Daniel E. Platt

activity

20202026

most citedGroup invariant machine learning by fundamental domain projections

2 citations · 3 across the 7 of their papers we have counts for

collaborators

7 papers

math.DG2026

Nowhere-vanishing harmonic 1-forms on real loci of K3-fibred Calabi-Yau 3-folds

Shih-Kai Chiu, Daniel Platt, Calum Spicer

We develop an analytic construction of nowhere-vanishing harmonic $1$ -forms on real loci of K3-fibred Calabi-Yau $3$ -folds with collapsing Ricci-flat Kähler metrics. We apply our c…

math.DG2024

Harmonic $1$ -forms on real loci of Calabi-Yau manifolds

Michael R. Douglas, Daniel Platt, Yidi Qi +1

We numerically study whether there exist nowhere vanishing harmonic $1$ -forms on the real locus of some carefully constructed examples of Calabi-Yau manifolds, which would then giv…

math.AG2022★ 1 cited

K3 surfaces with two involutions and low Picard number

Dino Festi, Wim Nijgh, Daniel Platt

Let $X$ be a complex algebraic K3 surface of degree $2 d$ and with Picard number $ρ$ . Assume that $X$ admits two commuting involutions: one holomorphic and one anti-holomorphic. In…

math.DG2022

$G_{2}$ -instantons on resolutions of $G_{2}$ -orbifolds

Daniel Platt

We explain a construction of $G_{2}$ -instantons on manifolds obtained by resolving $G_{2}$ -orbifolds. This includes the case of $G_{2}$ -instantons on resolutions of $T^{7} /Γ$ as a special…

cs.LG2022★ 2 cited

Group invariant machine learning by fundamental domain projections

Benjamin Aslan, Daniel Platt, David Sheard

We approach the well-studied problem of supervised group invariant and equivariant machine learning from the point of view of geometric topology. We propose a novel approach using…

math.DG2022

Associative submanifolds in Joyce's generalised Kummer constructions

Shubham Dwivedi, Daniel Platt, Thomas Walpuski

This article constructs examples of associative submanifolds in $G_{2}$ -manifolds obtained by resolving $G_{2}$ -orbifolds using Joyce's generalised Kummer construction. As the $G_{2}$ -ma…

math.DG2020

Improved Estimates for $G_{2}$ -structures on the Generalised Kummer Construction

Daniel Platt

The resolution of the $G_{2}$ -orbifold $T^{7} /Γ$ , where $Γ$ is a suitably chosen finite group, admits a $1$ -parameter family of $G_{2}$ -structures with small torsion $φ^{t}$ , obtained by g…