Daniel Platt
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). My postdoc supervisors are Richard Thomas and Toby Wiseman.
Publications and preprints
| Published | Publication | Text |
|---|---|---|
| 2024 | Towards a uniqueness theorem for static black holes in Kaluza-Klein theory with small circle size. Joint with Emma Albertini, Toby Wiseman. arXiv e-prints, arXiv:2410.20967. | |
| 2024 | Harmonic 1-forms on real loci of Calabi-Yau manifolds. Joint with Michael R. Douglas and Yidi Qi. arXiv e-prints, arXiv:2405.19402. | |
| 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. |
Publications and preprints where I am not a first author, and short papers
| Published | Publication | Text |
|---|---|---|
| 2024 | A New Canonical Log-Euclidean Kernel for Symmetric Positive Definite Matrices for EEG Analysis. Joint with Gabriel Leander Wagner vom Berg, Vera Röhr, Benjamin Blankertz. IEEE Transactions on Biomedical Engineering. | |
| 2024 | Group-invariant machine learning on the Kreuzer-Skarke dataset. Joint with Christian Ewert, Sumner Magruder, Vera Maiboroda, Yueyang Shen, Pragya Singh. Physics Letters B. |
Academic talks
| Date | Title | Event | Material |
|---|---|---|---|
| 31 Oct 2024 | New examples of G2-instantons | Mathematics Inspired by String Theory workshop, Chinese University of Hong Kong | |
| 25 Nov 2024 | Numerical approximations of harmonic 1-forms on real loci of Calabi-Yau manifolds | Imperial College Geometry and Topology Seminar | |
| 2 Jul 2024 | Numerical approximations of harmonic 1-forms on real loci of Calabi-Yau manifolds | Humboldt University Berlin Gauge Theory Research Seminar | Slides (most part was blackboard talk) |
| 15 May 2024 | New Spin(7)-instantons on compact manifolds | Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics (Durham, North Carolina) | Slides |
| 25 Apr 2024 | New Spin(7)-instantons on compact manifolds | 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 | An example of a G2-instanton on a resolution of (K3xT3)/Z22 coming from a stable bundle | 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 | Perturbing an approximate solution to a PDE in geometry obtained with computer aid | 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 |
Posters
| 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 |
Organised academic events and seminars
| 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 |
Miscellaneous
| 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 |