My
name is Gideon Simpson. I am a PhD candidate in the Department of Applied Physics and Applied
Mathematics. My current work
involves studying the stability properties of buoyantly ascending density
waves of magma in the Earth's interior. My
work is supervised by Michael
Weinstein and Marc Spiegelman.
My research interests include nonlinear partiatl differential equations, nonlinear waves, dynamical systems, homogenization, scientific computing, fluid mechanics, geophysics, and materials science.
Publications
G. Simpson and M.I. Weinstein. Asymptotic Stability of Ascending Solitary Magma Waves. Submitted to SIAM JMA[arXiv]
G. Simpson, M.I. Weinstein and P. Rosenau. On a Hamiltonian PDE arising in magma dynamics. Submitted to DCDS-B[arXiv]
G. Simpson, M. Spiegelman, and M.I. Weinstein. Degenerate dispersive equations arising in the study of magma dynamics. Nonlinearity, 20:21-49, 2007[pdf]
About Me
I received my BA in Mathematics from Cornell University in 2003. I did my honors thesis with John Hubbard. While at Cornell, I served as advertising manager, and later business manager, of the Cornell Daily Sun.
See my CV[pdf]
Links
Useful scientific computing software packages:
Buy my sister's book, 'cause she's got two kids.
LaTeX
A few tips that I wish I'd learned earlier.
Use the AMS packages: amsmath, amsfonts, amssymb. In particular, use \begin{align}...\end{align} in place of \begin{eqnarray}...\end{eqnarray} for grouping equations; I get better results with less work. Also, for a single equation that must be broken up across multiple lines, use \begin{split}...\end{split} within a \begin{equation}...\end{equation} environment.
Use the package showkeys to have your the labels you assign equations appear while working in draft mode.
Use the package cite to have references appear as [1--5] instead of [1,2,3,4,5].
Use the package hyperref. Without doing anything further, PDFs will now pick up the sections of your document.
Email me at grs2103(at)columbia(dot)edu