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math.AP2024
Hearing the shape of a drum by knocking around
Xing Wang, Emmett L. Wyman, Yakun Xi
We study a variation of Kac's question, "Can one hear the shape of a drum?" if we allow ourselves access to some additional information. In particular, we allow ourselves to ``hear…
math.CO2024
Cospectral vertices, walk-regular planar graphs and the echolocation problem
Shi-Lei Kong, Emmett L. Wyman, Yakun Xi
We study cospectral vertices on finite graphs in relation to the echolocation problem on Riemannian manifolds. First, We prove a computationally simple criterion to determine wheth…