## Carl McTague | |

Aspiring: | mathematician, composer, photographer, fiddler |

email: | first dot last name at rochester dot edu |

post: |
Mathematics Department University of Rochester Rochester, NY 14627, USA |

Interests: Topology & Algebraic Geometry, Geometric Methods in Generative Music Composition.

Blog: *Der Himmel über Rochester*, How to Recognize Generators for String Bordism, After *Laocoön* [or Before?], Binomial Coefficients & Villainy, Seminar Web Design, Comments on a Paper of Karcher, Noah in Norwich, Computing Hirzebruch *L*-Polynomials, Catullus of the Canopy, Dürer’s *Melencolia I*, Existential Angst, How to Optimize a Codex, … (RSS)

Compositions:
In Medias Res,
’Round Midnight,
The Lyre of Ur,
Ripples Through Pitch Space,
Portrait of Poincaré,
(ii-V-I)^{7},
Six Integers.

Publications:

- A New Approach to Euler Calculus for Continuous Integrands, preprint.
- On the Greatest Common Divisor of Binomial Coefficients
(

), (*n**q*

), (*n*2 *q*

),…,*n*3 *q**Amer. Math. Monthly*124-4 (2017) 353–356. - Shrinking the Fibers of a Submersion Splits the Riemann Tensor, preprint.
- tmf Is Not a Ring Spectrum Quotient of String Bordism, to appear in
*New Directions in Homotopy Theory*, Contemp. Math. (2017). - The Cayley Plane and String Bordism,
*Geometry & Topology*18-4 (2014) 2045–2078. - The Cayley plane and the Witten genus, preprint.
- Stiefel-Whitney Numbers for Singular Varieties,
*Math. Proc. Camb. Phil. Soc.*150 (2011) 273–289. - Stratified Morse Theory, unpublished expository essay written for Part III of the Cambridge Tripos, 2005.
- The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing, with DP Feldman and JP Crutchfield,
*Chaos*18-4 (2008) 59–73. - Automated Pattern Detection—An Algorithm for Constructing Optimally Synchronizing Multi-Regular Language Filters, with JP Crutchfield,
*Theoretical Computer Science*359 (2006) 306–328.

Talks:

- New Applications of Differential Geometry to Big Data, 2014 Topology Seminar, Edinburgh.
- A New Approach to Euler Calculus for Continuous Integrands, 2012 ATMCS 5, Edinburgh.
- How Twisted Is Infinity?, 2007 McMenemy Seminar, Trinity Hall Cambridge.
- Characteristic, Signature, and Singularity, 2006 Fulbright Seminar, Berlin.
- Music Through Computation, invited keynote speech at IMS2003, Imperial College London.

Teaching: Knot Theory, Honors Analysis, Honors Multivariable Calculus, Differential Equations, Linear Algebra.

Miscellanea: Signature Optimizer for Bookbinding, Topological Methods in Algebraic Advertising, Blow-up, Escaping the Flood of Time, Egon’s Twinkie, A Much Deserved Pie in the Face.

Fiddling: The Scholar (kitchen), Solo jigs, reels, and more reels (live). Duo reels and jigs with uilleann piper Tim Benson (studio).

Inspiration: Doug Ravenel, Jack Morava, Burt Totaro, Conlon Nancarrow.