I am a PhD candidate in the Department of Combinatorics and Optimization at the University of Waterloo, supervised by Peter Nelson. My research focuses on extremal and structural problems in matroid theory and graph theory. I am also interested in proof formalization and contribute to Peter Nelson's Lean repository on Matroids (see Lean section).
Before beginning my PhD, I completed a Master of Mathematics at the University of Waterloo in 2022, also under the supervision of Peter Nelson. I received my undergraduate degree from the Universidad Nacional Autónoma de México.
You can find my CV here. It was last updated August 2026.
You can contact me at mriverao (at) uwaterloo (dot) ca
Outside mathematics, I enjoy climbing, baking, going to the gym. I really like cats.
On the density of matroids omitting a complete-graphic minor
With Peter Nelson and Sergey Norin
Accepted for publication in Transactions of the American Mathematical Society
Modularity, extensions and connectivity in infinite matroids
With Mattias Ehatamm and Peter Nelson
[arXiv preprint]
An Erdős-Pósa Theorem for Matroids
With James Davies and Meike Hatzel
An Erdős-Pósa Theorem for all minors
With James Davies and Tony Huynh
I contribute to Matroids, a formalization project for matroid theory. My contributions include work on:
Projections and Quotients
You can view the full repository on GitHub here.