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SUMMARY:Diffeomorphisms of unit circle\, shape analysis and some  non-line
 ar PDEs - Irina Markina (Universitetet i Bergen)
DTSTART:20191010T150000Z
DTEND:20191010T160000Z
UID:TALK131878@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>In the talk\, we explain how univalent functions can be 
 used to&nbsp\;<br> analyze plain shapes. In its turn\, the univalent funct
 ions defined on&nbsp\;<br> the unit disc are closely related to the group 
 of oriented preserving&nbsp\;<br> diffeomorphisms of the unit circle. A mo
 ving plain shape gives rise to a&nbsp\;<br> curve on the group of diffeomo
 rphisms. The requirement to describe a&nbsp\;<br> shape modulo its rotatio
 n and/or scaling leads to a curve subordinated&nbsp\;<br> to some constrai
 nts. A geodesic curve of the motion of a shape is a&nbsp\;<br> solution to
  some non-linear partial differential equation. The choice of&nbsp\;<br> m
 etric leads to different PDEs\, that are generalizations of equations&nbsp
 \;<br> originated in fluid dynamics\, such us inviscid Burgers&#39\; equat
 ion\,&nbsp\;<br> Camassa-Holm\, Hunter-Saxton\, and KdV.</span><br><br><br
 ><br><br>
LOCATION:Seminar Room 2\, Newton Institute
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