https://neckpinch.com/authors/adam-thompson/New arXiv papers by Adam Thompson, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.21472arxiv:2609.21472Fri, 18 Sep 2026 00:00:00 GMTLucas Lavoyer, Adam Thompson — We prove linear stability of all steady and expanding gradient Kähler-Ricci solitons. In the expanding case, we prove strict linear stability under very general assumptions. In particular, every asymptotically conical expanding gradient Kähler-Ricci soliton is strictly linearly stable.Ricci solitonsKähler–Ricci solitonsKähler geometryStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2506.11362arxiv:2506.11362Thu, 12 Jun 2025 00:00:00 GMTRamiro A. Lafuente, Adam Thompson — Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are satisfied by Ricci flow limits, the equations dimension-reduce to the so-called twisted harmonic-Einstein equations. When the base is a surface, we establish a correspondence between solutions of the latter and a class of G-Higgs bundles. This allows us to produce infinite families of new examples that are not locally homogeneous, and in particular to obtain a complete description in dimension 4. We also show that all our examples admit Einstein one-dimensional extensions.Ricci flowRicci solitons4-manifoldsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2305.05923arxiv:2305.05923Wed, 10 May 2023 00:00:00 GMTAdam Thompson — For each non-flat, unimodular Ricci soliton solvmanifold (S₀,g₀), we construct a one-parameter family of complete, expanding, gradient Ricci solitons that admit a cohomogeneity one isometric action by S₀. The orbits of this action are hypersurfaces homothetic to (S₀,g₀). These metrics are asymptotic at one end to an Einstein solvmanifold. In the one-parameter family, exactly one metric is Einstein, and exactly one has orbits that are isometric to (S₀,g₀).Ricci solitonsHomogeneous spaces