Speaker: Ken Goodearl

Title: What are quantum groups?

This talk will be an elementary introduction to a slice of the subject of quantum groups, aimed particularly at those not familiar with the area. I'll take the perspective of the Cheshire Cat Principle: A quantum group is not a group at all, but something that remains when a group has faded away, leaving an algebra of functions behind. The type of algebra that results resembles an algebra of functions on a group, except that it is noncommutative.

The algebras known as quantum matrices, quantum GL_n, and quantum SL_n will be emphasized. In particular, I'll show how the relations in these algebras follow in a natural way from ``quantizing" functions on matrices, vectors, and matrix multiplication.