Sussex PDEs 15/09/14 – Maria J Esteban, Symmetry and Symmetry Breaking for Optimisers of Functional Inequalities

Setting and Scene

Lecture theatre in which all of the talks were held, formal talk

Participants

Audience of 35, all of equal status, one speaker.

Ends

To present research for peer review; to update others on developments in the field; to give a paper the status of having been presented

Act Sequence

Presentation with powerpoint slides, followed by short Q&A

Key

Formal and serious

Instrumentalities

Many technical terms, backed up with diagrams in the powerpoint presentation. Metaphorical explanations

Norms

No interruptions until the Q&A, at which two or three questions leading to 30-second answers is the norm.

Genre

Explanation of some research using metaphor and diagrams to aid understanding.

At the beginning, the speaker notes that “symmetry leads to simplifications”

Metaphorical language is used. For example, speaking of mathematical objects as having agency:

…so the potential tries to put this near to the…

There is competition between these ground state solutions

Description of phenomena using a particular characteristic:

Blow-up phenomena

Using language of location to talk about the work being done:

…many inequalities that we are used to, embedded in this class of inequalities.

…this little neighbourhood in which they could prove symmetry…

…you can work in this space over here…

…take one of these lumps and throw it very far away… (this referring to some alteration causing a lump-like structure in a graph to appear farther along one axis)

Many of these were around a certain diagram which showed regions in which symmetry or otherwise had been proved by area, labelled with a list of names of people who had done the work along with the years in which they had achieved this.

Also some interesting casual language:

…these are some very nice functions…

There was a reference to proving things by computation rather than theory.

…we did this numerically, playing around, and it was a surprise to everybody working in the area…

Some subtlety to what was in fact proved, which needed highlighting to the audience

We proved uniqueness, but it is not honest to say that it is a symmetry result.

And to the subjective experience of the mathematicians

There is this tiny region that remains to be studied. When you have been working at a thing for years you really really want to find the solution.

An image was used to illustrate the idea of a self-adaptive grid, something like this:

https://i0.wp.com/www.geocomputation.org/1999/042/gc042fig13b.gif

Points of interest

  • Descriptions carry certain features, for example personification of mathematical phenomena
  • An area of mathematical work was described in very geographical terms, then wedded to the historical aspect by labelling with names and years
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