Below is a list of the original research projects that students have worked on with me. Some project titles are linked to the final document. If you are a Colby student interested in low-dimensional topology, geometry, or knot theory, please don't hesitate to talk with me about research opportunities. Summer research positions fill up quickly, so I encourage you to speak with me in the fall if you are interested in summer research. In addition to honors projects and summer research students, I also often hire research assistants for the academic year. Those projects tend to be less ambitious and are not usually listed here.

Project Students Project Type Term
Heegaard splittings of certain 3-manifolds associated with the Cantor set Sarah Kirker '11 Honors January/Spring 2011
Low-dimensional topology and vector calculus Jennie Buskin '13
Philip Prosapio '13
Summer 2011
Quandles and Spatial Graphs Byoungwook Jang '14
Pratap Luitel '14
Summer 2012
Unknotting number and sutured manifold theory Alex Rasmussen '13 Honors 2012-2013
Brunnian Theta Graphs Anna Kronaeur '16
Dan Medici '16
Summer 2014
Thin position for triangulations Dan Medici '16
Nick Murphy '16
Haoyu Song '16
Summer 2015
The curve complex and bridge position Joseph Malionek '17
Muyuan Zhang '18
Summer 2016
Thin position and simplicial complexes Weiyan Huang '18
Muyuan Zhang '18
Summer 2017
Relationships between new knot invariants Qidong He '21
Charles Parham '20
Summer 2018
Bridge Trisections of Spun Knots Cindy Zhang '22
January 2021 - Fall 2021 jointly advised by Aranda and Pongtanapaisan.
Exploring the Additivity of Knot Invariants Matt Cerrato '23
Will Fitch '23
Summer 2021