Daniel Galvin

About me

I am a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn. 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 co-organise the MPIM low-dimensional topology seminar.

Papers and preprints

• Algorithms in 4-manifold topology, with the participants of the workshop `Algorithms in 4-manifold topology' held at Regensburg university in September 2024. Preprint.
• 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

• October 2024 - Gave a talk at the MPIM low-dimensional topology seminar on `Pseudo-isotopy of 3-manifolds'.
• September 2024 - Gave a talk at the workshop `Algorithms in 4-manifold topology' at the University of Regensburg on `Stable classification of 4-manifolds'.
• July 2024 - Gave 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 on `Non-smoothable homeomorphisms of 4-manifolds with boundary'.
• July 2024 - Gave a talk at the conference `New structures in low-dimensional topology' at the Rényi institute in Budapest on `Stable smooth isotopy of surfaces in 4-manifolds'.
• 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:

Max Planck Institute for Mathematics
Vivatsgasse 7
53111
Bonn
Germany

Email address: galvin@mpim-bonn.mpg.de