Postdoc in pure mathematics

**King's College London**, office K4L.12.4

E-mail: daniel.platt.berlin (at) gmail.com

I'm a postdoc at King's College London with a research interest in geometric analysis and applications of differential geometry to machine learning. I previously studied for a PhD at Imperial College where my advisors were Jason Lotay (University of Oxford) and Sir Simon Donaldson (Imperial College).

Published | Publication | Text |
---|---|---|

2022 | K3 surfaces with two involutions and low Picard number. Joint with Dino Festi and Wim Nijgh. arXiv e-prints, arXiv:2210.14623. | |

2022 | G2 -instantons on resolutions of G2-orbifolds. arXiv e-prints, arXiv:2208.10903. | |

2022 | Group invariant machine learning by fundamental domain projections. Joint with Benjamin Aslan and David Sheard. arXiv e-prints, arXiv:2202.02164. | |

2022 | Associative submanifolds in Joyce's generalised Kummer constructions. Joint with Shubham Dwivedi and Thomas Walpuski. arXiv e-prints, arXiv:2202.00522. | |

2020 | Improved Estimates for G2-structures on the Generalised Kummer Construction. arXiv e-prints, arXiv:2011.00482. |

Date | Title | Event | Material |
---|---|---|---|

15 Nov 2022 | An application of numerical techniques to rigorous proof in special holonomy | Computational Differential Geometry and its Applications in Physics, Simons Center for Geometry and Physics | Slides |

6 Oct 2022 | Associatives in the generalised Kummer construction | University of Waterloo Geometry Seminar | |

11 Sep 2022 | Associatives in the generalised Kummer construction | Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems 2022 | |

26 Apr 2022 | Associatives in the generalised Kummer construction | KCL Geometry Seminar | |

3 Apr 2022 | G2-instantons | Geometric Analysis: Past, Present and Future [5] | Video |

7 Jan 2022 | An example of a G2-instanton over (K3 × Tˆ3)/Z_2 | Junior Special Geometers Meeting | |

17 Nov 2021 | G2-instantons on resolutions of G2-orbifolds | Louisiana State University Geometry Seminar | |

15 Sep 2021 | New estimates for G2-structures on resolutions of orbifolds | Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems 2021 | Video |

24/25 Jun 2021 | Gluing Constructions in Gauge Theory | Oxford-London Gauge Assembly | |

13 May 2021 | Convolutions on manifolds and applications to geometric deep learning | KCL/UCL Junior Geometry Seminar | Video |

26 Mar 2021 | Elliptic Operators on Non-Compact Manifolds | Imperial College Junior Geometry Seminar | |

27 Nov 2020 | Gluing of ASD-instantons | Brussels-London Geometry Research Network Lecture Series on Gauge Theory | Video |

24 Jun 2020 | G2-instantons and Joyce-Karigiannis manifolds | LMBA workshop “Special Geometries and Gauge Theory” | Video |

8 May 2019 | G2-instantons on Joyce-Karigiannis manifolds | CMO BIRS workshop “G2 Geometry and Related Topics”, Oaxaca | Video |

14 Dec 2018 | Introduction to gauge theory | Imperial College Junior Geometry Seminar, London | Notes |

9 May 2018 | Cohomogeneity one actions on symmetric spaces, London | KCL/UCL Junior Geometry Seminar | |

2 Feb 2017 | The Tractor construction, conformal geodesics, and applications to conformal compactifications | Potsdam University Geometry Seminar, Potsdam |

Date | Title | Event | Material |
---|---|---|---|

1 Dec 2020 | Group Invariant Machine Learning through Near-Isometries | Imperial College Data Science Virtual Poster Competition |

Date | Title | Link |
---|---|---|

2022 | KCL Geometry Seminar | Link |

6-8 Jan 2022 | Junior Special Geometers Meeting | Link |

12–16 Jul 2021 | London Geometry and Machine Learning Workshop | Link |

24–25 Sep 2020 | Geometry and Machine Learning with Applications to Biomedical Engineering | Link |

20–21 Aug 2020 | Oxford-London Gauge Assembly | Link |

9–15 Jun 2019 | British Isles Graduate Workshop “Gauge Theory with a View to Higher Dimensions” | Link |

Sep 2018–Jun 2020 | KCL/UCL Junior Geometry Seminar | Link |

Title | Description | Link |
---|---|---|

G2-instantons on resolutions of G2-orbifolds (PhD thesis) | My PhD thesis in which I explain a new construction method for G2-instantons | Link |

Getting started in Machine Learning as a Pure Mathematician | My personal opinions on what you should do if you're a pure mathematician that wants to get into machine learning | Link |

Seiberg-Witten Invariants | Notes for a talk given in the London Geometric Analysis Reading Seminar | Link |

What is a group and why should I care? | Slides for an interactive talk given in several Royal Institution Masterclasses | Link |

Cohomogeneity one actions on symmetric spaces of noncompact type | Mini-project on the classification of cohomogeneity one actions on noncompact symmetric spaces, contains many pictures and explicit matrix calculations | Link |

G2-instantons on non-compact manifolds | Mini-project on G2-instantons on non-compact manifolds with holonomy G2 obtained as solutions of the Hitchin flow equations | Link |

Conformal Geodesics in Cartan Calculus | My master's thesis, giving the proof that conformal geodesics in a conformal manifold are the canonical curves in the associated Cartan geometry | Link |

Differentialgeometrie | Lecture notes on differential geometry, written together with four other students in German | Link |

Gesammelte Materialien aus der Mathematischen Schülergesellschaft | Course notes for a one year course in a mathematical enrichment programme featuring plane geometry, elementary number theory, combinatorial game theory, graph theory, and inequalities; in German | Link |