Ugignadl

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Hey everyone, thanks for reading my blog. For the first post I guess it’s a good idea to say a little about myself. Professionally, I’m a young academic. I live in the inner west of Sydney, Newtown, and commute to Wollongong to work at the University. I have many interests… an incurable nerd, and geek, so anything you can think of there I have most likely more than dabbled in. I’ve done more than my fair share of fantasy role playing, strategy trading card games, miniature battling, chess, and a huge number of video games.
Work has been great recently. I have funding to do some research into higher order geometric heat flows, which belong to the field of differential geometry. Geometric heat flows are the mathematical animals used to describe the complete behaviour of any geometric object evolving over time; under any force, any law. It’s quite difficult because it is so general. One of the key determining attributes on how we analyse these wacky critter is the `order’ of the flow. It is hard to explain, but first and second order geometric heat type flows are, for the most part, well understood (some people would vehemently disagree, that’s ok). There is still a rich area of research there for second order flows, and it could be argued that there are more natural phenomena that are explained by second order flows. But, going as far back as 1957, physicists have proposed fourth and sometimes even higher than fourth order flows to explain natural phenomena. So there is plenty of motivation. In the last few years there has been some research into the particular fourth order flow called the Willmore flow, which pushes objects into being locally spherical. There are other infamous fourth order flows like the surface diffusion flow, which I am working with right now. But I hope to be more general than that and apply our arguments to all kinds of higher order flows. Here’s hoping! Cheers.
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