My mathematical interests broadly lie in the realm of low-dimensional topology. I am particularly interested in algebraic invariants of knots in 3-manifolds and loops in surfaces. My recent projects have focused on problems in flat virtual knot theory, working with knots and links that are combinatorial models of curves on surfaces.

During my undergraduate career at the College of Wooster, I was involved with research on Klein links (links constructed using a rectangular representation of the punctured Klein bottle). Dr. Jennifer Bowen created a website with our collection of papers and publications about these links here.

**Talks**

Dartmouth Topology Seminar | Hanover, NH, February 1 and 8, 2018 | (Invited) |

Joint Mathematics Meetings | San Diego, CA, January 10-13, 2017 | |

Knots in Washington XLV | Washington, DC, December 10, 2017 | (Invited) |

Dartmouth Topology Seminar | Hanover, NH, November 16, 2017 | (Invited) |

AMS Fall Sectional Meeting | Riverside, CA, November 4-5, 2017 | (Invited) |

Seminar on Knots and Representation Theory | Moscow, Russia, October 17, 2017 | (Invited, Skype) |

Knots in Washington XLIV | Washington, DC, April 28-30, 2017 | (Invited) |

AMS Spring Sectional Meeting | Pullman, WA, April 22-23, 2017 | (Invited) |

Knots in Washington XLIII | Washington, DC, December 9-11, 2016 | (Invited) |

**Posters**

Graduate Poster Session | Hanover, NH, April 11, 2017 |

**Conferences Attended**

Knots in Hellas | Ancient Olympia, Greece, July 17-23, 2016 |

Joint Math Meetings | Seattle, WA, January 6-9, 2016 |

Knots in Washington XLI | Washington, DC, December 4-6, 2015 |

AMS Fall Sectional Meetings | Chicago, IL, October 3-4, 2015 |

UnKnot Conference II | Granville, OH, July 15-18, 2012 |

**Publications**

- Complexity of virtual multistrings,
*submitted*, arXiv:1709.01340 [math.GT]. - Multistring based matrices,
*submitted*, arXiv:1709.00564 [math.GT]. - Minimizing intersection points of curves under virtual homotopy, with V. Chernov and R. Sadykov,
*submitted*, arXiv:1708.03064 [math.GT]. - Klein link multiplicity and recursion, with S. Smith-Polderman,
*Rose-Hulman Undergraduate Mathematics Journal***17**(2) (2016), 146-156. - Klein links and braids, with S. Smith-Polderman,
*Rose-Hulman Undergraduate Mathematics Journal*,**14**(2013), 71-84. - A preliminary study of Klein knots, with L. Catalano, R. Ruzvidzo, J. Bowen, and J. Ramsay,
*Proc. Midstates Conference for Undergraduate Research in Computer Science and Mathematics*(2010), 10-17.

**Seminar Talks (Dartmouth College)**

Topology Seminar | |

Multistring Based Matrices (2 parts) | February 2017 |

Complexity of Virtual Multistrings | November 2017 |

Graduate Student Seminar | |

Hilbert's 1st Problem | February 2017 |

Counting Intersections of Loops on Surfaces | November 2016 |

Knots in Thickened Surfaces | May 2016 |

Classification of 3-Manifolds | July 2015 |

Understanding Geometry Through Linear Algebra | February 2015 |

Quaternion Geometry | July 2014 |

Kneser Graphs and Topological Combinatorics | January 2014 |