Hi, I am a PhD student at Oregon State University studying theoretical computer science, advised by Dr. Amir Nayyeri.
Research Interests
Combinatorics: Within combinatorics, graph theory is of particular interest to me. I spend time thinking about various problems in graph theory; extremal problems, coloring, optimization, forbidden substructures, etc.
Algorithms I enjoy thinking about algorithmic aspects, especially combinatorial algorithms. Combinatorial structures provide a rich playground for algorithms research.
Things I’m Currently Thinking About
I will try to keep this section udpated as frequently as possible; last update March 2026
The past year or so has still involved hidden graph reconstruction but I’ve really been mostly thinking about width parameters in graphs. A nice paper by David Eppstein, Michael Goodrich, and Alfred Liu from UCI on the width parameter BFS-width and its relation to the well-studied bandwidth was presented at ESA 2025 last year. This inspired our most recent paper (submitted to a conference recently, will post here as soon as appropriate) extending their work to study the relationship between BFS-width and the cutwidth and pathwidth parameters, with a tiny application in graph reconstruction at the end (as BFS-width is a natural parameter to study for many BFS-based algorithms like the simplest reconstruction algorithms).
Nov 2024
Thinking generally still about hidden graph reconstruction allowing for different oracles; many papers start using adversarial arguments and information theoretic arguments elegantly to prove lower bounds, which is always a blast to see! These techinques seem to play nicely with graph reconstruction problem variants, but there are probably bigger, more general sledgehammer techniques in this area out there.
Expanding from just graph reconstruction, there are a few interesting questions; using shortest path metric oracles, which properties of graphs can you verify in better than soft O(n^2) time? Connectivity properties seem natural to look at with shortest path metric oracles
Aug 2024
A neat conjecture in graph theory: for a nontrivial connected graph F, there exists an F-irregular graph if and only if F is not isomorphic to K2. The forward direction is easily provable and there exists a P3-irregular graph, but I have no idea beyond this and I can’t seem to find people seriously working on this.
General Updates
[Aug. 2024] I’ve created a blog containing my thoughts about (mostly) math things I find interesting.