Research

I like thinking about problems in low-dimensional topology related to knots, embeddings, and smooth objects in four dimensions, especially using the trisection technology originally developed by Gay and Kirby.

My recent work includes an exploration of weak reducibility for bridge-trisected knotted surfaces, with an eye toward a partial classification of four-bridge surface knots, and proving the first known triplane crossing number of a non-trivial 2-knot.

Publications and preprints

The 2-Twist Spun Trefoil has Crossing Number Six (joint with M. Gabbard, S. Gong, J. Osnes). in prep.
Weak Reducibility for Bridge-Trisected Knotted Surfaces. in prep.

Research Talks

Weak Reduction for 2-Knots. California Polytechnic University, AMS Western Sectional [invited], May 2025.
Weak Reductions of 4-Bridge Knotted S2’s in S4. University of Kansas, AMS Central Sectional, March 2025.
Weak Reductions of 4-Bridge Knotted S2’s in S4. UNL, Groups, Semigroups, and Topology Seminar, February 2025.
Weak Reductions of 4-Bridge Knotted S2’s in S4. UNL, Graduate Student Seminar, February 2025.
Low-Crossing Bridge Trisections. UNL, Graduate Students Talking about Groups, Semigroups, and Topology Seminar, February 2025.

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