arXiv subjects

Amandip Sangha

Publications and source records attributed to Amandip Sangha.

10 recordsLinked to original sources

arXiv2026

Spectral-Geometric Deformations of Function Algebras on Manifolds

We introduce an intrinsic deformation of the algebra of smooth functions on a compact Riemannian manifold using only the Laplace spectral decomposition. The construction twists the canonical multiplication-projection channels by unimodular phases, producing a well-defined bilinear product on the finite spectral core with values in $L^2(M)$. We give a simple condition for compatibility with complex conjugation and isolate a Sobolev boundedness hypothesis under which the product extends to a Sobolev algebra and admits iteration; in that setting, associativity is equivalent to an explicit identity for the twisted spectral channels. We analyze gauge and coboundary aspects for scalar twists and obtain rigidity statements in the action-free regime. We also compare with classical strict deformation frameworks arising from actions of locally compact abelian groups -- Rieffel's deformation for $\mathbb{R}^d$-actions, Connes-Landi's torus isospectral deformations, and Kasprzak's cocycle deformation via Landstad theory -- showing that, when the relevant abelian group action has a discrete spectral decomposition (in particular, in the compact abelian/periodic case where the algebra decomposes into homogeneous subspaces indexed by characters of the acting group), their deformed products are recovered uniformly as refined instances of our channel twist. Finally, we formulate a grading-based obstruction and classification for graded scalar twists.

math.OA↗

arXiv2026

Recovering Riemannian Geometry from Diffusion

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 second-order diffusion calculus, we recover the full weighted Riemannian structure of the underlying manifold. In particular, we show that the carre du champ determines a unique smooth Riemannian metric, that the iterated carre du champ encodes curvature, and that the symmetry of the diffusion fixes the Levi-Civita connection and reference measure. As a consequence, the diffusion semigroup determines the global Riemannian manifold uniquely up to isometry. The results provide an information-theoretic perspective on differential geometry in which geometric structure emerges from the intrinsic behavior of diffusion, without assuming any prior metric or coordinate description.

math.DG↗

arXiv2026

Entropy-Smooth Structures on Topological Manifolds

We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate functions and reconstructs a smooth atlas directly from the quadratic entropy response. We prove that this entropy-smooth structure is equivalent to the classical smooth structure, stable under perturbations, and compatible with products, submanifolds, immersions, and diffeomorphisms. This establishes smoothness as an information-theoretic phenomenon and forms the foundational layer of a broader program linking entropy, diffusion, and differential geometry.

math.DG↗

arXiv2026

Spectral Fusion Deformations for Locally Compact Quantum Groups

We develop a deformation framework for $C^*$-algebras equipped with a coaction of a locally compact quantum group, formulated intrinsically at the level of spectral subspaces determined by the coaction. The construction is defined algebraically on a finite spectral core and extended by continuity to a natural Fréchet $*$-algebra completion under mild analytic regularity assumptions. Deformations are governed by scalar fusion data assigning phases to fusion channels of irreducible corepresentations. Associativity and $*$-compatibility are characterized by explicit algebraic identities. The framework recovers a range of known deformation procedures, including Rieffel, Kasprzak, and Drinfeld-type constructions, and also yields genuinely new deformations that do not arise from dual $2$--cocycles or crossed-product methods. At the $C^*$-level, we identify a minimal reduced setting in which the deformed algebra admits a canonical completion, formulated in terms of boundedness of the deformed left regular action on the Haar--GNS space. This separates algebraic coherence from analytic implementability and clarifies the precise role of higher-order fusion data in deformation theory for locally compact quantum groups. In particular, the framework exhibits explicit associator-level deformations governed by fusion $3$--cocycles that cannot arise from any dual $2$--cocycle or crossed-product construction.

