I am an Associate Professor of Mathematics at the University of Oregon. My research interests are mathematical statistical physics and number theory.

I teach in the Clark Honors College.

I am currently the President of United Academics of the University of Oregon. I am the Secretary/Treasurer of the American Association of University Professors. I was the President of the University Senate 2017-2018.

Absolute Values and the Product Formula in Number Fields

We look at extending absolute values from base fields to extensions in the $K | \mathbb Q$ situation, and formulate a choice of absolute values for the places of $K$ which satisfy the Product Formula.

The Algebra and Geometry of $\mathbb Q_p$

Here we investigate the algebraic and geometric properties of the $p$-adic numbers.

Absolute Values and Completions of $\mathbb Q$

Notes on the places of $\mathbb Q$ and the analytic construction of the $p$-adic numbers.

Field Extensions and Number Fields

Here I am storing various basic facts about Number Fields that are useful in other notes. I hope this becomes more complete as time goes on.

Recalling Galois Theory

This is a brief reminder of the main ideas of Galois theory.

From Measures to Metrics on Pro-finite Completions

A note on how measures on pro finite completions of trees yield metrics.

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