Biography: Steve Butler is an award-winning teacher. He has given talks at numerous venues ranging from the AMS-MAA address at Mathfest 2021 to the Iowa State Fair and almost everything in between.

Steve particularly enjoys working with young researchers. He regularly participates in the Iowa State REU and maintains a listing of REU sites for students (mathreuprograms.org); he is also a lead organizer of the Graduate Research Workshop in Combinatorics (GRWC).

Steve’s mathematics was heavily influenced by his mentors, Fan Chung and Ron Graham. His mathematical research includes spectral graph theory, shuffling, juggling, origami, tiling, Apollonian circle packings, parking functions, and more. In 2015, he became the 512th mathematician to have an Erdős number of 1.

Steve Butler has been at Iowa State University since 2011 where he is a Morrill Professor and the Barbara J Janson Professor of Mathematics. More information about him can be found online (stevebutler.org).

Additional information can be found here.

Topics include:

Juggling Counts
Mathematics is a language which can help us describe and explore patterns. One source of patterns that mathematicians have been exploring comes from juggling (the tossing of objects, usually balls or clubs). In this talk we will look at multiple ways to describe juggling patterns that allow us to find new juggling patterns, and to count how many possible patterns exist. We can compare answers to various problems to give a combinatorial proof of Worpitzky’s identity. We will also look at a few juggling-based problems that mathematics has not yet succeeded in answering.

Every Game I’m Shufflin’, Shufflin’
Shuffling is a well-known aspect of gameplay to help make the decks “sufficiently random” to make the game interesting. Shuffling is also a source of mathematical exploration where shuffles are thought of as permutations of the cards. In this talk, we will take some tools of mathematics, modular arithmetic, and binary numbers, and show how we can apply these to shuffling, and in particular, some simple-to-learn mathematically-based card tricks, which will be performed live. Along the way, we will also learn why we should never work with jokers.