The International Conference on Trends in the Mathematical Representation of Space took place on December 1-2, 2007. This year marked the fiftieth anniversary of Alexander Grothendieck’s famed Tohoku paper.
Grothendieck was renowned for trying to tackle problems at the “correct” level of generality. Others have followed this same approach in order to unify diverse fields of mathematics, and address their most significant problems. Quite how this approach has impacted, and will impact, upon physics remains a matter of investigation.
The talks at this conference concern geometric, logical, and category- or topos-theoretical descriptions of reality. To start you off, why not try listening to Colin McLarty’s talk on generality versus unity?
More details are available at the conference website: http://www.bu.edu/cphs/ces/seminars-conferences/math-reps-space/