Papers

Research papers

Here are the research papers that I’ve written.

• Distinct distances between a line and strip [arXiv] [poster] [slides]
  with Adam Sheffer
• Exponents in the local properties problem for difference sets have a gap at 2 [arXiv]
• Expanding polynomials for sets with additive structure [arXiv] [poster]
  with Cosmin Pohoata and Adam Sheffer
• Bounds for the local properties problem for difference sets [arXiv] [slides]
• The distribution of $k$-free effective divisors and the summatory totient function in function fields [arXiv]
  with Hannah Lang, Hamilton Wan, and Nancy Xu
• The distribution of error terms of smoothed summatory totient functions [arXiv]
  with Hannah Lang, Hamilton Wan, and Nancy Xu
  Proceedings of the American Mathematical Society, to appear
• Asymptotic properties of maximal $p$-core $p'$-partitions [arXiv] [slides]
  Journal of Combinatorial Theory, Series A 193 (2023)

Expository writing

Here are some expository things I’ve written for class projects.

• The triangle-free process and lower bounds for $r(3, k)$ [pdf]
  Final project for 18.619 (Discrete Probability and Stochastic Processes).
• A faster combinatorial algorithm for triangle detection [pdf] [slides]
  Final project for 6.5350 (Matrix Multiplication and Graph Algorithms).
• Approximation algorithms for prize-collecting Steiner tree [pdf]
  Final project for 18.415 (Advanced Algorithms).
• Some results on anticoncentration [pdf]
  Final project for 18.204 (Undergraduate Seminar in Discrete Math).
• A survey on hardness magnification [pdf] [slides]
  Final project for 18.405 (Advanced Complexity Theory).