I am a fourth year PhD student at the University of Glasgow. For the first two years of my PhD I was at Durham University. My supervisor is Dr. Mark Powell. From September 2024 I will be a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. My interests are in topology, specifically in knot theory and manifolds, most often in dimensions 3 and 4.

- The Casson-Sullivan invariant for homeomorphisms of 4-manifolds. Preprint.
- Non-smoothable homeomorphisms of 4-manifolds with boundary, with Roberto Ladu. Preprint.

- July 2024 - Will give a talk at the special session `The Interface Between Smooth and Symplectic 4-manifolds' at the joint meeting of the AMS and UMI in Palermo.
- July 2024 - Will give a talk at the conference `New structures in low-dimensional topology' at the Rényi institute in Budapest.
- April 2024 - Attended the masterclass `Homotopical methods in manifold theory` at the University of Copenhagen.
- February 2024 - Gave a talk at the University of Glasgow Geometry and Topology seminar on `Generalised Dehn twists and Torelli groups of simply-connected 4-manifolds'.
- December 2023 - Gave a talk at the MPIM low-dimensional topology seminar on `The Casson-Sullivan invariant for self-homeomorphisms of 4-manifolds'.
- November 2023 - Gave at talk at the Durham University GANDALF Seminar on `Extending homeomorphisms in dimension 4'.
- July 2023 - Attended the conference `Gauge Theory and Topology: in Celebration of Peter Kronheimer's 60th Birthday'.
- June 2023 - Attended the focused research group `Algebraic Methods in 4-Manifold Topology' and gave a talk on 'Non-smoothable homeomorphisms of non-simply-connected 4-manifolds'.
- March 2023 - Attended `The low dimensional workshop' at the Rényi institute in Budapest and gave a lightning talk on `Non-smoothable homeomorphisms of non-simply-connected 4-manifolds'.
- January 2023 - Attended the conference `Morphisms in low-dimensional topology' at Oberwolfach and gave a lightning talk on `Non-isotopic but diffeomorphic smooth structures on 4-manifolds'.
- September 2022 - Attended the conference `4-manifolds: from above and below' in Luminy.
- June 2022 - Attended the conference `Surfaces in 4-manifolds' in Le Croisic.
- August 2021 - Visited the Max Planck Institute for Mathematics in Bonn.

- 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.

- 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.

**Mail address**:

School of Mathematics and Statistics

University of Glasgow

University Place

Glasgow

G12 8QQ

**Email address**: d.galvin.1@research.gla.ac.uk