Spectral Theory Archives - Quantum Calculus

discrete geometry, Graph theory, simplicial complex, Spectral Theory

Arboricity of spheres

By oliverknill September 17, 2023 September 21, 2023

We explain why the arboricity of 3 spheres can take values between 4 and 7 and mention that for 3 manifolds the upper bound is 9 (but believed to be 7).

almost periodicity, Differential equations, ergodic theory, physics, Spectral Theory

Measure and Category

By oliverknill July 2, 2023 July 2, 2023

Something about what happens typically in dynamical systems.

Graph theory, physics, quantum calculus, simplicial complex, Spectral Theory

Wave Equation

By oliverknill May 3, 2023 May 3, 2023

About the wave equation on discrete networks.

discrete geometry, Finite topology, Graph theory, Spectral Theory

Spectral Monotonicity for the Hodge Laplacian

By oliverknill April 1, 2023 April 3, 2023

We prove that the spectrum of the Hodge Laplacian dd* +d*d depends in a monotone way on the simplicial complex.