I've have to give a talk for our maths society. Topic suggestions?

[Tom Gilroy]

Hi everybody,

I'm a first year Ph.D student in mathematics and I've been asked to give an hour long talk for the university maths society. Speakers have the choice to talk about just about anything maths related, however the focus of most talks is usually the discussion of a classic maths problem (like Bachet's weighing problem, for example) or the speaker will give an introduction to the area they study (or another area they have become interested in), or they may possibly discuss a recent result in their own research.

I could give an introductory talk about the area I study (Vertex Operator Algebras), however, the basic definitions and axioms are quite long and involved, and the simplest non-trivial example also has quite a long construction. I'm not sure I could get through the basic terminology, definitions and an example in the hour and do so at a pace where the audience has time to digest and absorb the concepts. Also, the subject involves a lot of formal series, and I think some might lose interest just at the sight of them.

I think a discussion of a classic problem might make for an overall more enjoyable talk, but I'm at a loss for ideas. Ideally, I'd like to discuss something where the basic question is very easy to understand, the maths gets more involved and I have time to discuss the attempts to date if it's an open problem, or to outline the resolution if it has been solved.

 

[arildno]

Does it have to be technical?
Could you perhaps, prepare a historical treatise upon say, operator algebras in general, what motivated the formulation, what types of uses it has shown itself capable and so on?

 

[Tom Gilroy]

Actually no, it doesn't have to be technical at all, and that's a pretty good idea. The motivations for the formulation of Vertex Operator Algebras is quite an interesting story, and they've been a tremendously important tool in mathematics and physics in the last 25 years.

My only concern is that some might feel at the end of such a discussion people would want to know more about the technicalities.

 

[arildno]

My only concern is that some might feel at the end of such a discussion people would want to know more about the technicalities.

Well, and why can't you prepare some technical answers to your "concluding" question "Any questions?".

That is, reflect over what sort of technical issues might be raised on basis of your speech, and prepare appropriate answers, or at least sources of reference you might give the interested person.

 

[arildno]

Another, rather more technical topic could be to develop an answer to the question:
"Why are the definitions in VOA so complicated?"

After all, although I know nothing about VOA, I would think it started out as a cool idea that seemed simple enough.
But that when the exploration began, the topic was seen to be a logical minefield with numerous pitfalls and unfortunate explosions.
Thus, the winding path to today's definition has been one of trial and error that could be interesting to look at.
Not the least some of the spectacular errors made at the beginning.

 

[Tom Gilroy]

Thank you, those are both excellent ideas.