Elizabethan vortices

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• Maciej Dunajski (DAMTP)
• Tuesday 18 October 2022, 16:00-17:00
• MR11.

If you have a question about this talk, please contact Professor Maciej Dunajski.

Abelian vortices are solitons in two space dimensions, with finite core size.

I will explain how radial solutions to the sinh–Gordon equation and the elliptic Tzitzeica equation can be interpreted as abelian vortices on certain surfaces of revolution. These surfaces have a conical excess angle at infinity (in a way which makes them similar to Elizabethan ruff collars, or certain green algae). They can not be embedded in the Euclidean 3-space but can be globally embedded in the hyperbolic space. I will show pictures of these embeddings, and discuss their existence which follows from the asymptotic analysis of a Painleve III ODE .

This talk is part of the Mathematical Physics Seminar series.

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