https://neckpinch.com/authors/sebastien-picard/New arXiv papers by Sébastien Picard, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2511.21055arxiv:2511.21055Wed, 26 Nov 2025 00:00:00 GMTSpiro Karigiannis, Sébastien Picard, Caleb Suan — We study flows of G₂-structures guided by the principle of dimensional reduction: natural geometric flows in G₂-geometry reduce to natural flows in complex geometry. Our main examples are the G₂-Laplacian coflow, which lifts the Kähler–Ricci flow, and a 7-dimensional lift of the anomaly flow on complex threefolds. The G₂-lift of the anomaly flow deforms conformally coclosed G₂-structures. We compare the G₂-anomaly flow to the G₂-Laplacian coflow, and investigate short-time existence and fixed points.Ricci flowKähler–Ricci flowGeneralized & G₂ flows3-manifoldsKähler geometryHarmonic maps & DeTurck trick https://arxiv.org/abs/2402.17770arxiv:2402.17770Tue, 27 Feb 2024 00:00:00 GMTSébastien Picard — This is a survey on the Strominger system and a geometric flow known as the anomaly flow. We will discuss various aspects of non-Kähler geometry on Calabi-Yau threefolds. Along the way, we discuss balanced metrics and balanced classes, the Aeppli cohomology class associated to a solution to the Strominger system, the equations of motion of heterotic supergravity, and a version of Ricci flow in this special geometry.Ricci flowRicci-flat & Calabi–Yau3-manifoldsKähler geometryPhysics https://arxiv.org/abs/2209.03411arxiv:2209.03411Wed, 07 Sep 2022 00:00:00 GMTSébastien Picard, Caleb Suan — We establish a correspondence between a parabolic complex Monge-Ampère equation and the G₂-Laplacian flow for initial data produced from a Kähler metric on a complex 2- or 3-fold. By applying estimate for the complex Monge-Ampère equation, we show that for this class of initial data the G₂-Laplacian flow exists for all time and converges to a torsion-free G₂-structure induced by a Kähler Ricci-flat metric. Similar results are obtained for the G₂-Laplacian coflow, and in this case the coflow is related to the Kähler-Ricci flow.Ricci flowKähler–Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–YauKähler geometryLong-time existence & convergence