Kyle Huang

Mathematics PhD student at BTU Cottbus, supported by the DFG priority program SPP 2458 Project "Combinatorial Synergies", residing in Berlin. I am co-advised by Gennadiy Averkov, Giulia Codenotti, and Ansgar Freyer, with projected end date in Fall 2027. My research interests include smooth polytopes, lattice width, unimodular triangulations, and more broadly toric geometry and geometry of numbers.

Email: krhuang5@gmail.com

GitHub: https://github.com/krhuang

Last Update: 17.05.26

SmoothGeneration

As part of my Master's Thesis I implemented a novel algorithm to generate all smooth 3-polytopes with <= 50 lattice points (previous work by Lundman went to 16). The data and the codebase can be found on the GitHub repository.

UniTriSat: Unimodular Triangulations via SATISFIABILITY

Robert Lauff, Charles Zhang, and I implemented a novel algorithm to check if a lattice polytope has a unimodular triangulation, via SAT-solvers. This ongoing work can be found at the UniTriSat GitHub repository. Currently the working code can check if a 3-polytope with 35 lattice points has a unimodular triangulation in around .2 seconds! Please write us if you have any lattice polytopes for which you would like to check for unimodular triangulations.

Villa Student Seminar

Together with Matthew Dupraz and Katarina Krivokuća we organize the Villa Student Seminar. Please email me if you would like to attend or be added to the mailing list.

Publications

• G. Averkov, G. Codenotti, A. Freyer, K. Huang, Exact Flatness Constant for One-Point Convex Bodies and the Discrete Isominwidth Problem: The Planar Case, 2026 (preprint) arXiv:2604.27260
• C. Florez, J. Higgins, K. Huang, T. Keller, D. Shen, The prime graphs of some classes of finite groups, J. Pure Appl. Algebra 226 (2021), no. 7, 10.1016/j.jpaa.2021.106990
• C. Florez, J. Higgins, K. Huang, T. Keller, D. Shen, The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs. Minimal Prime Graphs of Solvable Groups, to appear in Involve, arXiv:2011:08938
• C. Florez, J. Higgins, K. Huang, T. Keller, D. Shen, Minimal Prime Graphs of Solvable Groups, 2020 (preprint) arXiv:2011.08938

Talks & Poster Presentations

• UniTriSat: Unimodular Triangulations via SATISFIABILITY at FPSAC 2026 Seattle -- this will be a software demonstration
• Computing Flatness Constants in the Plane at Young Researchers Conference on Combinatorial Synergies
• UniTriSat: Unimodular Triangulations via SATISFIABILITY at Polyhedral Geometry for Neural Networks
• UniTriSat: Unimodular Triangulations via SATISFIABILITY at Developments in Algorithmic, Discrete, and Tropical Geometry
• "Generating Smooth 3-Polytopes" at Modern Perspectives on Geometry of Numbers
• "Generating Smooth 3-Polytopes" at the Osnbruck Winter School and Workshop Polytopes 2025
• "Topologies on the Moduli Space of Delzant Polytopes" at the 2023 Chow Lectures
• "What is... a semialgebraic set?" (Video)
• "McMullen's Polytope Algebra", at the 2022 MIT Talbot Workshop: Scissors Congruence in K-Theory
• "Two Notions of Prime Graph Minimality", at the Young Mathematicians Conference