## Teaching

Teaching and presenting mathematics is a major part of my life - I love the challenge of presenting a difficult subject in an engaging and accessible way.

As well as teaching at Latymer Upper School in Hammersmith, I helped set up the charitable organisation London Maths Outreach during my PhD, and have designed and presented many lectures and advanced short courses in mathematics. I have worked part-time as a private mathematics tutor since 2015, teaching everything from school-level mathematics to Oxbridge entrance exams and undergraduate courses.

## Portfolio of Teaching, Outreach and Public Engagement

#### Secondary School Teaching

Upon graduating from my undergraduate degree, I worked as a secondary school teacher at Latymer Upper School in London. I taught students of all ages, including an A-level further mathematics set, and helped out in the academic mentoring department.

#### After-school Mathematics Masterclasses

From 2017 to 2020 I designed and ran weekly after-school maths courses with King's College School in Wimbledon. In these sessions, I aimed to teach university and graduate level topics (including Functional analysis, Riemannian geometry and Varieties in projective space) in an accessible way, inspiring interest in mathematics beyond that discussed at school.

#### London Maths Outreach

During my PhD, I helped set up and run the charitable organisation London Maths Outreach to teach advanced maths for free to students of schools in London. I have created and taught classes in a wide range of subjects, including projective geometry and regular shapes in higher dimensions. During the UK lockdown this year, I co-created a YouTube series for London Maths Outreach on groups and symmetries, together with David Sheard.

#### UCL Science Centre

I have given several talks for the UCL Science Centre - a university-affiliated lecture series on science and mathematics, free to attend for sixth form students and teachers. My talks have been on "Geometry in Curvy Space" and "Shapes in Higher Dimensions".

#### Chalkdust Writer

Chalkdust is a wonderfully wild mathematics magazine, founded by some of my friends at UCL. I was lucky enough to be invited to contribute some articles about the winners of the Fields medal in 2018 and 2022 - if you'd like to read them, you can find my author page here.

## Talks and Short Courses

#### Geometry in Curvy Space

Angles in a triangle add to 180 degrees - everybody knows this. Except it isn't always true! For example, there is a triangle one can draw on the surface of the Earth with three 90 degree angles!

In this talk we investigate all the ways in which geometry changes if we work on curved surfaces, such as the sphere and hyperbolic space. We discover that, although angles do not always add to 180, some even more exciting things are true instead.

#### Shapes in Higher Dimensions

In 2 dimensions, there is a regular shape with any number of sides that we choose. But strangely, in 3 dimensions this is no longer true - in fact there are only 5 regular shapes, known as the Platonic solids.

What happens if we look at even higher dimensions? How is a shape even defined? In this talk we answer these questions, and find every single regular shape that exists, in any number of dimensions!

#### The 17 Possible Wallpaper Patterns

Any artist could tell you that there are an endless number of repeating wallpaper patterns. However, no matter what pattern you come up with, it has to fall into one of 17 different groups, depending on its *symmetry type*. In this talk, we will understand what is meant by the symmetry type of a repeating pattern, and prove using geometry that there are only 17 possibilities!