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: 14.08.25

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 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 50 lattice points in around 30 seconds! Please write us if you have any lattice polytopes for which you would like to check for unimodular triangulations.

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

• "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