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 |