Daniel Galvin

About me

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.

Papers and preprints

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

Visits and talks

• 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.

Teaching and seminars

• 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

• 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.

Contact details

Mail address:

School of Mathematics and Statistics
University of Glasgow
University Place
Glasgow
G12 8QQ

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