arXiv subjects

Samit Ghosh

Publications and source records attributed to Samit Ghosh.

4 recordsLinked to original sources

arXiv2026

Lie algebroid Connections, Moduli of $\mathcal{L}$--twisted Principal Objects and motives

Let $X$ be an irreducible smooth complex projective variety, and let $G$ be a connected reductive linear algebraic group over $\mathbb{C}$. In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We then introduce Higgs bundles associated to a Lie algebroid and study their moduli spaces. In particular, we show that the category of vector bundles equipped with integrable $\mathcal{L}$-connections and the category of $\mathcal{L}$-twisted Higgs bundles of semiharmonic type on $X$ are neutral Tannakian categories, provided that $\mathcal{L}$ is a transitive Lie algebroid. Using this Tannakian framework, we obtain a characterization of principal $G$-bundles with integrable $\mathcal{L}$-connections and $\mathcal{L}$-twisted principal $G$-Higgs bundles of semiharmonic type on $X$, and construct their moduli spaces via Mumford's geometric invariant theory. We further introduce the notion of the $\mathcal{L}$-Hodge moduli space for principal $G$-bundles and prove that the moduli spaces of principal $G$-bundles with integrable $\mathcal{L}$-connections, $\mathcal{L}$-twisted principal $G$-Higgs bundles of harmonic type, and the associated $\mathcal{L}$-Hodge moduli spaces are semiprojective varieties. Finally, using the semiprojectivity of the $\mathcal{L}$-Hodge moduli spaces for principal $G$-bundles, we obtain a description of smooth locus of these moduli spaces in the Grothendieck ring of varieties and establish a motivic non-abelian Hodge correspondence type theorem.

math.AG↗

arXiv2026

Group evolving dynamics in biased condition: modeling and analysis

We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by group-specific bias terms, which can reflect social, economic, or reputational advantages. New entrants choose groups probabilistically based on these weighted attraction scores. We derive the conditions under which the system converges to a stationary equilibrium, where group proportions remain stable over time. The model exhibits rich nonlinear behavior, especially under varying bias strengths and inverse preference intensities. We analyze equilibrium conditions both theoretically and via simulations.

math.DS↗

arXiv2025

Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity

We present a new benchmarking study comparing a boundary-constrained Ehrenpreis--Palamodov Gaussian Process (B-EPGP) surrogate with a classical finite element method combined with Crank--Nicolson time stepping (CN-FEM) for solving the two-dimensional wave equation with homogeneous Dirichlet boundary conditions. The B-EPGP construction leverages exponential-polynomial bases derived from the characteristic variety to enforce the PDE and boundary conditions exactly and employs penalized least squares to estimate the coefficients. To ensure fairness across paradigms, we introduce a degrees-of-freedom (DoF) matching protocol. Under matched DoF, B-EPGP consistently attains lower space-time $L^2$-error and maximum-in-time $L^{2}$-error in space than CN-FEM, improving accuracy by roughly two orders of magnitude.

cs.LG↗

arXiv2025

Lie Algebroid Connections on Principal Bundles

Let $X$ be an irreducible smooth complex projective variety. Let $G$ be a linear algebraic group over $\mathbb{C}$. We define the notion of Lie algebroid valued connection on holomorphic principal $G$--bundles on $X$, and study their basic properties under extension and reduction of structure group. Finally we investigate criterions for existence of a Lie algebroid connection on principal $G$--bundles over smooth complex projective curves.

math.AG↗