I recently graduated with a PhD in mathematics from the Mathematical Sciences Institute of the Australian National University.

New, April 2018: The final version of my PhD thesis is available for open access.

July 2017: Slides from my PhD finishing talk

Dec 2016, subset of the above: Slides from my AustMS 2016 talk

My research is focused on (the theoretical analysis of) geometric flows, i.e. the application of nonlinear parabolic PDE to Riemannian Geometry. The preprint of my first paper (with Ben Andrews) on flowing diffeomorphisms of the flat torus is now available on the arχiv.

I'm also very interested in the interactive visualization of differential geometry. You can find a work-in-progress of an interactive demonstration of the diffeomorphism flow I mentioned above here. A more accessible flow-related curiosity is my demonstration of the Curve-shortening flow.

profile for Anthony Carapetis at Mathematics Stack Exchange, Q&A for people studying math at any level and professionals in related fields

The procrastination technique that causes me the least guilt is answering questions on Math.StackExchange.

Some older things I've written: