I am a tenure-track research fellow at the IBS Center for Geometry and Physics in Pohang, South Korea.

I received my PhD in 2010 under the supervision of John Terilla at the Graduate Center of the City University of New York (alternate site) and spent three years as an NSF postdoc at Northwestern University.

My research interests include operadic and homotopy algebra, quantum field theory, and the moduli space of Riemann surfaces.

Upcoming organizational work:

May 20–24, 2019:
Current directions in homotopical algebra

Feb 3–7, 2020:
Configuration spaces of graphs

Upcoming and recent travel plans:

2018 | November 5–9 | Hefei, Anhui |

July 16–20 | New York, New York | |

July 9–13 | Toulouse, Occitanie | |

July 2–6 | Cambridge, England | |

June 25–29 | Stockholm, Uppland | |

June 18–22 | Skye, Scotland | |

May 4–8 | Chengdu, Sichuan | |

January 24–30 | Cambridge, Massachusetts | |

January 22–23 | Irvine, California |

Publications:

2019 | A criterion for existence of right-induced model structures. With P. Hackney. Bull. London Math. Soc. 51, 309-326. |

2018 | An operadic approach to operator-valued free cumulants. Higher Structures 2, 42–56. |

A non-crossing word cooperad for free homotopy probability theory. MATRIX Book Series 1, 77–99. | |

2017 | Betti numbers of configuration spaces of surfaces. With B. Knudsen. J. London Math. Soc. 96 (2), 367–393. |

Homotopy probability theory on a Riemannian manifold and the Euler equation. With J. Terilla. New York J. Math. 23, 1065–1085. | |

2016 | Model structures for coalgebras. With J. Hirsh. Proc. Amer. Math. Soc 144, 1467–1481. |

2015 | Homotopy probability theory I. With J.-S. Park and J. Terilla. J. Homotopy Relat. Struct. 10 (3), 425–435. |

Homotopy probability theory II. With J.-S. Park and J. Terilla. J. Homotopy Relat. Struct. 10 (3), 623–635. | |

2014 | An update on domineering on rectangular boards. Integers 14, 13 pages. |

Formal formality of the hypercommutative algebras of low dimensional Calabi-Yau varieties. Comm. Math. Phys. 327, 433–441. | |

Homotopically trivializing the circle in the framed little disks. J. Topol. 7, 641–676. | |

2013 | The minimal model for the Batalin–Vilkovisky operad. With B. Vallette. Selecta Math. (N.S.) 19 (1), 1–47. |

2010 | Algebras over Ω(coFrob). With J. Terilla and T. Tradler. J. Homotopy Relat. Struct. 5, 15–36. |

2009 | Intrinsically n-linked complete graphs. With D. O'Donnol. Tokyo J. Math. 32, 113–125. |

2005 | Positions of value *2 in generalized domineering and chess. Integers 5 (1), 13 pages. |

Preprints:

2019 | An action of the Polishchuk differential operator via punctured surfaces. With M. Tavakol. ArXiv:1904.07520, 37 pages. |

Endomorphisms of functors ⊢ representations. With J. Hirsh and D. Lejay. ArXiv:1904.06987, 15 pages. | |

2018 | Dwyer–Kan homotopy theory for cyclic operads. With P. Hackney. ArXiv:1809.06322, 25 pages. |

Edge stabilization in the homology of graph braid groups. With B. H. An and B. Knudsen. ArXiv:1806.05585, 31 pages. | |

2017 | Subdivisional spaces and graph braid groups. With B. H. An and B. Knudsen. Accepted, Doc. Math., 63 pages. |

2015 | Chain level string topology operations. With K. Poirier and N. Rounds. ArXiv:1506.02596, 67 pages. |

2014 | Cones in homotopy probability theory. With J. Terilla. ArXiv:1410.5506, 8 pages. |

2004 | Temperature two in domineering. Unpublished note, 2 pages. |

ArXiv versions of most of these papers and preprints are available.

I can be contacted at gabriel_at_ibs.re.kr or gabriel.c.drummond.cole_at_gmail.

Research Statement (not necessarily current)

I compile and maintain notes in LaTeX of many conferences, seminars, workshops, and courses.

Here are notes for some talks I've given.