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October 2018

Events on Friday 19 October 2018

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11:10 Fri 19 Oct, 2018 :: Engineering North N132 :: Professor Herbert Huppert :: University of Cambridge

In many situations involving nonlinear partial differential equations, requiring much numerical calculation because there is no analytic solution, it is possible to find a similarity solution to the resulting (still nonlinear) ordinary differential equation; sometimes even analytically, but it is generally independent of the initial conditions. The similarity solution is said to approach the real solution for t >> tau, say. But what is tau? How does it depend on the parameters of the problem and the initial conditions? Answers will be presented for a variety of problems and the audience will be asked to suggest others if they know of them.
An Introduction to Ricci Flow
11:10 Fri 19 Oct, 2018 :: Barr Smith South Polygon Lecture theatre :: Miles Simon :: University of Magdeburg

In these three talks we give an introduction to Ricci flow and present some applications thereof. After introducing the Ricci flow we present some theorems and arguments from the theory of linear and non-linear parabolic equations. We explain why this theory guarantees that there is always a solution to the Ricci flow for a short time for any given smooth initial metric on a compact manifold without boundary. We calculate evolution equations for certain geometric quantities, and present some examples of maximum principle type arguments. In the last lecture we present some geometric results which are derived with the help of the Ricci flow.
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