Some notes on the relationship between different models of hyperbolic plane

Preliminaries Here's something I learned from Chongchun Zeng of Georgia Tech, while chatting over some hors-d'oeuvres at the AMS …

Some non-intuitive facts about periodic functions

A proof of a generalized form of Young's inequality is given without the need of interpolation theory.

A quick introduction of Newton-Cartan theory, which is a sort of Newtonian limit of general relativity from a geometric point of view.

A brief introduction to affine differential geometry and the notion of preferred volume forms.

A quick summary of the traceless version of general relativity.

The "Nirenberg trick" or "Nirenberg transformation" is the observation1 that the semilinear wave equation …

In this installment, we look at Schrödinger's equation with barriers, and study the decay of the solutions.

We use Laplace transform arguments to look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation …