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math.AG2026
Marvelous slices of orthogonal matrices
Taylor Brysiewicz, Fulvio Gesmundo
The space of special orthogonal matrices with zeros on the diagonal decomposes into the union of irreducible surfaces whose intersections are beautifully encoded…
math.AG2025
Homotopy Iterators
Paul Breiding, Taylor Brysiewicz, Hannah Friedman
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for…
math.AG2024
Monodromy Coordinates
Taylor Brysiewicz
We introduce the concept of monodromy coordinates for representing solutions to large polynomial systems. Representing solutions this way provides a time-memory trade-off in a mono…