I am interested in hyperbolic geometry, geometric topology, Teichmüller theory, and representations of fundamental groups. I mostly think about character varieties of surfaces and 3-manifolds. Character varieties provide a rich area of study and have been shown to reflect geometric and topological information of the manifold itself.

The pictures above and below are a visualisation of a collection of earthquakes on Teichmüller space of the once-punctured torus in two coordinate systems. Here Teichmüller space can be shown to be a specific component of the SL(2,C)-character variety of the once-punctured torus.

My CV is here.

• An invitation to Culler-Shalen theory in arbitrary characteristic (with Eric Chesebro, Ben Martin, Stephan Tillmann), in preparation.

• Earthquakes on the once-punctured torus, Experimental Mathematics, DOI: 10.1080/10586458.2023.2294491, 2024.

This work was also announced at the MATRIX-MFO tandem workshop Invariants and Structures in Low-Dimensional Topology in September 2021 here.

• I completed honours at the University of Sydney in 2015 under the supervision of Stephan Tillmann. My honours topic was The Mapping Class Group and its Action on the Character Variety of the Once-Punctured Torus, and my thesis is here.

• Character varieties and essential surfaces in arbitrary characteristic

67th Annual Meeting of the Australian Mathematical Society, University of Queensland (December, 2023)

Topology Seminar, Monash University (October, 2023)

• Earthquakes on the once-punctured torus

Institut de Mathématiques de Jussieu-Paris Rive Gauche (October, 2022)

Geometry and Topology Seminar, University of Warwick (October, 2022)

Nearly Carbon-Neutral Geometric Topology (September, 2022)

Recording can be found here.  

Dynamics, Foliations, and Geometry II (February, 2022)

Graduate Talks in Geometry and Topology (GT)^2 (September, 2021) 

Recording can be found here.

• What is dynamics on the character variety? 

What is…? Seminar, University of Queensland (June, 2020). 

Notes can be found here.

• Dynamics of character varieties for the once-punctured torus (poster), 

New Connections in Representation Theory (February, 2020) 

The poster can be found here.

• Mapping class group action on the character variety, 

63rd Annual Meeting of the Australiam Mathematical Society, Monash University (December 2019)

The slides can be found here. 

This talk received an honourable mention as part of the BH Neumann Award.

I am employed as a tutor in the School of Mathematics and Statistics, University of Sydney. I have tutored multiple classes including:

• MATH3061 Geometry and Topology

• MATH3066 Algebra and Logic

• MATH2022 Linear and Abstract Algebra and MATH2922 Linear and Abstract Algebra (Advanced)

• MATH2069 Discrete Mathematics and Graph Theory

• MATH1002 Linear Algebra and MATH1902 Linear Algebra (Advanced)

• MATH1003 Integral Calculus and Modelling and MATH1023 Multivariable Calculus and Modelling

• MATH1064 Discrete Mathematics for Computation

Student mentor in the School of Mathematics and Statistics, University of Sydney mentoring program for women and gender diverse students in advanced mathematics, 2022. 

Co-supervised AMSI Vacation Research Project by Youheng Yao titled ``The topology of character varieties of once-punctured torus bundles" (with Stephan Tillmann), 2020/2021.

• • I help organise the Mathematical Postgraduate Society (MaPS) at the University of Sydney.

  • I am one of the postgraduate representatives at the School of Mathematics and Statistics, University of Sydney.

  • Ellena Moskovsky, Yossi Bokor and I founded the Graduate Talks in Geometry and Topology (GT)^2 online seminar series in 2021 for Australian graduate students in geometry and topology. This was supported by MATRIX and AMSI. I continue to organise (GT)^2 with Em Thompson and James Morgan.

  • Em Thompson, James Morgan, and Yossi Bokor and I organised an in-person extension of (GT)^2 called Graduate Talks in Geometry and Topology Get-Together (GT)^3 held in July 2022. This was again supported by MATRIX and AMSI.

  • I was the student member of the Australian Mathematical Society Women in Mathematical Sciences Special Interest Group 2022 executive committee.

  • I used to post on MathsFeed.