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math.AG2026
Certifying Galois/monodromy Actions via Homotopy Graphs
Timothy Duff, Kisun Lee
We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guaran…
math.AG2026
Asymptotic rank bounds: a numerical census
Kisun Lee
We systematically compute improved asymptotic rank bounds for tensors. Using numerical implicitization, we implement the geometric framework of Kaski and Michałek across all comput…
math.AG2025
A priori bounds for certified Krawczyk homotopy tracking
Kisun Lee
We establish the first complexity analysis for Krawczyk-based certified homotopy tracking. It consists of explicit a priori stepsize bounds ensuring the success of the Krawczyk tes…