I'm interested in knotted surfaces and 4-manifolds, particularly branched covers, braided surfaces, Lefschetz fibrations, and trisections. Recently, I've been thinking about questions involving braid monodromy and extendable mapping class groups of surfaces in 4-manifolds.
Publications 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
- (Jun 2026) Australian Geometric Topology Webinar (virtual)
- (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 (virtual)
- (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
Seminars
I am one of the organizers of the GT GAPS online seminar — see Activities. Here are some other seminars I've organised at UT Austin.
- (Spring 2025) Reading group on mapping class groups of complex surfaces, with Aislinn Smith
- (Spring 2024) 3-Manifolds Learning Seminar, with Luis Torres
- (Spring 2023) Junior Topology Seminar
- (Fall 2022) Characteristic Classes learning seminar, with Casandra Monroe and Luis Torres
- (Fall 2021-Spring 2022) Sophex Seminar, with Jen Rozenblit