https://neckpinch.com/authors/mattia-pujia/New arXiv papers by Mattia Pujia, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2002.07210/arxiv:2002.07210Mon, 17 Feb 2020 00:00:00 GMTMattia Pujia — We study the positive Hermitian curvature flow of left-invariant metrics on complex 2-step nilpotent Lie groups. In this setting we completely characterize the long-time behaviour of the flow, showing that normalized solutions to the flow subconverge to a non-flat algebraic soliton, in Cheeger- Gromov topology. We also exhibit a uniqueness result for algebraic solitons on such Lie groups.Generalized & G₂ flowsHomogeneous spacesStability & uniquenessLong-time existence & convergence https://neckpinch.com/papers/1906.11676/arxiv:1906.11676Thu, 27 Jun 2019 00:00:00 GMTFrancesco Pediconi, Mattia Pujia — We study the Hermitian curvature flow of locally homogeneous non-Kähler metrics on compact complex surfaces. In particular, we characterize the long-time behavior of the solutions to the flow. We also provide the first example of a compact complex non-Kähler manifold admitting a finite time singularity for the Hermitian curvature flow. Finally, we compute the Gromov-Hausdorff limit of immortal solutions after a suitable normalization. Our results follow by a case-by-case analysis of the flow on each complex model geometry.Generalized & G₂ flowsSingularitiesKähler geometryLimit spaces & RCDHomogeneous spacesLong-time existence & convergence https://neckpinch.com/papers/1810.05063/arxiv:1810.05063Thu, 11 Oct 2018 00:00:00 GMTMattia Pujia — We investigate the algebraic structure of complex Lie groups equipped with left-invariant metrics which are expanding semi-algebraic solitons to the Hermitian curvature flow (HCF). We show that the Lie algebras of such Lie groups decompose in the semidirect product of a reductive Lie subalgebra with their nilradicals. Furthermore, we give a structural result concerning expanding semi-algebraic solitons on complex Lie groups. It turns out that the restriction of the soliton metric to the nilradical is also an expanding algebraic soliton and we explain how to construct expanding solitons on complex Lie groups starting from expanding solitons on their nilradicals.Generalized & G₂ flowsRicci solitonsHomogeneous spaces https://neckpinch.com/papers/1807.00059/arxiv:1807.00059Fri, 29 Jun 2018 00:00:00 GMTRamiro A. Lafuente, Mattia Pujia, Luigi Vezzoni — We investigate the Hermitian curvature flow (HCF) of left-invariant metrics on complex unimodular Lie groups. We show that in this setting the flow is governed by the Ricci-flow type equation ∂ₜgₜ=−rm Ric^(1,1) (gₜ). The solution gₜ always exist for all positive times, and (1 + t)⁻¹gₜ converges as t→ ∞ in Cheeger-Gromov sense to a non-flat left-invariant soliton (bar G, bar g). Moreover, up to homotheties on each of these groups there exists at most one left-invariant soliton solution, which is a static Hermitian metric if and only if the group is semisimple. In particular, compact quotients of complex semisimple Lie groups yield examples of compact non-Kähler manifolds with static Hermitian metrics. We also investigate the existence of static metrics on nilpotent Lie groups and we generalize a result in for the pluriclosed flow. In the last part of the paper we study HCF on Lie groups with abelian complex structures.Ricci flowGeneralized & G₂ flowsKähler geometryHomogeneous spacesLong-time existence & convergence