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Mathematical Sciences

Two Math Thesis Talks

Date: 3:30pm - 4:30pm PST November 19, 2014 Location: John Howard 135

John Howard 135

Singularities of the Mean Curvature Flow of Tori of Revolution
Colin Gavin ’15
Mathematics Major

Mean curvature flow deforms surfaces in space by decreasing their area as fast as possible, given local information. Generally this makes surfaces more spherical over time. Therefore, for tori, which cannot become spherical, one expects complex singularities to form and stop this process. My research involves classifying and analyzing the types of singularities which can develop.

 

 

Singularities of Wave Equations with Quadratic Nonlinearities
Sam Stewart ’15
Mathematics Major

We consider non-linear wave equations $ \phi_{tt} - \Delta \phi = Q(\partial\phi)$ in three spatial dimensions with the particular nonlinearity $Q(\partial\phi) = (\phi_t)^2 - (\phi_r)^2$, as it is an especially interesting example for studying the long-term behavior. For sufficiently small initial data, global existence of solutions is known, but for large initial data, it is expected that, generically, solutions blow up in finite time. In our work, we seek to understand this singularity formation using both numerical simulations and theoretical considerations.

 

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