_{See my first bonsai 'Paco'
(named after one of my favorite
mathematicians). I've grown quite
fond of these trees — I now have
4.5, including a Japanese maple,
redwood, and spruce.}

Ph.D. candidate at Cornell. I work on computational geometry (regular triangulations ❤️) and string compactifications, with a soft spot for problems where an efficient algorithm changes what's computationally possible.

Languages: C, C++, Python, Cython

• The DNA of Calabi-Yau Hypersurfaces — Applied the NTFE encoding (2-face restrictions) to the combinatorial optimization task of generating Batyrevian Calabi-Yau hypersurfaces (constructed via regular triangulations of 4D reflexive polytopes) targeting various objectives. Tested this encoding on search spaces up to ~500M candidates with a range of optimization methods, including genetic algorithms, best first search, simulated annealing, and MCMC. The GA significantly outperformed MCMC and simulated annealing.

• NTFE algorithm — Simple algorithm for generating regular triangulations of reflexive polytopes with distinct 2-face restrictions, exponentially quicker than previous methods. Such triangulations lead to potentially-inequivalent Calabi-Yau manifolds via Batyrev's construction. Bounds on NTFE counts established in this work. This algorithm is implemented in CYTools.
• CYTools — Lead developer and maintainer of the standard toolkit for studying Batyrevian CY compactifications in string theory. Major contributions include:
  1. a generalization to vex triangulations via regfans, and
  2. a significantly faster intersection number kernel (see fanroots for an application of this).
• latticepts — High-performance C/Cython implementation of Kannan's lattice point enumeration algorithm, substantially faster than Normaliz and OR-Tools CP-SAT with better scaling. As one performance example: latticepts generates ~107M lattice points in the strict interior of an example 7D cone (arXiv:2406.13751) in ~23s.
• regfans — Python package for regular triangulations of integral vector configurations, associated with Calabi-Yau Threefolds from Vex Triangulations.
• fanroots — Optimization library for finding roots of vector-valued functions defined over the secondary fan of point/vector configurations, designed for optimization tasks such as those occurring in Candidate de Sitter Vacua.
• pfvs (coming soon... when the rest of the paper is ready) — C/Cython algorithm (with some Python prep) for generating (coni-)PFVs orders of magnitude faster than previous methods, with significantly better scaling.
• FastAerosol — C++ 'advanced example' contributed to GEANT4 for stochastic simulation of particle transport through aerosol geometries via voxelized droplet generation, with attention to time and memory efficiency. Associated with this paper.

I put some more recreational projects in ntt. This includes a random, fine, pushing triangulation algorithm written in C and a cute game for visualizing flips of vector configurations and the vex triangulations that these flips lead to.