Research Interests

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

Joint Mathematics Meetings San Diego, CA, January 10-13, 2017
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 IIGranville, OH, July 15-18, 2012

Publications


Seminar Talks (Dartmouth College)

Topology Seminar
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 SurfacesMay 2016
Classification of 3-ManifoldsJuly 2015
Understanding Geometry Through Linear Algebra February 2015
Quaternion Geometry July 2014
Kneser Graphs and Topological Combinatorics January 2014