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math.AG2025
A stratified polyhedral homotopy method for sampling positive-dimensional zero sets of polynomial systems
Tianran Chen
Numerical algebraic geometry revolves around the study of solutions to polynomial systems via numerical methods. The polyhedral homotopy of Huber and Sturmfels for computing isolat…
math.AG2024
On the typical and atypical solutions to the Kuramoto equations
Tianran Chen, Evgeniia Korchevskaia, Julia Lindberg
The Kuramoto model is a dynamical system that models the interaction of coupled oscillators. There has been much work to effectively bound the number of equilibria to the Kuramoto…