Number Theory

Iterative Mathematics
Presentation for the UW Tacoma Math Enthusiast Series

A short presentation focused on iterative functions, with an introduction to fractals.

Counting Primitive Juggling Patterns
Invited to speak at the University of Toronto Undergraduate Seminar, Toronto, ON, Canada, February 8, 2023

A general review of the combinatorial aspects of juggling patterns, followed by some analytic results on primitive juggling patterns.

Making Juggling Mathematical
Invited to speak at the University of Toronto Undergraduate Seminar, Seattle, WA, November 21, 2019

This is a fun general review of the mathematical aspects of juggling. It has a more combinatorial bent than I usually give it.

The Prime Number Theorem for Juggling Patterns
AMS/MAA Joint Mathematics Meetings, San Diego, CA, January 11, 2018

This talk gives a brief introduction to the mathematics of juggling and presents my latest result on the asymptotic enumeration of primitive juggling patterns.

A Zeta Function for Juggling Patterns
MAA MathFest, Madison, WI, August 4, 2012

This is a (very brief) summary of my paper in the Journal of Number Theory and Combinatorics, with Dominic Klyve and Carsten Elsner. The paper's abstract is available here.

The Mathematics of Juggling
Invited to speak at Central Washington Univ., Ellensburg, WA, January 12, 2011

This was a preliminary report on the ideas that produced the paper cited above.

Zeta Functions on Cocompact Arithmetic Subgroups of SL\((3,\mathbb{R})\)
AMS/MAA Joint Mathematics Meetings, New Orleans, LA, January 5, 2007

My original job talk on my Ph.D. thesis.

A History of Riemann Zeta Function on the Positive Integers
Keene State College Mathematics Colloquium, October 27, 2006, and Buena Vista University, November 19, 2007

The origins of the Riemann Zeta Function can be traced back to the work of Leonhard Euler in the 18th century. Before Riemann, people were only interested in integer exponents. While we usually think of the zeta function from an analytic perspective today, research is still being done on the integer exponent case.

Measuring the Growth of Geodesic Lengths Associated to Selected Subgroups of SL\((3,\mathbb{R})\)
Québec-Maine Number Theory Conference, Laval University, Québec, September 30, 2006

History of Mathematics

A Tour of Joseph-Louis Lagrange's Recherches d'Arithmétique
West Coast Number Theory Conference, December 17, 2022
MAA Pacific Northwest Section Meeting, June 26, 2021

This is a survey of the contents of Joseph-Louis Lagrange's 1775 paper, "Recherches d'Arithmétique," in which he explored the representation problem for binary quadratic forms. My English translation of this work is available online at ArXiv.org.

Math Stories and Histories: How Historical Narratives Shape Mathematical Ideas
Invited to speak as part of the Grit City Think and Drink lecture series, Tacoma, WA, May 14, 2019

This is a survey of some ideas on historiography in mathematics, and how the underlying interpretive framework a teacher brings to the subject can affect its reception by students.

Leonhard Euler and the Invention of Modern Math
Invited to speak at the University of the Pacific, Stockton, CA, February 23, 2018

In this talk, I gave a brief overview of Euler's life and work, then explored some of his work on the Pell equation and its connections to some old (and ancient) number theory problems.

Euler's Publication Role During the Seven Years' War
Euler Society Conference, Garden City, NY, July 26, 2016

This is a review of the publication challenges in Berlin and St. Petersburg during the Seven Years' War (1756-63), including Euler's role in the war and the choices he made when sending his work to be published.

The Role of Geometry in Early Fluid Mechanics
Columbia History of Science Annual Mtg., Friday Harbor, WA, March 8, 2014
Euler Society Conference, Austin, TX, July 22, 2014

This talk covers one of the main threads of my fluid mechanics research, specifically the transition from heavily geometric models to heavily algebraic models during the mid-18th century. Leonhard Euler and Daniel Bernoulli feature prominently.

Relative Accuracy of Quadrilateral Area Measurement in the Ancient World
AMS-MAA Joint Mathematics Meetings, New Orleans, LA, January 8, 2011

This is a summary of my work on the Surveyor's Formula, which appeared early in 2014, in Mathematical Spectrum.

Navigation in the Time of Euler
Invited to speak at Adelphi University's Frederick V. Pohle Colloquium Series, March 3, 2010

A survey of navigational techniques from the Odyssey to the Enlightenment, including a method used by Leonhard Euler to calculate longitude. An extension of my talk from the previous year's Euler Society Conference.