Tona

Tonatiuh Matos Wiederhold

I'm a PhD candidate in mathematics at the University of Toronto. My research is in combinatorics, set theory, and theoretical computer science.

I care deeply about using my programming skills to solve hard problems and build tools that make abstract ideas useful.

Research Highlights

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.

Preprint

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

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.

Project website | Published paper

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? In this published paper 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.

Published paper

Machine Learning, Quantitative Finance, and AI

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.

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.

Project website

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.

Tools I built

MathNote

Markdown-based note sharing app with powerful LaTeX formatting. Share beautiful notes quick and easy, for free.

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