)

2024

In 2024 I began Master's studies in Mathematics at the University of Waterloo (Ontario, Canada), studying quantum information and cryptography. But I still also have interests in machine learning.

2023

• First author: BINDER: Hierarchical Concept Representation through Order Embedding of Binary Vectors (accepted in KDD 2024)
• Second author: Predicting the impact of retinal vessel density on retinal vessel and tissue oxygenation using a theoretical model. This project was mostly programming, and I decided that I wasn't interested in it (no offense to the collaborators!).

2022

• August-December:
  • Undergraduate capstone project: Paper proving that a problem in voting theory is NP-hard.
  • Machine learning research: Bit vector embeddings to predict noun hierarchies. This is a joint work with Niloy Talukder and Dr. Mohammad Al Hasan, both from IUPUI.
  • Traveling HyperSales: Created 2D hyperbolic geometry (\(\mathbb{H}^2\)) rendering engine using Minkowski model internally, rendering to Poincaré disk model.
• 2022 June-August: NSF REU (Research Experience for Undergraduates). Surveyed cryptographic attribute-based access control systems and learned about bilinear cryptography. Joint work with Dr. Xukai Zou (IUPUI) and Kritika Verma (Syracuse University).

2021 and earlier

• 2021 December: Scored 38 points (rank 112 out of 2975) on the Putnam Mathematical Competition.
• 2021 June-August: Completely independent work on an obscure problem involving intersecting families of finite sets. Not published, but paper can be found here.
• 2020 January-August: Numerical experiments to determine if a particular dynamical system is hyperbolic. Not published.

I have a lot of desires for my future development. One thing that recently piqued my curiosity is "Fully Homomorphic Encryption", which is a cipher (secret code) where you can add and multiply the encrypted forms to add the original numbers. For example, suppose 4 encrypts to \(x\) and 5 to \(y\); then if you decrypt \(x+y\) you get 9, and \(x \cdot y\) gives you 20. This allows you to do computations "in the cloud", on e.g. Amazon's servers, without selling your soul or giving your data to Amazon. They just run the computations (e.g. "find the average body weight of all participants over 60") and give you the encrypted result, and you decrypt it and get your answer!