# Posts

I am an associate professor of mathematics at the University of Oregon. My research interests include random spatial processes, mathematical statistical physics and number theory.

I am currently the Secretary/Treasurer of the American Association of University Professors.

## Non-archimedean electrostatics

I will be teaching a summer school course on $p$-adic electrostatics at the CIMPA-CIMAT Research School on $p$-adic Numbers, Ultrametric Analysis and Applications in Guanjuato, Mexico May 23-31, 2022. We will cover the following topics.… Read More »Non-archimedean electrostatics

## Basics of Probability

Some notes on foundational ideas and definitions in modern probability theory.

## Sample Spaces, Events & $\sigma$-Algebras

The set of possible outcomes of a random experiment is called the sample space. Subsets of the sample space are called events. We will eventually axiomatize probability measures, but for the moment we view probability… Read More »Sample Spaces, Events & $\sigma$-Algebras

## Measure & Probability

We begin with the sample space $\Omega$ of a random experiment, and a $\sigma$-algebra $\mathcal H$ on $\Omega$ consisting of subsets of $\Omega$ to which we want to assign probabilities. Definition: A probability measure on… Read More »Measure & Probability

## Random Variables & Measurable Functions

A measurable space consists of a set and a $\sigma$-algebra on that set. If $(E, \mathcal E)$ and $(F, \mathcal F)$ are measurable spaces, then we say $f: E \rightarrow F$ is measurable if for… Read More »Random Variables & Measurable Functions