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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

In this installment, we look at Schrödinger's equation with barriers, and study the decay of the solutions.
Last updated on 25 min read mathematical diversions

We use Laplace transform arguments to look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation …
Last updated on 11 min read mathematical diversions

We look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation to plane waves.
Last updated on 16 min read mathematical diversions