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Knotted surfaces and their profile curves


Speaker: Joel Hass, UC Davis
Location: 2112 MSB
Start time: Tue, Apr 16 2024, 2:10PM

The profile curve of a surface in R3 is formed from the points whose tangent plane is vertical.  This is the "outline" of a surface.  When a surface is transparent, this curve is what is most visible to the eye.  Profile curves play a role in surface reconstruction, the problem of reconstructing a surface from photographs. In this talk I will investigate the relationship between the knot type of a profile curve and that of the surface it lies on.  For example, I will answer the following question:  Is there an unknotted torus whose profile curves contain a component that is the standard trefoil knot?