Ancient solutions to geometric flows with small symmetry groups

Abstract: A useful method for the construction of examples of proper solutions to elliptic or parabolic (geometric) partial differential equations involves the reduction of the equation to a simpler one (typically, an algebraic equation or an ordinary differential equation) via the imposition of a suitable symmetry Ansatz. I will present some recent "genuinely parabolic" constructions of ancient solutions to geometric flows (mean curvature flow, fully nonlinear extrinsic flows and the Ricci flow) which rely on (sometimes much) weaker symmetry Ansätze. While the resulting equations are still parabolic partial differential equations, the imposed symmetries nonetheless yield crucial simplifications (e.g. allowing for the exploitation of special properties of geometric flow equations which only hold in low space dimensions).

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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