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The intrinsic allure of extrinsic curvature

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A 2D surface embedded in ordinary Euclidean 3-space carries an invariantly defined function that quantifies whether or not we can map it isometrically to the usual flat plane. This “intrinsic curvature” gets star billing in physics because its generalization to higher dimensions figures in the general theory of relativity. But a surface that is intrinsically flat may nevertheless be embedded in 3-space in a way that is clearly curved in the everyday sense. The “extrinsic curvature” needed to quantify this property has its own allure. For example, it appears in physical models appropriate for interfaces and fluid membranes. I’ll conclude by sketching some technological implications, both for biology and even in data science.

This talk is part of the Rouse Ball Lectures series.

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