Abstract: We will talk about a new general flow of $G_2$-structures which we call the Ricci-harmonic flow. The flow is a natural coupling of the Ricci flow of underlying metrics and the isometric flow of $G_2$-structures but with explicit lower order terms. We will explain how to obtain the lower order terms and how the flow can be interpreted as an analog of the Ricci flow of metrics for $G_2$-structures. We will discuss various analytic and geometric results for the flow including short-time existence and uniqueness of solutions, regularity theory and long time existence results. Time permitting, we will also talk about explicit solutions and singularities of the flow. The talk is based on arXiv:2601.05210 and arXiv:2601.16832 (joint with Ragini Singhal).

 

Link Information: Zoom Meeting https://us02web.zoom.us/j/84248932564?pwd=jgAVgDBtTJ2tjDtsytx7ctipASNUAx.1

Meeting ID: 842 4893 2564

Passcode: 335091

 

Organizers: Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chao-Ming Lin (NTU), Wei-Bo Su (NCU), Chung-Jun Tsai (NTU)