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Geometric Analysis Seminar

Testing long-time existence conjectures for geometric flows of G2-structures

Aaron Kennon (UCSB)

Location:  Hill 705
Date & time: Tuesday, 05 December 2023 at 2:50PM - 3:50PM

Abstract: A primary goal motivating the study of geometric flows of G2-structures is to better understand which 7-manifolds admit certain types of these metrics. Of particular interest are the cases of G2-holonomy metrics and nearly-parallel G2-structures, both of which are related to broader themes in differential geometry. I will survey what is known for specific geometric flows of G2-structures, motivate conditions on the initial data for these flows which I expect would make them promising for constructing these objects, and then discuss my work testing the behaviors of these flows under these initial conditions.