Daniel Galvin

About me

I am a Bing postdoctoral fellow at the University of Texas at Austin. Previously I was a postdoctoral fellow at the Max Planck Institute for Mathematics, and I completed my PhD at the University of Glasgow, where my supervisor was Dr. Mark Powell. For the first two years of my PhD I was at Durham University. My interests are in topology, specifically in knot theory and manifolds, most often in dimensions 3 and 4. Currently, I am particularly interested in diffeomorphisms and homeomorphisms of 4-manifolds. I will be visiting the Max Planck Institute for Mathematics in Bonn from mid May until mid August this year.

Papers and preprints

Non-smoothable surfaces in the 4-sphere, with Anthony Conway. Preprint.
Geometric obstructions for xi-fillings of 3-manifolds, with Peter Teichner and Simona Veselá. Preprint.
Pseudo-isotopy versus isotopy for homeomorphisms of 4-manifolds, with Isacco Nonino. Preprint.
Algorithms in 4-manifold topology, with the participants of the workshop `Algorithms in 4-manifold topology' held at Regensburg university in September 2024. Accepted for publication in Algebraic & Geometric Topology.
The Casson-Sullivan invariant for homeomorphisms of 4-manifolds. Preprint.
Non-smoothable homeomorphisms of 4-manifolds with boundary, with Roberto Ladu. Advances in Mathematics, Volume 467, 6 March 2025, 110191.

List of talks

Teaching and seminars

Austin Spring 2026: M367K Topology.
Austin Autumn 2025: M325K Discrete.
Glasgow 2023-2024 Multivariable calculus and linear algebra tutorials.
Glasgow 2022-2023 K-theory and applications learning seminar.
Durham 2021-2022: Analysis I tutorials.
Durham 2021-2022: Modified surgery learning seminar.

Projects and notes

My PhD thesis: Non-smoothable homeomorphisms of 4-manifolds.
Ronnie Lee's generator for L_5(Z[Z]). A freely available exposition on a result of Ronnie Lee's, previously only contained within a handwritten letter addressed to Martin Scharlemann from the 1970s.
Low dimensional applications of the torus trick. (Written for the MPIM topological manifolds seminar in collaboration with Weizhe Niu and Benjamin Ruppik.)
My Masters project: Groups of Homotopy Spheres.

The University of Texas at Austin, Department of Mathematics 2515 Speedway, PMA 9-164. Austin, TX 78712

Contact details

Mail address:

The University of Texas at Austin
Department of Mathematics
2515 Speedway
Austin, TX 78712
United States of America

Email address: daniel.galvin@austin.utexas.edu