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Geometric Analysis Seminar

Stability and moduli space of generalized Ricci solitons

Kuan-Hui Lee (UCI)

Location:  Hill-705
Date & time: Tuesday, 17 October 2023 at 2:50PM - 3:50PM

Abstract: The generalized Einstein-Hilbert action is an extension of the classic scalar curvature energy and Perelman’s F-functional which incorporates a closed three-form.  The critical points are known as generalized Ricci solitons, which arise naturally in mathematical physics, complex geometry, and generalized geometry. In this talk, we would like to study the local behavior of the generalized Ricci solitons and compute the second variation formula of the generalized Einstein-Hilbert action. As an application we show that all Bismut-flat manifolds are linearly stable critical points, and admit nontrivial deformations arising from Lie theory. Furthermore, this leads to extensions of classic results of Koiso, Podesta, Spiro, Kröncke to the moduli space of generalized Ricci solitons.

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