Writings

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As we all learned in a first course in PDEs, for "reasonable" initial data $u_0$, the solution to the linear heat equation …
Last updated on 4 min read mathematical diversions

This post is about the formulation of the dynamics of a rigid body, under rotations, as dynamics on a Lie group. I'm writing this to …
Last updated on 9 min read expository

Some notes on the relationship between different models of hyperbolic plane
Last updated on 6 min read expository

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …
Last updated on 6 min read expository

Some non-intuitive facts about periodic functions
Last updated on 4 min read mathematical diversions

A proof of a generalized form of Young's inequality is given without the need of interpolation theory.
Last updated on 6 min read expository

A quick introduction of Newton-Cartan theory, which is a sort of Newtonian limit of general relativity from a geometric point of view.
Last updated on 32 min read expository

A brief introduction to affine differential geometry and the notion of preferred volume forms.
Last updated on 13 min read expository

A quick summary of the traceless version of general relativity.
Last updated on 8 min read mathematical diversions

The "Nirenberg trick" or "Nirenberg transformation" is the observation1 that the semilinear wave equation …
Last updated on 5 min read mathematical diversions