# David Sheard

## Mentor

## University College London

David is a final year PhD student at University College London with a research background in pure mathematics, in particular geometric topology and group theory. He also does research in geometric machine learning, applying ideas from geometric topology to group invariant machine learning problems.

## Project

###### Group invariant machine learning for Calabi-Yau polyhedra

There are many group invariant machine learning models, i.e. learnable functions that give the same output if the input is acted on by a group. One novel approach is using fundamental domain projections - an approach which is particularly useful if the group which acts is very large [1]. There are many large string theory datasets with large symmetry groups, which make good benchmarks for group invariant machine learning models. One such example is the Kreuzer-Skarke dataset of Calabi-Yau three-folds coming from reflexive polyhedra and their Hodge numbers [2].

In this project, we will apply invariant machine learning via fundamental domain projections to the Kreuzer-Skarke dataset and compare this with other group invariant machine learning techniques (e.g. data augmentation and deep sets), as well models that are not group invariant.

**References**

[1] *Group invariant machine learning by fundamental domain projections**, *Benjamin Aslan, Daniel Platt, David Sheard, arXiv 2022

[2] __Calabi-Yau data__