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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Soliton equations and geometric flows

## Soliton equations and geometric flowsAdd to your list(s) Download to your calendar using vCal - Annalisa Calini (College of Charleston)
- Thursday 29 September 2022, 11:00-12:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. HYD2 - Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves Many classical objects in differential geometry are described by soliton equations: nonlinear PDEs with infinitely many conserved quantities that are (in some sense) solvable. Since the 1980s, studies of curve evolutions that are invariant under a group of transformations have unveiled more connections between geometric ﬂows and well-known integrable PDEs, such as the KdV, mKdV, sine-Gordon, and NLS equations. More recent studies have addressed discrete analogues coming from geometric discretizations of surfaces and curves, and associated evolutions. I will discuss a few natural geometric ﬂows for curves and polygons, highlighting the role of moving frames in integrability. The main examples are the vortex filament flow in Euclidean geometry and its relation to the NLS equation, Pinkall’s flow in centroaffine geometry and the KdV equation, and discretizations of the Adler-Gel’fand Dikii flows for curves in projective space. This talk is based on joint work with Tom Ivey and Gloria Marí-Beffa. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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