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.
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.
Here we investigate the algebraic and geometric properties of the $p$-adic numbers.
Notes on the places of $\mathbb Q$ and the analytic construction of the $p$-adic numbers.
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.
This is a brief reminder of the main ideas of Galois theory.
A note on how measures on pro finite completions of trees yield metrics.