Research
Research positions, original preprints and working papers, talks, and ongoing investigations.
Positions
Researcher — Algorithms & Graph Theory
GADA Lab (Geometric, Approximation & Distributed Algorithms) · University of Manitoba · Supervisor: Dr. Stephane Durocher
- –Developed a fast approximation algorithm for Hamiltonian path optimisation in spatially embedded graphs; built visualisation and randomised test-generation tooling across 100+ synthetic instances.
- –Delivered talks at weekly GADA lab meetings on wiggly permutations and space-efficient Eulerian circuits (works by other authors).
- –Contributed to noncrossing spanning trees library, improving performance by 30% and establishing Python best practices.
- –Engineered hypergraph visualisation tool for ML research.
Machine Learning Researcher
Terrabyte Machine Learning Research Group · University of Manitoba
- –Extended Graph Neural Diffusion architecture to Hypergraph Neural Diffusion networks using PyTorch and PyTorch Geometric, prototyping 4 model variants.
- –Tracked 25+ experiments across 5+ datasets for reproducibility using MLFlow.
Researcher — Combinatorics & Graph Theory
Department of Mathematics · University of Manitoba · Supervisors: Dr. Mahsa Nasrollahi-Shirazi & Dr. Andrii Arman
- –Proved a closed-form solution for the independence number of perfect binary trees and verified Hurlbert–Kamat's Conjecture using generating functions and computational analysis across 1,000+ cases.
Preprints & Working Papers
Original novel work. Unpublished and not yet peer-reviewed.
HK Property in Perfect Binary Trees
Preprint UnpublishedCombinatorics · Graph Theory
Proved a closed-form solution for the independence number of perfect binary trees and verified Hurlbert–Kamat's Conjecture using generating functions and computational analysis across 1,000+ cases.
Wiener Index
Preprint UnpublishedGraph Theory
Original research on the Wiener index — a topological graph invariant defined as the sum of pairwise distances between vertices — with novel combinatorial analysis and results.
Talks & Presentations
Talks given by me. Papers marked with an asterisk (*) are authored by others and were presented as reading-group talks.
Spectral Graph Theory for Maze Solving *
GADA Lab Research Meetings · EITC E2, University of Manitoba
Jul 28, 2025 · 1.7 MB
Wiggly Permutations *
GADA Lab Research Meetings · University of Manitoba
Oct 3, 2025 · 777 KB
Talk presenting the CCCG 2025 paper by its authors; presented as a reading-group talk.
Space-Efficient Eulerian Circuits *
GADA Lab Research Meetings · University of Manitoba
Feb 4, 2026 · 463 KB
Talk presenting the SOSA 2026 paper by its authors; presented as a reading-group talk.
Exploring Perfect Binary Trees with Relation to the HK-Property
UM Combinatorics Seminar · Machray Hall, University of Manitoba
Mar 28, 2024 · 233 KB
Git Fundamentals
Coding Kickoff · EITC E2, University of Manitoba
Sep 18, 2024 · 179 KB
Ongoing Work
Algorithmic Game Theory with Memory Pooling
Investigating game-theoretic models and their interaction with memory-pooling techniques in algorithm design.
Hypergraph Neural Networks
Extending diffusion-based GNN architectures to hypergraph settings via PyTorch Geometric; prototyping novel message-passing schemes.
HK-Property for Binary Trees
Continuing investigation into the Hurlbert–Kamat property for more general tree families beyond the perfect binary case.