Elizabethan vortices
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 Maciej Dunajski (DAMTP)
 Tuesday 18 October 2022, 16:0017:00
 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 sinhâ€“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 3space 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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