Submitted Papers
Published/Accepted Papers
-
New publication! Tactile Tools for Teaching: An Implementation of Knuth's Algorithm for Mastering Mastermind.
Joint with Alexander Lang and Antonella Perucca.
The College Mathematics Journal, to appear in 2018.
9 pages+several pages of supplement.
-
Commuting Groups and the Topos of Triads.
Joint with Thomas Noll.
Mathematics and Computation in Music, Third International Conference, MCM 2011, Proceedings. Edited by C. Agon, E. Amiot, M. Andreatta, G. Assayag, J. Bresson, J. Mandereau. Lecture Notes in Artificial Intelligence, Volume 6726, pages 69-83. Springer, Heidelberg, 2011. 15 pages.
-
What is the Jacobian of a Riemann Surface with Boundary?.
Joint with Igor Kriz.
Deformation spaces, Perspectives on algebro-geometric moduli. A publication of the Max-Planck-Institute for Mathematics, Bonn. Including papers from the workshops held at the Max-Planck-Institut für Mathematik, Bonn, July 2007 and August 2008. Edited by Hossein Abbaspour, Matilde Marcolli and Thomas Tradler. Pages 53--74. Aspects of Mathematics, E40. Vieweg + Teubner, Wiesbaden, 2010. 21 pages.
Other Writings
-
Transcription of my student seminar talk on Jacobians of Rigged Surfaces. 2004.
dvi, pdf, ps
-
Music and Mathematics, an introduction to mathematical music analysis aimed at undergraduates. 2004.
Musical examples can be found on my Music page.
pdf, ps
Talks
-
Voicing Transformations and a Linear Representation of Uniform Triadic Transformations, joint with Thomas Noll.
AMS Special Session on Mathematics and Music, January 6, 2017.
Joint Mathematics Meetings, Atlanta, GA.
Slides Large pdf File
-
Incorporating Voice Permutations into the Theory of Neo-Riemannian Groups and Lewinian Duality, joint with Thomas Noll and Ramon Satyendra.
Shulich School of Music, McGill University, June 14, 2013.
Fourth International Conference on Mathematics and Computation in Music.
-
Waldhausen Additivity and Approximation in Quasicategorical K-Theory.
Dalhousie University, June 7, 2013.
Canadian Mathematical Society Summer Meeting, Invited Speaker in Special Session "Progress in Higher Categories".
Slides Large pdf File
-
Morphisms in a Musical Analysis of Schoenberg, String Quartet No. 1, Opus 7.
Saginaw Valley State University, May 4, 2012.
Michigan Section MAA Meeting, Local Invited Speaker.
Slides Large pdf File
-
Waldhausen Additivity: Classical and Quasicategorical.
University of Western Ontario, April 9, 2012.
Geometry and Topology Seminar.
-
Morphisms in a Musical Analysis of Schoenberg, String Quartet No. 1, Opus 7.
Calvin College, March 15, 2012.
Colloquium.
Slides Large pdf File
-
Morphisms in a Musical Analysis of Schoenberg, String Quartet No. 1, Opus 7.
Wayne State University, January 18, 2012.
Applied Mathematics Seminar.
Slides Large pdf File
-
Commuting Groups and the Topos of Triads,
joint with Thomas Noll.
Institute for Research and Coordination of Acoustics and Music, Third International Conference on Mathematics and Computation in Music, Paris, France, June 17, 2011
-
Higher Categories, Homotopy Theory, and Applications.
Queens College, CUNY, January 28th, 2009.
Mathematics Colloquium.
Slides pdf, Illustrations pdf.
-
Group Actions in neo-Riemannian Music Theory.
Kalamazoo College, January 21st, 2009.
Mathematics Colloquium.
Slides pdf.
-
A Thomason Model Structure on the Category of Small n-fold Categories.
Notre Dame University, October 2nd, 2008.
Notre Dame Topology Seminar.
-
Model Structures on the Category of Small Double Categories.
Carvoeiro, Portugal, June 19th, 2007.
International Category Theory Meeting, CT2007.
Slides pdf.
-
Jacobians of Riemann Surfaces with Parametrized Boundary.
