John Bamberg, University of Western Australia will be lecturing at Summer School 2016 on Projective Geometry. He spoke to us about his work, why he choose mathematics as a career and why he feels lucky!
What are the most interesting “big questions” in your field?
In finite projective geometry, the general consensus is that the following problems are the “biggest” open problems in our field:
– Is the order of a finite projective plane always a prime power?
– Is a finite projective plane of prime order always Desarguesian?
– The classification of ovoids of finite projective 3-spaces.
– The classification of ovals of Desarguesian projective planes.
– The Buekenhout-Metz Conjecture.
– The “Small-blocking set” Conjecture.
– Does there exist a 430-cap of PG(6,4) with two intersection numbers with respect to hyperplanes?
– Do there exist non-classical generalised hexagons or generalised octagons?
What kind of problems are you interested in broadly in the field? (maths as a whole)
I’m interested in problems that show the interplay between different areas of mathematics. In my own field, this can be between geometry and group theory, or between algebraic number theory and combinatorics.
What are your favourite applications of your work?
Some of my work in finite group theory has been used to classify combinatorial objects. I did not know back then that it would be used in this way down the track!
What are some other areas of maths that are particularly interesting to you?
Group theory, representation theory, algebraic combinatorics, number theory, the list goes on!
Why did you become a mathematician?
I really enjoyed mathematics at university, more so than at school. So I followed what I enjoyed, and I still enjoy mathematics to this day.
Do you have any advice for future mathematicians?
Read as much as you can. It’s never a waste, you will somehow use what you read later, sometimes indirectly, sometimes you will see surprising connections.
Biggest mathematical/statistical regret?
I never took that differential geometry course in 3rd year!
Biggest mathematical/statistical success?
I’ve been lucky to have encountered four mathematicians early in my career that were very supportive and an excellent influence. They know who they are!