8 papers
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…
Spectral Fusion Deformations for Locally Compact Quantum Groups
Amandip Sangha
We develop a deformation framework for -algebras equipped with a coaction of a locally compact quantum group, formulated intrinsically at the level of spectral subspaces deter…
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…
Jet Functors and Weil Algebras in Automatic Differentiation: A Geometric Analysis
Amandip Sangha
We present a differential-geometric formulation of automatic differentiation (AD) based on jet functors and Weil algebras. In this framework, forward- and reverse-mode differentiat…