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PDE Real Analysis Seminar
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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2019/11/19
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Peter Topping (University of Warwick)
Starting Ricci flow with rough initial data (English)
Peter Topping (University of Warwick)
Starting Ricci flow with rough initial data (English)
[ Abstract ]
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.
Ricci flow is a nonlinear PDE that is traditionally used to deform a manifold we would like to understand into a manifold we already understand. For example, Hamilton showed that a simply connected closed 3-manifold with positive Ricci curvature is deformed into a manifold of constant sectional curvature, thus allowing us to identify it as topologically a sphere.
In this talk we take a look at a different use of Ricci flow. We would like to exploit the regularising effect of parabolic PDE to turn a rough space into a smooth space by running the Ricci flow. In practice, this revolves around proving good a priori estimates on solutions, and taking unorthodox approaches to solving parabolic PDE. We will see some theory, first in 2D, then in higher dimension, and some applications.
