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math.NA2023
The algebra of splines: duality, group actions and homology
Martina Lanini, Hal Schenck, Julianna Tymoczko
This survey gives an overview of three central algebraic themes related to the study of splines: duality, group actions, and homology. Splines are piecewise polynomial functions of…
math.DS2023
Algebraic aspects of homogeneous Kuramoto oscillators
Heather Harrington, Hal Schenck, Mike Stillman
We investigate algebraic and topological signatures of networks of coupled oscillators. Translating dynamics into a system of algebraic equations enables us to identify classes of…
math.AC2023
Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix
Fulvio Gesmundo, Hang, Huang +2
We describe the minimal free resolution of the ideal of subpermanents of a generic matrix . In contrast to the case of determinants, the $…