This is a collection some of the expository notes that I have written, they range in topic, some closer to my research and some farther away. As opposed to posts in "Mathematical Diversions", posts here are intended to be read by other people. I welcome comments and corrections.

Driving down the highway in upstate Michigan yesterday, I saw a State Police billboard that states (I paraphrase) Drivers who text are …

A follow up to my previous post on Young's inequality.

Some introductory notes about the definition and geometry of Lie groups, and their analysis.

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 …

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 …

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.

About the Einstein-Infeld-Hoffmann theorem characterizing geodesics.