Thomas M. Fiore


2009 REU, 2007 REU, 2006 REU, Student REU Projects,
Lectures on Transformational Theory

2011 MAA Mini-Course on Geometry and Algebra in Music Theory

2009 Chicago REU Lectures on Mathematical Music Theory

This year we incorporate recent work of Thomas Noll, David Clampitt, and Manuel Domínguez on scale theory and algebraic combinatorics on words.
I also plan to discuss Vuza canons and tiling problems in music. These are topics researched by Dan Tudor Vuza, Emmanuel Amiot,
Moreno Andretta, Harald Fripertinger, and many others. For other topics, see also:

Musical Actions of Dihedral Groups.
Joint with Alissa Crans and Ramon Satyendra.
American Mathematical Monthly, Volume 116, Number 6, June-July 2009, pp. 479-495. 17 pages.

Generalized Contextual Groups.
Joint with Ramon Satyendra.
Music Theory Online, Volume 11, Number 3, September 2005. 29 pages.

and the beginner lecture notes Music and Mathematics. Here is what we did in the 2009 REU:

2007 Chicago REU Lectures on Mathematical Music Theory

2006 Chicago REU Lectures on Mathematical Music Theory

Student REU Projects on Mathematical Music Theory

I mentored the following students on their projects during the 2006, 2007, and 2009 REU Programs. One student, inspired by my REU lectures, wrote his paper entirely independently:

Undergraduate Lectures on Transformational Theory at Michigan

The links below were created from a series of lectures I gave in Math 107 on applications of group theory to music theory as part of my VIGRE project at the University of Michigan. It was inspired by the work of music theorist David Lewin. These ideas are further developed in a joint paper with Ramon Satyendra, which has appeared in Music Theory Online. I also gave a talk on these topics in the Undergraduate Math Club at the University of Michigan.


Some of the material on this website is based upon work supported by the National Science Foundation under Grant DMS-0501208.