# Writings

### Colloquium Notes: Craig Evans

L. Craig Evans is a professor at UC Berkeley. For many students he is best known for his textbook on partial differential equations. I …

### Lengths of Parallel Curves

Let's start with something simple: Given a circle with radius $R$, draw a concentric circle with radius 1 larger. How much longer is …

### A Criterion for Real Roots

When does a polynomial with real coefficients have only real roots? Here's one way to determine it.

### You are 23 times more likely to crash

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

### A Tangent Identity

Here's a slightly non-obvious relation between some angles, that I ran into accidentally. Claim: (angles below given in degrees) \[ …

### An Implicit Assumption about Expectation Values

A short note about an implicit assumption behind the notion of expectation values, and how it relates to economics applications.

### Matter field from diffeomorphism: on a theme of Capoferri and Vassiliev

I try to reformulate an idea of Capoferri and Vassiliev in the infinitesimal limit and see where it goes.

### A Weighted/Interpolated Young's Inequality

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

### Lie Groups

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

### Oscillatory Solutions to the Heat Equation

As we all learned in a first course in PDEs, for "reasonable" initial data $u_0$, the solution to the linear heat equation …