https://neckpinch.com/authors/james-stanfield/New arXiv papers by James Stanfield, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.25619arxiv:2608.25619Wed, 26 Aug 2026 00:00:00 GMTElia Fusi, Ramiro A. Lafuente, James Stanfield — We relate the generalized Ricci curvature of left-invariant generalized metrics on a Lie group with the Ricci curvature of certain metric Lie algebras. As an application, we prove subconvergence of rescaled generalized Ricci flows to expanding generalized Ricci solitons on simply connected Lie groups with positive semi-definite Killing form. Under the same hypotheses, subconvergence of pluriclosed flows to expanding pluriclosed solitons is also shown. We further prove that left-invariant Bismut-Ricci flat metrics arise as critical points for the generalized scalar curvature functional on unimodular Lie groups. In view of this, we establish dynamical stability for the generalized Ricci flow of so-called standard bi-invariant, Bismut-flat metrics on compact, simply connected, semisimple Lie groups and construct examples of dynamically unstable Bismut-flat metrics which are non-standard.Ricci flowGeneralized & G₂ flowsRicci solitonsRicci-flat & Calabi–YauScalar curvatureHomogeneous spacesStability & uniqueness https://arxiv.org/abs/2404.15749arxiv:2404.15749Wed, 24 Apr 2024 00:00:00 GMTElia Fusi, Ramiro A. Lafuente, James Stanfield — We develop a framework inspired by Lauret's "bracket flow" to study the generalized Ricci flow, as introduced by Streets, on discrete quotients of Lie groups. As a first application, we establish global existence on solvmanifolds in arbitrary dimensions, a result which is new even for the pluriclosed flow. We also define a notion of generalized Ricci soliton on exact Courant algebroids that is geometrically meaningful and allows for non-trivial expanding examples. On nilmanifolds, we show that these solitons arise as rescaled limits of the generalized Ricci flow, provided the initial metrics have "harmonic torsion", and we classify them in low dimensions. Finally, we provide a new formula for the generalized Ricci curvature of invariant generalized metrics in terms of a moment map for the action of a non-reductive real Lie group.Ricci flowGeneralized & G₂ flowsRicci solitonsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2112.09344arxiv:2112.09344Fri, 17 Dec 2021 00:00:00 GMTJames Stanfield — We study invariant solutions to the Positive Hermitian Curvature Flow, introduced by Ustinovskiy, on complex Lie groups. We show in particular that the canonical scale-static metrics on the special linear groups, arising from the Killing form, are dynamically unstable. This disproves a conjecture of Ustinovskiy. We also construct certain perfect Lie groups that admit at least two distinct invariant solitons for the flow, only one of which is algebraic. This is the second known example of a geometric flow with non-algebraic, homogeneous solitons. The first being the G2-Laplacian flow.Generalized & G₂ flowsHomogeneous spacesStability & uniqueness