8 papers
Resolving Structural Uncertainty in Stochastic Dynamical Systems via Ensemble-Based Bayesian Inference
Francesco Zambelli, Valeria D'Andrea, Manlio De Domenico
Recovering the interaction structure of complex stochastic dynamical systems from sparse time-series observations is an inherently ill-posed inverse problem. The posterior over net…
Subarrangements of type A: the weak Lefschetz property of the Artinian Orlik-Terao algebra
Nicholas Gaubatz, Hal Schenck
In 1994, Orlik and Terao introduced a commutative Artinian analog S/I(A) of the Orlik-Solomon algebra of a hyperplane arrangement A to answer a question of Aomoto. A central topic…
The Vacuum Moduli Space of the Minimal Supersymmetric Standard Model
Yang-Hui He, Vishnu Jejjala, Brent D. Nelson +2
A starting point in the study of the minimal supersymmetric Standard Model (MSSM) is the vacuum moduli space, which is a highly complicated algebraic variety: it is the image of an…
Vacuum Geometry of the Standard Model
Yang-Hui He, Vishnu Jejjala, Brent D. Nelson +2
Vacuum structure of a quantum field theory is a crucial property. In theories with extended symmetries, such as supersymmetric gauge theories, the vacuum is typically a continuous…
The Likelihood Correspondence
Thomas Kahle, Hal Schenck, Bernd Sturmfels +1
An arrangement of hypersurfaces in projective space is strict normal crossing (SNC) if and only if its Euler discriminant is nonzero. We study the critical loci of arbitrary Lauren…
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…
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…
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 $…