University of Bonn, December 12th, 2006.
Bonn Topology Seminar.
-
Jacobians of Riemann Surfaces with Parametrized Boundary.
University of Pittsburgh, November 21st, 2006.
University of Pittsburgh Analytic Topology Seminar.
-
Topology and Algebra in Music Theory.
University of Pittsburgh, November 20th, 2006.
-
Topology and Algebra in Music Theory.
University of Chicago, November 7th, 2006.
-
2006 REU: Four Lectures on Mathematical Music Theory.
University of Chicago, July 5th, 7th, 11th, and 13th, 2006.
Slides.
-
Double Categories and Pseudo Algebras.
White Point, June 26th, 2006.
International Category Theory Meeting, CT2006.
Slides pdf.
-
Double Categories and Pseudo Algebras.
Northwestern University, March 27th, 2006.
Northwestern University Topology Seminar.
Slides dvi, pdf, ps.
See Mac Lane Conference above for expanded slides
-
Categories and Jacobians.
Notre Dame University, April 12th, 2005.
Notre Dame Topology Seminar.
-
Beethoven and the Torus.
University of Michigan Undergraduate Math Club, October 14th, 2004.
Slides dvi, pdf, ps.
Musical examples can be found on my Music page.
-
Three Multi-Media Lectures on Mathematics and Music
Math 107, Winter 2003, University of Michigan.
Lecture Notes pdf, ps.
-
Lax Algebraic Structures.
Purdue University, November 20th, 2003.
Purdue University Topology Seminar.
-
Lax Algebraic Structures.
Wayne State University, November 19th, 2003.
Wayne State University Topology Seminar.
Reviews
-
Zbl ...
Barwick, Clark. On left and right model categories and left and right Bousfield localizations.
Homology Homotopy Appl. 12 (2010), no. 2, 245--320.
-
Zbl 1197.18002.
Harper, John E. Bar constructions and Quillen homology of modules over operads.
Algebr. Geom. Topol. 10 (2010), no. 1, 87--136.
-
MR2350752.
Noll, Thomas. Musical intervals and special linear transformations.
J. Math. Music 1 (2007), no. 2, 121--137.
-
MR2298823.
Costello, Kevin. Topological conformal field theories and Calabi-Yau categories.
Adv. Math. 210 (2007), no. 1, 165--214.
-
MR2275690.
Schweigert, Christoph; Fuchs, Jürgen; Runkel, Ingo. Categorification and correlation functions in conformal field theory.
International Congress of Mathematicians. Vol. III, 443--458, Eur. Math. Soc., Zürich, 2006.
-
MR2230696.
Noll, Thomas.
The topos of triads.
Colloquium on Mathematical Music Theory, 103--135,
Grazer Math. Ber., 347, Karl-Franzens-Univ. Graz, Graz, 2005.
-
MR2236265.
Shahbazi, Zohreh.
Relative gerbes.
J. Geom. Phys. 56 (2006), no. 8, 1326--1356.
-
MR2201329.
Hu, Po; Kriz, Igor.
On modular functors and the ideal Teichmüller tower.
Pure Appl. Math. Q. 1 (2005), no. 3, 665--682.
-
MR2116744.
Hu, Po; Kriz, Igor.
Closed and open conformal field theories and their anomalies.
Comm. Math. Phys. 254 (2005), no. 1, 221--253.
-
MR2171638.
Shallit, Jeffrey.
The mathematics of Per Nørgård's rhythmic infinity system.
Fibonacci Quart. 43 (2005), no. 3, 262--268.
-
MR2137300.
Jakobsen, Per K. and Lychagin, Valentin V.
Quantizations in a category of relations.
Lobachevskii J. Math. 17 (2005), 61--148.
-
MR2079383 (with I. Kriz).
Segal, Graeme.
The definition of conformal field theory.
Topology, geometry and quantum field theory, 421--577,
London Math. Soc. Lecture Note Ser., 308,
Cambridge Univ. Press, Cambridge, 2004.
Acknowledgement
Some of the material on this website is based upon work supported by the National Science Foundation under Grant DMS-0501208.