Kyle Huang

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 and Giulia Codenotti. My research interests are smooth polytopes, lattice width, toric geometry, discrete geometry, and algebraic topology.

Email: krhuang5@gmail.com

GitHub: https://github.com/krhuang

Last Update: 18.09.25

SmoothGeneration

As part of my Master's Thesis I implemented a novel algorithm to generate all smooth 3-polytopes with <= 31 lattice points (previous work went to 16). The data and the codebase can be found on the GitHub repository

There is ongoing work to extend this to all smooth 3-polytopes with <= 50 lattice points

SATUNITRI: Unimodular Triangulations via SATISFIABILITY

Robert Lauff and I are implementing a program to quickly check if a lattice polytope has a unimodular triangulation, via SAT-solvers. This ongoing work can be found at the SATUNITRI 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 Krvokuca we organize the Villa Student Seminar.

Publications

• 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, . Higgins, K. Huang, T. Keller, D. Shen, Minimal Prime Graphs of Solvable Groups, 2020 (preprint) arXiv:2011.08938

Talks/Poster Presentations

• "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 MIT Talbot 2022 Conference
• "Type Cones and the Volume Polynomial"
• "Spanning Lattice Polytopes and the Uniform Position Principle"
• "Semigroup Rings, Toric Ideals, and their Groebner Bases"
• "Anisotropicity and Leftchetz Elements"
• "Two Notions of Prime Graph Minimality", at the Young Mathematicians Conference