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math.AP2026
Calculus on Wave Fronts
Oliver Knill
We define a deformation of the exterior derivative that is a bounded operator and preserves the symmetries of the geometry. It satisfies a modified wave equation that honors the st…
math-ph2026
Block Jacobi matrices, Barycentric limits and Manifolds
Oliver Knill
We deform block triangular Jacobi matrices appearing in geometry, look at multi-scale Barycentric limits of geometries and droplet boundary manifolds in Potts networks.
math.CO2026
Remarks about Connection and Dirac matrices
Oliver Knill
The connection Laplacian L and the Dirac matrix D are both n x n matrices defined from a given finite simplicial complex G with n sets. In both cases, there is interlacing of the e…