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gr-qc2024
Solving the area-length systems in discrete gravity using homotopy continuation
Seth K. Asante, Taylor Brysiewicz
Area variables are intrinsic to connection formulations of general relativity, in contrast to the fundamental length variables prevalent in metric formulations. Within 4D discrete…
gr-qc2024
Efficient Tensor Network Algorithms for Spin Foam Models
Seth K. Asante, Sebastian Steinhaus
Numerical computations and methods have become increasingly crucial in the study of spin foam models across various regimes. This paper adds to this field by introducing new algori…
math.AG2024
The algebraic matroid of the Heron variety
Seth K. Asante, Taylor Brysiewicz, Michelle Hatzel
We introduce the n-th Heron variety as the realization space of the (squared) volumes of faces of an n-simplex. Our primary goal is to understand the extent to which Heron's formul…