Research

I am currently a PhD student in Combinatorics and Optimization at the University of Waterloo, supervised by Stephen Melczer.

My present work studies critical points at infinity and toric compactifications in analytic combinatorics and algebraic geometry. More broadly, I am interested in how abstract mathematical structure can inform algorithms and symbolic methods.

Research Interests

  • Analytic combinatorics
  • Algebraic geometry
  • Symbolic computation
  • Automated theorem proving
  • Computational geometry and geometric processing

Current and Past Projects

  • Critical Points at Infinity, University of Waterloo, 2023 to present
    Using toric varieties to explore proper compactification reflecting the properties of infinity points of algebraic varieties.
  • Distance Measurement of Mesh Surfaces, New York University, 2023
    Proposed and implemented algorithms determining whether a surface deviates a certain distance from another surface in 3-dimensional Euclidean space.
  • Algebraic Geometry Solver, Google, Summer 2022
    Worked in Learning & Education on the math team and implemented polynomial division routines in a computer algebra system supporting Google’s math solver, together with an end-to-end algebraic geometry solver using Wu's Method.
  • Origami on Lattices, University of Michigan, 2019 to 2020
    Quantitatively studied the moduli space of an isolated origami hexagon, including energy bounds, deformation structure, and flip operators.
  • Efficient Eigensolvers and Applications, ICERM at Brown University, Summer 2020
    Implemented PageRank algorithms and related computational tools for ranking experiments on web domains. Project link.
  • Empirical Research on CoT Faithfulness
    Interactive project on chain-of-thought faithfulness stress tests under mathematical hints. Project link.

Selected Publications and Talks

  • Critical Points at Infinity in Analytic Combinatorics, Combinatorial Algebra Meets Algebraic Combinatorics, Halifax, January 2026. Talk.
  • An exceptional equinumerosity of lattice paths and Young tableaux, Journal of Integer Sequences, Volume 28, 2025.
  • Critical Points at Infinity in Analytic Combinatorics, Ontario Graduate Mathematics Conference, Toronto, June 2025. Talk.
  • Optimizing Surface Closeness Measurements: An Analysis of Distance Field and Adaptive Simplification Methods in Tetrahedral Meshing, master's thesis, 2023.
  • Deformations of the origami hexagon, flipping operations, and Pythagorean 4-tuples, preprint, 2021
  • Origami hexagon deformations and flip graph, SIAM Annual Meeting, 2021
  • Origami Hexagon Deformations and Flip Graph, Young Mathematicians Conference, Ohio State University, August 2020. Talk.
  • Origami on Lattices, Undergraduate Mathematics Symposium, University of Illinois Chicago, November 2019. Poster.