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SUMMARY:Soliton equations and geometric flows - Annalisa Calini (College o
 f Charleston)
DTSTART:20220929T100000Z
DTEND:20220929T110000Z
UID:TALK180404@talks.cam.ac.uk
DESCRIPTION:Many classical objects in differential geometry are described 
 by soliton equations: nonlinear PDEs with infinitely many conserved quanti
 ties that are (in some sense) solvable. Since the 1980s\, studies of curve
  evolutions that are invariant under a group of transformations have unvei
 led more connections between geometric flows and well-known integrable PD
 Es\, such as the KdV\, mKdV\, sine-Gordon\, and NLS equations.&nbsp\; More
  recent studies have addressed discrete analogues coming from geometric di
 scretizations of surfaces and curves\, and associated evolutions. I&nbsp\;
 will discuss a few natural geometric flows for curves and polygons\, high
 lighting the role of moving frames in integrability.&nbsp\; The main examp
 les are the vortex filament flow in Euclidean geometry and its relation to
  the NLS equation\, Pinkall&rsquo\;s flow in centroaffine geometry and the
  KdV equation\, and discretizations of the Adler-Gel&rsquo\;fand Dikii flo
 ws for curves in projective space. This talk is based on joint work with T
 om Ivey and Gloria Mar&iacute\;-Beffa.
LOCATION:Seminar Room 2\, Newton Institute
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