Sussex PDEs 16/09/14 – Yanyan Li

Setting and Scene

Lecture theatre, talk during conference of specialism


Speakers, academics, students


Presentation of new work on the Nirenberg problem – “On (s^2, g0) which K(x)70 on s^2 is the Gauss curvature of g=e^(2w)g?” – for critique, publication, information of other participants and discussion

Act Sequence

Talk with scattered questions, followed by formal Q&A at the end


Very formal


Technical language. Powerpoint presentation.

Several references to what can be done, what is possible – “the solvability of…” – as well as what can be asked

  • Which K can be Kg for some g on M
  • Which K, [backwards E] a diffeomorph e.m^2 -> m^2 s.t. k.g can be realised as Kg, g= e^(2wg)

Also use of names of historical mathematicians to refer to mathematical tools, sometimes with reference to history

Gauss – Bonnet gives necessary condition

D. Koutroufiotis (1872), who was a former student of Nirenbuerg…

This was discovered by Cafarelli-Silvester. This makes the equation, more generally, degenerate

Stronger than usual tendency to refer to who did what when, and then what happened, etc – possibly cultural?

Very rough diagram of “a manifold”, represented by an oval with another dotted oval drawn as if an equator, with a certain area highlighted with a dot.

This was discovered by Cafarelli-Silvester. This makes the equation, more generally, degenerate

During the Q&A, a disagreement bubbled up, with an audience member claiming already to have solved something that the other referred to as unsolved, but the presenter made it clear that he was familiar with the others’ work and emphasised that it was done 10 years ago, and did not show what the questioner was now claiming that it showed. An interesting insight in the difficulty even for experts in knowing the scope and applicability of their own work without spending some time reflecting on it.


No interruptions except short questions for clarification until Q&A, when participants raise hands to ask longer questions




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