math.OA↗

arXiv2025

An Information-Theoretic Reconstruction of Curvature

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 tangent space, we compare the heat mass transported along that plane with its Euclidean counterpart using the relative entropy of finite measures. We show that the leading small-time distortion of this directional entropy encodes precisely the local curvature of the manifold. In particular, the planar information imbalance determines both the scalar curvature and the sectional curvature at a point, and assembling these directional values produces a bilinear tensor that coincides exactly with the classical Riemannian curvature operator. The method is entirely analytic and avoids Jacobi fields, curvature identities, or variational formulas. Curvature appears solely through the behaviour of heat flow under the exponential map, providing a new viewpoint in which curvature is realized as an infinitesimal information defect of diffusion. This perspective suggests further connections between geometric analysis and information theory and offers a principled analytic mechanism for detecting and reconstructing curvature using only heat diffusion data.

math.DG↗

arXiv2025

An Information-Theoretic Route to Isoperimetric Inequalities via Heat Flow and Entropy Dissipation

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 measure how mutual information about set membership decays over time. This decay rate is shown to be determined by the boundary measure of the set, leading to a new proof of the Euclidean isoperimetric inequality with its sharp constant. The method extends to Riemannian manifolds satisfying curvature-dimension conditions, yielding Levy-Gromov and Gaussian isoperimetric results within a single analytic principle. Quantitative and stability bounds follow from refined entropy inequalities linking information loss to geometric rigidity. The approach connects geometric analysis and information theory, revealing how entropy dissipation encodes the geometry of diffusion and boundary.

math.DG↗

arXiv2025

Jet Functors and Weil Algebras in Automatic Differentiation: A Geometric Analysis

We present a differential-geometric formulation of automatic differentiation (AD) based on jet functors and Weil algebras. In this framework, forward- and reverse-mode differentiation arise naturally as pushforward and cotangent pullback, while higher-order differentiation corresponds to evaluation in a Weil algebra. This construction provides a unified, coordinate-free view of derivative propagation and clarifies the algebraic structure underlying AD. All results are realized in modern JAX code, where the Weil-mode formulation computes all mixed derivatives in a single forward pass with cost linear in the algebra dimension. The resulting implementation achieves algebraically exact and numerically stable differentiation with predictable scaling, demonstrating that geometric abstraction can yield more efficient and transparent computational differentiation systems. Code is available at https://git.nilu.no/geometric-ad/jet-weil-ad

cs.LG↗

arXiv2025

Data-Driven Energy Estimation for Virtual Servers Using Combined System Metrics and Machine Learning

This paper presents a machine learning-based approach to estimate the energy consumption of virtual servers without access to physical power measurement interfaces. Using resource utilization metrics collected from guest virtual machines, we train a Gradient Boosting Regressor to predict energy consumption measured via RAPL on the host. We demonstrate, for the first time, guest-only resource-based energy estimation without privileged host access with experiments across diverse workloads, achieving high predictive accuracy and variance explained ($0.90 \leq R^2 \leq 0.97$), indicating the feasibility of guest-side energy estimation. This approach can enable energy-aware scheduling, cost optimization and physical host independent energy estimates in virtualized environments. Our approach addresses a critical gap in virtualized environments (e.g. cloud) where direct energy measurement is infeasible.

cs.LG↗

arXiv2013

Deformation of operator algebras by Borel cocycles

Assume that we are given a coaction δof a locally compact group G on a C*-algebra A and a T-valued Borel 2-cocycle ωon G. Motivated by the approach of Kasprzak to Rieffel's deformation we define a deformation A_ωof A. Among other properties of A_ωwe show that A_ω\otimes K(L^2(G)) is canonically isomorphic to A\rtimes_δ\hat G\rtimes_{\hatδ,ω}G. This, together with a slight extension of a result of Echterhoff et al., implies that for groups satisfying the Baum-Connes conjecture the K-theory of A_ωremains invariant under homotopies of omega.

math.OA↗

arXiv2011

KK-fibrations arising from Rieffel deformations

The bundle map $π_{h}: Γ((A_{tJ})_{t\in [0,1]})\lra A_{hJ}$, for every $h\in [0,1]$, of the continuous field $(A_{tJ})_{t\in [0,1]}$ associated to the Rieffel deformation $A_{J}$ of a C*-algebra $A$ is shown to be a KK-equivalence by using a 2-cocycle twisting approach and RKK-fibrations.

math.OA↗