https://neckpinch.com/authors/ayush-khaitan/New arXiv papers by Ayush Khaitan, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.13897arxiv:2610.13897Fri, 09 Oct 2026 00:00:00 GMTYuan Liao, Ziyang Qin, Jui-Hui Chung, Ayush Khaitan, Zhengyang Zhang, Hongzhou Lin, Zijian Zhang, Ligeng Zhu, Peng Lu, Bennett Chow — We formalize the Hamilton–Perelman Ricci-flow proof of Thurston's geometrization conjecture. The public Lean declaration is reproduced in this paper. Its geometric interpretation follows, and verification is recorded in 4.Ricci flowGeometrization https://arxiv.org/abs/2609.33842arxiv:2609.33842Sun, 27 Sep 2026 00:00:00 GMTZiyang Qin, Yuan Liao, Ayush Khaitan, Bennett Chow — We formalize the smooth three-dimensional Poincaré conjecture, together with the Moise smoothing theorem, yielding the topological three-dimensional Poincaré conjecture. The smooth proof follows the Hamilton–Perelman route through Ricci flow with surgery and finite-time extinction.Ricci flowSingularitiesSurgeryPoincaré conjecture3-manifolds https://arxiv.org/abs/2308.02061arxiv:2308.02061Thu, 03 Aug 2023 00:00:00 GMTAyush Khaitan — We prove the existence and uniqueness of a weighted analogue of the Fefferman-Graham ambient metric for manifolds with density. We then show that this ambient metric forms the natural geometric framework for the singular Ricci flow: given a singular gradient Ricci flow spacetime in the Kleiner-Lott sense, we construct a unique global ambient half-space from it. We also prove the converse, that every global ambient space contains a singular gradient Ricci flow spacetime, thereby completing the correspondence. Our main application is the construction of infinite families of fully non-linear analogues of Perelman's 𝓕 and 𝓦 functionals. We extend Perelman's monotonicity result to these two families of functionals under several conditions, including for shrinking solitons and Einstein manifolds. We do so by constructing a "Ricci flow vector field" in the ambient space, which may be of independent research interest. We also prove that the weighted GJMS operators associated with the weighted ambient metric are formally self-adjoint, and that the associated weighted renormalized volume coefficients are variational.Ricci flowRicci solitonsEinstein metricsWeak & singular flowsStability & uniqueness