Smoothing properties of the Ricci flow have provided pointwise pinching results and extensions to pinching in the supercritical L^p, p>n/2 integral curvature cases. However, both here and in other geometric settings, differences arise at the critical, scale-invariant p=n/2 integral norm. I will describe some cases in which generalizations to curvature pinching in the critical, scale-invariant L^{n/2} sense can still be obtained using consequences of the monotonicity of Perelman's W-functional, such as in pinching to space forms and the Gromov--Ruh Theorem. This is joint work with Guofang Wei and Rugang Ye. 

Speaker: 

Eric Chen is currently an NSF postdoctoral scholar at UC Berkeley. He obtained his Ph.D. at Princeton University in 2019 under the supervision of Sun-Yung Alice Chang. His research focuses on differential geometry and geometric analysis.

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