I'm interested in low-dimensional topology and geometry, especially braids and surface mapping class groups in the context of 3- and 4-dimensional knot theory. Recently, I've been thinking about questions involving branched covers.
writing
papers and preprints
- Higher degree covering moves for 3-manifolds. arXiv:2507.15141 [math.GT], July 2025
- From braid groups to mapping class groups (with Lei Chen). Mathematische Zeitschrift 303, no. 2 (2023): 27.
notes
- Concordance of surfaces in 4-manifolds, expository notes written by Remy Bohm and myself following Maggie Miller's lectures for the New Structures Summer School in Budapest in 2024. To be published in a collection of notes by Springer.
talks
- (Nov 2025) Representing 3-manifolds via branched covers, University of Notre Dame Topology Seminar
- (Sep 2025) Representing 3-manifolds via branched covers, University of Nebraska-Lincoln Seminar on Groups, Semigroups, and Topology
- (Sep 2025) Representing 3-manifolds via branched covers, GT GAPS (online)
- (Jun 2025) Covering moves for 3-manifolds (lightning talk), Trisectors Workshop, UT Austin
- (Apr 2025) Covering moves for 3-manifolds (short talk), Graduate Student Topology and Geometry Conference, Indiana University Bloomington
expository
- (Spring 2025) Constructing taut foliations from branched surfaces, Foliations Log Cabin Workshop, St. George, Utah
- (Summer 2024) Trisected 4-manifolds as branched coverings of the 4-sphere (online lightning talk), Trisectors Zoom Pre-Workshop
- (Spring 2024) Universal Links, UT Austin Junior Topology Seminar