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).

From 2010 to 2013 I worked as an NSF postdoc at Northwestern University.

From 2013 to 2019 I worked as a research fellow at the IBS Center for Geometry and Physics in Pohang, South Korea.

Publications:

2020 | Edge stabilization in the homology of graph braid groups. With B. H. An and B. Knudsen. Geom. Topol. 24 (1), 421–469. |

2019 | Endomorphisms are adjoint to representations. With J. Hirsh and D. Lejay. J. Homotopy Relat. Struct. Online First, 17 pages. |

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

Subdivisional spaces and graph braid groups. With B. H. An and B. Knudsen. Doc. Math. 24, 1513–1583. | |

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:

2020 | Asymptotic homology of graph braid groups. With B. H. An and B. Knudsen. ArXiv:2005.08286, 19 pages. |

2019 | An action of the Polishchuk differential operator via punctured surfaces. With M. Tavakol. Accepted, Int. Math. Res. Not. IMRN, 37 pages. |

Endomorphism operads of functors. With J. Hirsh and D. Lejay. ArXiv:1906.09006, 20 pages. | |

Coextension of scalars in operad theory. With P. Hackney. ArXiv:1906.12275, 39 pages. | |

Betti numbers of unordered configuration spaces of small graphs. ArXiv:1906.00692, 728 pages. | |

Homotopy transfer and formality. With G. Horel. ArXiv:1906.03475, 20 pages. | |

2018 | Dwyer–Kan homotopy theory for cyclic operads. With P. Hackney. Accepted, Proc. Edinb. Math. Soc. (2), 25 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.

This is an atlas of Betti numbers of unordered configuration spaces of small graphs.

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

Here are notes for some talks I've given.