I am a first year PhD candidate at the University of Washington. I enjoy talking about mathematics, thinking about mathematics, teaching mathematics, and sometimes find myself dreaming about mathematics. My current areas of interest lie primarily in Algebra and Number Theory. I'm becoming increasingly interested in representation theory and algebraic number theory but I truly enjoy any and all math subjects that I study.
Aside from being a student, you can also find me at the beach, surfing and playing with my dog or watching a warriors basketball game. I also LOVE food, and I've become very interested in cooking and expanding my library of things I can cook.
My undergraduate research topic lives at the intersection of combinatorial group theory and recursion theory. The goal is to assess the algorithmic complexity of detecting orderability within computable groups, finitely recursively presented groups, and infinitely recursively presented groups. Informally, I investigate how "difficult" it would be for any given "computer" to find some given property within a group. For example, suppose I give some "computer" a presentation of a group and I want to ask the "computer" if every element has infinite order. By finding the appropriate placement of the group property of being torsion-free within the arithmetical hierarchy, I can know exactly how "difficult" it could be to answer this question for some given class of groups. At the moment, I spend my research efforts trying to assess how "difficult" the group property of being partially orderable is. In the process I also consider the same question for groups that admit a total bi-order.
Here is my CV