Email address butler@iastate.edu Office 400C Carver Hall Office Phone 5152944174 Office Hours Not available. 
Videos available on YouTube 
Mathematical interests combinatorics linear algebra discrete mathematics spectral graph theory 
I am an Assistant Professor in the Department of Mathematics at Iowa State University (ISU). Prior to coming to ISU I did a three year NSF PostDoc under the supervision of Benny Sudakov at UCLA. Before that I earned my doctorate degree in mathematics at UC San Diego under the supervision of Fan Chung where I also worked extensively with Ron Graham.
From September 2012February 2014, I maintained the Weekly Undergraduate Math Mailing (WUM^2) at Iowa State University. The archived announcements are available online.
A news story about by mathematics of juggling class I taught in the Fall of 2013.
Jump to Teaching, Publications, Miscellaneousresearch, Talks/presentations, Links.
Iowa State (2011present) 


UCLA (20082010) 

UCSD (2007) 

BYU (20012003) 

Papers that will appear:
Papers that have appeared:
Coauthors: AIM minimum rankspecial graphs work group, Wayne Barrett, Mireille BousquetMelou, Joe Buhler, Fan Chung, Kevin Costello, Warwick de Launey, Erik Demaine, Ron Graham, Jason Grout, Gerhard Guettler, Mohammad Hajiaghayi, H. Tracy Hall, Paul Horn, Pavel Karasik, Robert Kleinberg, Miklos Laczkovich, Tom Leighton, Colin Mallows, Jia Mao, Steven Osborne, John Sinkovic, Wasin So, Colin Starr, Richard Stong, Tomohiro Tachi, Eric Tressler, Amy Yielding, Nan Zang
Eigenvalues and structures of graphs  Ph.D. dissertation written at UC San Diego under the direction of Fan Chung. Much of this has shown up in various papers I have published. Bounding the number of graphs containing very long induced paths  Masters thesis written at Brigham Young University under the direction of Wayne Barrett. 



For the paper Finding patterns avoiding many monochromatic constellations we generated a Maple worksheet that gives a method to compute the coefficient of a block pattern given a constellation. We also have an extended Maple worksheet that contains more information about good block colorings. There is also an interactive JAVA applet that allows you to see what happens to the coefficient of a pattern as we perturb the pattern and/or the constellation. In addition we have the JAVA programs used to generate block patterns for 4APs as well as the general pattern [0,q,1]. 

For the paper Irreducible Apollonian configurations and packings we generated a Maple worksheet that automates finding the center and radii of a packing placed in standard position. We also have a list of all irreducible configuration of circles with between 10 and 15 circles that can be used in the worksheet. Finally, there is also a collection of packings with various curvatures marked in the circles. 

While visiting The Center for Combinatorics at Nankai University in September 2006 I gave three lectures that served as an introduction to the field of graph theory. 

I have posed various problems which have appeared. These include American Mathematical Monthly #11030, #11265 and Mathematics Magazine #1668, #1730, #1761, #Q1008. 

In Fall of 2004 Fan Chung taught a course about the combinatorics of patterns in subsets and graphs. I worked to collect and collate the notes for the course into a PDF document; of course Fan did all the hard work of teaching the course. 

A collection of the simplest aperiodic strongly connected directed graphs and their spectrums under the definition of the normalized Laplacian (as defined by Chung). 

Miscellaneous unpublished notes: 

A letter to the editor of my old school about the slogan do the math used for a fundraising campaign. 