Joshua Lau
I am currently a PhD student in the Department of Mathematics at the University of Toronto. I have a broad range of research interests, which mostly intersect geometry, representation theory, or mathematical physics. More specifically, my current projects concern aspects of 2d and 3d mirror symmetry, and their interaction with representation theory and various flavours of quantization.
An example of mirror symmetry.
In the past, I have also worked on operator algebras, interactions between topology and logic, as well as computational stellar astrophysics.
Publications & Preprints
- Continuous approximate roots of polynomial equations via shape theory. (with V. Marin-Marquez). Submitted.
- K-theory of co-existentially closed continua. (with C. Eagle). Journal of Logic and Analysis, Volume 16, Paper No. 1, February 2024, Pages 1-22. arXiv link.
- 3D hydrodynamic simulations of massive main-sequence stars – I. Dynamics and mixing of convection and internal gravity waves. (with F. Herwig, P.R. Woodward, H. Mao, W.R. Thompson, P. Denissenkov, S. Blouin, R. Andrassy, A. Paul). Monthly Notices of the Royal Astronomical Society, Volume 525, Issue 2, October 2023, Pages 1601–1629. arXiv link.
Teaching
TA work at the University of Toronto
| Term | Course |
|---|---|
| Winter 2026 | MAT437/MAT1016: K-theory and C*-algebras MAT247: Algebra II |
| Fall 2025 | MAT436/MAT1011: Introduction to Linear Operators MAT1312: Geometry of Quantum Mechanics (Joint with the Fields Institute) |
| Summer 2025 | MAT327: Introduction to Topology |
| Winter 2025 | MAT437/MAT1016: K-theory and C*-algebras MAT137: Calculus with Proofs |
| Fall 2024 | MAT436/MAT1011: Introduction to Linear Operators MAT137: Calculus with Proofs |
| Summer 2024 | MAT301: Groups and Symmetries |
| Winter 2024 | MAT246: Concepts in Abstract Mathematics MAT223: Linear Algebra I |
| Fall 2023 | MAT437/MAT1016: K-theory and C*-algebras (Joint with the Fields Institute) MAT223: Linear Algebra I |
| Summer 2023 | MAT246: Concepts in Abstract Mathematics |
| Winter 2023 | MAT223: Linear Algebra I MAT133: Calculus and Linear Algebra for Commerce |
| Fall 2022 | MAT133: Calculus and Linear Algebra for Commerce |
TA work at the University of Victoria
| Term | Course |
|---|---|
| Winter 2022 | Math 101: Calculus II |
| Fall 2021 | Math 236: Introduction to Real Analysis Math and Stats Assistance Centre Tutor |
| Winter 2021 | Math 101: Calculus II |
| Fall 2020 | Math 109: Introduction to Calculus |
Other
I am avid amateur violinist, interested in western classical music and Polish/Slovak folk music. I have performed with numerous community orchestras around Toronto. I especially enjoy playing chamber music, and I am always looking to play with others. I love all kinds of classical music but in particular I am a big fan of classical era composers (especially Mozart!), Brahms, and Johann Strauss II. Below are some examples of my playing, please do not take them too seriously!
A performance of Danse Macabre with the Rosedale Symphony Orchestra (RSO) in Toronto, November 9th 2024:
A performance of the Karlowicz Violin Concerto with the Rosedale Symphony Orchestra (RSO) in Toronto, November 1st 2025: