Welcome.
This site is part of an ongoing project created by me that aims to facilitate sharing academic content by implementing a live markdown editor with powerful sharing capabilities. You can test my free note sharing app here:
I’m also working on a framework that will allow researchers to transform any -based file into a beautifully-rendered live website like this one. Feel free to peruse my notes using the navigation panel on the left.
Please see my main website to explore my research projects:
Selected projects
Deep Computations
A unified framework linking machine learning and compactness, exemplifying how the topology of function spaces encodes the algorithmic and epistemic limits of prediction.
Border Tracer
A new border-tracing algorithm that generalizes classical image segmentation techniques from pixel-based grids to arbitrary polygonal tilings in abstract adjacency graphs.
Project website | Paper to be published
Merton Jump Diffusion Model Calibration with Machine Learning
Extended the Black-Scholes / geometric Brownian motion model by adding Poisson jumps to capture sudden market moves; calibrated the parameters on historical stock price data using a limited-memory BFGS optimization algorithm, using finite differences to estimate the Merton deltas; and compared hedging strategies across multiple assets, finding improved performance on jumpy stocks.
QuantGPT
An agentic AI framework that incorporates knowledge-graph reasoning with cryptographic vulnerability scanning through large language models (LLMs) to identify potential post-quantum security threats.
Developed as Visiting Scholar at the Fields Institute for Mathematical Sciences, in partnership with a major Canadian bank.
Fer Group
A comprehensive object-oriented framework for the study of graph automorphism groups and more, including an optimally indexed SQL database for statistical inference and hypothesis testing.
Neuro Shannon
We leveraged recent advancements in Graph Neural Networks to optimize a noisy communication network to estimate its Shannon capacity.
Wiki Explorer
A pipeline that fully automates educational video creation and streaming based off Wikipedia entries without any intervention.
Set Theory Forces Probability
Take the naturals as vertices of an infinite graph and flip a coin to decide whether each pair is an edge or not. Do this twice and you obtain two different infinite graphs. What is the probability that they are isomorphic? I give a new proof that the answer is, surprisingly, 100%.
Infinite Game Theory
We construct a dense linear order of arbitrary infinite cardinal on which Player II has a winning strategy on all payoff sets for the Cantor game.
You can see my full list of projects and publications here.