Mathematics

Background

I ranked in the top 100 in the nationwide William Lowell Putnam Mathematical Competition®, graduated from Carnegie Mellon University with an M.S. in mathematics (my thesis was on the modularity theorem in number theory), and I have published research papers on algebraic number theory and combinatorial game theory (which applies to board games such as Go).

In addition, I love teaching, especially mathematics. I regularly tutor a wide variety of mathematics topics both one-on-one and on mathematics help forums and chat servers. I also have managed and supported the creation of a variety of online mathematics courses for the Johns Hopkins Center for Talented Youth.

Highlighted Publications

• The positive discriminant case of Nagell's theorem for certain cubic orders

  
  

  • Journal of Number Theory 131 (3), 470-486
  • It is proved that a real cubic unit u, whose other two conjugates are also real, is almost always a fundamental unit of the order ℤ[u]. The exceptions are shown to consist of a single infinite family together with one sporadic case. This is an analogue of Nagell's theorem for the negative discriminant case i.e. the case where u does not have any real conjugate.
  • ScienceDirect page

  
  
• Equality Classes of Nim Positions under Misère Play

  
  

  • INTEGERS 16, G3
  • We determine the misère equivalence classes of Nim positions under two equivalence relations: one based on playing disjunctive sums with other impartial games, and one allowing sums with partizan games. In the impartial context, the only identifications we can make are those stemming from the known fact about adding a heap of size 1. In the partizan context, distinct Nim positions are inequivalent.
  • INTEGERS volume 16
  • arXiv page

  
  
• An Extension of the Normal Play Convention to N-player Combinatorial Games

  
  

  • INTEGERS 20A, A14
  • We examine short combinatorial games for three or more players under a new play convention in which a player who cannot move on their turn is the unique loser. We show that many theorems of impartial and partizan two-player games under normal play have natural analogues in this setting. For impartial games with three players, we investigate the possible outcomes of a sum in detail, and determine the outcomes and structure of three-player Nim.
  • INTEGERS volume 20A
  • arXiv page