https://neckpinch.com/authors/stuart-james-hall/New arXiv papers by Stuart James Hall, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2102.07168/arxiv:2102.07168Sun, 14 Feb 2021 00:00:00 GMTWafaa Batat, Stuart James Hall, Thomas Murphy, James Waldron — We prove that the bi-invariant Einstein metric on SU₂ₙ₊₁ is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of ℂP}²ⁿ×ℂP}¹ found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler–Einstein metrics on `odd' Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.Ricci flowEinstein metricsKähler geometryStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/1808.00344/arxiv:1808.00344Wed, 01 Aug 2018 00:00:00 GMTStuart James Hall — In this note we show that the bi-invariant Einstein metric on the compact Lie group G₂ is dynamically unstable as a fixed point of the Ricci flow. This completes the stability analysis for the bi-invariant metrics on the compact, connected, simple Lie groups. Interestingly, G₂ is the only unstable exceptional group.Ricci flowEinstein metricsHomogeneous spacesStability & uniqueness https://neckpinch.com/papers/1806.01722/arxiv:1806.01722Tue, 05 Jun 2018 00:00:00 GMTStuart James Hall, Thomas Murphy, James Waldron — Using a stability criterion due to Kröncke, we show, providing n≠ 2k, the Kähler–Einstein metric on the Grassmannian Grₖ(ℂⁿ) of complex k-planes in an n-dimensional complex vector space is dynamically unstable as a fixed point of the Ricci flow. This generalises the recent results of Kröncke and Knopf–Sesum on the instability of the Fubini–Study metric on ℂP}ⁿ for n>1. The key to the proof is using the description of Grassmannians as certain coadjoint orbits of SU(n). We are also able to prove that Kröncke's method will not work on any of the other compact, irreducible, Hermitian symmetric spaces.Ricci flowEinstein metricsKähler geometryStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/1607.05766/arxiv:1607.05766Tue, 19 Jul 2016 00:00:00 GMTWafaa Batat, Stuart James Hall, Thomas Murphy — The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstein metrics, quasi-Einstein metrics and Ricci solitons, we introduce a new destabilising perturbation (the Ricci variation) and show that certain infinite families of warped product Einstein metrics will be unstable in high dimensions.Ricci flowRicci solitonsEinstein metricsAlmost & η-Ricci solitonsStability & uniquenessRotational symmetry & warped products