Research

Graduate students (current):

• Sam Lewis-Monkman

• Nick Meyer

Graduate students (past):

• Vince Longo (PhD earned 2021, co-advised with Mark Brittenham)

• Jesse Moeller (PhD earned 2021, co-advised with Mark Brittenham)

• Marla Williams (PhD earned 2020, co-advised with Mark Brittenham)

• Ana Wright (PhD earned 2022, co-advised with Mark Brittenham)

Undergraduate research assistants (past):

• Gabriel Adams

• Derek Davies

• Lucy DePooter

• Hanna Hoffman

• Andrew Loken

• Kenji Nakagawa

• Mia Nguyen

• Rilee Potter

• Jack Rankin

• Ethan Romary

• Rebecca Sorsen

• Olivia Thiel

Preprints:

1. (with Jeffrey Meier) Knots bounding non-isotopic ribbon disks. [arXiv]

2. (with Ethan Romary) A family of Andrews-Curtis trivializations via 4-manifold trisections. [arXiv]

Publications:

1. Hexagonal lattice diagrams for complex curves in CP^2, to appear in Trans. Amer. Math. Soc. [arXiv]

2. (with Jason Joseph, Jeffrey Meier, and Maggie Miller) Bridge trisections and Seifert solids, to appear in Alg. & Geom. Top. [arXiv]

3. (with Maggie Miller) Equivalent characterizations of handle-ribbon knots, to appear in Comm. Anal. Geom. [arXiv]

4. (with Jeffrey Meier and Abigail Thompson)  Cubic graphs induced by bridge trisections, to appear in Math. Res. Lett. [arXiv]

5. (with W. Allred, M. Aragón, Z. Dooley, A. Goldman, Y. Lei, I. Martinez, N. Meyer, D. Peters, S. Warrander, and A. Wright) Tri-plane diagrams for simple surfaces in S^4,  J. Knot Theory Ramifications 32 (2023), no. 6, Paper No. 2350041, 28 pp. [arXiv] [journal]

6. (with Jeffrey Meier) Generalized square knots and homotopy 4-spheres,  J. Differential Geom. 122 (2022), no. 1, 69-129 [arXiv] [journal]

7. (with Jason Joseph, Jeffrey Meier, and Maggie Miller) Bridge trisections and classical knotted surface theory, Pacific J. Math 319 (2022), no. 2, 343-369. [arXiv] [journal]

8.  (with Rebecca Sorsen) The Kauffman bracket expansion of a generalized crossing, Top. Proc. 58 (2021), 298-301. [journal]

9. The Powell conjecture and reducing sphere complexes, J. London Math. Soc. (2)  101 (2020), 328-348. [arXiv] [journal]

10. (with Jeffrey Meier) Bridge trisections of knotted surfaces in 4-manifolds, Proc. Nat. Acad. Sci. 115 (2018), no. 43, 10880-10886. [arXiv] [journal]

11. (with Jeffrey Meier) Characterizing Dehn surgeries on links via trisections, Proc. Nat. Acad. Sci. 115 (2018), no. 43, 10887-10893. [arXiv] [journal]

12. (with Jeffrey Meier) Genus-two trisections are standard, Geom. Topol. 21 (2017), no. 3, 1583-1630. [arXiv] [journal]

13. (with Jeffrey Meier) Bridge trisections of knotted surfaces in S^4, Trans. Amer. Math. Soc. 369 (2017), no. 10, 7343-7386. [arXiv] [journal]

14. (with Jessica Purcell) Independence of volume and genus g bridge numbers, Proc. Amer. Math. Soc. 145 (2017), no. 4, 1805-1818. [arXiv] [journal]

15. (with Derek Davies) Natural properties of the trunk of the knot, J. Knot Theory Ramifications 26 (2017), no. 12, 1750080, 9 pp. [arXiv] [journal]

16. (with Jeffrey Meier and Trent Schirmer) Classification of trisections and the generalized property R conjecture, Proc. Amer. Math. Soc. 144 (2016), no. 11, 4983-4997. [arXiv] [journal]

17. (with B. Jang, A. Kronaeur, P. Luitel, D. Medici, and S. A. Taylor) New examples of Brunnian theta graphs, Involve 9 (2016), no. 5, 857-875. [arXiv] [journal]

18. (with Samuel Taylor) Products of Farey graphs are totally geodesic in the pants graph, J. Topol. Anal. 8 (2016), no. 2, 287-311. [arXiv] [journal]

19. Uniqueness of higher genus bridge surfaces for torus knots, Math Proc. Cambridge Philos. Soc. 159 (2015), no. 1, 79-88. [arXiv] [journal]

20. (with Ryan Blair) Knots with compressible thin levels, Alg. Geom. Top. 15 (2015), no. 3, 1691-1715. [arXiv] [journal]

21. (with R. Sean Bowman and Scott A. Taylor) Bridge spectra of twisted torus knots, Int. Math. Res. Notices (2015), no. 16, 7336-7356. [arXiv] [journal]

22. Bridge spectra of iterated torus knots, Comm. Anal. Geom. 22 (2014), no. 5, 931-963. [arXiv] [journal]

23. Infinite cardinalities in the Hausdorff metric geometry, Involve 7 (2014), 285-293. [journal]

24. Bridge and pants complexities of knots, J. London Math. Soc. (2) 87 (2013), 43-68. [arXiv] [journal]

25. A lower bound on the width of satellite knots, Top. Proc. 40 (2012), 179-188. [arXiv] [journal]

26. Unexpected local minima in the width complexes for knots, Alg. Geom. Top. 11 (2011), no. 2, 1097-1106. [arXiv] [journal]

27. Properties of knots preserved by cabling, Comm. Anal. Geom. 19 (2011), no. 3, 541-562. [arXiv] [journal]

28. (with C. Blackburn, K. Lund, S. Schlicker, and P. Sigmon) A missing prime configuration in the Hausdorff Metric Geometry, J. Geom. 92 (2009), no. 1-2, 28-59. [journal]