Thomas M. Fiore

Published Papers, Submitted Papers, Papers in Progress,

Talks, Reviews, Expository Essays

Published/Accepted Papers

Click on article title for abstract and paper.

What is the Jacobian of a Riemann Surface with Boundary?.
Joint with Igor Kriz.
Slightly revised version will appear in the Proceedings of the 2007 Max-Planck Workshop on
Hochschild and Cyclic (co-)homology and Applications to Geometry and Physics,
Aspects of Mathematics, Viehweg, Braunschweig. 27 pages.

Model Structures on the Category of Small Double Categories.
Joint with Simona Paoli and Dorette Pronk.
Slightly revised version in press at Algebraic and Geometric Topology. 103 pages.

Laplaza Sets, or How to Select Coherence Diagrams for Pseudo Algebras.
Joint with Po Hu and Igor Kriz.
Advances in Mathematics, Volume 218, Number 6, pages 1705-1722, 2008. 17 pages.

Musical Actions of Dihedral Groups.
Joint with Alissa Crans and Ramon Satyendra.
In press at the American Mathematical Monthly. 27 pages.

Pseudo Algebras and Pseudo Double Categories.
Journal of Homotopy and Related Structures, Volume 2, Number 2, pages 119-170, 2007. 51 pages.

On the Cobordism and Commutative Monoid with Cancellation Approaches to Conformal Field Theory.
Journal of Pure and Applied Algebra, Volume 209 Number 3, pages 583-620, 2007. 37 pages.

Pseudo Limits, Biadjoints, and Pseudo Algebras: Categorical Foundations of Conformal Field Theory.
Memoirs of the American Mathematical Society 182 (2006), no. 860. 171 pages.

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

Submitted Papers

A Thomason Model Structure on the Category of Small n-fold Categories.
Joint with Simona Paoli.
CRM Preprint. 54 pages.

Papers in Progress

Fundamental Double Category of a Bisimplicial Set.
Joint with Simona Paoli.

Monads in Double Categories.
Joint with Nicola Gambino and Joachim Kock.

Double Categorical K-Theory.
Joint with Mark Johnson.

Euler Characteristics of Categories.
Joint with Roman Sauer.

Talks

Homotopy Theory of Double Categories.
Centre de Recerca Matemàtica, Spain, June 30th, 2008.
HOCAT 2008. Homotopy Structures in Geometry and Algebra; Derived Categories, Higher Categories.

Selecting Coherence Diagrams for Pseudo Algebras over Theories.
Centre de Recerca Matemàtica, Spain, May 21st, 2008.
Passe-partout Seminar.

Homotopy Theory of Double Categories.
Københavns Universitet, Denmark, December 17th, 2007.
Topology Seminar.

Generalized Rings for Arakelov Geometry.
Universitat Autònoma de Barcelona, Spain, October 15th, 2007.
Tropical Geometry Seminar.

Homotopy Theory of Double Categories.
Centre de Recerca Matemàtica, Spain, October 4th, 2007.
Passe-partout Seminar.

Model Structures on the Category of Small Double Categories.
Carvoeiro, Portugal, June 19th, 2007.
International Category Theory Meeting, CT2007.
Slides pdf.

2007 REU: Seven Lectures on Mathematical Music Theory.
University of Chicago, July 16th-26th, 2007.
Slides, Problems, and other Material.

The Homotopy Theory of Double Categories.
University of Michigan, March 8th, 2007.
University of Michigan Topology Seminar.

The Homotopy Theory of Double Categories.
Wayne State University, March 6th, 2007.
Wayne State Topology Seminar.

Double Categories and Pseudo Algebras.
Fields Institute, February 20th, 2007.
Seminar Up to Homotopy.
Slides Part 1 Part 2

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.
Pennsylvania State University Altoona, November 17th, 2006.
Pennsylvania State University Altoona, Colloquium.

Jacobians of Riemann Surfaces with Parametrized Boundary.
Pennsylvania State University Altoona, November 16th, 2006.
Pennsylvania State University Topology Seminar.

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.
University of Chicago, April 11th, 2006.
Category theory and its applications:
A conference in memory of Saunders Mac Lane.
Slides dvi, pdf, ps.

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.

Categories and Jacobians.
Michigan State University, February 14th, 2005.
MSU Topology Seminar.

On Jacobians of Complex Curves with Boundary.
AMS Central Section Meeting, October 23rd, 2004.
Special Session on Algebraic Topology.

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.

Pseudo Algebraic Structures in Conformal Field Theory.
IMA Summer Program on n-Categories, June 11th, 2004.
Introduction dvi, pdf, ps.
Slides dvi, pdf, ps.

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

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.

Expository Essays

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

Music and Knowledge in Two Texts by Franz Kafka. An Honors Thesis at the University of Pittsburgh
in the subject of Germanic Languages and Literatures. 1998.