Mathematical Field Notes

Archive for February 2013

Convex Integration (talk notes)

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In case you were unable to take notes from my talk (either because you were unable to attend or because you were present) I’ve written them up below in some detail. They’re basically just a summary of Borrelli’s notes.

Also relevant is the preliminary cartoon which contains many of the essential ideaas.

Warning: Images are large may take some time to load.

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Written by Jonny Evans

February 15, 2013 at 1:32 pm

Posted in Geometry, h-principle

Convex integration

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On Thursday I’ll be giving a talk on convex integration at the London h-principle learning seminar. This will be a dry and technical subject, so I thought I’d create some light-hearted preliminary reading. Here then, in cartoon-form, is the simplest version of 1-dimensional convex integration, used to construct an immersed loop in the plane whose tangent vector has winding number zero.

The technical details of the talk will be heavily based on these notes by Vincent Borrelli, which is an excellent place to learn all this stuff from.

Warning: The cartoon is big (about 1MB) and may take time to load.

Read the rest of this entry »

Written by Jonny Evans

February 10, 2013 at 9:06 pm