About
From November 2026, I am a Postdoctoral Research Assistant at University College London (UCL), working with Mikhail Karpukhin. I recently completed my Ph.D. at the University of Warwick.
My research focuses on mean curvature flow and related topics. I am broadly interested in problems in geometric analysis.
You can reach me at joshua.daniels-holgate.15(at)ucl.ac.uk
Published Articles
- Approximation of mean curvature flow with generic singularities by smooth flows with surgery. (2021). Advances in Mathematics, Volume 410, Part A, 2022, doi:10.1016/j.aim.2022.108715, [arXiv:2104.11647].
- Mean Curvature Flow from Conical Singularities. (2024). Joint with Otis Chodosh and Felix Schulze. Inventiones Mathematicae, Volume 238, 1041–1066, 2024, doi:10.1007/s00222-024-01296-8, [arXiv:2312.00759].
- How close is too close for singular mean curvature flows? (2025). Joint with Or Hershkovits. Calculus of Varations and Partial Differential Equations, Volume 65, article 234 (2026) doi:10.1007/s00526-026-03403-4 [arXiv:2503.11522].
Preprints
- Generic mean curvature flow has finitely many singularities (2026). Joint with Or Hershkovits and Gábor Székelyhidi [arXiv:2610.12763].
- Non-uniqueness in Mean Curvature Flow: Non-canonical solutions via the parabolic Allen--Cahn (2025). [arXiv:2510.06979].
- Backwards uniqueness for Mean curvature flow with asymptotically conical singularities (2025). Joint with Or Hershkovits [arXiv:2507.16805].
Invited Talks
- Mean Curvature Flow from Conical Singularities
- London PDE Seminar, Imperial College London, UK (2025)
- Geometric Analysis Seminar, Cambridge University, UK (2025)
- GANG Seminar, QMUL, UK (2025)
- Pisan Workshop Saga Ep. V, Pisa, Italy (2024)
- Topology and Geometry Seminar, Hebrew University of Jerusalem, (Online) (2024)
- Geometry Seminar, Leeds, UK (2024)
- Geometry Seminar, Stanford, USA (2023)
- Approximation of mean curvature flow with generic singularities by smooth flows with surgery
- Junior Analysis Seminar, Imperial College, London, UK (2023)
- Geometry Seminar, Sorbonne, Paris, France (2023)
- Geometry Seminar, University of Copenhagen, (Online) (2022)
- Topology and Geometry Seminar, Hebrew University of Jerusalem, (Online) (2022)
- Geometric Analysis Seminar, OvGU Magdeburg, Germany (2022)
- Partial Differential Equations (Hybrid Meeting), MFO, Oberwolfach, Germany (2021)
- PDE CDT Seminar, University of Oxford, UK (2021)
- Geometric Analysis Seminar, Rutgers, (Online) (2021)