Math Projects
Bi-Automorphisms Project
I am working on a collaborative research project that started from Canada/USA Mathcamp on deciding when a mathematical structure S is affable, which is when it has a bi-automorphism: a map * : S -> S where for any a in S, x -> a*x and x -> x*a are automorphisms on S. A paper is in progress.
Kuratowski Closure-Complement Theorem
In this collaborative project, inspired by Kuratowski’s Closure-Complement Theorem, we investigated the amount of different sets that can be created in a topological space by applying finite collections of topological operators to a single original set. We presented our results in my school’s math symposium.
Fractal Dimension
In the Euler Circle Independent Research and Paper Writing program, I wrote an expository paper on fractal dimension and presented the topic to my peers.
3-Player Nim
I worked on a group project to create strategies for 3-player Nim. We created a framework to generalize players' positions during specific game states and used that to create a strategy of collusion and betrayal.
