# Brett Parker

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## About

Brett Parker received his undergraduate degree in mathematics and physics from Monash University in 2000. He went on to earn his PhD in mathematics from Stanford University in 2005, under the supervision of Yakov Eliashberg. Over the next 15 years, he worked as a postdoctoral researcher and lecturer at several institutions, including MIT, Berkeley, MSRI, University of Zurich, the Max Plank Institute at Bonn, ANU, and Monash University. In 2020, he joined ANU as a permanent faculty member. In 2021, he was awarded the Gavin Brown prize for the best Australian mathematics paper published in the previous ten years.

## Affiliations

- Analysis & geometry, Researcher
- Mathematical physics, Researcher
- Algebra & topology, Researcher

## Research interests

My research interests are focused on differential geometry and topology, mathematical physics, and symplectic geometry. I specialize in J-holomorphic curves, which are a powerful tool for understanding the structure of symplectic manifolds and are also important in string theory as they represent the worldsheets traced out over time by strings. To study J-holomorphic curves, I use degenerations where they limit to piecewise linear graphs, which are reminiscent of interacting particle trajectories and are known as tropical curves. To handle this mathematics, I have developed a technical tool called an exploded manifold, related to something called a log scheme in algebraic geometry. Exploded manifolds allow me to apply differential geometric techniques in degenerate and singular situations.

## Projects

## Teaching information

I have taught courses on many topics, including

- Real Analysis
- Analysis on manifolds
- Ordinary differential equations and vector calculus
- Algebra 1
- Galois Theory
- Symplectic geometry and classical mechanics
- Differential topology
- 4-Manifolds
- Calculus
- Complex analyis
- Topology

## Location

Room 2.80, Hanna Neumann Building 145

## Publications

- Parker, B 2018, 'De Rham theory of exploded manifolds', Geometry and Topology, vol. 22, no. 1, pp. 1-54.
- Parker, B 2017, 'Three Dimensional Tropical Correspondence Formula', Communications in Mathematical Physics, vol. 353, no. 2, pp. 791-819.
- Parker, B 2015, 'Holomorphic curves in exploded manifolds: Compactness', Advances in Mathematics, vol. 283, pp. 377-457.
- Parker, B 2012, 'Log geometry and exploded manifolds', Abhandlungen aus dem Mathematischen Seminar der UniversitÃ¤t Hamburg, vol. 82, no. 1, pp. 43-81.
- Parker, B 2012, 'Exploded Manifolds', Advances in Mathematics, vol. 229, no. 6, pp. 3256-3319.