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.

Publications:

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. | |

2013 | Homotopically trivializing the circle in the framed little disks. J. Topol. DOI: 10.1112/jtopol/jtt040, 36 pages. |

The minimal model for the Batalin-Vilkovisky operad. With B. Vallette. Selecta Math. 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:

2016 | An operadic approach to operator-valued free cumulants. In preparation. |

A non-crossing word cooperad for free homotopy probability theory. ArXiv:1602.08867, 17 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 Unpublished note, 2 pages.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.

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.