4 papers · 1 filter
Recovering Riemannian Geometry from Diffusion
Amandip Sangha
We present an intrinsic reconstruction of Riemannian geometry from a symmetric, strongly local diffusion semigroup. Starting from a diffusion operator and its associated first- and…
Entropy-Smooth Structures on Topological Manifolds
Amandip Sangha
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probe…
An Information-Theoretic Reconstruction of Curvature
Amandip Sangha
We develop an intrinsic information-theoretic approach for recovering Riemannian curvature from the small-time behaviour of heat diffusion. Given a point and a two-plane in the tan…
An Information-Theoretic Route to Isoperimetric Inequalities via Heat Flow and Entropy Dissipation
Amandip Sangha
We develop an information-theoretic approach to isoperimetric inequalities based on entropy dissipation under heat flow. By viewing diffusion as a noisy information channel, we mea…