Local estimates on the higher temporal derivatives of the Ricci flow and unique continuation (Brett L. Kotschwar, Arizona State University)

Source: CACM Publish Date：2026-06-05 13

Speaker: Brett L. Kotschwar, Arizona State University

Time: June 12, 2026 (Friday), 16:00–18:00

Venue (In-person): Room 20-200

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Abstract: We will discuss the problem of unique continuation for general complete Ricci flows and establish local estimates on the spatio-temporal derivatives of general smooth Ricci flows which interpolate between two existing sets of bounds: one a set of local estimates which imply the instantaneous local real-analyticity of the solution, and the other a set of global estimates on complete solutions of bounded curvature which imply the instantaneous analytic analyticity (and full space-time analyticity) of the solution. The coefficients of these bounds are sharp in the orders of the derivatives, and imply that the solution is of second Gevrey class in the temporal variables. When the solution is complete and of bounded curvature, the estimates recover in the limit global spatio-temporal bounds which imply the instantaneous space-time analyticity of the solution.

Speaker Bio: Brett L. Kotschwar specializes in differential geometry, partial differential equations, and geometric analysis. He received his Ph.D. in Mathematics from the University of California, San Diego in 2007. He has served as a lecturer at MIT and a researcher at the Max Planck Institute in Germany. He joined Arizona State University in 2011, where he is currently an Associate Professor with upcoming promotion to Full Professor. He has been awarded multiple NSF and Simons Foundation grants, authored one monograph, and published numerous papers in top-tier journals. In addition to supervising graduate students and teaching undergraduate and graduate mathematics courses, he holds several administrative and academic service roles within his department and serves as a reviewer for multiple leading mathematics journals.

Host: Ni Lei