Em K. Thompson

About me

I am a PhD candidate at Monash University, Melbourne.  My supervisors are Prof. Jessica Purcell and Assoc. Prof. Daniel Mathews. You can contact me at em dot thompson at monash dot edu. I live and work on the stolen lands of the Kulin Nations.

Research interests

I am a low-dimensional topologist, with a particular interest in knot theory and 3-manifold triangulations. I have spent a lot of time thinking about A-polynomials. I frequently work with hyperbolic geometry and also think about character varieties. I am interested in connections to other areas such as cluster algebras, symplectic geometry and quantum invariants. 

Publications and preprints

Twisting, ladder graphs and A-polynomials // New York Journal of Mathematics 29 (2023) 739-770 // NYJM // arXiv

A-polynomials of fillings of the Whitehead sister (with Josh Howie, Dan Mathews and Jessica Purcell) // International Journal of Mathematics 34 (2023) 2350085 // IJM // arXiv

An algorithm to construct one-vertex triangulations of Heegaard splittings (with Alex He and James Morgan) // preprint // arXiv 

On a volume invariant of 3-manifolds (with Marc Kegel, Arunima Ray, Jonathan Spreer and Stephan Tillmann) // preprint // arXiv 

Talks

Mar 2023 - The magic manifold, twisted torus knots, and minimal triangulations // Monash Topology Seminar

Dec 2023 - An algorithm to construct one-vertex triangulations of Heegaard splittings // AustMS Conference // Slides

Sep 2023 - An algorithm to construct one-vertex triangulations of Heegaard splittings // Monash Topology Seminar

Sep 2023 - Layered solid tori: a generalisation and an application // Monash Milestone Review Seminar

Feb 2023 - Describing deformations // MATRIX Dynamics, Foliations and Geometry Workshop III

Jun 2022 - A-polynomials and cluster algebras (lightning talk) // Geometry, Arithmetic, and Groups // Slides

Jun 2022 - Describing deformations // The 39th Annual Workshop in Geometric Topology // Slides 

Feb 2022 - Twisting, ladder graphs and A-polynomials // MATRIX Dynamics, Foliations and Geometry Workshop II

Dec 2021 - Twisting and A-polynomials // AustMS Conference // Notes

Nov 2021 - Twisting, ladder graphs and A-polynomials // CUNY Geometry and Topology Seminar // Slides

Sep 2021 - Ten minute intro to calculating A-polynomials // MATRIX-MFO Invariants and Structures in Low Dimensional Topology // Notes 

Jun 2021 - Untangling algebra // Monash Faculty of Science 3MT // Vimeo

May 2021 - What is a hyperbolic knot? // UQ What is...? Seminar // Notes

Mar 2021 - Simplifying A-polynomial calculations for knots related by Dehn filling // Graduate Talks on Geometry and Topology // YouTube

Dec 2020 - A-polynomials of knots related by Dehn filling // AustMS Conference // Slides

Awards

2022 AustMS WIMSIG Cheryl E. Praeger Travel Award - This award is designed to provide full or partial support for women, trans and gender diverse mathematicians based in Australia to attend conferences or to visit collaborators, with approximately eight domestic Travel Awards and four international Travel Awards awarded annually.

2022 Faculty of Science Young Science Leader Award - This award recognises students who have actively participated or promoted social inclusion initiatives including social justice, enterprise and efforts towards charitable or not-for-profit groups.

2022 Faculty of Science Award for Outstanding Contributions by a Graduate Research Student to the Life of the Faculty/School Community (joint with Ellena Moskovsky) - This award celebrates outstanding contribution/s to the life of the Faculty of Science/School community, by individuals or teams of graduate research students within the Faculty of Science, that are above and beyond their own research and the expectations of a postgraduate student.

Teaching

I am passionate about quality maths education at all levels. At university level I enjoy teaching board-tutorials. I also enjoy working with secondary school students, particularly in my role at the National Mathematics Summer School. 

I have been a teaching associate at Monash University for several years, teaching the following classes at various times:

Service

I am the student representative on the Monash School of Maths Equity Committee. In this role, I started the GEMs (Gender Equity in Maths) Mentoring Program for undergraduate maths students at Monash who identify as any gender that is underrepresented in maths.  

I was an organiser of the Graduate Talks in Geometry and Topology seminar series, and the associated (GT)^2 Get-Together, which was held at MATRIX in Creswick in July 2022.