Speaker:

Tom Leinster (Glasgow)

Date/Time:

Mon, 06/02/2012 - 16:30

Room:

M103

Seminar series:

Many invariants of "size" in mathematics are tied together by a single

invariant, the Euler characteristic of a category. This phenomenon can be

found in contexts from orbifolds to associative algebras, taking in such

concrete invariants as volume and (conjecturally) perimeter of convex

sets. Closely related are invariants of "spread", typified by information

entropy. For example, the original category-theoretic invariant turns out

to solve a problem in mathematical ecology: that of how (theoretically) to

maximize biological diversity. I will conduct a tour through all of this,

assuming no knowledge of anything in particular.