# Dr Benjamin Aslan

## Mentor

## University College London

Benjamin is a recent PhD graduate from University College London in differential geometry. His research aims to understand higher dimensional geometric structures, that are models for spacetime in string theory, by the lower-dimensional objects it contains. He is also interested in applications of geometry to equivariant and invariant machine learning.

## 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__