Sussex PDEs 15/09/14 – Giuseppe Mingione, Recent Progresses in Nonlinear Potential Theory

Setting and Scene

Formal talk in lecture theatre


Speaker and audience, all addressees


To present recent work with a collaborator, make it public and available for peer review

Act Sequence

Formal talk followed by Q&A


Quite formal with surprising moments of informal language


Many references to history of the topic, often used as terminology. Occasional colloquialisms (“this guy” to refer to a mathematical object). Heavy mathematical terminology, difficult to penetrate. Interludes of much more informal jokes provoked by technical issues.


Very occasional brief questions from older peers in the audience restricted to quick elucidation, longer questions in the Q&A


Describes how some kind of work done with classic PDEs can be extended to a broader field, non-linear PDEs.

In this talk were many interesting references to the history of the subject, both in the terminology constantly used

Riesz potential

reproduced pages of particular papers, reference made to what was “left open” and what happened next

and explicit references to the well-known tendency in the maths world for a mathematical discovery to be named after someone other than the initial discoverer. The tendency to use names as terminology sso frequently seems to be unique to mathematics, not so pronounced in Physics, for example.

Early in the talk some work was outlined and described as a

…completely trivial argument. This is just another way of writing down the Reisz potential… there’s no trick here.

Interestingly, it seems to be worthwhile to simply rearrange an expression in a way described as “trivial”, but will presumably offer some advantage to understanding or future work.

Much reference was made to estimates described as “sharp”, meaning that they would “return exact values” – at a guess this would suggest something locally accurate but more simple and manageable.

More than once, mathematical objects were personified, referred to as “this guy”.

Many references were made to Italian mathematicians. In fact, there were many Italian-sounding names on the list of attendees of this conference, although affiliations were largely to British Universities.


Points of Interest

  • Constant historical situation – every sentence is a series of references to history and to the work that has been done by others. This seems to tie in with a certain deference to the establishment observed by a computer scientist I met, who mentioned that mathematicians seemed much more likely to say that something was true because somebody respected said so than people working in his own field.
  • Rearranging an expression, without really changing it, sometimes seems to confer some advantage


Responses to this observation:


Three Narrators

Three Narrators



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s