REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
Ben Webster
ABSTRACT: It's
a long established principle that an interesting way to think about
numbers as the sizes of sets or dimensions of vector spaces, or better
yet, the Euler characteristic of complexes. You can't have a map
between numbers, but you can have one between sets or vector spaces.
For example, Euler characteristic of topological spaces is not
functorial, but homology is.
One can try to extend this idea to a bigger stage, by, say, taking a
vector space, and trying to make a category by defining morphisms
between its vectors. This approach (interpreted suitably) has
been a remarkable success with the representation theory of semi-simple
Lie algebras (and their associated quantum groups). I'll give an
introduction to this area, with a view toward applications in topology;
in particular to replacing polynomial invariants of knots that come
from representation theory with vector space valued invariants that
reduce to knot polynomials under Euler characteristic.
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu