Postdoc in pure mathematics

**Imperial College London**

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

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

Published | Publication | Text |
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2024 | K3 surfaces with two involutions and low Picard number. Joint with Dino Festi and Wim Nijgh. Geometriae Dedicata. | |

2024 | G2-instantons on resolutions of G2-orbifolds. Communications in Mathematical Physics. | |

2023 | Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds. Joint with Mateo Galdeano, Yuuji Tanaka, and Luya Wang. arXiv e-prints, arXiv:2310.03451. | |

2022 | Group invariant machine learning by fundamental domain projections. Joint with Benjamin Aslan and David Sheard. NeurIPS 2022 proceedings. | |

2022 | Associative submanifolds in Joyce's generalised Kummer constructions. Joint with Shubham Dwivedi and Thomas Walpuski. Communications in Mathematical Physics. | Link |

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

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

22-26 Apr 2024 | tba | Special Riemannian geometries in dimensions 6,7,8 | |

20 Mar 2024 | Numerical approximations of harmonic 1-forms on real loci of Calabi-Yau manifolds | Loughborough University | Slides |

8 Feb 2024 | Group invariant machine learning on pure maths datasets | University of Hong Kong | Slides |

29 Nov 2023 | New examples of Spin(7)-instantons on compact manifolds | University of Leeds Geometry Seminar | |

16 Nov 2023 | Numerically verified proofs | Faculty of Natural Sciences Postdoc Showcase | |

31 Oct 2023 | K3 surfaces with two involutions and low Picard number | University of Kyoto Algebraic Geometry Seminar | |

30 Oct 2023 | G2-instantons on resolutions of G2-orbifolds | University of Kyoto Geometry and Topology Seminar | |

20 Sep 2023 | G2-instantons on the Generalised Kummer Construction | Rutgers University Gauge Theory Seminar | |

13 Sep 2023 | Approximations of harmonic 1-forms on real loci of Calabi-Yau 3-folds | Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics: Progress and Open Problems | |

19-23 Jun 2023 | K3 surfaces with low Picard number | Workshop BRIDGES: Specials geometries and gauge theories | |

13 Jun 2023 | K3 surfaces with low Picard number | Geometry Seminar at Universita degli studi di Milano | |

29 May 2023 | tba | Spinorial and Octonionic Aspects of G2 and Spin(7) Geometry | Slides Video |

12 May 2023 | An Explicit Example of a G2-instanton on a resolution of K3×T^3/Z_2 coming from a stable bundle | Gauge Seminar at Humboldt University Berlin | |

10 May 2023 | K3 surfaces with low Picard number | Geometry Seminar at Humboldt University Berlin | |

3 May 2023 | Group invariant machine learning by fundamental domain projections | University of Nottingham Online Machine Learning Seminar | Video Slides |

27 Apr 2023 | tba | King's College London Analysis Seminar | |

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 (step 2 is false as stated) |

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 |
---|---|---|---|

29 Mar 2023 | A Numerically Verifiable Proof for M-theory Compactifications (Poster) | Kings and Queens of Gravity | |

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

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

11 Aug 2023 | Calibrated Geometry Fun Day | Link |

3-7 Jul 2023 | British Isles Graduate Workshop “Geometric flows and related topics ” | Link (archive) |

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 |
---|---|---|

From Zero to Riemannian Manifolds in 8 Pages | 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 |