Steve Butler


Office: Carver 420

Pronouns: he/him

I am a Morrill Professor and the Barbara J. Janson Professor in the Department of Mathematics at Iowa State University. Prior to coming to Iowa State 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. In addition I worked extensively with Ron Graham and am current proprietor of Ron's archival material.

My primary mathematical interests are spectral graph theory, enumerative combinatorics, mathematics of juggling, discrete geometry, and generally mathematics of fun things.  Among other things, I can do eight perfect faro shuffles in a row, and is willing to teach this to anyone who stops by my office.

From Fall of 2018 through Fall of 2020 I was the calculus coordinator for Iowa State University. Many of my lectures during that time were recorded and are available online.

One of my main areas of research is spectral graph theory. A graph looks at the connections (edges) between objects (vertices). One way to understand a graph is by storing it as an array. A linear algebraist sees an array and says "Hey, let's call it a matrix" (matrix = array with benefits), and then a whole new world of exploration opens up by looking at the eigenvalues of the matrix, and this is the area of spectral graph theory.

Other math related talks I have given:

I have worked in mathematics of juggling (currently one of only a few mathematicians who have published more papers about the mathematics of juggling than the number of balls that they can juggle).

Coming in the near(?) future from Princeton University Press -- Juggling Counts

I have a lot of fun working with students; and a few of the students have had a lot of fun and been creative with me. You can find a few of the videos online:

A lot of fun and interesting mathematics can be done and explored by using decks of cards and perfect shuffles. I have a few videos that talk about some of these (aimed at young people in STEM):

Fan Chung (my PhD advisor) and me in December 2020.

Self portrait (2023)

The L'Hospital shirt